TSTP Solution File: RNG018-6 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : RNG018-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 20:36:17 EDT 2022
% Result : Unsatisfiable 31.09s 31.06s
% Output : Proof 31.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG018-6 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n021.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 : 600
% 0.13/0.34 % DateTime : Mon May 30 13:20:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 31.09/31.06 % SZS status Unsatisfiable
% 31.09/31.06 % SZS output start Proof
% 31.09/31.06 The input problem is unsatisfiable because
% 31.09/31.06
% 31.09/31.06 [1] the following set of Horn clauses is unsatisfiable:
% 31.09/31.06
% 31.09/31.06 add(additive_identity, X) = X
% 31.09/31.06 add(X, additive_identity) = X
% 31.09/31.06 multiply(additive_identity, X) = additive_identity
% 31.09/31.06 multiply(X, additive_identity) = additive_identity
% 31.09/31.06 add(additive_inverse(X), X) = additive_identity
% 31.09/31.06 add(X, additive_inverse(X)) = additive_identity
% 31.09/31.06 additive_inverse(additive_inverse(X)) = X
% 31.09/31.06 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 31.09/31.06 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 31.09/31.06 add(X, Y) = add(Y, X)
% 31.09/31.06 add(X, add(Y, Z)) = add(add(X, Y), Z)
% 31.09/31.06 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 31.09/31.06 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y))
% 31.09/31.06 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 31.09/31.06 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 31.09/31.06 multiply(add(x, y), additive_inverse(z)) = add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))) ==> \bottom
% 31.09/31.06
% 31.09/31.06 This holds because
% 31.09/31.06
% 31.09/31.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 31.09/31.06
% 31.09/31.06 E:
% 31.09/31.06 add(X, Y) = add(Y, X)
% 31.09/31.06 add(X, add(Y, Z)) = add(add(X, Y), Z)
% 31.09/31.06 add(X, additive_identity) = X
% 31.09/31.06 add(X, additive_inverse(X)) = additive_identity
% 31.09/31.06 add(additive_identity, X) = X
% 31.09/31.06 add(additive_inverse(X), X) = additive_identity
% 31.09/31.06 additive_inverse(additive_inverse(X)) = X
% 31.09/31.06 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 31.09/31.06 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 31.09/31.06 f1(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z)))) = false__
% 31.09/31.06 f1(multiply(add(x, y), additive_inverse(z))) = true__
% 31.09/31.06 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 31.09/31.06 multiply(X, additive_identity) = additive_identity
% 31.09/31.06 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 31.09/31.06 multiply(additive_identity, X) = additive_identity
% 31.09/31.06 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y))
% 31.09/31.06 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 31.09/31.06 G:
% 31.09/31.06 true__ = false__
% 31.09/31.06
% 31.09/31.06 This holds because
% 31.09/31.06
% 31.09/31.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 31.09/31.06
% 31.09/31.06 add(X, Y) = add(Y, X)
% 31.09/31.06 add(Y0, add(Y2, additive_inverse(X0))) = add(additive_inverse(X0), add(Y2, Y0))
% 31.09/31.06 add(Y0, add(additive_inverse(X1), Y1)) = add(Y1, add(additive_inverse(X1), Y0))
% 31.09/31.06 add(Y0, additive_inverse(X1)) = add(additive_inverse(X1), Y0)
% 31.09/31.06 add(Y0, additive_inverse(multiply(X0, X1))) = add(additive_inverse(multiply(X0, X1)), Y0)
% 31.09/31.06 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2))
% 31.09/31.06 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2))
% 31.09/31.06 add(additive_inverse(Y0), add(X2, add(additive_inverse(X1), Y0))) = add(additive_inverse(X1), X2)
% 31.09/31.06 add(additive_inverse(Y0), add(Y1, add(Y0, additive_inverse(Y2)))) = add(additive_inverse(Y2), Y1)
% 31.09/31.06 add(additive_inverse(Y0), add(additive_inverse(X2), add(X1, Y0))) = add(X1, additive_inverse(X2))
% 31.09/31.06 add(additive_inverse(Y0), add(additive_inverse(Y1), add(Y0, Y2))) = add(Y2, additive_inverse(Y1))
% 31.09/31.06 add(X, additive_identity) -> X
% 31.09/31.06 add(X, additive_inverse(X)) -> additive_identity
% 31.09/31.06 add(X0, add(X1, add(Y1, add(Y2, add(additive_inverse(X1), additive_inverse(X0)))))) -> add(Y1, Y2)
% 31.09/31.06 add(Y0, add(X1, add(X2, additive_inverse(Y0)))) -> add(X1, X2)
% 31.09/31.06 add(Y0, add(Y1, additive_inverse(Y0))) -> Y1
% 31.09/31.06 add(Y0, add(additive_inverse(Y0), Y2)) -> Y2
% 31.09/31.06 add(Y1, add(Y0, add(additive_inverse(Y1), X1))) -> add(Y0, X1)
% 31.09/31.06 add(add(X, Y), Z) -> add(X, add(Y, Z))
% 31.09/31.06 add(additive_identity, X) -> X
% 31.09/31.06 add(additive_inverse(X), X) -> additive_identity
% 31.09/31.06 add(additive_inverse(Y0), add(Y2, add(Y0, additive_inverse(Y1)))) -> add(Y2, additive_inverse(Y1))
% 31.09/31.06 add(additive_inverse(Y0), add(additive_inverse(Y2), add(Y0, Y1))) -> add(additive_inverse(Y2), Y1)
% 31.09/31.06 add(additive_inverse(Y1), add(Y1, Y2)) -> Y2
% 31.09/31.06 add(additive_inverse(Y2), add(Y1, add(additive_inverse(Y0), Y2))) -> add(Y1, additive_inverse(Y0))
% 31.09/31.06 additive_inverse(add(X1, Y0)) -> add(additive_inverse(Y0), additive_inverse(X1))
% 31.09/31.06 additive_inverse(additive_identity) -> additive_identity
% 31.09/31.06 additive_inverse(additive_inverse(X)) -> X
% 31.09/31.06 associator(X, Y, Z) -> add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 31.09/31.06 commutator(X, Y) -> add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 31.09/31.06 f1(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z)))) -> false__
% 31.09/31.06 f1(add(additive_inverse(multiply(y, z)), additive_inverse(multiply(x, z)))) -> false__
% 31.09/31.06 f1(multiply(add(x, y), additive_inverse(z))) -> true__
% 31.09/31.06 f1(multiply(add(y, x), additive_inverse(z))) -> true__
% 31.09/31.06 false__ -> true__
% 31.09/31.06 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z))
% 31.09/31.06 multiply(X, additive_identity) -> additive_identity
% 31.09/31.06 multiply(X0, additive_inverse(X1)) -> additive_inverse(multiply(X0, X1))
% 31.09/31.06 multiply(add(X, Y), Z) -> add(multiply(X, Z), multiply(Y, Z))
% 31.09/31.06 multiply(additive_identity, X) -> additive_identity
% 31.09/31.06 multiply(additive_inverse(X0), X1) -> additive_inverse(multiply(X0, X1))
% 31.09/31.06 multiply(multiply(X, X), Y) -> multiply(X, multiply(X, Y))
% 31.09/31.06 multiply(multiply(X, Y), Y) -> multiply(X, multiply(Y, Y))
% 31.09/31.06 multiply(multiply(X0, multiply(X0, Y1)), Y1) -> multiply(X0, multiply(X0, multiply(Y1, Y1)))
% 31.09/31.06 multiply(multiply(X0, multiply(X0, multiply(X0, X0))), Y1) -> multiply(X0, multiply(X0, multiply(X0, multiply(X0, Y1))))
% 31.09/31.06 multiply(multiply(X0, multiply(Y1, Y1)), Y1) -> multiply(multiply(X0, Y1), multiply(Y1, Y1))
% 31.09/31.06 with the LPO induced by
% 31.09/31.06 commutator > associator > multiply > additive_inverse > add > additive_identity > z > y > x > f1 > false__ > true__
% 31.09/31.06
% 31.09/31.06 % SZS output end Proof
% 31.09/31.06
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