TSTP Solution File: GRP513-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP513-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n032.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 10:55:56 EDT 2022
% Result : Unsatisfiable 6.01s 6.14s
% Output : Proof 6.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : GRP513-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.09 % Command : moca.sh %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Mon Jun 13 16:11:57 EDT 2022
% 0.08/0.28 % CPUTime :
% 6.01/6.14 % SZS status Unsatisfiable
% 6.01/6.14 % SZS output start Proof
% 6.01/6.14 The input problem is unsatisfiable because
% 6.01/6.14
% 6.01/6.14 [1] the following set of Horn clauses is unsatisfiable:
% 6.01/6.14
% 6.01/6.14 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B
% 6.01/6.14 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 6.01/6.14
% 6.01/6.14 This holds because
% 6.01/6.14
% 6.01/6.14 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 6.01/6.14
% 6.01/6.14 E:
% 6.01/6.14 f1(multiply(inverse(a1), a1)) = true__
% 6.01/6.14 f1(multiply(inverse(b1), b1)) = false__
% 6.01/6.14 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) = B
% 6.01/6.14 G:
% 6.01/6.14 true__ = false__
% 6.01/6.14
% 6.01/6.14 This holds because
% 6.01/6.14
% 6.01/6.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 6.01/6.14
% 6.01/6.14 inverse(multiply(X0, inverse(X0))) = multiply(Y1, inverse(Y1))
% 6.01/6.14 multiply(X0, multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, multiply(X2, inverse(multiply(X2, X1))))
% 6.01/6.14 multiply(X1, Y2) = multiply(multiply(Y0, Y2), inverse(multiply(Y0, inverse(X1))))
% 6.01/6.14 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, inverse(multiply(Y0, inverse(X1))))
% 6.01/6.14 multiply(X1, multiply(Y2, inverse(Y0))) = multiply(Y2, multiply(X1, inverse(Y0)))
% 6.01/6.14 multiply(Y0, X0) = multiply(X0, Y0)
% 6.01/6.14 multiply(Y0, X0) = multiply(X0, multiply(X1, inverse(multiply(X1, inverse(Y0)))))
% 6.01/6.14 multiply(Y0, inverse(Y0)) = multiply(X1, inverse(X1))
% 6.01/6.14 multiply(Y0, multiply(X0, inverse(multiply(X0, X1)))) = multiply(Y0, multiply(X2, inverse(multiply(X2, X1))))
% 6.01/6.14 multiply(Y0, multiply(multiply(X2, X1), inverse(multiply(Y0, multiply(X2, inverse(X0)))))) = multiply(X0, X1)
% 6.01/6.14 multiply(multiply(X0, X1), multiply(Y1, inverse(X0))) = multiply(Y1, X1)
% 6.01/6.14 multiply(multiply(X0, Y1), X1) = multiply(multiply(Y2, Y1), multiply(multiply(X0, X1), inverse(Y2)))
% 6.01/6.14 multiply(multiply(X2, X1), Y2) = multiply(multiply(multiply(X0, X1), Y2), multiply(X2, inverse(X0)))
% 6.01/6.14 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, multiply(X2, inverse(X0)))
% 6.01/6.14 multiply(multiply(X2, X1), multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(X0)))))) = multiply(X0, X1)
% 6.01/6.14 multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))) = multiply(multiply(Y2, Y1), multiply(Y0, inverse(Y2)))
% 6.01/6.14 multiply(multiply(Y0, Y1), X0) = multiply(multiply(X0, multiply(X1, inverse(multiply(X1, inverse(Y0))))), Y1)
% 6.01/6.14 multiply(multiply(Y0, Y1), multiply(multiply(X0, inverse(Y0)), X1)) = multiply(multiply(X0, X1), Y1)
% 6.01/6.14 multiply(multiply(Y0, Y1), multiply(multiply(X2, inverse(Y0)), multiply(Y2, inverse(X2)))) = multiply(Y2, Y1)
% 6.01/6.14 multiply(multiply(Y1, Y0), Y2) = multiply(multiply(Y0, Y2), Y1)
% 6.01/6.14 multiply(multiply(Y1, Y2), X1) = multiply(multiply(Y1, X1), Y2)
% 6.01/6.14 multiply(multiply(inverse(X0), Y1), multiply(Y2, X0)) = multiply(Y2, Y1)
% 6.01/6.14 multiply(multiply(multiply(X0, Y1), X1), multiply(Y2, inverse(multiply(X0, X1)))) = multiply(Y2, Y1)
% 6.01/6.14 multiply(multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))), Y2) = multiply(multiply(Y0, Y2), Y1)
% 6.01/6.14 multiply(multiply(multiply(X2, Y1), multiply(Y0, inverse(X2))), multiply(Y2, inverse(Y0))) = multiply(Y2, Y1)
% 6.01/6.14 f1(multiply(X1, inverse(X1))) -> false__
% 6.01/6.14 f1(multiply(X1, inverse(X1))) -> true__
% 6.01/6.14 f1(multiply(false__, inverse(false__))) -> false__
% 6.01/6.14 f1(multiply(false__, inverse(false__))) -> true__
% 6.01/6.14 f1(multiply(inverse(a1), a1)) -> true__
% 6.01/6.14 f1(multiply(inverse(b1), b1)) -> false__
% 6.01/6.14 f1(multiply(multiply(X2, a1), multiply(inverse(a1), inverse(X2)))) -> true__
% 6.01/6.14 f1(multiply(multiply(X2, b1), multiply(inverse(b1), inverse(X2)))) -> false__
% 6.01/6.14 f1(multiply(multiply(multiply(X0, b1), X1), multiply(inverse(b1), inverse(multiply(X0, X1))))) -> false__
% 6.01/6.14 inverse(inverse(Y0)) -> Y0
% 6.01/6.14 multiply(A, multiply(multiply(B, C), inverse(multiply(A, C)))) -> B
% 6.01/6.14 multiply(X0, inverse(inverse(X1))) -> multiply(X0, X1)
% 6.01/6.14 multiply(X0, multiply(Y2, inverse(multiply(Y2, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1)
% 6.01/6.14 multiply(X1, inverse(inverse(multiply(Y0, inverse(X1))))) -> Y0
% 6.01/6.14 multiply(X1, multiply(Y2, inverse(multiply(Y2, multiply(X1, inverse(Y0)))))) -> Y0
% 6.01/6.14 multiply(X1, multiply(Y2, inverse(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2))))))) -> Y0
% 6.01/6.14 multiply(X2, multiply(Y2, inverse(multiply(Y2, multiply(X1, inverse(multiply(Y0, multiply(X1, inverse(X2))))))))) -> Y0
% 6.01/6.14 multiply(Y0, inverse(multiply(X0, Y0))) -> inverse(X0)
% 6.01/6.14 multiply(Y0, inverse(multiply(Y0, X0))) -> inverse(X0)
% 6.01/6.14 multiply(Y0, inverse(multiply(Y1, inverse(Y1)))) -> Y0
% 6.01/6.14 multiply(Y0, inverse(multiply(inverse(Y1), Y0))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(X0, inverse(multiply(Y0, multiply(X2, inverse(multiply(X2, X1))))))) -> multiply(X0, X1)
% 6.01/6.14 multiply(Y0, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2))))))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(X1, inverse(multiply(Y1, multiply(X1, inverse(X2)))))) -> multiply(Y0, multiply(X2, inverse(Y1)))
% 6.01/6.14 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X1, inverse(multiply(Y3, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))))))))) -> Y3
% 6.01/6.14 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(X2, inverse(multiply(Y3, multiply(X1, inverse(multiply(Y1, multiply(X1, inverse(X2)))))))))))) -> Y3
% 6.01/6.14 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
% 6.01/6.14 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y1, inverse(Y3)))))) -> Y3
% 6.01/6.14 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(Y2, inverse(multiply(Y3, multiply(Y2, inverse(Y1))))))))) -> Y3
% 6.01/6.14 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
% 6.01/6.14 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
% 6.01/6.14 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y4))), inverse(Y2)))))) -> Y4
% 6.01/6.14 multiply(Y0, multiply(Y1, inverse(multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y3, X2)))), inverse(X1)))))) -> Y3
% 6.01/6.14 multiply(Y0, multiply(inverse(Y0), Y1)) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(X0, inverse(Y0)), X1)) -> multiply(X0, X1)
% 6.01/6.14 multiply(Y0, multiply(multiply(X1, X2), inverse(X1))) -> multiply(Y0, X2)
% 6.01/6.14 multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y1, X2)))) -> multiply(Y0, multiply(X1, inverse(Y1)))
% 6.01/6.14 multiply(Y0, multiply(multiply(X1, multiply(X2, inverse(Y1))), inverse(X2))) -> multiply(Y0, multiply(X1, inverse(Y1)))
% 6.01/6.14 multiply(Y0, multiply(multiply(X1, multiply(Y2, inverse(Y0))), inverse(X1))) -> Y2
% 6.01/6.14 multiply(Y0, multiply(multiply(X2, inverse(Y0)), multiply(Y1, inverse(X2)))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(X2, inverse(Y1)), multiply(multiply(Y1, Y2), inverse(X2)))) -> multiply(Y0, Y2)
% 6.01/6.14 multiply(Y0, multiply(multiply(X2, inverse(multiply(Y0, Y2))), multiply(multiply(Y1, Y2), inverse(X2)))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, Y2), inverse(multiply(multiply(X2, Y2), multiply(Y0, inverse(X2)))))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, inverse(Y1)), Y2)) -> multiply(Y0, Y2)
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(X1, inverse(X2)))))), inverse(X2))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(X3, X2))))))), inverse(X3))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, multiply(X3, inverse(multiply(Y0, multiply(X1, inverse(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(X3, X2)))))))))), inverse(Y2))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, multiply(Y2, inverse(Y0))), inverse(Y2))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, multiply(multiply(X1, multiply(X2, inverse(Y0))), inverse(X2))), inverse(X1))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(Y1, multiply(multiply(Y2, multiply(multiply(X1, X2), inverse(multiply(Y0, X2)))), inverse(X1))), inverse(Y2))) -> Y1
% 6.01/6.14 multiply(Y0, multiply(multiply(multiply(X0, Y2), X1), inverse(multiply(Y0, Y2)))) -> multiply(X0, X1)
% 6.01/6.14 multiply(Y0, multiply(multiply(multiply(X2, Y2), multiply(Y1, inverse(X2))), inverse(multiply(Y0, Y2)))) -> Y1
% 6.01/6.14 multiply(Y1, inverse(multiply(Y1, inverse(Y0)))) -> Y0
% 6.01/6.14 multiply(Y3, multiply(Y1, inverse(Y1))) -> Y3
% 6.01/6.14 multiply(inverse(X0), multiply(Y1, X0)) -> Y1
% 6.01/6.14 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1
% 6.01/6.14 multiply(inverse(multiply(X0, inverse(X0))), Y1) -> Y1
% 6.01/6.14 multiply(multiply(X0, X1), inverse(multiply(multiply(X0, inverse(Y1)), X1))) -> Y1
% 6.01/6.14 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(X0))), inverse(multiply(X2, X1)))) -> Y1
% 6.01/6.14 multiply(multiply(X0, X1), multiply(multiply(Y1, multiply(X2, inverse(multiply(X2, X1)))), inverse(X0))) -> Y1
% 6.01/6.14 multiply(multiply(X0, Y1), inverse(X0)) -> Y1
% 6.01/6.14 multiply(multiply(X1, inverse(X1)), Y1) -> Y1
% 6.01/6.14 multiply(multiply(X2, multiply(Y2, inverse(multiply(Y2, Y1)))), multiply(multiply(Y0, Y1), inverse(X2))) -> Y0
% 6.01/6.14 multiply(multiply(Y0, Y2), Y1) -> multiply(Y2, multiply(Y0, Y1))
% 6.01/6.14 multiply(multiply(Y0, multiply(X1, inverse(multiply(Y2, multiply(X1, inverse(X2)))))), multiply(Y2, inverse(X2))) -> Y0
% 6.01/6.14 multiply(multiply(Y0, multiply(X2, inverse(multiply(X2, X1)))), X1) -> Y0
% 6.01/6.14 multiply(multiply(Y0, multiply(multiply(X1, X2), inverse(multiply(Y2, X2)))), multiply(Y2, inverse(X1))) -> Y0
% 6.01/6.14 multiply(multiply(Y1, X1), inverse(X1)) -> Y1
% 6.01/6.14 multiply(multiply(Y1, multiply(Y2, inverse(X2))), multiply(X2, inverse(Y2))) -> Y1
% 6.01/6.14 multiply(multiply(Y2, multiply(X2, inverse(X0))), multiply(multiply(X0, X1), inverse(Y2))) -> multiply(X2, X1)
% 6.01/6.14 multiply(multiply(Y3, Y2), multiply(Y1, inverse(multiply(Y1, Y2)))) -> Y3
% 6.01/6.14 multiply(multiply(false__, Y2), multiply(multiply(Y0, inverse(false__)), multiply(X0, inverse(multiply(X0, Y2))))) -> Y0
% 6.01/6.14 multiply(multiply(multiply(X0, Y1), X1), multiply(Y2, inverse(multiply(Y2, Y1)))) -> multiply(X0, X1)
% 6.01/6.14 multiply(multiply(multiply(X0, multiply(Y1, inverse(multiply(Y1, Y2)))), X1), Y2) -> multiply(X0, X1)
% 6.01/6.14 multiply(multiply(multiply(Y2, inverse(X1)), Y1), X1) -> multiply(Y2, Y1)
% 6.01/6.14 true__ -> false__
% 6.01/6.14 with the LPO induced by
% 6.01/6.14 a1 > b1 > f1 > inverse > multiply > true__ > false__
% 6.01/6.14
% 6.01/6.14 % SZS output end Proof
% 6.01/6.14
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