TSTP Solution File: GRP001-4 by Moca---0.1
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% File : Moca---0.1
% Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 10:51:40 EDT 2022
% Result : Unsatisfiable 0.76s 0.90s
% Output : Proof 0.76s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : moca.sh %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 06:06:42 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.76/0.90 % SZS status Unsatisfiable
% 0.76/0.90 % SZS output start Proof
% 0.76/0.90 The input problem is unsatisfiable because
% 0.76/0.90
% 0.76/0.90 [1] the following set of Horn clauses is unsatisfiable:
% 0.76/0.90
% 0.76/0.90 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.76/0.90 multiply(identity, X) = X
% 0.76/0.90 multiply(X, X) = identity
% 0.76/0.90 multiply(a, b) = c
% 0.76/0.90 multiply(b, a) = c ==> \bottom
% 0.76/0.90
% 0.76/0.90 This holds because
% 0.76/0.90
% 0.76/0.90 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.76/0.90
% 0.76/0.90 E:
% 0.76/0.90 f1(c) = false__
% 0.76/0.90 f1(multiply(b, a)) = true__
% 0.76/0.90 multiply(X, X) = identity
% 0.76/0.90 multiply(a, b) = c
% 0.76/0.90 multiply(identity, X) = X
% 0.76/0.90 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.76/0.90 G:
% 0.76/0.90 true__ = false__
% 0.76/0.90
% 0.76/0.90 This holds because
% 0.76/0.90
% 0.76/0.90 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.76/0.90
% 0.76/0.90 multiply(X1, multiply(Y0, X1)) = multiply(Y1, multiply(Y0, Y1))
% 0.76/0.90 multiply(Y0, X1) = multiply(X1, Y0)
% 0.76/0.90 multiply(Y0, identity) = multiply(X1, multiply(Y0, X1))
% 0.76/0.90 multiply(Y1, multiply(Y0, Y2)) = multiply(Y0, multiply(Y1, Y2))
% 0.76/0.90 multiply(Y2, multiply(Y0, Y1)) = multiply(Y0, multiply(Y1, Y2))
% 0.76/0.90 c -> multiply(a, b)
% 0.76/0.90 f1(c) -> false__
% 0.76/0.90 f1(multiply(a, b)) -> false__
% 0.76/0.90 f1(multiply(b, a)) -> true__
% 0.76/0.90 multiply(X, X) -> identity
% 0.76/0.90 multiply(X0, multiply(X1, multiply(Y1, multiply(X0, multiply(X1, Y2))))) -> multiply(Y1, Y2)
% 0.76/0.90 multiply(X0, multiply(X1, multiply(Y1, multiply(Y2, multiply(X0, X1))))) -> multiply(Y1, Y2)
% 0.76/0.90 multiply(X1, multiply(Y0, multiply(Y1, X1))) -> multiply(Y0, Y1)
% 0.76/0.90 multiply(Y0, multiply(X0, multiply(X1, multiply(Y0, Y2)))) -> multiply(X0, multiply(X1, Y2))
% 0.76/0.90 multiply(Y0, multiply(X0, multiply(X1, multiply(Y0, multiply(X0, multiply(X1, Y2)))))) -> Y2
% 0.76/0.90 multiply(Y0, multiply(X1, multiply(Y0, multiply(X1, identity)))) -> identity
% 0.76/0.90 multiply(Y0, multiply(Y1, multiply(X1, multiply(Y0, Y1)))) -> X1
% 0.76/0.90 multiply(Y0, multiply(Y1, multiply(X1, multiply(Y0, multiply(Y1, X1))))) -> identity
% 0.76/0.90 multiply(Y0, multiply(Y1, multiply(Y0, X1))) -> multiply(Y1, X1)
% 0.76/0.90 multiply(Y0, multiply(Y1, multiply(Y0, Y1))) -> identity
% 0.76/0.90 multiply(Y0, multiply(Y1, multiply(Y0, multiply(X1, multiply(Y1, X1))))) -> identity
% 0.76/0.90 multiply(Y0, multiply(Y1, multiply(Y0, multiply(Y1, X1)))) -> X1
% 0.76/0.90 multiply(Y1, identity) -> Y1
% 0.76/0.90 multiply(Y1, multiply(Y0, Y1)) -> Y0
% 0.76/0.90 multiply(Y1, multiply(Y1, Y2)) -> Y2
% 0.76/0.90 multiply(identity, X) -> X
% 0.76/0.90 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 0.76/0.90 true__ -> false__
% 0.76/0.90 with the LPO induced by
% 0.76/0.90 f1 > c > a > b > multiply > identity > true__ > false__
% 0.76/0.90
% 0.76/0.90 % SZS output end Proof
% 0.76/0.90
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