TSTP Solution File: GRP525-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n006.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 10:56:01 EDT 2022
% Result : Unsatisfiable 1.98s 2.12s
% Output : Proof 1.98s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 08:46:27 EDT 2022
% 0.12/0.35 % CPUTime :
% 1.98/2.12 % SZS status Unsatisfiable
% 1.98/2.12 % SZS output start Proof
% 1.98/2.12 The input problem is unsatisfiable because
% 1.98/2.12
% 1.98/2.12 [1] the following set of Horn clauses is unsatisfiable:
% 1.98/2.12
% 1.98/2.12 divide(A, divide(divide(A, B), divide(C, B))) = C
% 1.98/2.12 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 1.98/2.12 inverse(A) = divide(divide(B, B), A)
% 1.98/2.12 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 1.98/2.12
% 1.98/2.12 This holds because
% 1.98/2.12
% 1.98/2.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.98/2.12
% 1.98/2.12 E:
% 1.98/2.12 divide(A, divide(divide(A, B), divide(C, B))) = C
% 1.98/2.12 f1(multiply(inverse(a1), a1)) = true__
% 1.98/2.12 f1(multiply(inverse(b1), b1)) = false__
% 1.98/2.12 inverse(A) = divide(divide(B, B), A)
% 1.98/2.12 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 1.98/2.12 G:
% 1.98/2.12 true__ = false__
% 1.98/2.12
% 1.98/2.12 This holds because
% 1.98/2.12
% 1.98/2.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 divide(A, divide(divide(A, B), divide(C, B))) -> C
% 1.98/2.12 divide(X1, X1) -> g1
% 1.98/2.12 divide(Y0, divide(divide(Y0, Y1), inverse(Y1))) -> g1
% 1.98/2.12 divide(Y0, g1) -> Y0
% 1.98/2.12 divide(Y0, inverse(divide(X1, inverse(inverse(X1))))) -> Y0
% 1.98/2.12 divide(Y0, inverse(inverse(Y0))) -> g1
% 1.98/2.12 divide(Y1, inverse(divide(Y2, Y1))) -> Y2
% 1.98/2.12 divide(divide(B, B), A) -> inverse(A)
% 1.98/2.12 divide(divide(X1, inverse(inverse(X1))), Y1) -> inverse(Y1)
% 1.98/2.12 divide(divide(Y0, divide(X2, X1)), X1) -> divide(Y0, X2)
% 1.98/2.12 divide(g1, Y1) -> inverse(Y1)
% 1.98/2.12 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1)
% 1.98/2.12 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1
% 1.98/2.12 divide(inverse(divide(g1, Y1)), g1) -> Y1
% 1.98/2.12 divide(inverse(inverse(Y1)), g1) -> Y1
% 1.98/2.12 divide(inverse(inverse(Y1)), inverse(divide(X1, X1))) -> Y1
% 1.98/2.12 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1)
% 1.98/2.12 f1(divide(X1, inverse(inverse(X1)))) -> false__
% 1.98/2.12 f1(divide(X1, inverse(inverse(X1)))) -> true__
% 1.98/2.12 f1(divide(inverse(a1), inverse(a1))) -> true__
% 1.98/2.12 f1(g1) -> false__
% 1.98/2.12 f1(g1) -> true__
% 1.98/2.12 f1(multiply(inverse(a1), a1)) -> true__
% 1.98/2.12 f1(multiply(inverse(b1), b1)) -> false__
% 1.98/2.12 inverse(divide(g1, divide(Y1, g1))) -> Y1
% 1.98/2.12 inverse(divide(inverse(Y0), g1)) -> Y0
% 1.98/2.12 inverse(divide(inverse(Y1), divide(Y2, Y1))) -> Y2
% 1.98/2.12 inverse(divide(inverse(inverse(divide(X1, Y1))), X1)) -> Y1
% 1.98/2.12 inverse(g1) -> g1
% 1.98/2.12 inverse(inverse(divide(X1, divide(Y0, Y0)))) -> X1
% 1.98/2.12 inverse(inverse(divide(X1, inverse(divide(Y0, Y0))))) -> X1
% 1.98/2.12 multiply(A, B) -> divide(A, inverse(B))
% 1.98/2.12 true__ -> false__
% 1.98/2.12 with the LPO induced by
% 1.98/2.12 a1 > b1 > multiply > divide > g1 > f1 > inverse > true__ > false__
% 1.98/2.12
% 1.98/2.12 % SZS output end Proof
% 1.98/2.12
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