TSTP Solution File: GRP536-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP536-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n014.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 10:56:06 EDT 2022
% Result : Unsatisfiable 3.01s 3.13s
% Output : Proof 3.01s
% 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 : GRP536-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n014.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 12:55:52 EDT 2022
% 0.14/0.34 % CPUTime :
% 3.01/3.13 % SZS status Unsatisfiable
% 3.01/3.13 % SZS output start Proof
% 3.01/3.13 The input problem is unsatisfiable because
% 3.01/3.13
% 3.01/3.13 [1] the following set of Horn clauses is unsatisfiable:
% 3.01/3.13
% 3.01/3.13 divide(divide(A, divide(divide(A, B), C)), B) = C
% 3.01/3.13 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 3.01/3.13 inverse(A) = divide(divide(B, B), A)
% 3.01/3.13 identity = divide(A, A)
% 3.01/3.13 multiply(a, b) = multiply(b, a) ==> \bottom
% 3.01/3.13
% 3.01/3.13 This holds because
% 3.01/3.13
% 3.01/3.13 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.01/3.13
% 3.01/3.13 E:
% 3.01/3.13 divide(divide(A, divide(divide(A, B), C)), B) = C
% 3.01/3.13 f1(multiply(a, b)) = true__
% 3.01/3.13 f1(multiply(b, a)) = false__
% 3.01/3.13 identity = divide(A, A)
% 3.01/3.13 inverse(A) = divide(divide(B, B), A)
% 3.01/3.13 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 3.01/3.13 G:
% 3.01/3.13 true__ = false__
% 3.01/3.13
% 3.01/3.13 This holds because
% 3.01/3.13
% 3.01/3.13 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.01/3.13
% 3.01/3.13 divide(X0, Y1) = divide(inverse(Y1), inverse(X0))
% 3.01/3.13 divide(X1, Y0) = inverse(divide(Y0, X1))
% 3.01/3.13 divide(Y0, inverse(X0)) = divide(X0, inverse(Y0))
% 3.01/3.13 divide(inverse(Y1), Y2) = divide(inverse(Y2), Y1)
% 3.01/3.13 inverse(divide(X1, divide(Y0, Y1))) = inverse(divide(Y1, divide(Y0, X1)))
% 3.01/3.13 divide(A, A) -> identity
% 3.01/3.13 divide(Y0, divide(Y0, Y1)) -> Y1
% 3.01/3.13 divide(Y0, inverse(divide(Y1, Y0))) -> Y1
% 3.01/3.13 divide(Y1, divide(X0, inverse(Y1))) -> inverse(X0)
% 3.01/3.13 divide(Y1, identity) -> Y1
% 3.01/3.13 divide(divide(Y0, Y1), divide(X1, Y1)) -> divide(Y0, X1)
% 3.01/3.13 divide(divide(Y0, Y2), Y1) -> inverse(divide(Y2, divide(Y0, Y1)))
% 3.01/3.13 divide(divide(Y0, divide(X0, X1)), divide(X1, X0)) -> Y0
% 3.01/3.13 divide(identity, Y1) -> inverse(Y1)
% 3.01/3.13 divide(identity, divide(Y1, divide(Y0, divide(identity, Y1)))) -> Y0
% 3.01/3.13 divide(inverse(X0), divide(Y1, X0)) -> inverse(Y1)
% 3.01/3.13 divide(inverse(X0), divide(inverse(Y1), X0)) -> Y1
% 3.01/3.13 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1)
% 3.01/3.13 divide(inverse(Y1), Y0) -> inverse(divide(Y1, inverse(Y0)))
% 3.01/3.13 f1(divide(a, divide(identity, b))) -> true__
% 3.01/3.13 f1(divide(b, inverse(a))) -> false__
% 3.01/3.13 f1(divide(identity, divide(divide(identity, b), a))) -> true__
% 3.01/3.13 f1(inverse(divide(inverse(b), a))) -> true__
% 3.01/3.13 f1(multiply(a, b)) -> true__
% 3.01/3.13 inverse(divide(X0, inverse(divide(inverse(X0), Y1)))) -> Y1
% 3.01/3.13 inverse(divide(inverse(Y1), divide(Y0, Y1))) -> Y0
% 3.01/3.13 inverse(divide(inverse(Y1), inverse(divide(Y1, Y0)))) -> Y0
% 3.01/3.13 inverse(identity) -> identity
% 3.01/3.13 inverse(inverse(Y1)) -> Y1
% 3.01/3.13 multiply(Y0, Y2) -> divide(Y0, inverse(Y2))
% 3.01/3.13 true__ -> false__
% 3.01/3.13 with the LPO induced by
% 3.01/3.13 a > b > f1 > multiply > divide > inverse > identity > true__ > false__
% 3.01/3.13
% 3.01/3.13 % SZS output end Proof
% 3.01/3.13
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