TSTP Solution File: GRP514-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n022.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 10:55:57 EDT 2022
% Result : Unsatisfiable 4.73s 4.92s
% Output : Proof 4.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP514-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : moca.sh %s
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jun 13 13:48:03 EDT 2022
% 0.11/0.32 % CPUTime :
% 4.73/4.92 % SZS status Unsatisfiable
% 4.73/4.92 % SZS output start Proof
% 4.73/4.92 The input problem is unsatisfiable because
% 4.73/4.92
% 4.73/4.92 [1] the following set of Horn clauses is unsatisfiable:
% 4.73/4.92
% 4.73/4.92 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B
% 4.73/4.92 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 4.73/4.92
% 4.73/4.92 This holds because
% 4.73/4.92
% 4.73/4.92 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 4.73/4.92
% 4.73/4.92 E:
% 4.73/4.92 f1(a2) = false__
% 4.73/4.92 f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 4.73/4.92 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B
% 4.73/4.92 G:
% 4.73/4.92 true__ = false__
% 4.73/4.92
% 4.73/4.92 This holds because
% 4.73/4.92
% 4.73/4.92 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 4.73/4.92
% 4.73/4.92 inverse(multiply(X0, inverse(X0))) = multiply(Y1, inverse(Y1))
% 4.73/4.92 multiply(X1, inverse(inverse(X0))) = multiply(X0, X1)
% 4.73/4.92 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, multiply(X1, inverse(Y0)))
% 4.73/4.92 multiply(Y0, X0) = multiply(X0, Y0)
% 4.73/4.92 multiply(Y0, X0) = multiply(X0, multiply(X1, inverse(multiply(X1, inverse(Y0)))))
% 4.73/4.92 multiply(Y0, inverse(Y0)) = multiply(X1, inverse(X1))
% 4.73/4.92 multiply(Y0, multiply(X0, inverse(multiply(X0, X1)))) = multiply(Y0, multiply(X2, inverse(multiply(X2, X1))))
% 4.73/4.92 multiply(Y0, multiply(X0, inverse(multiply(Y0, Y2)))) = multiply(X0, multiply(X1, inverse(multiply(X1, Y2))))
% 4.73/4.92 multiply(Y0, multiply(multiply(X2, X1), inverse(multiply(Y0, multiply(X2, inverse(X0)))))) = multiply(X0, X1)
% 4.73/4.92 multiply(Y1, multiply(Y2, inverse(multiply(X0, inverse(X0))))) = multiply(Y2, Y1)
% 4.73/4.92 multiply(multiply(X0, X1), multiply(Y1, inverse(X0))) = multiply(Y1, X1)
% 4.73/4.92 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, multiply(X2, inverse(X0)))
% 4.73/4.92 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(X0)))))) = multiply(X0, X1)
% 4.73/4.92 multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))) = multiply(multiply(Y2, Y1), multiply(Y0, inverse(Y2)))
% 4.73/4.92 multiply(multiply(Y0, Y1), multiply(multiply(X2, inverse(Y0)), multiply(Y2, inverse(X2)))) = multiply(Y2, Y1)
% 4.73/4.92 multiply(multiply(inverse(X0), Y1), multiply(Y2, X0)) = multiply(Y2, Y1)
% 4.73/4.92 multiply(multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))), multiply(Y2, inverse(Y0))) = multiply(Y2, Y1)
% 4.73/4.92 f1(a2) -> false__
% 4.73/4.92 f1(multiply(inverse(false__), multiply(false__, a2))) -> true__
% 4.73/4.92 f1(multiply(multiply(X2, a2), multiply(multiply(multiply(false__, b2), multiply(inverse(b2), inverse(false__))), inverse(X2)))) -> true__
% 4.73/4.92 f1(multiply(multiply(false__, a2), multiply(multiply(multiply(X2, b2), multiply(inverse(b2), inverse(X2))), inverse(false__)))) -> true__
% 4.73/4.92 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 4.73/4.92 inverse(inverse(Y0)) -> Y0
% 4.73/4.92 inverse(multiply(X1, inverse(Y0))) -> multiply(Y0, inverse(X1))
% 4.73/4.92 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) -> B
% 4.73/4.92 multiply(X0, inverse(inverse(X1))) -> multiply(X0, X1)
% 4.73/4.92 multiply(X0, inverse(multiply(X0, X1))) -> inverse(X1)
% 4.73/4.92 multiply(X0, multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1)
% 4.73/4.92 multiply(X1, inverse(multiply(X0, X1))) -> inverse(X0)
% 4.73/4.92 multiply(X1, multiply(Y2, inverse(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2))))))) -> Y0
% 4.73/4.92 multiply(X2, multiply(Y2, inverse(multiply(Y2, multiply(X1, inverse(multiply(Y0, multiply(X1, inverse(X2))))))))) -> Y0
% 4.73/4.92 multiply(Y0, inverse(multiply(X0, inverse(X0)))) -> Y0
% 4.73/4.92 multiply(Y0, inverse(multiply(Y0, inverse(Y1)))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(X0, inverse(multiply(Y0, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1)
% 4.73/4.92 multiply(Y0, multiply(X1, inverse(multiply(X1, inverse(Y1))))) -> multiply(Y0, Y1)
% 4.73/4.92 multiply(Y0, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2))))))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X1, inverse(multiply(Y3, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))))))))) -> Y3
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X2, inverse(multiply(Y3, multiply(X1, inverse(multiply(Y1, multiply(X1, inverse(X2)))))))))))) -> Y3
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X3, inverse(multiply(Y3, multiply(X1, inverse(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))))))))) -> Y3
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y1, inverse(Y3)))))) -> Y3
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y2, inverse(multiply(Y3, multiply(Y2, inverse(Y1))))))))) -> Y3
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y2, inverse(multiply(Y3, multiply(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))), inverse(X1))))))))) -> Y3
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y3, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))), inverse(X3)))))) -> Y3
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y4))), inverse(Y2)))))) -> Y4
% 4.73/4.92 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y3, X2)))), inverse(X1)))))) -> Y3
% 4.73/4.92 multiply(Y0, multiply(inverse(Y0), Y1)) -> Y1
% 4.73/4.92 multiply(Y0, multiply(multiply(X1, X2), inverse(X1))) -> multiply(Y0, X2)
% 4.73/4.92 multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))) -> multiply(Y0, multiply(X1, inverse(Y1)))
% 4.73/4.92 multiply(Y0, multiply(multiply(X1, multiply(Y2, inverse(Y0))), inverse(X1))) -> Y2
% 4.73/4.92 multiply(Y0, multiply(multiply(X2, inverse(Y0)), multiply(Y1, inverse(X2)))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(multiply(X2, inverse(multiply(Y0, Y2))), multiply(multiply(Y1, Y2), inverse(X2)))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))), inverse(X3))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y0))), inverse(Y2))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(multiply(Y0, multiply(Y2, inverse(Y4)))))), inverse(Y4))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(multiply(Y2, multiply(X1, inverse(Y0))), inverse(X1))), inverse(Y2))) -> Y1
% 4.73/4.92 multiply(Y0, multiply(multiply(Y1, multiply(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))), inverse(Y2))) -> Y1
% 4.73/4.92 multiply(Y2, multiply(Y1, inverse(multiply(Y1, multiply(Y2, inverse(Y3)))))) -> Y3
% 4.73/4.92 multiply(Y3, multiply(Y1, inverse(Y1))) -> Y3
% 4.73/4.92 multiply(inverse(X0), multiply(Y1, X0)) -> Y1
% 4.73/4.92 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1
% 4.73/4.92 multiply(inverse(multiply(X0, inverse(X0))), Y1) -> Y1
% 4.73/4.92 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(X0))), inverse(multiply(X2, X1)))) -> Y1
% 4.73/4.92 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(multiply(X2, X1)))), inverse(X0))) -> Y1
% 4.73/4.92 multiply(multiply(X0, multiply(X1, inverse(multiply(X1, Y2)))), multiply(multiply(Y1, Y2), inverse(X0))) -> Y1
% 4.73/4.92 multiply(multiply(X1, inverse(X1)), Y0) -> Y0
% 4.73/4.92 multiply(multiply(Y0, Y1), inverse(Y0)) -> Y1
% 4.73/4.92 multiply(multiply(Y0, multiply(X2, inverse(multiply(X2, X1)))), X1) -> Y0
% 4.73/4.92 multiply(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y2, X2)))), multiply(Y2, inverse(X1))) -> Y0
% 4.73/4.92 multiply(multiply(Y1, Y2), inverse(Y2)) -> Y1
% 4.73/4.92 multiply(multiply(Y2, multiply(X2, inverse(X0))), multiply(multiply(X0, X1), inverse(Y2))) -> multiply(X2, X1)
% 4.73/4.92 multiply(multiply(Y3, Y2), multiply(Y1, inverse(multiply(Y1, Y2)))) -> Y3
% 4.73/4.92 multiply(multiply(Y3, multiply(Y2, inverse(Y1))), multiply(Y1, inverse(Y2))) -> Y3
% 4.73/4.92 true__ -> false__
% 4.73/4.92 with the LPO induced by
% 4.73/4.92 b2 > a2 > f1 > inverse > multiply > true__ > false__
% 4.73/4.92
% 4.73/4.92 % SZS output end Proof
% 4.73/4.92
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