TSTP Solution File: GRP542-1 by Moca---0.1
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% File : Moca---0.1
% Problem : GRP542-1 : TPTP v8.1.0. Released v2.6.0.
% 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 10:56:09 EDT 2022
% Result : Unsatisfiable 0.86s 1.00s
% Output : Proof 0.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP542-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 08:08:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.86/1.00 % SZS status Unsatisfiable
% 0.86/1.00 % SZS output start Proof
% 0.86/1.00 The input problem is unsatisfiable because
% 0.86/1.00
% 0.86/1.00 [1] the following set of Horn clauses is unsatisfiable:
% 0.86/1.00
% 0.86/1.00 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B
% 0.86/1.00 multiply(A, B) = divide(A, divide(identity, B))
% 0.86/1.00 inverse(A) = divide(identity, A)
% 0.86/1.00 identity = divide(A, A)
% 0.86/1.00 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 0.86/1.00
% 0.86/1.00 This holds because
% 0.86/1.00
% 0.86/1.00 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.86/1.00
% 0.86/1.00 E:
% 0.86/1.00 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B
% 0.86/1.00 f1(a2) = false__
% 0.86/1.00 f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 0.86/1.00 identity = divide(A, A)
% 0.86/1.00 inverse(A) = divide(identity, A)
% 0.86/1.00 multiply(A, B) = divide(A, divide(identity, B))
% 0.86/1.00 G:
% 0.86/1.00 true__ = false__
% 0.86/1.00
% 0.86/1.00 This holds because
% 0.86/1.00
% 0.86/1.00 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.86/1.00
% 0.86/1.00 divide(X0, Y1) = divide(inverse(divide(Y1, identity)), inverse(X0))
% 0.86/1.00 divide(X0, inverse(Y1)) = divide(Y1, inverse(X0))
% 0.86/1.00 divide(inverse(X1), inverse(X0)) = divide(X0, X1)
% 0.86/1.00 divide(inverse(Y2), Y1) = divide(inverse(divide(Y1, identity)), Y2)
% 0.86/1.00 divide(A, A) -> identity
% 0.86/1.00 divide(Y0, divide(Y0, Y1)) -> Y1
% 0.86/1.00 divide(Y1, identity) -> Y1
% 0.86/1.00 divide(divide(divide(X0, X1), Y2), X0) -> divide(inverse(divide(X1, identity)), Y2)
% 0.86/1.00 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) -> B
% 0.86/1.00 divide(divide(inverse(Y1), Y2), identity) -> divide(inverse(divide(Y1, identity)), Y2)
% 0.86/1.00 divide(identity, A) -> inverse(A)
% 0.86/1.00 divide(inverse(X0), divide(inverse(X0), Y1)) -> Y1
% 0.86/1.00 divide(inverse(Y0), identity) -> inverse(Y0)
% 0.86/1.00 divide(inverse(divide(Y1, identity)), divide(Y0, Y1)) -> inverse(Y0)
% 0.86/1.00 divide(inverse(divide(divide(divide(Y0, Y1), Y2), Y0)), Y2) -> Y1
% 0.86/1.00 divide(inverse(divide(divide(inverse(Y1), Y2), identity)), Y2) -> Y1
% 0.86/1.00 divide(inverse(divide(inverse(Y2), Y1)), Y2) -> Y1
% 0.86/1.00 divide(inverse(inverse(Y0)), divide(Y0, Y1)) -> Y1
% 0.86/1.00 divide(inverse(inverse(Y1)), identity) -> Y1
% 0.86/1.00 divide(inverse(inverse(inverse(inverse(X0)))), X1) -> divide(X0, X1)
% 0.86/1.00 f1(a2) -> false__
% 0.86/1.00 f1(inverse(inverse(a2))) -> true__
% 0.86/1.00 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 0.86/1.00 inverse(identity) -> identity
% 0.86/1.00 inverse(inverse(Y1)) -> Y1
% 0.86/1.00 multiply(A, B) -> divide(A, divide(identity, B))
% 0.86/1.00 true__ -> false__
% 0.86/1.00 with the LPO induced by
% 0.86/1.00 b2 > a2 > f1 > multiply > divide > identity > inverse > true__ > false__
% 0.86/1.00
% 0.86/1.00 % SZS output end Proof
% 0.86/1.00
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