TSTP Solution File: GRP012-4 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : GRP012-4 : 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 10:51:49 EDT 2022
% Result : Unsatisfiable 0.60s 0.77s
% Output : Proof 0.60s
% 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 : GRP012-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 14:24:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/0.77 % SZS status Unsatisfiable
% 0.60/0.77 % SZS output start Proof
% 0.60/0.77 The input problem is unsatisfiable because
% 0.60/0.77
% 0.60/0.77 [1] the following set of Horn clauses is unsatisfiable:
% 0.60/0.77
% 0.60/0.77 multiply(identity, X) = X
% 0.60/0.77 multiply(inverse(X), X) = identity
% 0.60/0.77 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.60/0.77 multiply(X, identity) = X
% 0.60/0.77 multiply(X, inverse(X)) = identity
% 0.60/0.77 inverse(multiply(a, b)) = multiply(inverse(b), inverse(a)) ==> \bottom
% 0.60/0.77
% 0.60/0.77 This holds because
% 0.60/0.77
% 0.60/0.77 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.60/0.77
% 0.60/0.77 E:
% 0.60/0.77 f1(inverse(multiply(a, b))) = true__
% 0.60/0.77 f1(multiply(inverse(b), inverse(a))) = false__
% 0.60/0.77 multiply(X, identity) = X
% 0.60/0.77 multiply(X, inverse(X)) = identity
% 0.60/0.77 multiply(identity, X) = X
% 0.60/0.77 multiply(inverse(X), X) = identity
% 0.60/0.77 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.60/0.77 G:
% 0.60/0.77 true__ = false__
% 0.60/0.77
% 0.60/0.77 This holds because
% 0.60/0.77
% 0.60/0.77 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.60/0.77
% 0.60/0.77
% 0.60/0.77 f1(inverse(multiply(a, b))) -> true__
% 0.60/0.77 f1(multiply(inverse(b), inverse(a))) -> false__
% 0.60/0.77 inverse(identity) -> identity
% 0.60/0.77 inverse(inverse(Y1)) -> Y1
% 0.60/0.77 inverse(multiply(X1, Y0)) -> multiply(inverse(Y0), inverse(X1))
% 0.60/0.77 inverse(multiply(X1, inverse(Y0))) -> multiply(Y0, inverse(X1))
% 0.60/0.77 inverse(multiply(inverse(X1), Y0)) -> multiply(inverse(Y0), X1)
% 0.60/0.77 inverse(multiply(inverse(X1), inverse(Y0))) -> multiply(Y0, X1)
% 0.60/0.77 inverse(multiply(inverse(multiply(Y1, Y2)), Y1)) -> Y2
% 0.60/0.77 multiply(X, identity) -> X
% 0.60/0.77 multiply(X, inverse(X)) -> identity
% 0.60/0.77 multiply(X1, inverse(multiply(Y0, X1))) -> inverse(Y0)
% 0.60/0.77 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0
% 0.60/0.77 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 0.60/0.77 multiply(Y0, multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(Y1, X1)))))) -> identity
% 0.60/0.77 multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1
% 0.60/0.77 multiply(Y0, multiply(inverse(Y0), Y2)) -> Y2
% 0.60/0.77 multiply(identity, X) -> X
% 0.60/0.77 multiply(inverse(X), X) -> identity
% 0.60/0.77 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 0.60/0.77 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 0.60/0.77 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1
% 0.60/0.77 multiply(inverse(multiply(Y0, Y1)), Y0) -> inverse(Y1)
% 0.60/0.77 multiply(inverse(multiply(Y0, inverse(Y2))), Y0) -> Y2
% 0.60/0.77 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.60/0.77 true__ -> false__
% 0.60/0.77 with the LPO induced by
% 0.60/0.77 a > b > f1 > inverse > identity > multiply > true__ > false__
% 0.60/0.77
% 0.60/0.77 % SZS output end Proof
% 0.60/0.77
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