TSTP Solution File: RNG023-7 by Toma---0.4
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% File : Toma---0.4
% Problem : RNG023-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n013.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 13:58:10 EDT 2023
% Result : Unsatisfiable 0.21s 0.76s
% 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
% 0.00/0.13 % Problem : RNG023-7 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 03:05:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.76 % SZS status Unsatisfiable
% 0.21/0.76 % SZS output start Proof
% 0.21/0.76 original problem:
% 0.21/0.76 axioms:
% 0.21/0.76 add(additive_identity(), X) = X
% 0.21/0.76 add(X, additive_identity()) = X
% 0.21/0.76 multiply(additive_identity(), X) = additive_identity()
% 0.21/0.76 multiply(X, additive_identity()) = additive_identity()
% 0.21/0.76 add(additive_inverse(X), X) = additive_identity()
% 0.21/0.76 add(X, additive_inverse(X)) = additive_identity()
% 0.21/0.76 additive_inverse(additive_inverse(X)) = X
% 0.21/0.76 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.21/0.76 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 0.21/0.76 add(X, Y) = add(Y, X)
% 0.21/0.76 add(X, add(Y, Z)) = add(add(X, Y), Z)
% 0.21/0.76 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 0.21/0.76 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y))
% 0.21/0.76 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 0.21/0.76 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 0.21/0.76 multiply(additive_inverse(X), additive_inverse(Y)) = multiply(X, Y)
% 0.21/0.76 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 0.21/0.76 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 0.21/0.76 multiply(X, add(Y, additive_inverse(Z))) = add(multiply(X, Y), additive_inverse(multiply(X, Z)))
% 0.21/0.76 multiply(add(X, additive_inverse(Y)), Z) = add(multiply(X, Z), additive_inverse(multiply(Y, Z)))
% 0.21/0.76 multiply(additive_inverse(X), add(Y, Z)) = add(additive_inverse(multiply(X, Y)), additive_inverse(multiply(X, Z)))
% 0.21/0.76 multiply(add(X, Y), additive_inverse(Z)) = add(additive_inverse(multiply(X, Z)), additive_inverse(multiply(Y, Z)))
% 0.21/0.76 goal:
% 0.21/0.76 associator(x(), x(), y()) != additive_identity()
% 0.21/0.76 To show the unsatisfiability of the original goal,
% 0.21/0.76 it suffices to show that associator(x(), x(), y()) = additive_identity() (skolemized goal) is valid under the axioms.
% 0.21/0.76 Here is an equational proof:
% 0.21/0.76 5: add(X0, additive_inverse(X0)) = additive_identity().
% 0.21/0.76 Proof: Axiom.
% 0.21/0.76
% 0.21/0.76 9: add(X0, X1) = add(X1, X0).
% 0.21/0.76 Proof: Axiom.
% 0.21/0.76
% 0.21/0.76 12: multiply(multiply(X0, X0), X1) = multiply(X0, multiply(X0, X1)).
% 0.21/0.76 Proof: Axiom.
% 0.21/0.76
% 0.21/0.76 13: associator(X0, X1, X2) = add(multiply(multiply(X0, X1), X2), additive_inverse(multiply(X0, multiply(X1, X2)))).
% 0.21/0.76 Proof: Axiom.
% 0.21/0.76
% 0.21/0.76 16: multiply(additive_inverse(X0), X1) = additive_inverse(multiply(X0, X1)).
% 0.21/0.76 Proof: Axiom.
% 0.21/0.76
% 0.21/0.76 17: multiply(X0, additive_inverse(X1)) = additive_inverse(multiply(X0, X1)).
% 0.21/0.76 Proof: Axiom.
% 0.21/0.76
% 0.21/0.76 22: associator(X0, X1, X2) = add(multiply(multiply(X0, X1), X2), multiply(additive_inverse(X0), multiply(X1, X2))).
% 0.21/0.76 Proof: Rewrite equation 13,
% 0.21/0.76 lhs with equations []
% 0.21/0.76 rhs with equations [16].
% 0.21/0.76
% 0.21/0.76 24: multiply(additive_inverse(X0), X1) = multiply(X0, additive_inverse(X1)).
% 0.21/0.76 Proof: Rewrite equation 16,
% 0.21/0.76 lhs with equations []
% 0.21/0.76 rhs with equations [17].
% 0.21/0.76
% 0.21/0.76 42: associator(X0, X1, X2) = add(additive_inverse(multiply(X0, multiply(X1, X2))), multiply(multiply(X0, X1), X2)).
% 0.21/0.76 Proof: Rewrite equation 22,
% 0.21/0.76 lhs with equations []
% 0.21/0.76 rhs with equations [24,17,9].
% 0.21/0.76
% 0.21/0.76 44: associator(x(), x(), y()) = additive_identity().
% 0.21/0.76 Proof: Rewrite lhs with equations [42,12,9,5]
% 0.21/0.76 rhs with equations [].
% 0.21/0.76
% 0.21/0.76 % SZS output end Proof
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