TSTP Solution File: GRP521-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP521-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n023.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 10:56:00 EDT 2022
% Result : Unsatisfiable 0.59s 0.79s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP521-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : moca.sh %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 09:05:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.59/0.79 % SZS status Unsatisfiable
% 0.59/0.79 % SZS output start Proof
% 0.59/0.79 The input problem is unsatisfiable because
% 0.59/0.79
% 0.59/0.79 [1] the following set of Horn clauses is unsatisfiable:
% 0.59/0.79
% 0.59/0.79 divide(A, divide(B, divide(C, divide(A, B)))) = C
% 0.59/0.79 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.59/0.79 inverse(A) = divide(divide(B, B), A)
% 0.59/0.79 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 0.59/0.79
% 0.59/0.79 This holds because
% 0.59/0.79
% 0.59/0.79 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.59/0.79
% 0.59/0.79 E:
% 0.59/0.79 divide(A, divide(B, divide(C, divide(A, B)))) = C
% 0.59/0.79 f1(multiply(inverse(a1), a1)) = true__
% 0.59/0.79 f1(multiply(inverse(b1), b1)) = false__
% 0.59/0.79 inverse(A) = divide(divide(B, B), A)
% 0.59/0.79 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.59/0.79 G:
% 0.59/0.79 true__ = false__
% 0.59/0.79
% 0.59/0.79 This holds because
% 0.59/0.79
% 0.59/0.79 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.59/0.79
% 0.59/0.79 divide(Y0, divide(Y1, inverse(divide(Y0, Y1)))) = divide(X0, X0)
% 0.59/0.79 inverse(divide(Y0, inverse(inverse(Y0)))) = divide(X0, X0)
% 0.59/0.79 inverse(divide(Y0, inverse(inverse(Y0)))) = inverse(divide(X0, X0))
% 0.59/0.79 inverse(inverse(divide(X0, X0))) = inverse(divide(Y1, inverse(inverse(Y1))))
% 0.59/0.79 inverse(inverse(inverse(inverse(divide(X0, X0))))) = divide(Y1, Y1)
% 0.59/0.79 inverse(inverse(inverse(inverse(inverse(divide(X0, X0)))))) = divide(Y1, Y1)
% 0.59/0.79 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.59/0.79 divide(A, divide(B, divide(C, divide(A, B)))) -> C
% 0.59/0.79 divide(Y0, divide(divide(X2, divide(Y2, Y0)), X2)) -> Y2
% 0.59/0.79 divide(Y0, inverse(divide(Y2, divide(Y0, divide(X0, X0))))) -> Y2
% 0.59/0.79 divide(divide(B, B), A) -> inverse(A)
% 0.59/0.79 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1)
% 0.59/0.79 divide(inverse(divide(X1, inverse(inverse(X1)))), Y1) -> inverse(Y1)
% 0.59/0.79 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1)
% 0.59/0.79 divide(inverse(inverse(inverse(divide(X0, X0)))), Y1) -> inverse(Y1)
% 0.59/0.79 f1(divide(inverse(a1), inverse(a1))) -> true__
% 0.59/0.79 f1(divide(inverse(b1), inverse(b1))) -> false__
% 0.59/0.79 f1(inverse(divide(X1, inverse(inverse(X1))))) -> false__
% 0.59/0.79 f1(inverse(divide(X1, inverse(inverse(X1))))) -> true__
% 0.59/0.79 f1(inverse(divide(divide(X0, divide(X1, inverse(X0))), inverse(X1)))) -> false__
% 0.59/0.79 f1(inverse(divide(divide(X0, divide(X1, inverse(X0))), inverse(X1)))) -> true__
% 0.59/0.79 f1(inverse(inverse(inverse(inverse(divide(X0, X0)))))) -> false__
% 0.59/0.79 f1(inverse(inverse(inverse(inverse(divide(X0, X0)))))) -> true__
% 0.59/0.79 f1(inverse(inverse(inverse(inverse(inverse(divide(X0, X0))))))) -> false__
% 0.59/0.79 f1(inverse(inverse(inverse(inverse(inverse(divide(X0, X0))))))) -> true__
% 0.59/0.79 f1(multiply(inverse(a1), a1)) -> true__
% 0.59/0.79 f1(multiply(inverse(b1), b1)) -> false__
% 0.59/0.79 inverse(divide(Y1, divide(Y2, inverse(Y1)))) -> Y2
% 0.59/0.79 inverse(divide(divide(X0, divide(X1, inverse(X0))), divide(Y1, X1))) -> Y1
% 0.59/0.79 inverse(divide(divide(Y1, divide(Y2, divide(X0, X0))), Y1)) -> Y2
% 0.59/0.79 inverse(inverse(divide(Y1, inverse(divide(X0, X0))))) -> Y1
% 0.59/0.79 inverse(inverse(divide(Y1, inverse(inverse(divide(X0, X0)))))) -> Y1
% 0.59/0.79 true__ -> false__
% 0.59/0.79 with the LPO induced by
% 0.59/0.79 a1 > b1 > f1 > multiply > divide > inverse > true__ > false__
% 0.59/0.79
% 0.59/0.79 % SZS output end Proof
% 0.59/0.79
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