TSTP Solution File: BOO001-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : BOO001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.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 : Thu Jul 14 23:46:10 EDT 2022
% Result : Unsatisfiable 3.79s 3.89s
% Output : Proof 3.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : moca.sh %s
% 0.13/0.34 % Computer : n020.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 : Wed Jun 1 20:09:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.79/3.89 % SZS status Unsatisfiable
% 3.79/3.89 % SZS output start Proof
% 3.79/3.89 The input problem is unsatisfiable because
% 3.79/3.89
% 3.79/3.89 [1] the following set of Horn clauses is unsatisfiable:
% 3.79/3.89
% 3.79/3.89 multiply(multiply(V, W, X), Y, multiply(V, W, Z)) = multiply(V, W, multiply(X, Y, Z))
% 3.79/3.89 multiply(Y, X, X) = X
% 3.79/3.89 multiply(X, X, Y) = X
% 3.79/3.89 multiply(inverse(Y), Y, X) = X
% 3.79/3.89 multiply(X, Y, inverse(Y)) = X
% 3.79/3.89 inverse(inverse(a)) = a ==> \bottom
% 3.79/3.89
% 3.79/3.89 This holds because
% 3.79/3.89
% 3.79/3.89 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.79/3.89
% 3.79/3.89 E:
% 3.79/3.89 f1(a) = false__
% 3.79/3.89 f1(inverse(inverse(a))) = true__
% 3.79/3.89 multiply(X, X, Y) = X
% 3.79/3.89 multiply(X, Y, inverse(Y)) = X
% 3.79/3.89 multiply(Y, X, X) = X
% 3.79/3.89 multiply(inverse(Y), Y, X) = X
% 3.79/3.89 multiply(multiply(V, W, X), Y, multiply(V, W, Z)) = multiply(V, W, multiply(X, Y, Z))
% 3.79/3.89 G:
% 3.79/3.89 true__ = false__
% 3.79/3.89
% 3.79/3.89 This holds because
% 3.79/3.89
% 3.79/3.89 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.79/3.89
% 3.79/3.89 multiply(Y0, Y1, Y2) = multiply(Y2, Y0, Y1)
% 3.79/3.89 multiply(Y0, Y1, Y3) = multiply(Y0, Y3, Y1)
% 3.79/3.89 multiply(Y0, Y1, multiply(Y1, Y0, Y2)) = multiply(Y1, Y2, Y0)
% 3.79/3.89 multiply(Y0, Y3, multiply(Y0, Y1, Y4)) = multiply(Y0, Y1, multiply(inverse(Y1), Y3, Y4))
% 3.79/3.89 multiply(Y0, inverse(X0), multiply(X0, Y2, Y3)) = multiply(Y0, Y2, multiply(Y0, inverse(X0), Y3))
% 3.79/3.89 multiply(Y2, Y3, multiply(Y0, Y2, Y4)) = multiply(Y0, Y2, multiply(Y2, Y3, Y4))
% 3.79/3.89 f1(a) -> false__
% 3.79/3.89 f1(inverse(inverse(a))) -> true__
% 3.79/3.89 inverse(inverse(Y0)) -> Y0
% 3.79/3.89 multiply(X, X, Y) -> X
% 3.79/3.89 multiply(X, Y, inverse(Y)) -> X
% 3.79/3.89 multiply(Y, X, X) -> X
% 3.79/3.89 multiply(Y0, Y1, multiply(Y0, Y1, Y2)) -> multiply(Y0, Y1, Y2)
% 3.79/3.89 multiply(Y0, Y1, multiply(Y0, Y2, multiply(inverse(Y2), Y1, Y2))) -> multiply(Y0, Y1, Y2)
% 3.79/3.89 multiply(Y0, Y1, multiply(Y2, Y1, inverse(multiply(Y0, Y1, Y2)))) -> Y1
% 3.79/3.89 multiply(Y0, Y1, multiply(Y2, multiply(Y0, Y1, Y2), Y4)) -> multiply(Y0, Y1, Y2)
% 3.79/3.89 multiply(Y0, Y1, multiply(Y2, multiply(Y0, Y1, Y4), Y4)) -> multiply(Y0, Y1, Y4)
% 3.79/3.89 multiply(Y0, Y2, inverse(Y0)) -> Y2
% 3.79/3.89 multiply(Y0, inverse(Y0), Y2) -> Y2
% 3.79/3.89 multiply(Y0, inverse(Y1), Y1) -> Y0
% 3.79/3.89 multiply(Y1, Y2, multiply(Y0, Y1, inverse(Y2))) -> Y1
% 3.79/3.89 multiply(Y1, Y2, multiply(Y0, Y2, Y1)) -> multiply(Y0, Y2, Y1)
% 3.79/3.89 multiply(Y1, Y2, multiply(Y1, Y3, inverse(multiply(Y1, Y2, Y3)))) -> Y1
% 3.79/3.89 multiply(Y1, Y2, multiply(inverse(Y2), Y1, Y3)) -> Y1
% 3.79/3.89 multiply(Y1, Y2, multiply(multiply(Y1, Y2, Y3), Y1, Y3)) -> multiply(Y1, Y2, Y3)
% 3.79/3.89 multiply(Y1, Y3, Y1) -> Y1
% 3.79/3.89 multiply(Y1, Y3, multiply(Y0, Y1, Y3)) -> multiply(Y0, Y1, Y3)
% 3.79/3.89 multiply(Y2, Y1, multiply(Y2, Y3, Y1)) -> multiply(Y2, Y3, Y1)
% 3.79/3.89 multiply(Y3, Y0, multiply(Y0, Y1, Y3)) -> multiply(Y0, Y1, Y3)
% 3.79/3.89 multiply(inverse(Y), Y, X) -> X
% 3.79/3.89 multiply(inverse(Y2), Y1, Y2) -> Y1
% 3.79/3.89 multiply(inverse(Y3), Y0, multiply(Y0, Y1, Y3)) -> Y0
% 3.79/3.89 multiply(multiply(V, W, X), Y, multiply(V, W, Z)) -> multiply(V, W, multiply(X, Y, Z))
% 3.79/3.89 multiply(multiply(X2, Y1, Y2), Y1, multiply(X2, Y2, Y1)) -> multiply(X2, Y1, Y2)
% 3.79/3.89 multiply(multiply(Y0, Y1, Y2), Y3, Y0) -> multiply(Y0, Y1, multiply(Y2, Y3, inverse(Y1)))
% 3.79/3.89 multiply(multiply(Y0, Y4, Y2), Y3, Y4) -> multiply(Y0, Y4, multiply(Y2, Y3, Y4))
% 3.79/3.89 true__ -> false__
% 3.79/3.89 with the LPO induced by
% 3.79/3.89 multiply > inverse > a > f1 > true__ > false__
% 3.79/3.89
% 3.79/3.89 % SZS output end Proof
% 3.79/3.89
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