TSTP Solution File: GRP526-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP526-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n009.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 10:56:02 EDT 2022
% Result : Unsatisfiable 2.55s 2.70s
% Output : Proof 2.55s
% 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 : GRP526-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 09:25:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.55/2.70 % SZS status Unsatisfiable
% 2.55/2.70 % SZS output start Proof
% 2.55/2.70 The input problem is unsatisfiable because
% 2.55/2.70
% 2.55/2.70 [1] the following set of Horn clauses is unsatisfiable:
% 2.55/2.70
% 2.55/2.70 divide(A, divide(divide(A, B), divide(C, B))) = C
% 2.55/2.70 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 2.55/2.70 inverse(A) = divide(divide(B, B), A)
% 2.55/2.70 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 2.55/2.70
% 2.55/2.70 This holds because
% 2.55/2.70
% 2.55/2.70 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 2.55/2.70
% 2.55/2.70 E:
% 2.55/2.70 divide(A, divide(divide(A, B), divide(C, B))) = C
% 2.55/2.70 f1(a2) = false__
% 2.55/2.70 f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 2.55/2.70 inverse(A) = divide(divide(B, B), A)
% 2.55/2.70 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 2.55/2.70 G:
% 2.55/2.70 true__ = false__
% 2.55/2.70
% 2.55/2.70 This holds because
% 2.55/2.70
% 2.55/2.70 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 2.55/2.70
% 2.55/2.70
% 2.55/2.70 divide(A, divide(divide(A, B), divide(C, B))) -> C
% 2.55/2.70 divide(X1, X1) -> g1
% 2.55/2.70 divide(Y0, divide(X2, divide(Y2, divide(divide(Y0, X1), divide(X2, X1))))) -> Y2
% 2.55/2.70 divide(Y0, divide(Y0, Y1)) -> Y1
% 2.55/2.70 divide(Y0, divide(Y3, divide(Y2, divide(Y0, Y3)))) -> Y2
% 2.55/2.70 divide(Y0, divide(g1, divide(Y1, Y0))) -> Y1
% 2.55/2.70 divide(Y0, g1) -> Y0
% 2.55/2.70 divide(Y3, divide(Y1, divide(Y2, divide(g1, divide(Y1, Y3))))) -> Y2
% 2.55/2.70 divide(divide(X1, X0), X1) -> divide(g1, X0)
% 2.55/2.70 divide(divide(Y0, Y3), divide(Y1, Y3)) -> divide(Y0, Y1)
% 2.55/2.70 divide(divide(Y0, divide(X2, X1)), X1) -> divide(Y0, X2)
% 2.55/2.70 divide(divide(g1, X1), divide(Y1, X1)) -> divide(g1, Y1)
% 2.55/2.70 divide(divide(g1, divide(Y0, Y1)), divide(g1, Y0)) -> Y1
% 2.55/2.70 divide(g1, divide(X0, divide(Y2, divide(g1, X0)))) -> Y2
% 2.55/2.70 divide(g1, divide(g1, Y0)) -> Y0
% 2.55/2.70 f1(a2) -> false__
% 2.55/2.70 f1(divide(g1, divide(g1, a2))) -> true__
% 2.55/2.70 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 2.55/2.70 g2 -> g1
% 2.55/2.70 inverse(Y1) -> divide(g1, Y1)
% 2.55/2.70 inverse(divide(inverse(inverse(divide(X1, Y1))), X1)) -> Y1
% 2.55/2.70 multiply(A, B) -> divide(A, divide(g1, B))
% 2.55/2.70 true__ -> false__
% 2.55/2.70 with the LPO induced by
% 2.55/2.70 b2 > multiply > g2 > inverse > divide > g1 > a2 > f1 > true__ > false__
% 2.55/2.70
% 2.55/2.70 % SZS output end Proof
% 2.55/2.70
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