TSTP Solution File: GRP548-1 by Moca---0.1
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- Process Solution
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% File : Moca---0.1
% Problem : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n008.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 10:56:11 EDT 2022
% Result : Unsatisfiable 12.96s 13.06s
% Output : Proof 12.96s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.08/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n008.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 09:28:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 12.96/13.06 % SZS status Unsatisfiable
% 12.96/13.06 % SZS output start Proof
% 12.96/13.06 The input problem is unsatisfiable because
% 12.96/13.06
% 12.96/13.06 [1] the following set of Horn clauses is unsatisfiable:
% 12.96/13.06
% 12.96/13.06 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) = C
% 12.96/13.06 multiply(A, B) = divide(A, divide(identity, B))
% 12.96/13.06 inverse(A) = divide(identity, A)
% 12.96/13.06 identity = divide(A, A)
% 12.96/13.06 multiply(a, b) = multiply(b, a) ==> \bottom
% 12.96/13.06
% 12.96/13.06 This holds because
% 12.96/13.06
% 12.96/13.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 12.96/13.06
% 12.96/13.06 E:
% 12.96/13.06 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) = C
% 12.96/13.06 f1(multiply(a, b)) = true__
% 12.96/13.06 f1(multiply(b, a)) = false__
% 12.96/13.06 identity = divide(A, A)
% 12.96/13.06 inverse(A) = divide(identity, A)
% 12.96/13.06 multiply(A, B) = divide(A, divide(identity, B))
% 12.96/13.06 G:
% 12.96/13.06 true__ = false__
% 12.96/13.06
% 12.96/13.06 This holds because
% 12.96/13.06
% 12.96/13.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 12.96/13.06
% 12.96/13.06 divide(X0, Y1) = divide(divide(identity, Y1), divide(identity, X0))
% 12.96/13.06 divide(X1, divide(Y1, divide(identity, X1))) = divide(identity, Y1)
% 12.96/13.06 divide(Y0, divide(identity, X1)) = divide(X1, divide(identity, Y0))
% 12.96/13.06 divide(divide(X1, X0), Y1) = divide(divide(identity, Y1), divide(X0, X1))
% 12.96/13.06 divide(divide(identity, X0), X1) = divide(divide(identity, X1), X0)
% 12.96/13.06 divide(identity, divide(X1, Y0)) = divide(Y0, X1)
% 12.96/13.06 divide(A, A) -> identity
% 12.96/13.06 divide(Y0, divide(Y0, Y1)) -> Y1
% 12.96/13.06 divide(Y0, divide(divide(identity, Y1), divide(identity, Y0))) -> Y1
% 12.96/13.06 divide(Y0, divide(identity, divide(Y1, Y0))) -> Y1
% 12.96/13.06 divide(Y0, identity) -> Y0
% 12.96/13.06 divide(divide(X0, X1), X0) -> divide(identity, X1)
% 12.96/13.06 divide(divide(X0, X1), divide(identity, divide(X1, X0))) -> identity
% 12.96/13.06 divide(divide(X1, X0), divide(Y1, divide(X0, X1))) -> divide(identity, Y1)
% 12.96/13.06 divide(divide(Y0, divide(X0, X1)), divide(X1, X0)) -> Y0
% 12.96/13.06 divide(divide(Y1, X1), divide(identity, X1)) -> Y1
% 12.96/13.06 divide(divide(false__, divide(Y0, divide(identity, false__))), divide(identity, Y0)) -> identity
% 12.96/13.06 divide(divide(identity, Y0), divide(X0, Y0)) -> divide(identity, X0)
% 12.96/13.06 divide(divide(identity, Y0), divide(divide(identity, Y1), Y0)) -> Y1
% 12.96/13.06 divide(divide(identity, Y1), divide(identity, divide(Y1, X1))) -> divide(identity, X1)
% 12.96/13.06 divide(divide(identity, divide(A, B)), divide(divide(B, C), A)) -> C
% 12.96/13.06 divide(divide(identity, divide(Y0, Y1)), divide(Y1, Y0)) -> identity
% 12.96/13.06 divide(divide(identity, divide(Y0, Y1)), divide(identity, Y0)) -> Y1
% 12.96/13.06 divide(divide(identity, divide(divide(identity, Y0), Y1)), Y0) -> Y1
% 12.96/13.06 divide(divide(identity, divide(divide(identity, Y1), X1)), X1) -> Y1
% 12.96/13.06 divide(false__, multiply(divide(X1, Y0), false__)) -> divide(Y0, X1)
% 12.96/13.06 divide(identity, divide(divide(identity, X1), Y0)) -> divide(X1, divide(identity, Y0))
% 12.96/13.06 divide(identity, divide(divide(identity, X1), divide(Y1, X1))) -> Y1
% 12.96/13.06 divide(identity, divide(divide(identity, X1), divide(identity, X0))) -> divide(X1, X0)
% 12.96/13.06 divide(inverse(divide(divide(Y1, Y2), Y1)), identity) -> Y2
% 12.96/13.06 divide(inverse(identity), divide(divide(Y1, Y2), Y1)) -> Y2
% 12.96/13.06 f1(divide(a, divide(identity, b))) -> true__
% 12.96/13.06 f1(divide(b, divide(identity, a))) -> false__
% 12.96/13.06 f1(divide(identity, divide(divide(identity, b), a))) -> true__
% 12.96/13.06 inverse(A) -> divide(identity, A)
% 12.96/13.06 inverse(divide(divide(Y0, Y1), Y0)) -> Y1
% 12.96/13.06 multiply(A, B) -> divide(A, divide(identity, B))
% 12.96/13.06 multiply(divide(false__, multiply(Y1, false__)), Y1) -> identity
% 12.96/13.06 true__ -> false__
% 12.96/13.06 with the LPO induced by
% 12.96/13.06 a > b > f1 > multiply > inverse > divide > identity > true__ > false__
% 12.96/13.06
% 12.96/13.06 % SZS output end Proof
% 12.96/13.06
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