TSTP Solution File: RNG026-7 by Toma---0.4
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% File : Toma---0.4
% Problem : RNG026-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n015.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 13:58:12 EDT 2023
% Result : Unsatisfiable 1.70s 2.01s
% Output : CNFRefutation 1.70s
% 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 : RNG026-7 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n015.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
% 0.13/0.35 % DateTime : Sun Aug 27 01:57:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.70/2.01 % SZS status Unsatisfiable
% 1.70/2.01 % SZS output start Proof
% 1.70/2.01 original problem:
% 1.70/2.01 axioms:
% 1.70/2.01 add(additive_identity(), X) = X
% 1.70/2.01 add(X, additive_identity()) = X
% 1.70/2.01 multiply(additive_identity(), X) = additive_identity()
% 1.70/2.01 multiply(X, additive_identity()) = additive_identity()
% 1.70/2.01 add(additive_inverse(X), X) = additive_identity()
% 1.70/2.01 add(X, additive_inverse(X)) = additive_identity()
% 1.70/2.01 additive_inverse(additive_inverse(X)) = X
% 1.70/2.01 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 1.70/2.01 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 1.70/2.01 add(X, Y) = add(Y, X)
% 1.70/2.01 add(X, add(Y, Z)) = add(add(X, Y), Z)
% 1.70/2.01 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 1.70/2.01 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y))
% 1.70/2.01 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 1.70/2.01 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 1.70/2.01 multiply(additive_inverse(X), additive_inverse(Y)) = multiply(X, Y)
% 1.70/2.01 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 1.70/2.01 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 1.70/2.01 multiply(X, add(Y, additive_inverse(Z))) = add(multiply(X, Y), additive_inverse(multiply(X, Z)))
% 1.70/2.01 multiply(add(X, additive_inverse(Y)), Z) = add(multiply(X, Z), additive_inverse(multiply(Y, Z)))
% 1.70/2.01 multiply(additive_inverse(X), add(Y, Z)) = add(additive_inverse(multiply(X, Y)), additive_inverse(multiply(X, Z)))
% 1.70/2.01 multiply(add(X, Y), additive_inverse(Z)) = add(additive_inverse(multiply(X, Z)), additive_inverse(multiply(Y, Z)))
% 1.70/2.01 goal:
% 1.70/2.01 add(add(associator(multiply(a(), b()), c(), d()), associator(a(), b(), multiply(c(), d()))), additive_inverse(add(add(associator(a(), multiply(b(), c()), d()), multiply(a(), associator(b(), c(), d()))), multiply(associator(a(), b(), c()), d())))) != additive_identity()
% 1.70/2.01 To show the unsatisfiability of the original goal,
% 1.70/2.01 it suffices to show that add(add(associator(multiply(a(), b()), c(), d()), associator(a(), b(), multiply(c(), d()))), additive_inverse(add(add(associator(a(), multiply(b(), c()), d()), multiply(a(), associator(b(), c(), d()))), multiply(associator(a(), b(), c()), d())))) = additive_identity() (skolemized goal) is valid under the axioms.
% 1.70/2.01 Here is an equational proof:
% 1.70/2.01 0: add(additive_identity(), X0) = X0.
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 5: add(X0, additive_inverse(X0)) = additive_identity().
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 7: multiply(X0, add(X1, X2)) = add(multiply(X0, X1), multiply(X0, X2)).
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 8: multiply(add(X0, X1), X2) = add(multiply(X0, X2), multiply(X1, X2)).
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 9: add(X0, X1) = add(X1, X0).
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 10: add(X0, add(X1, X2)) = add(add(X0, X1), X2).
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 13: associator(X0, X1, X2) = add(multiply(multiply(X0, X1), X2), additive_inverse(multiply(X0, multiply(X1, X2)))).
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 16: multiply(additive_inverse(X0), X1) = additive_inverse(multiply(X0, X1)).
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 17: multiply(X0, additive_inverse(X1)) = additive_inverse(multiply(X0, X1)).
% 1.70/2.01 Proof: Axiom.
% 1.70/2.01
% 1.70/2.01 22: associator(X0, X1, X2) = add(multiply(multiply(X0, X1), X2), multiply(additive_inverse(X0), multiply(X1, X2))).
% 1.70/2.01 Proof: Rewrite equation 13,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [16].
% 1.70/2.01
% 1.70/2.01 24: multiply(additive_inverse(X0), X1) = multiply(X0, additive_inverse(X1)).
% 1.70/2.01 Proof: Rewrite equation 16,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [17].
% 1.70/2.01
% 1.70/2.01 34: add(X3, add(additive_inverse(X3), X2)) = add(additive_identity(), X2).
% 1.70/2.01 Proof: A critical pair between equations 10 and 5.
% 1.70/2.01
% 1.70/2.01 35: add(X5, add(X3, X4)) = add(X3, add(X4, X5)).
% 1.70/2.01 Proof: A critical pair between equations 9 and 10.
% 1.70/2.01
% 1.70/2.01 40: add(X3, add(additive_inverse(X3), X2)) = X2.
% 1.70/2.01 Proof: Rewrite equation 34,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [0].
% 1.70/2.01
% 1.70/2.01 42: associator(X0, X1, X2) = add(additive_inverse(multiply(X0, multiply(X1, X2))), multiply(multiply(X0, X1), X2)).
% 1.70/2.01 Proof: Rewrite equation 22,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [24,17,9].
% 1.70/2.01
% 1.70/2.01 43: multiply(additive_inverse(X0), X1) = additive_inverse(multiply(X0, X1)).
% 1.70/2.01 Proof: Rewrite equation 24,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [17].
% 1.70/2.01
% 1.70/2.01 47: add(additive_identity(), add(X6, X5)) = add(X5, X6).
% 1.70/2.01 Proof: A critical pair between equations 35 and 0.
% 1.70/2.01
% 1.70/2.01 55: add(X3, add(X4, X2)) = add(add(X4, X3), X2).
% 1.70/2.01 Proof: A critical pair between equations 10 and 9.
% 1.70/2.01
% 1.70/2.01 56: add(X3, add(X4, X2)) = add(X4, add(X3, X2)).
% 1.70/2.01 Proof: Rewrite equation 55,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [10].
% 1.70/2.01
% 1.70/2.01 58: multiply(additive_inverse(X0), X1) = multiply(X0, additive_inverse(X1)).
% 1.70/2.01 Proof: Rewrite equation 43,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [17].
% 1.70/2.01
% 1.70/2.01 59: associator(X0, X1, X2) = add(multiply(X0, multiply(X1, additive_inverse(X2))), multiply(multiply(X0, X1), X2)).
% 1.70/2.01 Proof: Rewrite equation 42,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [17,17].
% 1.70/2.01
% 1.70/2.01 63: add(X6, X5) = add(X5, X6).
% 1.70/2.01 Proof: Rewrite equation 47,
% 1.70/2.01 lhs with equations [0]
% 1.70/2.01 rhs with equations [].
% 1.70/2.01
% 1.70/2.01 80: associator(X0, X1, X2) = add(additive_inverse(multiply(X0, multiply(X1, X2))), multiply(multiply(X0, X1), X2)).
% 1.70/2.01 Proof: Rewrite equation 59,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [17,17].
% 1.70/2.01
% 1.70/2.01 81: multiply(additive_inverse(X0), X1) = additive_inverse(multiply(X0, X1)).
% 1.70/2.01 Proof: Rewrite equation 58,
% 1.70/2.01 lhs with equations []
% 1.70/2.01 rhs with equations [17].
% 1.70/2.01
% 1.70/2.01 89: add(add(associator(multiply(a(), b()), c(), d()), associator(a(), b(), multiply(c(), d()))), additive_inverse(add(add(associator(a(), multiply(b(), c()), d()), multiply(a(), associator(b(), c(), d()))), multiply(associator(a(), b(), c()), d())))) = additive_identity().
% 1.70/2.01 Proof: Rewrite lhs with equations [80,80,10,56,63,56,56,40,80,80,7,17,10,56,63,56,56,40,80,8,81,10,40,5]
% 1.70/2.01 rhs with equations [].
% 1.70/2.01
% 1.70/2.01 % SZS output end Proof
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