TSTP Solution File: GRP576-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n009.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 10:56:23 EDT 2022
% Result : Unsatisfiable 6.23s 6.24s
% Output : Proof 6.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 13:23:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.23/6.24 % SZS status Unsatisfiable
% 6.23/6.24 % SZS output start Proof
% 6.23/6.24 The input problem is unsatisfiable because
% 6.23/6.24
% 6.23/6.24 [1] the following set of Horn clauses is unsatisfiable:
% 6.23/6.24
% 6.23/6.24 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) = B
% 6.23/6.24 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 6.23/6.24 inverse(A) = double_divide(A, identity)
% 6.23/6.24 identity = double_divide(A, inverse(A))
% 6.23/6.24 multiply(a, b) = multiply(b, a) ==> \bottom
% 6.23/6.24
% 6.23/6.24 This holds because
% 6.23/6.24
% 6.23/6.24 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 6.23/6.24
% 6.23/6.24 E:
% 6.23/6.24 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) = B
% 6.23/6.24 f1(multiply(a, b)) = true__
% 6.23/6.24 f1(multiply(b, a)) = false__
% 6.23/6.24 identity = double_divide(A, inverse(A))
% 6.23/6.24 inverse(A) = double_divide(A, identity)
% 6.23/6.24 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 6.23/6.24 G:
% 6.23/6.24 true__ = false__
% 6.23/6.24
% 6.23/6.24 This holds because
% 6.23/6.24
% 6.23/6.24 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 6.23/6.24
% 6.23/6.24 double_divide(Y0, X0) = double_divide(X0, Y0)
% 6.23/6.24 double_divide(double_divide(identity, double_divide(X1, inverse(identity))), inverse(identity)) = double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), inverse(X2)))
% 6.23/6.24 double_divide(identity, double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity))
% 6.23/6.24 double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))) = double_divide(inverse(identity), inverse(identity))
% 6.23/6.24 double_divide(inverse(Y2), double_divide(inverse(Y1), inverse(Y2))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity))
% 6.23/6.24 inverse(double_divide(Y0, inverse(X0))) = double_divide(X0, inverse(Y0))
% 6.23/6.24 double_divide(A, identity) -> inverse(A)
% 6.23/6.24 double_divide(A, inverse(A)) -> identity
% 6.23/6.24 double_divide(X0, double_divide(identity, X0)) -> identity
% 6.23/6.24 double_divide(X0, double_divide(inverse(X1), X0)) -> inverse(X1)
% 6.23/6.24 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1)
% 6.23/6.24 double_divide(X1, double_divide(X0, double_divide(inverse(X1), X0))) -> identity
% 6.23/6.24 double_divide(X1, double_divide(X0, inverse(double_divide(X1, inverse(X0))))) -> identity
% 6.23/6.24 double_divide(X1, double_divide(X1, Y0)) -> Y0
% 6.23/6.24 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X1, X0)))) -> identity
% 6.23/6.24 double_divide(Y0, double_divide(X0, Y0)) -> X0
% 6.23/6.24 double_divide(Y0, inverse(double_divide(inverse(Y0), Y1))) -> inverse(Y1)
% 6.23/6.24 double_divide(Y0, inverse(inverse(inverse(Y0)))) -> identity
% 6.23/6.24 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y2, Y1)), inverse(Y2))) -> double_divide(inverse(identity), inverse(identity))
% 6.23/6.24 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(C, A)), double_divide(C, identity))), double_divide(identity, identity)) -> B
% 6.23/6.24 double_divide(double_divide(X0, double_divide(inverse(X1), X0)), X1) -> identity
% 6.23/6.24 double_divide(double_divide(X0, inverse(double_divide(X1, inverse(X0)))), X1) -> identity
% 6.23/6.24 double_divide(double_divide(X1, Y1), X1) -> Y1
% 6.23/6.24 double_divide(double_divide(X1, inverse(Y1)), X1) -> inverse(Y1)
% 6.23/6.24 double_divide(double_divide(Y0, X0), X0) -> Y0
% 6.23/6.24 double_divide(double_divide(Y0, double_divide(X0, Y0)), inverse(X0)) -> identity
% 6.23/6.24 double_divide(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y2, Y0)), inverse(Y2))), inverse(identity)) -> Y1
% 6.23/6.24 double_divide(double_divide(Y0, inverse(Y1)), inverse(Y1)) -> Y0
% 6.23/6.24 double_divide(double_divide(identity, X0), inverse(inverse(X0))) -> identity
% 6.23/6.24 double_divide(double_divide(identity, double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2))), inverse(identity)) -> Y1
% 6.23/6.24 double_divide(double_divide(identity, double_divide(identity, inverse(X0))), X0) -> identity
% 6.23/6.24 double_divide(double_divide(identity, double_divide(identity, inverse(Y1))), inverse(identity)) -> Y1
% 6.23/6.24 double_divide(double_divide(inverse(X0), double_divide(inverse(X1), inverse(X0))), X1) -> identity
% 6.23/6.24 double_divide(double_divide(inverse(X0), inverse(double_divide(X1, X0))), X1) -> identity
% 6.23/6.24 double_divide(double_divide(inverse(X1), Y1), inverse(X1)) -> Y1
% 6.23/6.24 double_divide(double_divide(inverse(Y2), double_divide(inverse(Y1), inverse(Y2))), inverse(identity)) -> Y1
% 6.23/6.24 double_divide(double_divide(inverse(identity), X0), inverse(identity)) -> inverse(inverse(X0))
% 6.23/6.24 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y0, Y1), inverse(double_divide(identity, double_divide(double_divide(Y1, inverse(Y3)), inverse(Y3)))))), inverse(identity)) -> Y0
% 6.23/6.24 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y1, X0), inverse(inverse(inverse(inverse(X0)))))), inverse(identity)) -> Y1
% 6.23/6.24 double_divide(double_divide(inverse(identity), double_divide(double_divide(Y1, X1), inverse(double_divide(X0, double_divide(double_divide(X1, double_divide(X2, X0)), inverse(X2)))))), inverse(identity)) -> Y1
% 6.23/6.24 double_divide(double_divide(inverse(identity), double_divide(inverse(Y0), inverse(double_divide(Y2, double_divide(double_divide(identity, double_divide(Y3, Y2)), inverse(Y3)))))), inverse(identity)) -> Y0
% 6.23/6.24 double_divide(identity, X0) -> inverse(X0)
% 6.23/6.24 double_divide(identity, double_divide(double_divide(X0, inverse(false__)), inverse(false__))) -> inverse(inverse(inverse(X0)))
% 6.23/6.24 double_divide(identity, double_divide(double_divide(Y1, inverse(false__)), inverse(false__))) -> double_divide(identity, double_divide(identity, inverse(Y1)))
% 6.23/6.24 double_divide(identity, double_divide(double_divide(identity, inverse(Y1)), inverse(Y1))) -> double_divide(inverse(identity), inverse(identity))
% 6.23/6.24 double_divide(identity, double_divide(identity, inverse(X0))) -> inverse(inverse(inverse(X0)))
% 6.23/6.24 double_divide(identity, double_divide(identity, inverse(false__))) -> inverse(inverse(inverse(false__)))
% 6.23/6.24 double_divide(identity, double_divide(identity, inverse(inverse(Y1)))) -> Y1
% 6.23/6.24 double_divide(inverse(X0), X0) -> identity
% 6.23/6.24 double_divide(inverse(X0), double_divide(Y1, double_divide(X0, Y1))) -> identity
% 6.23/6.24 double_divide(inverse(X0), double_divide(inverse(X1), inverse(X0))) -> inverse(inverse(inverse(X1)))
% 6.23/6.24 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1)
% 6.23/6.24 double_divide(inverse(X1), double_divide(inverse(X1), Y0)) -> Y0
% 6.23/6.24 double_divide(inverse(Y0), X1) -> inverse(double_divide(Y0, inverse(X1)))
% 6.23/6.24 double_divide(inverse(Y0), double_divide(identity, inverse(Y0))) -> identity
% 6.23/6.24 double_divide(inverse(Y0), inverse(double_divide(Y0, Y1))) -> inverse(Y1)
% 6.23/6.24 double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))) -> identity
% 6.23/6.24 double_divide(inverse(identity), inverse(identity)) -> identity
% 6.23/6.24 double_divide(inverse(inverse(X0)), inverse(X0)) -> identity
% 6.23/6.24 double_divide(inverse(inverse(identity)), inverse(identity)) -> inverse(inverse(identity))
% 6.23/6.24 double_divide(inverse(inverse(inverse(X0))), X0) -> identity
% 6.23/6.24 double_divide(inverse(inverse(inverse(X0))), inverse(inverse(X0))) -> identity
% 6.23/6.24 double_divide(inverse(inverse(inverse(Y1))), inverse(identity)) -> Y1
% 6.23/6.24 f1(inverse(double_divide(a, b))) -> false__
% 6.23/6.24 f1(inverse(double_divide(b, a))) -> true__
% 6.23/6.24 f1(multiply(a, b)) -> true__
% 6.23/6.24 f1(multiply(b, a)) -> false__
% 6.23/6.24 inverse(double_divide(X0, double_divide(inverse(Y1), X0))) -> Y1
% 6.23/6.24 inverse(double_divide(Y0, double_divide(X0, Y0))) -> inverse(inverse(inverse(X0)))
% 6.23/6.24 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y2, Y0)), inverse(Y2)))) -> Y1
% 6.23/6.24 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(inverse(X0), Y0)), X0))) -> Y1
% 6.23/6.24 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1
% 6.23/6.24 inverse(double_divide(Y0, inverse(double_divide(inverse(Y0), Y1)))) -> Y1
% 6.23/6.24 inverse(double_divide(double_divide(X1, inverse(Y1)), X1)) -> Y1
% 6.23/6.24 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0))
% 6.23/6.24 inverse(double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0
% 6.23/6.24 inverse(double_divide(inverse(X0), inverse(double_divide(Y1, X0)))) -> Y1
% 6.23/6.24 inverse(double_divide(inverse(Y0), double_divide(X0, inverse(Y0)))) -> inverse(inverse(inverse(X0)))
% 6.23/6.24 inverse(double_divide(inverse(Y0), double_divide(identity, inverse(Y0)))) -> identity
% 6.23/6.24 inverse(double_divide(inverse(Y0), double_divide(inverse(Y1), inverse(Y0)))) -> Y1
% 6.23/6.24 inverse(double_divide(inverse(Y0), inverse(double_divide(Y0, Y1)))) -> Y1
% 6.23/6.24 inverse(identity) -> identity
% 6.23/6.24 inverse(inverse(Y0)) -> Y0
% 6.23/6.24 inverse(inverse(double_divide(double_divide(Y0, inverse(Y1)), inverse(Y1)))) -> Y0
% 6.23/6.24 inverse(inverse(identity)) -> identity
% 6.23/6.24 inverse(inverse(inverse(identity))) -> identity
% 6.23/6.24 inverse(inverse(inverse(inverse(Y0)))) -> Y0
% 6.23/6.24 inverse(inverse(inverse(inverse(identity)))) -> identity
% 6.23/6.24 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 6.23/6.24 true__ -> false__
% 6.23/6.24 with the LPO induced by
% 6.23/6.24 a > b > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 6.23/6.24
% 6.23/6.24 % SZS output end Proof
% 6.23/6.24
%------------------------------------------------------------------------------