TSTP Solution File: GRP572-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP572-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n026.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 : Sat Jul 16 10:56:21 EDT 2022
% Result : Unsatisfiable 7.09s 7.07s
% Output : Proof 7.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP572-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.14 % Command : moca.sh %s
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 10:06:06 EDT 2022
% 0.15/0.36 % CPUTime :
% 7.09/7.07 % SZS status Unsatisfiable
% 7.09/7.07 % SZS output start Proof
% 7.09/7.07 The input problem is unsatisfiable because
% 7.09/7.07
% 7.09/7.07 [1] the following set of Horn clauses is unsatisfiable:
% 7.09/7.07
% 7.09/7.07 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B
% 7.09/7.07 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 7.09/7.07 inverse(A) = double_divide(A, identity)
% 7.09/7.07 identity = double_divide(A, inverse(A))
% 7.09/7.07 multiply(a, b) = multiply(b, a) ==> \bottom
% 7.09/7.07
% 7.09/7.07 This holds because
% 7.09/7.07
% 7.09/7.07 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 7.09/7.07
% 7.09/7.07 E:
% 7.09/7.07 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B
% 7.09/7.07 f1(multiply(a, b)) = true__
% 7.09/7.07 f1(multiply(b, a)) = false__
% 7.09/7.07 identity = double_divide(A, inverse(A))
% 7.09/7.07 inverse(A) = double_divide(A, identity)
% 7.09/7.07 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 7.09/7.07 G:
% 7.09/7.07 true__ = false__
% 7.09/7.07
% 7.09/7.07 This holds because
% 7.09/7.07
% 7.09/7.07 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 7.09/7.07
% 7.09/7.07 double_divide(Y0, X0) = double_divide(X0, Y0)
% 7.09/7.07 double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity))
% 7.09/7.07 double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))) = double_divide(false__, double_divide(double_divide(Y1, inverse(false__)), inverse(identity)))
% 7.09/7.07 double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity))
% 7.09/7.07 double_divide(Y0, inverse(double_divide(X1, X0))) = inverse(double_divide(double_divide(X0, X1), inverse(Y0)))
% 7.09/7.07 double_divide(double_divide(identity, double_divide(X1, inverse(identity))), inverse(identity)) = double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2)))
% 7.09/7.07 double_divide(false__, double_divide(double_divide(X1, inverse(false__)), inverse(identity))) = double_divide(X0, double_divide(inverse(X1), inverse(inverse(X0))))
% 7.09/7.07 double_divide(false__, inverse(X0)) = inverse(double_divide(X0, inverse(false__)))
% 7.09/7.07 inverse(double_divide(X1, inverse(X0))) = double_divide(X0, inverse(X1))
% 7.09/7.07 inverse(double_divide(Y0, X0)) = inverse(double_divide(X0, Y0))
% 7.09/7.07 inverse(double_divide(Y0, inverse(double_divide(X1, X0)))) = double_divide(double_divide(X0, X1), inverse(Y0))
% 7.09/7.07 inverse(double_divide(false__, inverse(X0))) = double_divide(X0, inverse(false__))
% 7.09/7.07 double_divide(A, identity) -> inverse(A)
% 7.09/7.07 double_divide(A, inverse(A)) -> identity
% 7.09/7.07 double_divide(X0, double_divide(X0, inverse(X1))) -> inverse(X1)
% 7.09/7.07 double_divide(X0, double_divide(X0, inverse(false__))) -> inverse(false__)
% 7.09/7.07 double_divide(X0, double_divide(X1, X0)) -> X1
% 7.09/7.07 double_divide(X0, double_divide(X2, double_divide(X1, double_divide(X0, inverse(X2))))) -> inverse(X1)
% 7.09/7.07 double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2))) -> inverse(X1)
% 7.09/7.07 double_divide(X0, double_divide(inverse(X1), X0)) -> inverse(X1)
% 7.09/7.07 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1)
% 7.09/7.07 double_divide(X1, double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2)))) -> identity
% 7.09/7.07 double_divide(X1, double_divide(X0, double_divide(inverse(X1), X0))) -> identity
% 7.09/7.07 double_divide(X1, double_divide(X1, Y0)) -> Y0
% 7.09/7.07 double_divide(Y0, double_divide(double_divide(identity, inverse(Y0)), inverse(identity))) -> identity
% 7.09/7.07 double_divide(Y0, double_divide(identity, Y0)) -> identity
% 7.09/7.07 double_divide(Y0, double_divide(identity, inverse(inverse(Y0)))) -> identity
% 7.09/7.07 double_divide(Y0, double_divide(inverse(false__), Y0)) -> inverse(false__)
% 7.09/7.07 double_divide(Y0, double_divide(inverse(identity), inverse(inverse(Y0)))) -> identity
% 7.09/7.07 double_divide(Y0, inverse(double_divide(double_divide(Y0, X0), X0))) -> identity
% 7.09/7.07 double_divide(Y0, inverse(double_divide(double_divide(Y0, inverse(X0)), inverse(X0)))) -> identity
% 7.09/7.07 double_divide(Y0, inverse(double_divide(identity, inverse(Y0)))) -> identity
% 7.09/7.07 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y1, Y2)), inverse(Y2))) -> double_divide(inverse(identity), inverse(identity))
% 7.09/7.07 double_divide(Y1, double_divide(inverse(false__), inverse(inverse(Y1)))) -> inverse(false__)
% 7.09/7.07 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) -> B
% 7.09/7.07 double_divide(double_divide(X0, double_divide(X1, X0)), inverse(X1)) -> identity
% 7.09/7.07 double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2))), X1) -> identity
% 7.09/7.07 double_divide(double_divide(X0, double_divide(inverse(X1), X0)), X1) -> identity
% 7.09/7.07 double_divide(double_divide(X0, inverse(false__)), double_divide(false__, inverse(X0))) -> identity
% 7.09/7.07 double_divide(double_divide(X0, inverse(false__)), inverse(double_divide(double_divide(false__, inverse(X0)), inverse(Y1)))) -> Y1
% 7.09/7.07 double_divide(double_divide(X1, Y1), X1) -> Y1
% 7.09/7.07 double_divide(double_divide(X1, inverse(Y1)), X1) -> inverse(Y1)
% 7.09/7.07 double_divide(double_divide(X1, inverse(false__)), X1) -> inverse(false__)
% 7.09/7.07 double_divide(double_divide(Y0, X0), X0) -> Y0
% 7.09/7.07 double_divide(double_divide(Y0, double_divide(X0, inverse(false__))), inverse(double_divide(false__, inverse(X0)))) -> Y0
% 7.09/7.07 double_divide(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), inverse(Y2))), inverse(identity)) -> Y1
% 7.09/7.07 double_divide(double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))), inverse(identity)) -> Y1
% 7.09/7.07 double_divide(double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))), inverse(identity)) -> Y1
% 7.09/7.07 double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2)) -> Y1
% 7.09/7.07 double_divide(double_divide(Y1, inverse(false__)), inverse(false__)) -> Y1
% 7.09/7.07 double_divide(double_divide(double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), inverse(X2))), double_divide(double_divide(Y1, X1), inverse(inverse(identity)))), inverse(identity)) -> Y1
% 7.09/7.07 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))), double_divide(double_divide(Y3, Y1), inverse(inverse(identity)))), inverse(identity)) -> Y3
% 7.09/7.07 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(identity, double_divide(Y0, Y2)), inverse(Y2))), double_divide(inverse(Y3), inverse(inverse(identity)))), inverse(identity)) -> Y3
% 7.09/7.07 double_divide(double_divide(double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))), double_divide(double_divide(Y3, Y1), inverse(inverse(identity)))), inverse(identity)) -> Y3
% 7.09/7.07 double_divide(double_divide(false__, inverse(X0)), double_divide(X0, inverse(false__))) -> identity
% 7.09/7.07 double_divide(double_divide(identity, X0), X0) -> identity
% 7.09/7.07 double_divide(double_divide(identity, X0), double_divide(identity, inverse(X0))) -> identity
% 7.09/7.07 double_divide(double_divide(inverse(X0), double_divide(double_divide(Y1, X0), inverse(inverse(identity)))), inverse(identity)) -> Y1
% 7.09/7.07 double_divide(double_divide(inverse(X1), Y1), inverse(X1)) -> Y1
% 7.09/7.07 double_divide(double_divide(inverse(false__), Y1), inverse(false__)) -> Y1
% 7.09/7.07 double_divide(double_divide(inverse(identity), double_divide(inverse(Y1), inverse(inverse(identity)))), inverse(identity)) -> Y1
% 7.09/7.07 double_divide(double_divide(inverse(inverse(Y1)), double_divide(identity, inverse(inverse(identity)))), inverse(identity)) -> Y1
% 7.09/7.07 double_divide(false__, double_divide(double_divide(X0, inverse(false__)), inverse(identity))) -> inverse(X0)
% 7.09/7.07 double_divide(false__, double_divide(false__, Y1)) -> Y1
% 7.09/7.07 double_divide(false__, inverse(double_divide(Y0, inverse(false__)))) -> inverse(Y0)
% 7.09/7.07 double_divide(identity, X0) -> inverse(X0)
% 7.09/7.07 double_divide(identity, false__) -> inverse(false__)
% 7.09/7.07 double_divide(identity, inverse(inverse(false__))) -> inverse(false__)
% 7.09/7.07 double_divide(inverse(X0), X0) -> identity
% 7.09/7.07 double_divide(inverse(X0), double_divide(double_divide(identity, X0), inverse(inverse(identity)))) -> identity
% 7.09/7.07 double_divide(inverse(X0), double_divide(identity, inverse(X0))) -> identity
% 7.09/7.07 double_divide(inverse(X0), double_divide(inverse(false__), inverse(X0))) -> inverse(false__)
% 7.09/7.07 double_divide(inverse(X0), false__) -> inverse(double_divide(X0, inverse(false__)))
% 7.09/7.07 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1)
% 7.09/7.07 double_divide(inverse(X1), double_divide(X0, double_divide(X1, X0))) -> identity
% 7.09/7.07 double_divide(inverse(Y0), X1) -> inverse(double_divide(Y0, inverse(X1)))
% 7.09/7.07 double_divide(inverse(Y0), inverse(double_divide(identity, Y0))) -> identity
% 7.09/7.07 double_divide(inverse(Y0), inverse(identity)) -> Y0
% 7.09/7.07 double_divide(inverse(double_divide(X0, inverse(false__))), inverse(X0)) -> false__
% 7.09/7.07 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity)))) -> identity
% 7.09/7.07 double_divide(inverse(inverse(identity)), double_divide(identity, inverse(inverse(identity)))) -> identity
% 7.09/7.07 f1(inverse(double_divide(a, b))) -> false__
% 7.09/7.07 f1(inverse(double_divide(b, a))) -> true__
% 7.09/7.07 f1(multiply(a, b)) -> true__
% 7.09/7.07 f1(multiply(b, a)) -> false__
% 7.09/7.07 inverse(double_divide(X0, double_divide(X0, Y1))) -> inverse(Y1)
% 7.09/7.07 inverse(double_divide(Y0, double_divide(X0, Y0))) -> inverse(X0)
% 7.09/7.07 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), inverse(Y2)))) -> Y1
% 7.09/7.07 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, inverse(X0))), X0))) -> Y1
% 7.09/7.07 inverse(double_divide(Y0, double_divide(inverse(Y1), Y0))) -> Y1
% 7.09/7.07 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1
% 7.09/7.07 inverse(double_divide(double_divide(X1, Y1), X1)) -> inverse(Y1)
% 7.09/7.07 inverse(double_divide(double_divide(X1, inverse(Y1)), X1)) -> Y1
% 7.09/7.07 inverse(double_divide(double_divide(false__, inverse(X0)), inverse(double_divide(double_divide(X0, inverse(false__)), Y1)))) -> Y1
% 7.09/7.07 inverse(double_divide(identity, Y1)) -> Y1
% 7.09/7.07 inverse(double_divide(inverse(X0), inverse(double_divide(Y1, X0)))) -> Y1
% 7.09/7.07 inverse(double_divide(inverse(Y0), inverse(X1))) -> double_divide(Y0, X1)
% 7.09/7.07 inverse(double_divide(inverse(double_divide(X1, Y1)), inverse(X1))) -> Y1
% 7.09/7.07 inverse(double_divide(inverse(false__), X1)) -> double_divide(false__, inverse(X1))
% 7.09/7.07 inverse(identity) -> identity
% 7.09/7.07 inverse(inverse(Y0)) -> Y0
% 7.09/7.07 inverse(inverse(identity)) -> identity
% 7.09/7.07 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 7.09/7.07 true__ -> false__
% 7.09/7.07 with the LPO induced by
% 7.09/7.07 a > b > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 7.09/7.07
% 7.09/7.07 % SZS output end Proof
% 7.09/7.07
%------------------------------------------------------------------------------