TSTP Solution File: GRP564-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP564-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n027.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 10:56:18 EDT 2022
% Result : Unsatisfiable 2.22s 2.30s
% Output : Proof 2.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP564-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : moca.sh %s
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % 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 : Tue Jun 14 14:08:48 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.22/2.30 % SZS status Unsatisfiable
% 2.22/2.30 % SZS output start Proof
% 2.22/2.30 The input problem is unsatisfiable because
% 2.22/2.30
% 2.22/2.30 [1] the following set of Horn clauses is unsatisfiable:
% 2.22/2.30
% 2.22/2.30 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B
% 2.22/2.30 multiply(A, B) = divide(A, inverse(B))
% 2.22/2.30 multiply(a, b) = multiply(b, a) ==> \bottom
% 2.22/2.30
% 2.22/2.30 This holds because
% 2.22/2.30
% 2.22/2.30 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.22/2.30
% 2.22/2.30 E:
% 2.22/2.30 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B
% 2.22/2.30 f1(multiply(a, b)) = true__
% 2.22/2.30 f1(multiply(b, a)) = false__
% 2.22/2.30 multiply(A, B) = divide(A, inverse(B))
% 2.22/2.30 G:
% 2.22/2.30 true__ = false__
% 2.22/2.30
% 2.22/2.30 This holds because
% 2.22/2.30
% 2.22/2.30 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.22/2.30
% 2.22/2.30 divide(Y0, X1) = divide(inverse(X1), inverse(Y0))
% 2.22/2.30 divide(Y1, inverse(Y0)) = divide(Y0, inverse(Y1))
% 2.22/2.30 divide(X1, divide(Y0, divide(inverse(X1), inverse(divide(Y0, inverse(Y1)))))) -> Y1
% 2.22/2.30 divide(X1, divide(divide(X0, inverse(X1)), divide(X0, inverse(Y1)))) -> Y1
% 2.22/2.30 divide(X1, divide(divide(inverse(Y2), inverse(divide(Y1, inverse(X1)))), Y1)) -> Y2
% 2.22/2.30 divide(X1, divide(inverse(Y1), inverse(X1))) -> Y1
% 2.22/2.30 divide(X1, inverse(divide(X0, X0))) -> X1
% 2.22/2.30 divide(X2, divide(Y0, divide(divide(X1, inverse(divide(Y0, inverse(Y1)))), divide(X1, inverse(X2))))) -> Y1
% 2.22/2.30 divide(Y0, divide(X1, divide(divide(inverse(Y0), inverse(X1)), inverse(Y2)))) -> Y2
% 2.22/2.30 divide(Y0, divide(Y0, Y1)) -> Y1
% 2.22/2.30 divide(Y0, divide(Y0, inverse(inverse(Y1)))) -> Y1
% 2.22/2.30 divide(Y0, divide(divide(divide(inverse(Y2), inverse(X1)), inverse(Y0)), X1)) -> Y2
% 2.22/2.30 divide(Y0, multiply(inverse(inverse(Y0)), inverse(Y1))) -> Y1
% 2.22/2.30 divide(Y1, divide(Y2, Y2)) -> Y1
% 2.22/2.30 divide(Y1, inverse(inverse(Y0))) -> divide(Y1, Y0)
% 2.22/2.30 divide(divide(X1, X1), inverse(Y1)) -> Y1
% 2.22/2.30 divide(divide(X1, Y2), divide(divide(inverse(Y1), inverse(X1)), Y2)) -> Y1
% 2.22/2.30 divide(divide(Y1, X0), inverse(X0)) -> Y1
% 2.22/2.30 divide(divide(Y1, inverse(Y0)), Y0) -> Y1
% 2.22/2.30 divide(divide(Y1, inverse(Y3)), Y1) -> Y3
% 2.22/2.30 divide(divide(divide(A, inverse(B)), C), divide(A, C)) -> B
% 2.22/2.30 divide(divide(divide(Y0, inverse(Y1)), divide(divide(X1, inverse(Y0)), divide(X1, inverse(X2)))), X2) -> Y1
% 2.22/2.30 divide(divide(divide(Y0, inverse(Y1)), divide(inverse(X1), inverse(Y0))), X1) -> Y1
% 2.22/2.30 divide(divide(divide(Y0, inverse(divide(X1, X1))), inverse(Y2)), Y0) -> Y2
% 2.22/2.30 divide(divide(divide(divide(Y2, inverse(X1)), inverse(Y1)), Y2), X1) -> Y1
% 2.22/2.30 divide(divide(divide(divide(divide(X0, inverse(X1)), X2), inverse(Y1)), divide(X0, X2)), X1) -> Y1
% 2.22/2.30 divide(inverse(Y0), inverse(divide(Y0, inverse(Y1)))) -> Y1
% 2.22/2.30 divide(inverse(Y0), inverse(divide(inverse(inverse(Y1)), inverse(Y0)))) -> Y1
% 2.22/2.30 divide(inverse(divide(X1, X1)), inverse(Y0)) -> Y0
% 2.22/2.30 divide(inverse(inverse(X0)), inverse(X1)) -> divide(X0, inverse(X1))
% 2.22/2.30 divide(inverse(inverse(X0)), inverse(divide(Y1, X0))) -> Y1
% 2.22/2.30 divide(inverse(inverse(X1)), inverse(divide(X0, X0))) -> X1
% 2.22/2.30 divide(multiply(inverse(inverse(Y1)), Y0), Y0) -> Y1
% 2.22/2.30 f1(divide(a, inverse(b))) -> true__
% 2.22/2.30 f1(divide(b, inverse(a))) -> false__
% 2.22/2.30 multiply(A, B) -> divide(A, inverse(B))
% 2.22/2.30 multiply(inverse(inverse(Y1)), divide(Y0, Y0)) -> Y1
% 2.22/2.30 true__ -> false__
% 2.22/2.30 with the LPO induced by
% 2.22/2.30 multiply > inverse > divide > a > b > f1 > true__ > false__
% 2.22/2.30
% 2.22/2.30 % SZS output end Proof
% 2.22/2.30
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