TSTP Solution File: GRP541-1 by Moca---0.1
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% File : Moca---0.1
% Problem : GRP541-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n010.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 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP541-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : moca.sh %s
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 14 02:39:09 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 The input problem is unsatisfiable because
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% 0.12/0.37 [1] the following set of Horn clauses is unsatisfiable:
% 0.12/0.37
% 0.12/0.37 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B
% 0.12/0.37 multiply(A, B) = divide(A, divide(identity, B))
% 0.12/0.37 inverse(A) = divide(identity, A)
% 0.12/0.37 identity = divide(A, A)
% 0.12/0.37 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 0.12/0.37
% 0.12/0.37 This holds because
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% 0.12/0.37 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.12/0.37
% 0.12/0.37 E:
% 0.12/0.37 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B
% 0.12/0.37 f1(multiply(inverse(a1), a1)) = true__
% 0.12/0.37 f1(multiply(inverse(b1), b1)) = false__
% 0.12/0.37 identity = divide(A, A)
% 0.12/0.37 inverse(A) = divide(identity, A)
% 0.12/0.37 multiply(A, B) = divide(A, divide(identity, B))
% 0.12/0.37 G:
% 0.12/0.37 true__ = false__
% 0.12/0.37
% 0.12/0.37 This holds because
% 0.12/0.37
% 0.12/0.37 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.12/0.37
% 0.12/0.37 divide(inverse(X1), inverse(X0)) = divide(X0, X1)
% 0.12/0.37 divide(A, A) -> identity
% 0.12/0.37 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) -> B
% 0.12/0.37 divide(identity, A) -> inverse(A)
% 0.12/0.37 divide(inverse(divide(X1, identity)), divide(X0, X1)) -> inverse(X0)
% 0.12/0.37 divide(inverse(divide(divide(divide(Y0, Y1), Y2), Y0)), Y2) -> Y1
% 0.12/0.37 divide(inverse(divide(divide(inverse(Y1), Y2), identity)), Y2) -> Y1
% 0.12/0.37 divide(inverse(divide(inverse(Y2), Y1)), Y2) -> Y1
% 0.12/0.37 divide(inverse(inverse(Y0)), divide(Y0, Y1)) -> Y1
% 0.12/0.37 divide(inverse(inverse(Y1)), identity) -> Y1
% 0.12/0.37 divide(inverse(inverse(inverse(divide(inverse(Y1), X1)))), X1) -> Y1
% 0.12/0.37 divide(inverse(inverse(inverse(inverse(X0)))), X1) -> divide(X0, X1)
% 0.12/0.37 f1(identity) -> false__
% 0.12/0.37 f1(identity) -> true__
% 0.12/0.37 f1(multiply(inverse(a1), a1)) -> true__
% 0.12/0.37 f1(multiply(inverse(b1), b1)) -> false__
% 0.12/0.37 inverse(identity) -> identity
% 0.12/0.37 inverse(inverse(Y1)) -> Y1
% 0.12/0.37 multiply(A, B) -> divide(A, divide(identity, B))
% 0.12/0.37 true__ -> false__
% 0.12/0.37 with the LPO induced by
% 0.12/0.37 a1 > b1 > f1 > multiply > divide > identity > inverse > true__ > false__
% 0.12/0.37
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37
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