TSTP Solution File: GRP522-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n003.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 10:56:00 EDT 2022
% Result : Unsatisfiable 2.23s 2.38s
% Output : Proof 2.23s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.14 % Command : moca.sh %s
% 0.14/0.35 % Computer : n003.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 : Tue Jun 14 07:54:40 EDT 2022
% 0.14/0.36 % CPUTime :
% 2.23/2.38 % SZS status Unsatisfiable
% 2.23/2.38 % SZS output start Proof
% 2.23/2.38 The input problem is unsatisfiable because
% 2.23/2.38
% 2.23/2.38 [1] the following set of Horn clauses is unsatisfiable:
% 2.23/2.38
% 2.23/2.38 divide(A, divide(B, divide(C, divide(A, B)))) = C
% 2.23/2.38 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 2.23/2.38 inverse(A) = divide(divide(B, B), A)
% 2.23/2.38 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 2.23/2.38
% 2.23/2.38 This holds because
% 2.23/2.38
% 2.23/2.38 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.23/2.38
% 2.23/2.38 E:
% 2.23/2.38 divide(A, divide(B, divide(C, divide(A, B)))) = C
% 2.23/2.38 f1(a2) = false__
% 2.23/2.38 f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 2.23/2.38 inverse(A) = divide(divide(B, B), A)
% 2.23/2.38 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 2.23/2.38 G:
% 2.23/2.38 true__ = false__
% 2.23/2.38
% 2.23/2.38 This holds because
% 2.23/2.38
% 2.23/2.38 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.23/2.38
% 2.23/2.38 divide(X1, X1) = divide(Y0, Y0)
% 2.23/2.38 divide(X1, X1) = inverse(divide(Y0, Y0))
% 2.23/2.38 divide(A, divide(B, divide(C, divide(A, B)))) -> C
% 2.23/2.38 divide(X0, divide(X1, inverse(X0))) -> inverse(X1)
% 2.23/2.38 divide(Y0, divide(X1, X1)) -> Y0
% 2.23/2.38 divide(Y0, divide(divide(X1, divide(X2, divide(Y0, X1))), divide(Y2, X2))) -> Y2
% 2.23/2.38 divide(Y0, divide(divide(X2, divide(Y2, Y0)), X2)) -> Y2
% 2.23/2.38 divide(Y0, inverse(divide(X1, X1))) -> Y0
% 2.23/2.38 divide(Y0, inverse(divide(Y2, Y0))) -> Y2
% 2.23/2.38 divide(Y1, divide(Y1, Y2)) -> Y2
% 2.23/2.38 divide(divide(B, B), A) -> inverse(A)
% 2.23/2.38 divide(divide(X0, X1), X0) -> inverse(X1)
% 2.23/2.38 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1)
% 2.23/2.38 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1
% 2.23/2.38 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1
% 2.23/2.38 f1(a2) -> false__
% 2.23/2.38 f1(inverse(inverse(a2))) -> true__
% 2.23/2.38 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 2.23/2.38 inverse(divide(Y1, divide(Y2, inverse(Y1)))) -> Y2
% 2.23/2.38 inverse(divide(divide(Y1, Y2), Y1)) -> Y2
% 2.23/2.38 inverse(divide(divide(Y1, divide(Y2, divide(X0, X0))), Y1)) -> Y2
% 2.23/2.38 inverse(divide(inverse(X0), divide(Y1, X0))) -> Y1
% 2.23/2.38 inverse(inverse(Y1)) -> Y1
% 2.23/2.38 multiply(A, B) -> divide(A, inverse(B))
% 2.23/2.38 true__ -> false__
% 2.23/2.38 with the LPO induced by
% 2.23/2.38 b2 > multiply > divide > inverse > a2 > f1 > true__ > false__
% 2.23/2.38
% 2.23/2.38 % SZS output end Proof
% 2.23/2.38
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