TSTP Solution File: GRP010-4 by Moca---0.1
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% File : Moca---0.1
% Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n016.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 0.46s 0.65s
% Output : Proof 0.46s
% 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 : GRP010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n016.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 : Mon Jun 13 06:54:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/0.65 % SZS status Unsatisfiable
% 0.46/0.65 % SZS output start Proof
% 0.46/0.65 The input problem is unsatisfiable because
% 0.46/0.65
% 0.46/0.65 [1] the following set of Horn clauses is unsatisfiable:
% 0.46/0.65
% 0.46/0.65 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.46/0.65 multiply(identity, X) = X
% 0.46/0.65 multiply(inverse(X), X) = identity
% 0.46/0.65 multiply(c, b) = identity
% 0.46/0.65 multiply(b, c) = identity ==> \bottom
% 0.46/0.65
% 0.46/0.65 This holds because
% 0.46/0.65
% 0.46/0.65 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.46/0.65
% 0.46/0.65 E:
% 0.46/0.65 f1(identity) = false__
% 0.46/0.65 f1(multiply(b, c)) = true__
% 0.46/0.65 multiply(c, b) = identity
% 0.46/0.65 multiply(identity, X) = X
% 0.46/0.65 multiply(inverse(X), X) = identity
% 0.46/0.65 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.46/0.65 G:
% 0.46/0.65 true__ = false__
% 0.46/0.65
% 0.46/0.65 This holds because
% 0.46/0.65
% 0.46/0.65 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.46/0.65
% 0.46/0.65
% 0.46/0.65 f1(identity) -> false__
% 0.46/0.65 f1(multiply(b, c)) -> true__
% 0.46/0.65 f1(multiply(c, b)) -> false__
% 0.46/0.65 identity -> multiply(c, b)
% 0.46/0.65 inverse(b) -> c
% 0.46/0.65 inverse(c) -> b
% 0.46/0.65 inverse(inverse(Y1)) -> Y1
% 0.46/0.65 inverse(multiply(b, c)) -> multiply(b, c)
% 0.46/0.65 multiply(Y0, inverse(Y0)) -> multiply(c, b)
% 0.46/0.65 multiply(Y0, multiply(b, c)) -> Y0
% 0.46/0.65 multiply(Y1, multiply(c, b)) -> Y1
% 0.46/0.65 multiply(c, b) -> multiply(b, c)
% 0.46/0.65 multiply(c, multiply(b, Y0)) -> Y0
% 0.46/0.65 multiply(identity, X) -> X
% 0.46/0.65 multiply(inverse(X), X) -> identity
% 0.46/0.65 multiply(inverse(Y1), multiply(Y1, Y2)) -> multiply(c, multiply(b, Y2))
% 0.46/0.65 multiply(inverse(c), X0) -> multiply(b, X0)
% 0.46/0.65 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1)
% 0.46/0.65 multiply(inverse(inverse(Y1)), multiply(c, b)) -> Y1
% 0.46/0.65 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1
% 0.46/0.65 multiply(inverse(multiply(Y0, c)), multiply(Y0, X0)) -> multiply(b, X0)
% 0.46/0.65 multiply(inverse(multiply(Y0, inverse(Y2))), multiply(Y0, multiply(c, b))) -> Y2
% 0.46/0.65 multiply(inverse(multiply(Y0, multiply(c, b))), multiply(Y0, Y2)) -> Y2
% 0.46/0.65 multiply(inverse(multiply(b, c)), Y0) -> Y0
% 0.46/0.65 multiply(inverse(multiply(c, b)), Y1) -> Y1
% 0.46/0.65 multiply(inverse(multiply(inverse(multiply(Y1, Y2)), Y1)), multiply(c, b)) -> Y2
% 0.46/0.65 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.46/0.65 true__ -> false__
% 0.46/0.65 with the LPO induced by
% 0.46/0.65 f1 > inverse > identity > c > b > multiply > true__ > false__
% 0.46/0.65
% 0.46/0.65 % SZS output end Proof
% 0.46/0.65
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