TSTP Solution File: RNG007-4 by Toma---0.4
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% File : Toma---0.4
% Problem : RNG007-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:58:06 EDT 2023
% Result : Unsatisfiable 0.21s 0.65s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : RNG007-4 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14 % Command : toma --casc %s
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 01:53:08 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.65 % SZS status Unsatisfiable
% 0.21/0.65 % SZS output start Proof
% 0.21/0.65 original problem:
% 0.21/0.65 axioms:
% 0.21/0.65 add(additive_identity(), X) = X
% 0.21/0.65 add(additive_inverse(X), X) = additive_identity()
% 0.21/0.65 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.21/0.65 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 0.21/0.65 additive_inverse(additive_identity()) = additive_identity()
% 0.21/0.65 additive_inverse(additive_inverse(X)) = X
% 0.21/0.65 multiply(X, additive_identity()) = additive_identity()
% 0.21/0.65 multiply(additive_identity(), X) = additive_identity()
% 0.21/0.65 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y))
% 0.21/0.65 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 0.21/0.65 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 0.21/0.65 add(add(X, Y), Z) = add(X, add(Y, Z))
% 0.21/0.65 add(X, Y) = add(Y, X)
% 0.21/0.65 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.21/0.65 multiply(X, X) = X
% 0.21/0.65 goal:
% 0.21/0.65 add(a(), a()) != additive_identity()
% 0.21/0.65 To show the unsatisfiability of the original goal,
% 0.21/0.65 it suffices to show that add(a(), a()) = additive_identity() (skolemized goal) is valid under the axioms.
% 0.21/0.65 Here is an equational proof:
% 0.21/0.65 1: add(additive_inverse(X0), X0) = additive_identity().
% 0.21/0.65 Proof: Axiom.
% 0.21/0.65
% 0.21/0.65 5: additive_inverse(additive_inverse(X0)) = X0.
% 0.21/0.65 Proof: Axiom.
% 0.21/0.65
% 0.21/0.65 9: multiply(X0, additive_inverse(X1)) = additive_inverse(multiply(X0, X1)).
% 0.21/0.65 Proof: Axiom.
% 0.21/0.65
% 0.21/0.65 10: multiply(additive_inverse(X0), X1) = additive_inverse(multiply(X0, X1)).
% 0.21/0.65 Proof: Axiom.
% 0.21/0.65
% 0.21/0.65 12: add(X0, X1) = add(X1, X0).
% 0.21/0.65 Proof: Axiom.
% 0.21/0.65
% 0.21/0.65 14: multiply(X0, X0) = X0.
% 0.21/0.65 Proof: Axiom.
% 0.21/0.65
% 0.21/0.65 15: add(X0, additive_inverse(X0)) = additive_identity().
% 0.21/0.65 Proof: Rewrite equation 1,
% 0.21/0.65 lhs with equations [12]
% 0.21/0.65 rhs with equations [].
% 0.21/0.65
% 0.21/0.65 18: additive_inverse(multiply(X0, additive_inverse(X0))) = additive_inverse(X0).
% 0.21/0.65 Proof: A critical pair between equations 10 and 14.
% 0.21/0.65
% 0.21/0.65 32: X0 = additive_inverse(X0).
% 0.21/0.65 Proof: Rewrite equation 18,
% 0.21/0.65 lhs with equations [9,14,5]
% 0.21/0.65 rhs with equations [].
% 0.21/0.65
% 0.21/0.65 33: add(X0, X0) = additive_identity().
% 0.21/0.65 Proof: Rewrite equation 15,
% 0.21/0.65 lhs with equations [32]
% 0.21/0.65 rhs with equations [].
% 0.21/0.65
% 0.21/0.65 34: add(a(), a()) = additive_identity().
% 0.21/0.65 Proof: Rewrite lhs with equations [33]
% 0.21/0.65 rhs with equations [].
% 0.21/0.65
% 0.21/0.65 % SZS output end Proof
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