TSTP Solution File: GRP558-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP558-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 10:56:15 EDT 2022
% Result : Unsatisfiable 3.13s 3.23s
% Output : Proof 3.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP558-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n019.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 : Mon Jun 13 16:36:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.13/3.23 % SZS status Unsatisfiable
% 3.13/3.23 % SZS output start Proof
% 3.13/3.23 The input problem is unsatisfiable because
% 3.13/3.23
% 3.13/3.23 [1] the following set of Horn clauses is unsatisfiable:
% 3.13/3.23
% 3.13/3.23 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B
% 3.13/3.23 multiply(A, B) = divide(A, inverse(B))
% 3.13/3.23 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 3.13/3.23
% 3.13/3.23 This holds because
% 3.13/3.23
% 3.13/3.23 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.13/3.23
% 3.13/3.23 E:
% 3.13/3.23 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B
% 3.13/3.23 f1(a2) = false__
% 3.13/3.23 f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 3.13/3.23 multiply(A, B) = divide(A, inverse(B))
% 3.13/3.23 G:
% 3.13/3.23 true__ = false__
% 3.13/3.23
% 3.13/3.23 This holds because
% 3.13/3.23
% 3.13/3.23 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.13/3.23
% 3.13/3.23 divide(X1, X1) = divide(Y1, Y1)
% 3.13/3.23 divide(Y0, X1) = divide(divide(divide(false__, false__), X1), divide(divide(false__, false__), Y0))
% 3.13/3.23 divide(Y0, X1) = divide(inverse(X1), inverse(Y0))
% 3.13/3.23 divide(Y0, divide(divide(false__, false__), X0)) = divide(X0, divide(divide(false__, false__), Y0))
% 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(Y1))))) = inverse(divide(X1, X1))
% 3.13/3.23 divide(divide(Y0, X1), Y0) = divide(divide(X0, X0), X1)
% 3.13/3.23 divide(divide(divide(X1, X1), Y0), divide(divide(false__, false__), Y1)) = divide(Y1, Y0)
% 3.13/3.23 divide(divide(divide(false__, false__), Y0), divide(divide(X1, X1), Y0)) = divide(Y1, Y1)
% 3.13/3.23 divide(divide(divide(false__, false__), Y0), divide(divide(X1, X1), Y1)) = divide(Y1, Y0)
% 3.13/3.23 divide(false__, false__) = divide(Y1, Y1)
% 3.13/3.23 divide(inverse(X1), inverse(X1)) = divide(Y1, Y1)
% 3.13/3.23 divide(inverse(X1), inverse(X1)) = divide(inverse(Y1), inverse(Y1))
% 3.13/3.23 divide(inverse(Y0), inverse(Y0)) = inverse(divide(X1, X1))
% 3.13/3.23 divide(inverse(false__), inverse(false__)) = divide(Y1, Y1)
% 3.13/3.23 inverse(X1) = divide(divide(Y0, Y0), X1)
% 3.13/3.23 inverse(divide(Y0, Y0)) = divide(X1, X1)
% 3.13/3.23 inverse(divide(Y0, Y0)) = inverse(divide(X1, X1))
% 3.13/3.23 inverse(inverse(divide(Y0, Y0))) = divide(X1, X1)
% 3.13/3.23 divide(A, inverse(divide(divide(B, C), divide(A, C)))) -> B
% 3.13/3.23 divide(Y0, divide(X1, X1)) -> Y0
% 3.13/3.23 divide(Y0, divide(Y0, Y2)) -> Y2
% 3.13/3.23 divide(Y0, divide(divide(X1, X1), divide(Y1, Y0))) -> Y1
% 3.13/3.23 divide(Y0, divide(inverse(Y2), inverse(Y0))) -> Y2
% 3.13/3.23 divide(Y0, inverse(divide(X1, divide(Y0, inverse(divide(divide(X1, X2), divide(Y1, X2))))))) -> Y1
% 3.13/3.23 divide(Y0, inverse(divide(Y1, Y0))) -> Y1
% 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(X1, divide(Y3, inverse(divide(divide(X1, X2), divide(Y1, X2)))))))))) -> Y3
% 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(X3, divide(Y3, inverse(divide(X1, divide(Y1, inverse(divide(divide(X1, X2), divide(X3, X2))))))))))))) -> Y3
% 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y1, Y3)))))) -> Y3
% 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y1, inverse(divide(divide(inverse(divide(X1, X1)), Y3), divide(Y4, Y3))))))))) -> Y4
% 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y2, divide(Y3, inverse(divide(Y2, Y1))))))))) -> Y3
% 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(divide(Y1, inverse(divide(X1, divide(Y3, inverse(divide(divide(X1, X2), divide(X3, X2))))))), X3)))))) -> Y3
% 3.13/3.23 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(X1, X2), divide(Y3, X2)))), X1)))))) -> Y3
% 3.13/3.23 divide(Y0, inverse(divide(Y1, inverse(divide(divide(inverse(divide(X1, X1)), Y3), divide(Y0, Y3)))))) -> Y1
% 3.13/3.23 divide(Y0, inverse(divide(divide(Y1, inverse(divide(X1, divide(Y0, inverse(divide(divide(X1, X2), divide(X3, X2))))))), X3))) -> Y1
% 3.13/3.23 divide(Y0, inverse(divide(divide(Y1, inverse(divide(Y2, Y0))), Y2))) -> Y1
% 3.13/3.23 divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(X1, X2), divide(Y0, X2)))), X1))) -> Y1
% 3.13/3.23 divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(Y2, inverse(divide(divide(X1, X2), divide(Y0, X2)))), X1))), Y2))) -> Y1
% 3.13/3.23 divide(Y0, inverse(inverse(divide(X1, X1)))) -> Y0
% 3.13/3.23 divide(Y0, inverse(inverse(inverse(divide(X1, X1))))) -> Y0
% 3.13/3.23 divide(Y0, inverse(inverse(inverse(inverse(divide(X1, X1)))))) -> Y0
% 3.13/3.23 divide(Y3, inverse(divide(Y1, Y1))) -> Y3
% 3.13/3.23 divide(divide(X1, X1), divide(divide(Y0, Y0), Y1)) -> Y1
% 3.13/3.23 divide(divide(X1, X1), inverse(Y1)) -> Y1
% 3.13/3.23 divide(divide(X1, inverse(Y1)), X1) -> Y1
% 3.13/3.23 divide(divide(Y0, Y1), divide(divide(X1, X1), Y1)) -> Y0
% 3.13/3.23 divide(divide(Y0, divide(divide(X1, X1), Y1)), Y1) -> Y0
% 3.13/3.23 divide(divide(Y1, X1), inverse(X1)) -> Y1
% 3.13/3.23 divide(divide(Y1, inverse(X1)), X1) -> Y1
% 3.13/3.23 divide(divide(divide(X1, X1), divide(Y0, Y1)), divide(divide(false__, false__), Y0)) -> Y1
% 3.13/3.23 divide(divide(divide(divide(false__, false__), Y0), divide(divide(false__, false__), Y1)), divide(divide(X1, X1), Y0)) -> Y1
% 3.13/3.23 divide(divide(divide(false__, false__), X0), divide(X1, X0)) -> divide(divide(false__, false__), X1)
% 3.13/3.23 divide(divide(false__, false__), divide(divide(X1, X1), Y1)) -> Y1
% 3.13/3.23 divide(divide(inverse(X0), inverse(X1)), X1) -> inverse(X0)
% 3.13/3.23 divide(divide(inverse(Y1), inverse(Y2)), inverse(Y1)) -> Y2
% 3.13/3.23 divide(inverse(Y1), inverse(Y1)) -> divide(false__, false__)
% 3.13/3.23 divide(inverse(divide(X1, X1)), inverse(Y1)) -> Y1
% 3.13/3.23 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1
% 3.13/3.23 divide(inverse(divide(divide(X1, X2), divide(Y1, X2))), inverse(X1)) -> Y1
% 3.13/3.23 divide(inverse(inverse(divide(X1, X1))), inverse(Y1)) -> Y1
% 3.13/3.23 divide(inverse(inverse(inverse(divide(X1, X1)))), inverse(Y1)) -> Y1
% 3.13/3.23 f1(a2) -> false__
% 3.13/3.23 f1(divide(divide(X1, X1), inverse(a2))) -> true__
% 3.13/3.23 f1(divide(divide(false__, false__), inverse(a2))) -> true__
% 3.13/3.23 f1(divide(divide(inverse(b2), inverse(b2)), inverse(a2))) -> true__
% 3.13/3.23 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 3.13/3.23 inverse(X1) -> divide(divide(false__, false__), X1)
% 3.13/3.23 inverse(divide(X1, Y0)) -> divide(inverse(X1), inverse(Y0))
% 3.13/3.23 inverse(divide(divide(X1, X1), Y1)) -> Y1
% 3.13/3.23 multiply(A, B) -> divide(A, inverse(B))
% 3.13/3.23 true__ -> false__
% 3.13/3.23 with the LPO induced by
% 3.13/3.23 b2 > a2 > f1 > multiply > inverse > divide > true__ > false__
% 3.13/3.23
% 3.13/3.23 % SZS output end Proof
% 3.13/3.23
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