TSTP Solution File: GRP011-4 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP011-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n023.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 10:51:47 EDT 2022
% Result : Unsatisfiable 1.82s 1.96s
% Output : Proof 1.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP011-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n023.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 : Tue Jun 14 05:31:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.82/1.96 % SZS status Unsatisfiable
% 1.82/1.96 % SZS output start Proof
% 1.82/1.96 The input problem is unsatisfiable because
% 1.82/1.96
% 1.82/1.96 [1] the following set of Horn clauses is unsatisfiable:
% 1.82/1.96
% 1.82/1.96 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 1.82/1.96 multiply(identity, X) = X
% 1.82/1.96 multiply(inverse(X), X) = identity
% 1.82/1.96 multiply(b, c) = multiply(d, c)
% 1.82/1.96 b = d ==> \bottom
% 1.82/1.96
% 1.82/1.96 This holds because
% 1.82/1.96
% 1.82/1.96 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.82/1.96
% 1.82/1.96 E:
% 1.82/1.96 f1(b) = true__
% 1.82/1.96 f1(d) = false__
% 1.82/1.96 multiply(b, c) = multiply(d, c)
% 1.82/1.96 multiply(identity, X) = X
% 1.82/1.96 multiply(inverse(X), X) = identity
% 1.82/1.96 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 1.82/1.96 G:
% 1.82/1.96 true__ = false__
% 1.82/1.96
% 1.82/1.96 This holds because
% 1.82/1.96
% 1.82/1.96 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.82/1.96
% 1.82/1.96 multiply(inverse(X1), Y0) = inverse(multiply(inverse(Y0), X1))
% 1.82/1.96 multiply(inverse(X1), inverse(X0)) = inverse(multiply(X0, X1))
% 1.82/1.96 d -> b
% 1.82/1.96 f1(b) -> true__
% 1.82/1.96 f1(d) -> false__
% 1.82/1.96 inverse(identity) -> identity
% 1.82/1.96 inverse(inverse(Y0)) -> Y0
% 1.82/1.96 inverse(multiply(X1, inverse(multiply(Y0, X1)))) -> Y0
% 1.82/1.97 multiply(X0, multiply(inverse(X0), Y1)) -> Y1
% 1.82/1.97 multiply(X1, inverse(multiply(Y1, X1))) -> inverse(Y1)
% 1.82/1.97 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0
% 1.82/1.97 multiply(Y0, inverse(Y0)) -> identity
% 1.82/1.97 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity
% 1.82/1.97 multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1
% 1.82/1.97 multiply(Y1, identity) -> Y1
% 1.82/1.97 multiply(b, c) -> inverse(multiply(inverse(c), inverse(b)))
% 1.82/1.97 multiply(identity, X) -> X
% 1.82/1.97 multiply(inverse(X), X) -> identity
% 1.82/1.97 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 1.82/1.97 multiply(inverse(multiply(X0, X1)), X0) -> inverse(X1)
% 1.82/1.97 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1
% 1.82/1.97 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 1.82/1.97 true__ -> false__
% 1.82/1.97 with the LPO induced by
% 1.82/1.97 multiply > identity > d > b > c > inverse > f1 > true__ > false__
% 1.82/1.97
% 1.82/1.97 % SZS output end Proof
% 1.82/1.97
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