TSTP Solution File: RNG011-5 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n025.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 20:36:14 EDT 2022
% Result : Unsatisfiable 2.13s 2.25s
% Output : Proof 2.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : moca.sh %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon May 30 20:01:57 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.13/2.25 % SZS status Unsatisfiable
% 2.13/2.25 % SZS output start Proof
% 2.13/2.25 The input problem is unsatisfiable because
% 2.13/2.25
% 2.13/2.25 [1] the following set of Horn clauses is unsatisfiable:
% 2.13/2.25
% 2.13/2.25 add(X, Y) = add(Y, X)
% 2.13/2.25 add(add(X, Y), Z) = add(X, add(Y, Z))
% 2.13/2.25 add(X, additive_identity) = X
% 2.13/2.25 add(additive_identity, X) = X
% 2.13/2.25 add(X, additive_inverse(X)) = additive_identity
% 2.13/2.25 add(additive_inverse(X), X) = additive_identity
% 2.13/2.25 additive_inverse(additive_identity) = additive_identity
% 2.13/2.25 add(X, add(additive_inverse(X), Y)) = Y
% 2.13/2.25 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y))
% 2.13/2.25 additive_inverse(additive_inverse(X)) = X
% 2.13/2.25 multiply(X, additive_identity) = additive_identity
% 2.13/2.25 multiply(additive_identity, X) = additive_identity
% 2.13/2.25 multiply(additive_inverse(X), additive_inverse(Y)) = multiply(X, Y)
% 2.13/2.25 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 2.13/2.25 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 2.13/2.25 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 2.13/2.25 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 2.13/2.25 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 2.13/2.25 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 2.13/2.25 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 2.13/2.25 multiply(multiply(associator(X, X, Y), X), associator(X, X, Y)) = additive_identity
% 2.13/2.25 multiply(multiply(associator(a, a, b), a), associator(a, a, b)) = additive_identity ==> \bottom
% 2.13/2.25
% 2.13/2.25 This holds because
% 2.13/2.25
% 2.13/2.25 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.13/2.25
% 2.13/2.25 E:
% 2.13/2.25 add(X, Y) = add(Y, X)
% 2.13/2.25 add(X, add(additive_inverse(X), Y)) = Y
% 2.13/2.25 add(X, additive_identity) = X
% 2.13/2.25 add(X, additive_inverse(X)) = additive_identity
% 2.13/2.25 add(add(X, Y), Z) = add(X, add(Y, Z))
% 2.13/2.25 add(additive_identity, X) = X
% 2.13/2.25 add(additive_inverse(X), X) = additive_identity
% 2.13/2.25 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y))
% 2.13/2.25 additive_inverse(additive_identity) = additive_identity
% 2.13/2.25 additive_inverse(additive_inverse(X)) = X
% 2.13/2.25 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 2.13/2.25 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 2.13/2.25 f1(additive_identity) = false__
% 2.13/2.25 f1(multiply(multiply(associator(a, a, b), a), associator(a, a, b))) = true__
% 2.13/2.25 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 2.13/2.25 multiply(X, additive_identity) = additive_identity
% 2.13/2.25 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y))
% 2.13/2.25 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 2.13/2.25 multiply(additive_identity, X) = additive_identity
% 2.13/2.25 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y))
% 2.13/2.25 multiply(additive_inverse(X), additive_inverse(Y)) = multiply(X, Y)
% 2.13/2.25 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 2.13/2.25 multiply(multiply(associator(X, X, Y), X), associator(X, X, Y)) = additive_identity
% 2.13/2.25 G:
% 2.13/2.25 true__ = false__
% 2.13/2.25
% 2.13/2.25 This holds because
% 2.13/2.25
% 2.13/2.25 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.13/2.25
% 2.13/2.25 add(X, Y) = add(Y, X)
% 2.13/2.25 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2))
% 2.13/2.25 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2))
% 2.13/2.25 add(multiply(X0, X1), multiply(Y2, additive_inverse(X1))) = multiply(add(additive_inverse(X0), Y2), additive_inverse(X1))
% 2.13/2.25 add(multiply(X0, X1), multiply(additive_inverse(X0), Y2)) = multiply(additive_inverse(X0), add(additive_inverse(X1), Y2))
% 2.13/2.25 add(multiply(X0, multiply(Y2, Y2)), multiply(multiply(X0, Y2), Y1)) = multiply(multiply(X0, Y2), add(Y1, Y2))
% 2.13/2.25 multiply(X0, additive_inverse(Y1)) = multiply(additive_inverse(X0), Y1)
% 2.13/2.25 multiply(Y2, add(Y1, Y1)) = multiply(add(Y2, Y2), Y1)
% 2.13/2.25 multiply(multiply(X0, X1), additive_inverse(X1)) = multiply(additive_inverse(X0), multiply(X1, X1))
% 2.13/2.25 add(X, add(additive_inverse(X), Y)) -> Y
% 2.13/2.25 add(X, additive_identity) -> X
% 2.13/2.25 add(X, additive_inverse(X)) -> additive_identity
% 2.13/2.25 add(Y0, add(Y1, add(additive_inverse(add(Y0, Y1)), X1))) -> X1
% 2.13/2.25 add(Y0, add(Y1, additive_inverse(Y0))) -> Y1
% 2.13/2.25 add(Y0, add(Y1, additive_inverse(add(Y0, Y1)))) -> additive_identity
% 2.13/2.25 add(Y0, additive_inverse(add(Y0, X1))) -> additive_inverse(X1)
% 2.13/2.25 add(add(X, Y), Z) -> add(X, add(Y, Z))
% 2.13/2.25 add(additive_identity, X) -> X
% 2.13/2.25 add(additive_inverse(X), X) -> additive_identity
% 2.13/2.25 add(additive_inverse(X), additive_inverse(Y)) -> additive_inverse(add(X, Y))
% 2.13/2.25 add(additive_inverse(X0), add(X0, Y1)) -> Y1
% 2.13/2.25 add(additive_inverse(Y0), X0) -> additive_inverse(add(Y0, additive_inverse(X0)))
% 2.13/2.25 add(additive_inverse(Y0), multiply(X0, additive_inverse(X1))) -> additive_inverse(add(Y0, multiply(X0, X1)))
% 2.13/2.25 add(additive_inverse(Y0), multiply(additive_inverse(X0), X1)) -> additive_inverse(add(Y0, multiply(X0, X1)))
% 2.13/2.25 add(additive_inverse(add(X0, X1)), Y2) -> add(additive_inverse(X0), add(additive_inverse(X1), Y2))
% 2.13/2.25 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 2.13/2.25 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z)
% 2.13/2.25 add(multiply(X0, X1), add(multiply(X0, additive_inverse(X1)), Y1)) -> Y1
% 2.13/2.25 add(multiply(X0, X1), add(multiply(additive_inverse(X0), X1), Y1)) -> Y1
% 2.13/2.25 add(multiply(X0, add(X1, X2)), Y2) -> add(multiply(X0, X1), add(multiply(X0, X2), Y2))
% 2.13/2.25 add(multiply(X0, additive_inverse(X1)), additive_inverse(Y1)) -> additive_inverse(add(multiply(X0, X1), Y1))
% 2.13/2.25 add(multiply(X0, multiply(Y1, Y1)), multiply(Y2, Y1)) -> multiply(add(multiply(X0, Y1), Y2), Y1)
% 2.13/2.25 add(multiply(X0, multiply(Y1, Y1)), multiply(multiply(X0, Y1), Y2)) -> multiply(multiply(X0, Y1), add(Y1, Y2))
% 2.13/2.25 add(multiply(Y0, Y1), multiply(X0, multiply(Y1, Y1))) -> multiply(add(Y0, multiply(X0, Y1)), Y1)
% 2.13/2.25 add(multiply(Y0, additive_inverse(X1)), multiply(X0, X1)) -> multiply(add(Y0, additive_inverse(X0)), additive_inverse(X1))
% 2.13/2.25 add(multiply(add(X0, X2), X1), Y2) -> add(multiply(X0, X1), add(multiply(X2, X1), Y2))
% 2.13/2.25 add(multiply(additive_inverse(X0), X1), additive_inverse(Y1)) -> additive_inverse(add(multiply(X0, X1), Y1))
% 2.13/2.25 add(multiply(additive_inverse(X0), Y1), multiply(X0, X1)) -> multiply(additive_inverse(X0), add(Y1, additive_inverse(X1)))
% 2.13/2.25 additive_inverse(add(additive_inverse(X0), Y1)) -> add(X0, additive_inverse(Y1))
% 2.13/2.25 additive_inverse(additive_identity) -> additive_identity
% 2.13/2.25 additive_inverse(additive_inverse(X)) -> X
% 2.13/2.25 additive_inverse(multiply(X, Y)) -> multiply(X, additive_inverse(Y))
% 2.13/2.25 additive_inverse(multiply(X, Y)) -> multiply(additive_inverse(X), Y)
% 2.13/2.25 associator(X, Y, Z) -> add(multiply(multiply(X, Y), Z), multiply(X, multiply(Y, additive_inverse(Z))))
% 2.13/2.25 commutator(X, Y) -> add(multiply(Y, X), multiply(X, additive_inverse(Y)))
% 2.13/2.25 f1(additive_identity) -> false__
% 2.13/2.25 f1(multiply(multiply(add(multiply(multiply(a, a), b), multiply(a, multiply(a, additive_inverse(b)))), a), add(multiply(multiply(a, a), b), multiply(a, multiply(a, additive_inverse(b)))))) -> true__
% 2.13/2.25 f1(multiply(multiply(associator(a, a, b), a), associator(a, a, b))) -> true__
% 2.13/2.25 multiply(X, additive_identity) -> additive_identity
% 2.13/2.25 multiply(add(Y0, multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0)), add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))) -> multiply(Y0, add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))))
% 2.13/2.25 multiply(add(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), Y2), add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))) -> multiply(Y2, add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))))
% 2.13/2.25 multiply(additive_identity, X) -> additive_identity
% 2.13/2.25 multiply(additive_inverse(X), additive_inverse(Y)) -> multiply(X, Y)
% 2.13/2.25 multiply(additive_inverse(Y0), multiply(X0, additive_inverse(X1))) -> multiply(Y0, multiply(X0, X1))
% 2.13/2.25 multiply(additive_inverse(Y0), multiply(additive_inverse(X0), X1)) -> multiply(Y0, multiply(X0, X1))
% 2.13/2.25 multiply(multiply(X, Y), Y) -> multiply(X, multiply(Y, Y))
% 2.13/2.25 multiply(multiply(X0, additive_inverse(X1)), additive_inverse(Y1)) -> multiply(multiply(X0, X1), Y1)
% 2.13/2.25 multiply(multiply(X0, multiply(Y1, Y1)), Y1) -> multiply(multiply(X0, Y1), multiply(Y1, Y1))
% 2.13/2.25 multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), add(Y1, add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))))) -> multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), Y1)
% 2.13/2.25 multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), add(multiply(multiply(X0, X0), X1), add(multiply(X0, multiply(X0, additive_inverse(X1))), Y2))) -> multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), Y2)
% 2.13/2.25 multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), additive_inverse(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))))) -> additive_identity
% 2.13/2.25 multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))))) -> additive_identity
% 2.13/2.25 multiply(multiply(add(multiply(multiply(Y0, Y0), Y1), multiply(Y0, multiply(Y0, additive_inverse(Y1)))), Y0), add(multiply(multiply(Y0, Y0), Y1), multiply(Y0, multiply(Y0, additive_inverse(Y1))))) -> additive_identity
% 2.13/2.25 multiply(multiply(additive_inverse(X0), X1), additive_inverse(Y1)) -> multiply(multiply(X0, X1), Y1)
% 2.13/2.25 multiply(multiply(additive_inverse(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))), X0), add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))) -> additive_identity
% 2.13/2.25 multiply(multiply(associator(X, X, Y), X), associator(X, X, Y)) -> additive_identity
% 2.13/2.25 true__ -> false__
% 2.13/2.25 with the LPO induced by
% 2.13/2.25 b > commutator > a > associator > add > additive_identity > additive_inverse > multiply > f1 > true__ > false__
% 2.13/2.25
% 2.13/2.25 % SZS output end Proof
% 2.13/2.25
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