TSTP Solution File: GRP001-2 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n004.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 10:51:39 EDT 2022
% Result : Unsatisfiable 0.88s 1.06s
% Output : Proof 0.88s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : moca.sh %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 18:33:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.88/1.06 % SZS status Unsatisfiable
% 0.88/1.06 % SZS output start Proof
% 0.88/1.06 The input problem is unsatisfiable because
% 0.88/1.06
% 0.88/1.06 [1] the following set of Horn clauses is unsatisfiable:
% 0.88/1.06
% 0.88/1.06 multiply(identity, X) = X
% 0.88/1.06 multiply(inverse(X), X) = identity
% 0.88/1.06 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.88/1.06 multiply(X, identity) = X
% 0.88/1.06 multiply(X, inverse(X)) = identity
% 0.88/1.06 multiply(X, X) = identity
% 0.88/1.06 multiply(a, b) = c
% 0.88/1.06 multiply(b, a) = c ==> \bottom
% 0.88/1.06
% 0.88/1.06 This holds because
% 0.88/1.06
% 0.88/1.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.88/1.06
% 0.88/1.06 E:
% 0.88/1.06 f1(c) = false__
% 0.88/1.06 f1(multiply(b, a)) = true__
% 0.88/1.06 multiply(X, X) = identity
% 0.88/1.06 multiply(X, identity) = X
% 0.88/1.06 multiply(X, inverse(X)) = identity
% 0.88/1.06 multiply(a, b) = c
% 0.88/1.06 multiply(identity, X) = X
% 0.88/1.06 multiply(inverse(X), X) = identity
% 0.88/1.06 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.88/1.06 G:
% 0.88/1.06 true__ = false__
% 0.88/1.06
% 0.88/1.06 This holds because
% 0.88/1.06
% 0.88/1.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.88/1.06
% 0.88/1.06 multiply(Y0, X1) = multiply(X1, Y0)
% 0.88/1.06 multiply(Y1, multiply(Y0, Y2)) = multiply(Y0, multiply(Y1, Y2))
% 0.88/1.06 multiply(Y2, multiply(Y0, Y1)) = multiply(Y0, multiply(Y1, Y2))
% 0.88/1.06 c -> multiply(a, b)
% 0.88/1.06 f1(c) -> false__
% 0.88/1.06 f1(multiply(a, b)) -> false__
% 0.88/1.06 f1(multiply(b, a)) -> true__
% 0.88/1.06 inverse(Y1) -> Y1
% 0.88/1.06 inverse(identity) -> identity
% 0.88/1.06 inverse(inverse(Y1)) -> Y1
% 0.88/1.06 multiply(X, X) -> identity
% 0.88/1.06 multiply(X, identity) -> X
% 0.88/1.06 multiply(X, inverse(X)) -> identity
% 0.88/1.06 multiply(X1, inverse(multiply(Y0, X1))) -> Y0
% 0.88/1.06 multiply(X1, multiply(Y0, X1)) -> Y0
% 0.88/1.06 multiply(X1, multiply(Y0, X1)) -> inverse(Y0)
% 0.88/1.06 multiply(Y0, multiply(X0, multiply(X1, Y0))) -> multiply(X0, X1)
% 0.88/1.06 multiply(Y0, multiply(X0, multiply(X1, multiply(Y0, multiply(X0, X1))))) -> identity
% 0.88/1.06 multiply(Y0, multiply(X0, multiply(X1, multiply(Y0, multiply(X0, multiply(X1, Y2)))))) -> Y2
% 0.88/1.06 multiply(Y0, multiply(X0, multiply(X1, multiply(Y2, multiply(Y0, multiply(X0, X1)))))) -> Y2
% 0.88/1.06 multiply(Y0, multiply(X1, multiply(X2, multiply(Y0, multiply(X1, Y2))))) -> multiply(X2, Y2)
% 0.88/1.06 multiply(Y0, multiply(X1, multiply(Y0, Y2))) -> multiply(X1, Y2)
% 0.88/1.06 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 0.88/1.06 multiply(Y0, multiply(Y1, multiply(X0, multiply(X1, multiply(Y0, Y1))))) -> multiply(X0, X1)
% 0.88/1.06 multiply(Y0, multiply(Y1, multiply(X1, multiply(Y0, Y1)))) -> X1
% 0.88/1.06 multiply(Y0, multiply(Y1, multiply(Y0, Y1))) -> identity
% 0.88/1.06 multiply(Y0, multiply(Y1, multiply(Y0, multiply(Y1, X1)))) -> X1
% 0.88/1.06 multiply(Y0, multiply(inverse(Y0), Y2)) -> Y2
% 0.88/1.06 multiply(Y1, multiply(Y1, Y2)) -> Y2
% 0.88/1.06 multiply(identity, X) -> X
% 0.88/1.06 multiply(inverse(X), X) -> identity
% 0.88/1.06 multiply(inverse(Y0), X1) -> multiply(Y0, X1)
% 0.88/1.06 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 0.88/1.06 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 0.88/1.06 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.88/1.06 true__ -> false__
% 0.88/1.06 with the LPO induced by
% 0.88/1.06 f1 > c > a > b > multiply > identity > inverse > true__ > false__
% 0.88/1.06
% 0.88/1.06 % SZS output end Proof
% 0.88/1.06
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