TSTP Solution File: GRP457-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : GRP457-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n015.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 10:55:35 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% 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 : GRP457-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n015.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 07:25:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 The input problem is unsatisfiable because
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% 0.12/0.39 [1] the following set of Horn clauses is unsatisfiable:
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% 0.12/0.39 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(identity, A), C)))), C) = B
% 0.12/0.39 multiply(A, B) = divide(A, divide(identity, B))
% 0.12/0.39 inverse(A) = divide(identity, A)
% 0.12/0.39 identity = divide(A, A)
% 0.12/0.39 multiply(inverse(a1), a1) = identity ==> \bottom
% 0.12/0.39
% 0.12/0.39 This holds because
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% 0.12/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.12/0.39 E:
% 0.12/0.39 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(identity, A), C)))), C) = B
% 0.12/0.39 f1(identity) = false__
% 0.12/0.39 f1(multiply(inverse(a1), a1)) = true__
% 0.12/0.39 identity = divide(A, A)
% 0.12/0.39 inverse(A) = divide(identity, A)
% 0.12/0.39 multiply(A, B) = divide(A, divide(identity, B))
% 0.12/0.39 G:
% 0.12/0.39 true__ = false__
% 0.12/0.39
% 0.12/0.39 This holds because
% 0.12/0.39
% 0.12/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39 divide(A, A) -> identity
% 0.12/0.39 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(identity, A), C)))), C) -> B
% 0.12/0.39 divide(divide(inverse(identity), inverse(divide(Y1, divide(inverse(identity), Y2)))), Y2) -> Y1
% 0.12/0.39 divide(divide(inverse(identity), inverse(divide(Y1, inverse(Y2)))), Y2) -> Y1
% 0.12/0.39 divide(identity, A) -> inverse(A)
% 0.12/0.39 divide(inverse(Y0), inverse(divide(Y0, identity))) -> identity
% 0.12/0.39 divide(inverse(divide(Y0, divide(Y1, divide(inverse(Y0), Y2)))), Y2) -> Y1
% 0.12/0.39 divide(inverse(divide(Y0, divide(Y1, identity))), inverse(Y0)) -> Y1
% 0.12/0.39 divide(inverse(divide(Y0, identity)), Y2) -> divide(inverse(Y0), Y2)
% 0.12/0.39 divide(inverse(divide(Y0, inverse(divide(inverse(Y0), Y2)))), Y2) -> identity
% 0.12/0.39 divide(inverse(inverse(divide(X0, identity))), Y1) -> divide(inverse(inverse(X0)), Y1)
% 0.12/0.39 divide(inverse(inverse(divide(Y0, inverse(Y1)))), Y1) -> Y0
% 0.12/0.39 divide(inverse(inverse(divide(Y1, identity))), identity) -> Y1
% 0.12/0.39 divide(inverse(inverse(inverse(inverse(Y1)))), Y1) -> identity
% 0.12/0.39 f1(identity) -> false__
% 0.12/0.39 f1(multiply(inverse(a1), a1)) -> true__
% 0.12/0.39 inverse(identity) -> identity
% 0.12/0.39 inverse(inverse(divide(Y1, identity))) -> Y1
% 0.12/0.39 multiply(A, B) -> divide(A, divide(identity, B))
% 0.12/0.39 true__ -> false__
% 0.12/0.39 with the LPO induced by
% 0.12/0.39 a1 > f1 > multiply > divide > identity > inverse > true__ > false__
% 0.12/0.39
% 0.12/0.39 % SZS output end Proof
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