TSTP Solution File: GRP022-2 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP022-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n028.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 10:51:54 EDT 2022
% Result : Unsatisfiable 0.37s 0.62s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP022-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 14:08:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.37/0.62 % SZS status Unsatisfiable
% 0.37/0.62 % SZS output start Proof
% 0.37/0.62 The input problem is unsatisfiable because
% 0.37/0.62
% 0.37/0.62 [1] the following set of Horn clauses is unsatisfiable:
% 0.37/0.62
% 0.37/0.62 multiply(identity, X) = X
% 0.37/0.62 multiply(inverse(X), X) = identity
% 0.37/0.62 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.37/0.62 multiply(X, identity) = X
% 0.37/0.62 multiply(X, inverse(X)) = identity
% 0.37/0.62 inverse(inverse(a)) = a ==> \bottom
% 0.37/0.62
% 0.37/0.62 This holds because
% 0.37/0.62
% 0.37/0.62 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.37/0.62
% 0.37/0.62 E:
% 0.37/0.62 f1(a) = false__
% 0.37/0.62 f1(inverse(inverse(a))) = true__
% 0.37/0.62 multiply(X, identity) = X
% 0.37/0.62 multiply(X, inverse(X)) = identity
% 0.37/0.62 multiply(identity, X) = X
% 0.37/0.62 multiply(inverse(X), X) = identity
% 0.37/0.62 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.37/0.62 G:
% 0.37/0.62 true__ = false__
% 0.37/0.62
% 0.37/0.62 This holds because
% 0.37/0.62
% 0.37/0.62 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.37/0.62
% 0.37/0.62
% 0.37/0.62 f1(a) -> false__
% 0.37/0.62 f1(inverse(inverse(a))) -> true__
% 0.37/0.62 inverse(identity) -> identity
% 0.37/0.62 inverse(inverse(Y1)) -> Y1
% 0.37/0.62 inverse(multiply(X1, Y0)) -> multiply(inverse(Y0), inverse(X1))
% 0.37/0.62 inverse(multiply(X1, inverse(Y0))) -> multiply(Y0, inverse(X1))
% 0.37/0.62 inverse(multiply(inverse(X1), Y0)) -> multiply(inverse(Y0), X1)
% 0.37/0.62 inverse(multiply(inverse(multiply(Y1, Y2)), Y1)) -> Y2
% 0.37/0.62 multiply(X, identity) -> X
% 0.37/0.62 multiply(X, inverse(X)) -> identity
% 0.37/0.62 multiply(X1, inverse(multiply(Y0, X1))) -> inverse(Y0)
% 0.37/0.62 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0
% 0.37/0.62 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 0.37/0.62 multiply(Y0, multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(Y1, X1)))))) -> identity
% 0.37/0.62 multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1
% 0.37/0.62 multiply(Y0, multiply(inverse(Y0), Y2)) -> Y2
% 0.37/0.62 multiply(identity, X) -> X
% 0.37/0.62 multiply(inverse(X), X) -> identity
% 0.37/0.62 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 0.37/0.62 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 0.37/0.62 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1
% 0.37/0.62 multiply(inverse(multiply(Y0, Y1)), Y0) -> inverse(Y1)
% 0.37/0.62 multiply(inverse(multiply(Y0, inverse(Y2))), Y0) -> Y2
% 0.37/0.62 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.37/0.62 true__ -> false__
% 0.37/0.62 with the LPO induced by
% 0.37/0.62 a > f1 > inverse > identity > multiply > true__ > false__
% 0.37/0.62
% 0.37/0.62 % SZS output end Proof
% 0.37/0.62
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