TSTP Solution File: GRP540-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP540-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 10:56:08 EDT 2022
% Result : Unsatisfiable 2.52s 2.61s
% Output : Proof 2.52s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP540-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 12:25:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.52/2.61 % SZS status Unsatisfiable
% 2.52/2.61 % SZS output start Proof
% 2.52/2.61 The input problem is unsatisfiable because
% 2.52/2.61
% 2.52/2.61 [1] the following set of Horn clauses is unsatisfiable:
% 2.52/2.61
% 2.52/2.61 divide(divide(A, B), divide(divide(A, C), B)) = C
% 2.52/2.61 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 2.52/2.61 inverse(A) = divide(divide(B, B), A)
% 2.52/2.61 identity = divide(A, A)
% 2.52/2.61 multiply(a, b) = multiply(b, a) ==> \bottom
% 2.52/2.61
% 2.52/2.61 This holds because
% 2.52/2.61
% 2.52/2.61 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.52/2.61
% 2.52/2.61 E:
% 2.52/2.61 divide(divide(A, B), divide(divide(A, C), B)) = C
% 2.52/2.61 f1(multiply(a, b)) = true__
% 2.52/2.61 f1(multiply(b, a)) = false__
% 2.52/2.61 identity = divide(A, A)
% 2.52/2.61 inverse(A) = divide(divide(B, B), A)
% 2.52/2.61 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 2.52/2.61 G:
% 2.52/2.61 true__ = false__
% 2.52/2.61
% 2.52/2.61 This holds because
% 2.52/2.61
% 2.52/2.61 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.52/2.61
% 2.52/2.61 divide(Y0, X0) = divide(inverse(X0), inverse(Y0))
% 2.52/2.61 divide(Y0, X1) = inverse(divide(X1, Y0))
% 2.52/2.61 divide(Y0, inverse(X0)) = divide(X0, inverse(Y0))
% 2.52/2.61 divide(A, A) -> identity
% 2.52/2.61 divide(X0, inverse(divide(Y0, X0))) -> Y0
% 2.52/2.61 divide(X2, divide(divide(divide(X0, X1), Y2), divide(divide(X0, X2), X1))) -> Y2
% 2.52/2.61 divide(Y0, divide(Y0, Y1)) -> Y1
% 2.52/2.61 divide(Y0, divide(divide(Y1, Y3), divide(Y1, Y0))) -> Y3
% 2.52/2.61 divide(Y0, divide(divide(divide(Y0, Y2), Y3), divide(identity, Y2))) -> Y3
% 2.52/2.61 divide(Y0, divide(divide(identity, Y3), divide(divide(Y2, Y0), Y2))) -> Y3
% 2.52/2.61 divide(Y0, divide(identity, divide(divide(Y1, Y0), Y2))) -> divide(Y1, Y2)
% 2.52/2.61 divide(Y0, divide(inverse(Y1), inverse(Y0))) -> Y1
% 2.52/2.61 divide(Y0, identity) -> Y0
% 2.52/2.61 divide(Y1, divide(X0, inverse(Y1))) -> inverse(X0)
% 2.52/2.61 divide(divide(X0, X1), X0) -> inverse(X1)
% 2.52/2.61 divide(divide(Y0, Y1), divide(X1, Y1)) -> divide(Y0, X1)
% 2.52/2.61 divide(divide(Y0, divide(divide(Y0, Y2), X1)), X1) -> Y2
% 2.52/2.61 divide(divide(Y0, inverse(X1)), X1) -> Y0
% 2.52/2.61 divide(divide(Y1, X1), inverse(X1)) -> Y1
% 2.52/2.61 divide(identity, Y1) -> inverse(Y1)
% 2.52/2.61 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1)
% 2.52/2.61 divide(inverse(X0), inverse(divide(X0, inverse(Y1)))) -> Y1
% 2.52/2.61 divide(inverse(X1), divide(X0, X1)) -> inverse(X0)
% 2.52/2.61 f1(divide(a, divide(identity, b))) -> true__
% 2.52/2.61 f1(divide(b, inverse(a))) -> false__
% 2.52/2.61 f1(divide(b, inverse(a))) -> true__
% 2.52/2.61 f1(inverse(divide(inverse(b), a))) -> true__
% 2.52/2.61 f1(multiply(a, b)) -> true__
% 2.52/2.61 inverse(divide(X0, divide(Y0, inverse(X0)))) -> Y0
% 2.52/2.61 inverse(divide(Y1, inverse(divide(inverse(Y1), Y0)))) -> Y0
% 2.52/2.61 inverse(divide(inverse(Y1), divide(Y0, Y1))) -> Y0
% 2.52/2.61 inverse(identity) -> identity
% 2.52/2.61 inverse(inverse(X1)) -> X1
% 2.52/2.61 multiply(Y0, Y2) -> divide(Y0, inverse(Y2))
% 2.52/2.61 true__ -> false__
% 2.52/2.61 with the LPO induced by
% 2.52/2.61 a > b > f1 > multiply > divide > inverse > identity > true__ > false__
% 2.52/2.61
% 2.52/2.61 % SZS output end Proof
% 2.52/2.61
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