42 lines
No EOL
1 KiB
Text
42 lines
No EOL
1 KiB
Text
%--------------------------------------------------------------------------
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% File : NUM-ROZEK : TPTP v8.1.2.
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% Domain : Number Theory
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% Axioms : Number theory - Equality and Addition
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%--------------------------------------------------------------------------
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%-- Constants
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fof(c1, axiom, "one" = successor("zero")).
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fof(c1, axiom, "two" = successor("one")).
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fof(c1, axiom, "three" = successor("two")).
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fof(c1, axiom, "four" = successor("three")).
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fof(c1, axiom, "five" = successor("four")).
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%-- Equality with respect to natural numbers
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fof(zero, axiom,
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![X] : "zero" != successor(X)
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).
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fof(successor_equality, axiom,
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![A, B]: (
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(successor(A) = successor(B)) =>
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(A = B)
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)
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).
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% Note: Also shows that successor is an injective function
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%-- Addition Axioms
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fof(adding_zero, axiom,
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![A]: add(A,"zero") = A
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).
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fof(addition, axiom,
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![A, B]:
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(add(A,successor(B)) =
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successor(add(A,B)))
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).
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%-------------------------------------------------------------------------- |