TSTP Solution File: RNG023-6 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : RNG023-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n027.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 : 600s
% DateTime : Mon Jul 18 20:36:19 EDT 2022
% Result : Unsatisfiable 1.58s 1.74s
% Output : Proof 1.58s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG023-6 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 12:54:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.58/1.74 % SZS status Unsatisfiable
% 1.58/1.74 % SZS output start Proof
% 1.58/1.74 The input problem is unsatisfiable because
% 1.58/1.74
% 1.58/1.74 [1] the following set of Horn clauses is unsatisfiable:
% 1.58/1.74
% 1.58/1.74 add(additive_identity, X) = X
% 1.58/1.74 add(X, additive_identity) = X
% 1.58/1.74 multiply(additive_identity, X) = additive_identity
% 1.58/1.74 multiply(X, additive_identity) = additive_identity
% 1.58/1.74 add(additive_inverse(X), X) = additive_identity
% 1.58/1.74 add(X, additive_inverse(X)) = additive_identity
% 1.58/1.74 additive_inverse(additive_inverse(X)) = X
% 1.58/1.74 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 1.58/1.74 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 1.58/1.74 add(X, Y) = add(Y, X)
% 1.58/1.74 add(X, add(Y, Z)) = add(add(X, Y), Z)
% 1.58/1.74 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 1.58/1.74 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y))
% 1.58/1.74 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 1.58/1.74 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 1.58/1.74 associator(x, x, y) = additive_identity ==> \bottom
% 1.58/1.74
% 1.58/1.74 This holds because
% 1.58/1.74
% 1.58/1.74 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.58/1.74
% 1.58/1.74 E:
% 1.58/1.74 add(X, Y) = add(Y, X)
% 1.58/1.74 add(X, add(Y, Z)) = add(add(X, Y), Z)
% 1.58/1.74 add(X, additive_identity) = X
% 1.58/1.74 add(X, additive_inverse(X)) = additive_identity
% 1.58/1.74 add(additive_identity, X) = X
% 1.58/1.74 add(additive_inverse(X), X) = additive_identity
% 1.58/1.74 additive_inverse(additive_inverse(X)) = X
% 1.58/1.74 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 1.58/1.74 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 1.58/1.74 f1(additive_identity) = false__
% 1.58/1.74 f1(associator(x, x, y)) = true__
% 1.58/1.74 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 1.58/1.74 multiply(X, additive_identity) = additive_identity
% 1.58/1.74 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 1.58/1.74 multiply(additive_identity, X) = additive_identity
% 1.58/1.74 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y))
% 1.58/1.74 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 1.58/1.74 G:
% 1.58/1.74 true__ = false__
% 1.58/1.74
% 1.58/1.74 This holds because
% 1.58/1.74
% 1.58/1.74 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.58/1.74
% 1.58/1.74 add(X, Y) = add(Y, X)
% 1.58/1.74 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2))
% 1.58/1.74 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2))
% 1.58/1.74 add(multiply(X0, multiply(Y2, Y2)), multiply(multiply(X0, Y2), Y1)) = multiply(multiply(X0, Y2), add(Y1, Y2))
% 1.58/1.74 multiply(Y2, add(Y1, Y1)) = multiply(add(Y2, Y2), Y1)
% 1.58/1.74 add(X, additive_identity) -> X
% 1.58/1.74 add(X, additive_inverse(X)) -> additive_identity
% 1.58/1.74 add(Y0, add(Y1, additive_inverse(add(Y0, Y1)))) -> additive_identity
% 1.58/1.74 add(Y0, add(additive_inverse(Y0), Y2)) -> Y2
% 1.58/1.74 add(add(X, Y), Z) -> add(X, add(Y, Z))
% 1.58/1.74 add(additive_identity, X) -> X
% 1.58/1.74 add(additive_inverse(X), X) -> additive_identity
% 1.58/1.74 add(additive_inverse(Y1), add(Y1, Y2)) -> Y2
% 1.58/1.74 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 1.58/1.74 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z)
% 1.58/1.74 add(multiply(X0, add(X1, X2)), Y2) -> add(multiply(X0, X1), add(multiply(X0, X2), Y2))
% 1.58/1.74 add(multiply(X0, multiply(X0, Y1)), multiply(Y2, Y1)) -> multiply(add(multiply(X0, X0), Y2), Y1)
% 1.58/1.74 add(multiply(X0, multiply(Y1, Y1)), multiply(Y2, Y1)) -> multiply(add(multiply(X0, Y1), Y2), Y1)
% 1.58/1.74 add(multiply(X0, multiply(Y1, Y1)), multiply(multiply(X0, Y1), Y2)) -> multiply(multiply(X0, Y1), add(Y1, Y2))
% 1.58/1.74 add(multiply(Y0, Y1), multiply(X0, multiply(X0, Y1))) -> multiply(add(Y0, multiply(X0, X0)), Y1)
% 1.58/1.74 add(multiply(Y0, Y1), multiply(X0, multiply(Y1, Y1))) -> multiply(add(Y0, multiply(X0, Y1)), Y1)
% 1.58/1.74 add(multiply(add(X0, X2), X1), Y2) -> add(multiply(X0, X1), add(multiply(X2, X1), Y2))
% 1.58/1.74 additive_inverse(additive_identity) -> additive_identity
% 1.58/1.74 additive_inverse(additive_inverse(X)) -> X
% 1.58/1.74 associator(X, Y, Z) -> add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 1.58/1.74 commutator(X, Y) -> add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 1.58/1.74 f1(additive_identity) -> false__
% 1.58/1.74 f1(associator(x, x, y)) -> true__
% 1.58/1.74 multiply(X, additive_identity) -> additive_identity
% 1.58/1.74 multiply(additive_identity, X) -> additive_identity
% 1.58/1.74 multiply(multiply(X, X), Y) -> multiply(X, multiply(X, Y))
% 1.58/1.74 multiply(multiply(X, Y), Y) -> multiply(X, multiply(Y, Y))
% 1.58/1.74 multiply(multiply(X0, multiply(X0, Y1)), Y1) -> multiply(X0, multiply(X0, multiply(Y1, Y1)))
% 1.58/1.74 multiply(multiply(X0, multiply(X0, multiply(X0, X0))), Y1) -> multiply(X0, multiply(X0, multiply(X0, multiply(X0, Y1))))
% 1.58/1.74 multiply(multiply(X0, multiply(Y1, Y1)), Y1) -> multiply(multiply(X0, Y1), multiply(Y1, Y1))
% 1.58/1.74 true__ -> false__
% 1.58/1.74 with the LPO induced by
% 1.58/1.74 y > x > f1 > commutator > associator > additive_inverse > add > multiply > additive_identity > true__ > false__
% 1.58/1.74
% 1.58/1.74 % SZS output end Proof
% 1.58/1.74
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