TSTP Solution File: GRP448-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP448-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n015.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 10:55:31 EDT 2022
% Result : Unsatisfiable 2.72s 2.81s
% Output : Proof 2.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP448-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : moca.sh %s
% 0.14/0.34 % Computer : n015.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 10:38:37 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.72/2.81 % SZS status Unsatisfiable
% 2.72/2.81 % SZS output start Proof
% 2.72/2.81 The input problem is unsatisfiable because
% 2.72/2.81
% 2.72/2.81 [1] the following set of Horn clauses is unsatisfiable:
% 2.72/2.81
% 2.72/2.81 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) = B
% 2.72/2.81 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 2.72/2.81 inverse(A) = divide(divide(B, B), A)
% 2.72/2.81 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 2.72/2.81
% 2.72/2.81 This holds because
% 2.72/2.81
% 2.72/2.81 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.72/2.81
% 2.72/2.81 E:
% 2.72/2.81 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) = B
% 2.72/2.81 f1(multiply(inverse(a1), a1)) = true__
% 2.72/2.81 f1(multiply(inverse(b1), b1)) = false__
% 2.72/2.81 inverse(A) = divide(divide(B, B), A)
% 2.72/2.81 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 2.72/2.81 G:
% 2.72/2.81 true__ = false__
% 2.72/2.81
% 2.72/2.81 This holds because
% 2.72/2.81
% 2.72/2.81 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.72/2.81
% 2.72/2.81
% 2.72/2.81 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) -> B
% 2.72/2.81 divide(X1, X1) -> g1
% 2.72/2.81 divide(Y0, divide(divide(inverse(Y1), Y2), divide(inverse(Y0), Y2))) -> Y1
% 2.72/2.81 divide(Y0, divide(g1, divide(divide(g1, Y0), X0))) -> divide(g1, divide(g1, divide(g1, X0)))
% 2.72/2.81 divide(Y0, divide(g1, divide(g1, Y0))) -> g1
% 2.72/2.81 divide(Y0, inverse(divide(inverse(Y0), inverse(Y1)))) -> Y1
% 2.72/2.81 divide(Y1, g1) -> Y1
% 2.72/2.81 divide(divide(divide(g1, X0), X1), divide(g1, X1)) -> divide(g1, divide(g1, divide(g1, X0)))
% 2.72/2.81 divide(divide(g1, Y0), divide(g1, divide(Y0, divide(g1, Y1)))) -> Y1
% 2.72/2.81 divide(divide(g1, Y0), divide(g1, divide(Y0, g1))) -> g1
% 2.72/2.81 divide(divide(g1, divide(g1, Y0)), g1) -> divide(Y0, g1)
% 2.72/2.81 divide(g1, divide(divide(X0, Y1), divide(g1, Y1))) -> divide(g1, divide(g1, divide(g1, X0)))
% 2.72/2.81 divide(g1, divide(g1, divide(g1, divide(g1, Y0)))) -> Y0
% 2.72/2.81 divide(g1, inverse(divide(g1, inverse(Y1)))) -> Y1
% 2.72/2.81 divide(inverse(X0), inverse(divide(X0, inverse(Y1)))) -> Y1
% 2.72/2.81 divide(inverse(Y0), inverse(divide(Y0, g1))) -> g1
% 2.72/2.81 divide(inverse(inverse(Y0)), g1) -> divide(Y0, g1)
% 2.72/2.81 divide(inverse(inverse(Y0)), inverse(X1)) -> divide(Y0, divide(g1, X1))
% 2.72/2.81 f1(divide(inverse(a1), inverse(a1))) -> true__
% 2.72/2.81 f1(g1) -> false__
% 2.72/2.81 f1(g1) -> true__
% 2.72/2.81 f1(inverse(divide(X1, X1))) -> false__
% 2.72/2.81 f1(inverse(divide(X1, X1))) -> true__
% 2.72/2.81 f1(multiply(inverse(a1), a1)) -> true__
% 2.72/2.81 f1(multiply(inverse(b1), b1)) -> false__
% 2.72/2.81 g2 -> g1
% 2.72/2.81 inverse(Y1) -> divide(g1, Y1)
% 2.72/2.81 inverse(divide(divide(inverse(Y0), inverse(inverse(inverse(X0)))), X0)) -> Y0
% 2.72/2.81 inverse(divide(divide(inverse(Y1), Y2), divide(inverse(divide(X0, X0)), Y2))) -> Y1
% 2.72/2.81 inverse(divide(divide(inverse(Y1), Y2), divide(inverse(inverse(divide(X0, X0))), Y2))) -> Y1
% 2.72/2.81 inverse(divide(divide(inverse(Y1), Y2), inverse(Y2))) -> Y1
% 2.72/2.81 inverse(inverse(divide(inverse(inverse(divide(X0, X0))), inverse(Y1)))) -> Y1
% 2.72/2.81 inverse(inverse(inverse(inverse(Y1)))) -> Y1
% 2.72/2.81 multiply(A, B) -> divide(A, divide(g1, B))
% 2.72/2.81 true__ -> false__
% 2.72/2.81 with the LPO induced by
% 2.72/2.81 a1 > b1 > multiply > g2 > inverse > divide > g1 > f1 > true__ > false__
% 2.72/2.81
% 2.72/2.81 % SZS output end Proof
% 2.72/2.81
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