TSTP Solution File: GRP568-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 : Sat Jul 16 10:56:20 EDT 2022
% Result : Unsatisfiable 8.11s 8.10s
% Output : Proof 8.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.08/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 21:18:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 8.11/8.10 % SZS status Unsatisfiable
% 8.11/8.10 % SZS output start Proof
% 8.11/8.10 The input problem is unsatisfiable because
% 8.11/8.10
% 8.11/8.10 [1] the following set of Horn clauses is unsatisfiable:
% 8.11/8.10
% 8.11/8.10 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) = B
% 8.11/8.10 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 8.11/8.10 inverse(A) = double_divide(A, identity)
% 8.11/8.10 identity = double_divide(A, inverse(A))
% 8.11/8.10 multiply(a, b) = multiply(b, a) ==> \bottom
% 8.11/8.10
% 8.11/8.10 This holds because
% 8.11/8.10
% 8.11/8.10 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.11/8.10
% 8.11/8.10 E:
% 8.11/8.10 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) = B
% 8.11/8.10 f1(multiply(a, b)) = true__
% 8.11/8.10 f1(multiply(b, a)) = false__
% 8.11/8.10 identity = double_divide(A, inverse(A))
% 8.11/8.10 inverse(A) = double_divide(A, identity)
% 8.11/8.10 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 8.11/8.10 G:
% 8.11/8.10 true__ = false__
% 8.11/8.10
% 8.11/8.10 This holds because
% 8.11/8.10
% 8.11/8.10 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.11/8.10
% 8.11/8.10 double_divide(Y0, X0) = double_divide(X0, Y0)
% 8.11/8.10 double_divide(Y0, double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), inverse(Y0)))
% 8.11/8.10 double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity))
% 8.11/8.10 double_divide(Y0, double_divide(inverse(Y1), double_divide(identity, inverse(Y0)))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity))
% 8.11/8.10 double_divide(Y0, inverse(double_divide(X1, X0))) = inverse(double_divide(double_divide(X0, X1), inverse(Y0)))
% 8.11/8.10 double_divide(Y0, inverse(double_divide(Y1, double_divide(Y0, inverse(identity))))) = double_divide(double_divide(identity, double_divide(Y1, inverse(identity))), inverse(identity))
% 8.11/8.10 double_divide(double_divide(identity, double_divide(X1, inverse(identity))), inverse(identity)) = double_divide(X0, double_divide(double_divide(X1, double_divide(X0, X2)), double_divide(identity, X2)))
% 8.11/8.10 double_divide(false__, inverse(double_divide(X0, double_divide(false__, inverse(identity))))) = double_divide(identity, inverse(inverse(X0)))
% 8.11/8.10 inverse(double_divide(X1, inverse(Y1))) = double_divide(Y1, inverse(X1))
% 8.11/8.10 inverse(double_divide(Y0, X0)) = inverse(double_divide(X0, Y0))
% 8.11/8.10 inverse(double_divide(Y0, double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), inverse(Y0))
% 8.11/8.10 inverse(double_divide(Y0, inverse(double_divide(X1, X0)))) = double_divide(double_divide(X0, X1), inverse(Y0))
% 8.11/8.10 double_divide(A, identity) -> inverse(A)
% 8.11/8.10 double_divide(A, inverse(A)) -> identity
% 8.11/8.10 double_divide(X0, double_divide(X0, inverse(Y1))) -> inverse(Y1)
% 8.11/8.10 double_divide(X0, double_divide(X1, X0)) -> X1
% 8.11/8.10 double_divide(X0, double_divide(X2, double_divide(X1, double_divide(X0, inverse(X2))))) -> inverse(X1)
% 8.11/8.10 double_divide(X0, double_divide(identity, X0)) -> identity
% 8.11/8.10 double_divide(X0, double_divide(inverse(X1), X0)) -> inverse(X1)
% 8.11/8.10 double_divide(X0, inverse(double_divide(X1, inverse(X0)))) -> inverse(X1)
% 8.11/8.10 double_divide(X1, double_divide(X0, double_divide(inverse(X1), X0))) -> identity
% 8.11/8.10 double_divide(X1, double_divide(X1, Y0)) -> Y0
% 8.11/8.10 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X1, X0)))) -> identity
% 8.11/8.10 double_divide(X1, double_divide(inverse(double_divide(X0, X1)), inverse(X0))) -> identity
% 8.11/8.10 double_divide(X1, double_divide(inverse(double_divide(inverse(X0), X1)), X0)) -> identity
% 8.11/8.10 double_divide(Y0, double_divide(double_divide(identity, inverse(Y0)), inverse(identity))) -> identity
% 8.11/8.10 double_divide(Y0, double_divide(identity, double_divide(identity, inverse(Y0)))) -> identity
% 8.11/8.10 double_divide(Y0, double_divide(inverse(identity), double_divide(identity, inverse(Y0)))) -> identity
% 8.11/8.10 double_divide(Y0, inverse(double_divide(double_divide(Y0, Y1), Y1))) -> identity
% 8.11/8.10 double_divide(Y0, inverse(double_divide(identity, double_divide(Y0, inverse(identity))))) -> identity
% 8.11/8.10 double_divide(Y0, inverse(double_divide(identity, inverse(Y0)))) -> identity
% 8.11/8.10 double_divide(Y1, double_divide(double_divide(Y0, double_divide(Y1, Y2)), inverse(Y2))) -> inverse(Y0)
% 8.11/8.10 double_divide(Y1, double_divide(double_divide(identity, double_divide(Y1, Y2)), double_divide(identity, Y2))) -> double_divide(inverse(identity), inverse(identity))
% 8.11/8.10 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity)) -> B
% 8.11/8.10 double_divide(double_divide(X0, double_divide(X1, X0)), inverse(X1)) -> identity
% 8.11/8.10 double_divide(double_divide(X0, double_divide(inverse(X1), X0)), X1) -> identity
% 8.11/8.10 double_divide(double_divide(X0, false__), double_divide(inverse(X0), inverse(false__))) -> identity
% 8.11/8.10 double_divide(double_divide(X0, inverse(false__)), double_divide(false__, inverse(X0))) -> identity
% 8.11/8.10 double_divide(double_divide(X1, Y1), X1) -> Y1
% 8.11/8.10 double_divide(double_divide(X1, inverse(Y1)), X1) -> inverse(Y1)
% 8.11/8.10 double_divide(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), double_divide(identity, Y2))), inverse(identity)) -> Y1
% 8.11/8.10 double_divide(double_divide(Y0, double_divide(double_divide(Y1, inverse(Y0)), inverse(identity))), inverse(identity)) -> Y1
% 8.11/8.10 double_divide(double_divide(Y0, double_divide(inverse(Y1), double_divide(identity, inverse(Y0)))), inverse(identity)) -> Y1
% 8.11/8.10 double_divide(double_divide(Y0, inverse(double_divide(Y1, double_divide(Y0, inverse(identity))))), inverse(identity)) -> Y1
% 8.11/8.10 double_divide(double_divide(Y1, X0), X0) -> Y1
% 8.11/8.10 double_divide(double_divide(Y1, inverse(Y2)), inverse(Y2)) -> Y1
% 8.11/8.10 double_divide(double_divide(double_divide(X0, double_divide(double_divide(X1, inverse(X0)), inverse(identity))), inverse(double_divide(Y1, X1))), inverse(identity)) -> Y1
% 8.11/8.10 double_divide(double_divide(identity, X0), X0) -> identity
% 8.11/8.10 double_divide(double_divide(identity, inverse(X0)), inverse(X0)) -> identity
% 8.11/8.10 double_divide(double_divide(identity, inverse(inverse(Y1))), inverse(identity)) -> Y1
% 8.11/8.10 double_divide(double_divide(inverse(X0), X0), inverse(identity)) -> identity
% 8.11/8.10 double_divide(double_divide(inverse(X0), X0), inverse(inverse(identity))) -> identity
% 8.11/8.10 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(X0, X1)) -> identity
% 8.11/8.10 double_divide(double_divide(inverse(X0), inverse(double_divide(X1, X0))), X1) -> identity
% 8.11/8.10 double_divide(double_divide(inverse(X0), inverse(double_divide(Y1, X0))), inverse(identity)) -> Y1
% 8.11/8.10 double_divide(double_divide(inverse(X0), inverse(false__)), double_divide(X0, false__)) -> identity
% 8.11/8.10 double_divide(double_divide(inverse(X1), Y1), inverse(X1)) -> Y1
% 8.11/8.10 double_divide(double_divide(inverse(double_divide(X0, X1)), inverse(X0)), X1) -> identity
% 8.11/8.10 double_divide(double_divide(inverse(double_divide(inverse(X0), X1)), X0), X1) -> identity
% 8.11/8.10 double_divide(double_divide(inverse(false__), X0), double_divide(false__, inverse(X0))) -> identity
% 8.11/8.10 double_divide(double_divide(inverse(identity), inverse(inverse(Y1))), inverse(identity)) -> Y1
% 8.11/8.10 double_divide(double_divide(inverse(inverse(identity)), inverse(X0)), inverse(identity)) -> inverse(X0)
% 8.11/8.10 double_divide(false__, inverse(double_divide(X0, double_divide(false__, inverse(identity))))) -> inverse(X0)
% 8.11/8.10 double_divide(false__, inverse(double_divide(Y0, inverse(false__)))) -> inverse(Y0)
% 8.11/8.10 double_divide(identity, X0) -> inverse(X0)
% 8.11/8.10 double_divide(identity, inverse(X0)) -> X0
% 8.11/8.10 double_divide(identity, inverse(inverse(identity))) -> identity
% 8.11/8.10 double_divide(inverse(X0), X0) -> identity
% 8.11/8.10 double_divide(inverse(X0), double_divide(identity, inverse(X0))) -> identity
% 8.11/8.10 double_divide(inverse(X0), false__) -> inverse(double_divide(X0, inverse(false__)))
% 8.11/8.10 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1)
% 8.11/8.10 double_divide(inverse(X0), inverse(double_divide(identity, X0))) -> identity
% 8.11/8.10 double_divide(inverse(X0), inverse(false__)) -> inverse(double_divide(X0, false__))
% 8.11/8.10 double_divide(inverse(X1), double_divide(X0, double_divide(X1, X0))) -> identity
% 8.11/8.10 double_divide(inverse(Y0), X1) -> inverse(double_divide(Y0, inverse(X1)))
% 8.11/8.10 double_divide(inverse(Y0), inverse(X1)) -> inverse(double_divide(Y0, X1))
% 8.11/8.10 double_divide(inverse(Y0), inverse(identity)) -> Y0
% 8.11/8.10 double_divide(inverse(double_divide(X0, X1)), inverse(X0)) -> inverse(X1)
% 8.11/8.10 double_divide(inverse(double_divide(X0, inverse(false__))), inverse(X0)) -> false__
% 8.11/8.10 double_divide(inverse(double_divide(inverse(X0), X1)), X0) -> inverse(X1)
% 8.11/8.10 double_divide(inverse(double_divide(inverse(X0), inverse(false__))), X0) -> false__
% 8.11/8.10 double_divide(inverse(false__), X0) -> inverse(double_divide(false__, inverse(X0)))
% 8.11/8.10 f1(inverse(double_divide(a, b))) -> false__
% 8.11/8.10 f1(inverse(double_divide(b, a))) -> true__
% 8.11/8.10 f1(multiply(a, b)) -> true__
% 8.11/8.10 f1(multiply(b, a)) -> false__
% 8.11/8.10 inverse(double_divide(X0, double_divide(X0, Y1))) -> inverse(Y1)
% 8.11/8.10 inverse(double_divide(X0, inverse(double_divide(Y1, inverse(X0))))) -> Y1
% 8.11/8.10 inverse(double_divide(X1, double_divide(X1, inverse(Y0)))) -> Y0
% 8.11/8.10 inverse(double_divide(Y0, double_divide(X0, Y0))) -> inverse(X0)
% 8.11/8.10 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, Y2)), inverse(Y2)))) -> Y1
% 8.11/8.10 inverse(double_divide(Y0, double_divide(double_divide(Y1, double_divide(Y0, inverse(X0))), X0))) -> Y1
% 8.11/8.10 inverse(double_divide(Y0, double_divide(inverse(Y1), Y0))) -> Y1
% 8.11/8.10 inverse(double_divide(Y0, inverse(double_divide(double_divide(Y0, Y2), Y2)))) -> identity
% 8.11/8.10 inverse(double_divide(double_divide(X1, Y1), X1)) -> inverse(Y1)
% 8.11/8.10 inverse(double_divide(double_divide(X1, inverse(Y1)), X1)) -> Y1
% 8.11/8.10 inverse(double_divide(identity, Y0)) -> Y0
% 8.11/8.10 inverse(double_divide(identity, inverse(Y0))) -> inverse(Y0)
% 8.11/8.10 inverse(double_divide(identity, inverse(inverse(Y0)))) -> Y0
% 8.11/8.10 inverse(double_divide(inverse(X0), double_divide(inverse(Y1), inverse(X0)))) -> Y1
% 8.11/8.10 inverse(double_divide(inverse(X0), inverse(false__))) -> double_divide(X0, false__)
% 8.11/8.10 inverse(double_divide(inverse(Y0), X0)) -> double_divide(Y0, inverse(X0))
% 8.11/8.10 inverse(double_divide(inverse(Y0), inverse(X1))) -> double_divide(Y0, X1)
% 8.11/8.10 inverse(double_divide(inverse(Y0), inverse(double_divide(Y1, Y0)))) -> Y1
% 8.11/8.10 inverse(double_divide(inverse(double_divide(X1, Y1)), inverse(X1))) -> Y1
% 8.11/8.10 inverse(double_divide(inverse(double_divide(inverse(X0), Y1)), X0)) -> Y1
% 8.11/8.10 inverse(double_divide(inverse(false__), X1)) -> double_divide(false__, inverse(X1))
% 8.11/8.10 inverse(identity) -> identity
% 8.11/8.10 inverse(inverse(Y0)) -> Y0
% 8.11/8.10 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 8.11/8.10 true__ -> false__
% 8.11/8.10 with the LPO induced by
% 8.11/8.10 a > b > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 8.11/8.10
% 8.11/8.10 % SZS output end Proof
% 8.11/8.10
%------------------------------------------------------------------------------