TSTP Solution File: GRP561-1 by Moca---0.1
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% File : Moca---0.1
% Problem : GRP561-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n004.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 10:56:17 EDT 2022
% Result : Unsatisfiable 3.02s 3.19s
% Output : Proof 3.02s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP561-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.09 % Command : moca.sh %s
% 0.08/0.29 % Computer : n004.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 600
% 0.08/0.29 % DateTime : Tue Jun 14 05:57:09 EDT 2022
% 0.08/0.29 % CPUTime :
% 3.02/3.19 % SZS status Unsatisfiable
% 3.02/3.19 % SZS output start Proof
% 3.02/3.19 The input problem is unsatisfiable because
% 3.02/3.19
% 3.02/3.19 [1] the following set of Horn clauses is unsatisfiable:
% 3.02/3.19
% 3.02/3.19 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B
% 3.02/3.19 multiply(A, B) = divide(A, inverse(B))
% 3.02/3.19 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 3.02/3.19
% 3.02/3.19 This holds because
% 3.02/3.19
% 3.02/3.19 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.02/3.19
% 3.02/3.19 E:
% 3.02/3.19 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B
% 3.02/3.19 f1(multiply(inverse(a1), a1)) = true__
% 3.02/3.19 f1(multiply(inverse(b1), b1)) = false__
% 3.02/3.19 multiply(A, B) = divide(A, inverse(B))
% 3.02/3.19 G:
% 3.02/3.19 true__ = false__
% 3.02/3.19
% 3.02/3.19 This holds because
% 3.02/3.19
% 3.02/3.19 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.02/3.19
% 3.02/3.19 divide(Y0, X1) = multiply(inverse(X1), Y0)
% 3.02/3.19 divide(A, inverse(B)) -> multiply(A, B)
% 3.02/3.19 divide(X1, divide(Y0, divide(inverse(X1), inverse(divide(Y0, inverse(Y1)))))) -> Y1
% 3.02/3.19 divide(X1, divide(divide(X0, inverse(X1)), divide(X0, inverse(Y1)))) -> Y1
% 3.02/3.19 divide(X1, divide(divide(inverse(Y2), inverse(divide(Y1, inverse(X1)))), Y1)) -> Y2
% 3.02/3.19 divide(X1, divide(inverse(Y1), inverse(X1))) -> Y1
% 3.02/3.19 divide(X2, divide(Y0, divide(divide(X1, inverse(divide(Y0, inverse(Y1)))), divide(X1, inverse(X2))))) -> Y1
% 3.02/3.19 divide(X2, divide(divide(divide(X0, inverse(inverse(Y1))), inverse(X2)), X0)) -> Y1
% 3.02/3.19 divide(Y0, Y0) -> g2
% 3.02/3.19 divide(Y0, divide(X1, divide(divide(inverse(Y0), inverse(X1)), inverse(Y2)))) -> Y2
% 3.02/3.19 divide(Y0, divide(Y0, Y2)) -> Y2
% 3.02/3.19 divide(Y0, divide(divide(divide(inverse(Y2), inverse(X1)), inverse(Y0)), X1)) -> Y2
% 3.02/3.19 divide(Y0, divide(divide(inverse(Y1), inverse(divide(X1, X1))), inverse(Y0))) -> Y1
% 3.02/3.19 divide(Y0, g2) -> Y0
% 3.02/3.19 divide(Y0, multiply(inverse(Y1), Y0)) -> Y1
% 3.02/3.19 divide(Y1, divide(Y2, Y2)) -> Y1
% 3.02/3.19 divide(divide(X1, X1), inverse(Y1)) -> Y1
% 3.02/3.19 divide(divide(X1, Y2), divide(divide(inverse(Y1), inverse(X1)), Y2)) -> Y1
% 3.02/3.19 divide(divide(X1, inverse(Y2)), divide(inverse(divide(Y1, Y1)), inverse(X1))) -> Y2
% 3.02/3.19 divide(divide(Y1, Y2), divide(divide(X0, X0), Y2)) -> Y1
% 3.02/3.19 divide(divide(Y1, inverse(X1)), X1) -> Y1
% 3.02/3.19 divide(divide(Y1, inverse(Y3)), Y1) -> Y3
% 3.02/3.19 divide(divide(divide(A, inverse(B)), C), divide(A, C)) -> B
% 3.02/3.19 divide(divide(divide(Y0, inverse(Y1)), divide(divide(X1, inverse(Y0)), divide(X1, inverse(X2)))), X2) -> Y1
% 3.02/3.19 divide(divide(divide(Y0, inverse(Y1)), divide(inverse(X1), inverse(Y0))), X1) -> Y1
% 3.02/3.19 divide(divide(divide(Y0, inverse(divide(X1, X1))), inverse(Y2)), Y0) -> Y2
% 3.02/3.19 divide(divide(divide(divide(X1, X1), inverse(Y1)), inverse(Y2)), Y1) -> Y2
% 3.02/3.19 divide(divide(divide(divide(Y0, inverse(divide(X1, X1))), Y2), inverse(Y3)), divide(Y0, Y2)) -> Y3
% 3.02/3.19 divide(divide(divide(divide(Y2, inverse(X1)), inverse(Y1)), Y2), X1) -> Y1
% 3.02/3.19 divide(divide(divide(divide(divide(X0, inverse(X1)), X2), inverse(Y1)), divide(X0, X2)), X1) -> Y1
% 3.02/3.19 f1(divide(a1, a1)) -> true__
% 3.02/3.19 f1(divide(b1, b1)) -> false__
% 3.02/3.19 f1(divide(inverse(a1), inverse(a1))) -> true__
% 3.02/3.19 f1(divide(inverse(b1), inverse(b1))) -> false__
% 3.02/3.19 f1(g1) -> false__
% 3.02/3.19 f1(g1) -> true__
% 3.02/3.19 f1(g2) -> false__
% 3.02/3.19 f1(g2) -> true__
% 3.02/3.19 f1(multiply(inverse(a1), a1)) -> true__
% 3.02/3.19 g1 -> g2
% 3.02/3.19 inverse(Y1) -> divide(g2, Y1)
% 3.02/3.19 multiply(Y0, multiply(inverse(X1), X1)) -> Y0
% 3.02/3.19 multiply(g2, Y1) -> Y1
% 3.02/3.19 multiply(inverse(Y0), Y0) -> g1
% 3.02/3.19 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1
% 3.02/3.19 multiply(inverse(Y0), multiply(inverse(inverse(Y1)), Y0)) -> Y1
% 3.02/3.19 multiply(inverse(divide(X1, X1)), Y0) -> Y0
% 3.02/3.19 multiply(inverse(multiply(inverse(X1), X1)), Y0) -> Y0
% 3.02/3.19 multiply(inverse(multiply(inverse(X1), Y0)), Y0) -> X1
% 3.02/3.19 true__ -> false__
% 3.02/3.19 with the LPO induced by
% 3.02/3.19 inverse > g1 > divide > g2 > a1 > b1 > multiply > f1 > true__ > false__
% 3.02/3.19
% 3.02/3.19 % SZS output end Proof
% 3.02/3.19
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