TSTP Solution File: GRP550-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP550-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n013.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 10:56:12 EDT 2022
% Result : Unsatisfiable 1.11s 1.26s
% Output : Proof 1.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP550-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 20:10:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.11/1.26 % SZS status Unsatisfiable
% 1.11/1.26 % SZS output start Proof
% 1.11/1.26 The input problem is unsatisfiable because
% 1.11/1.26
% 1.11/1.26 [1] the following set of Horn clauses is unsatisfiable:
% 1.11/1.26
% 1.11/1.26 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) = C
% 1.11/1.26 multiply(A, B) = divide(A, divide(identity, B))
% 1.11/1.26 inverse(A) = divide(identity, A)
% 1.11/1.26 identity = divide(A, A)
% 1.11/1.26 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 1.11/1.26
% 1.11/1.26 This holds because
% 1.11/1.26
% 1.11/1.26 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.11/1.26
% 1.11/1.26 E:
% 1.11/1.26 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) = C
% 1.11/1.26 f1(a2) = false__
% 1.11/1.26 f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 1.11/1.26 identity = divide(A, A)
% 1.11/1.26 inverse(A) = divide(identity, A)
% 1.11/1.26 multiply(A, B) = divide(A, divide(identity, B))
% 1.11/1.26 G:
% 1.11/1.26 true__ = false__
% 1.11/1.26
% 1.11/1.26 This holds because
% 1.11/1.26
% 1.11/1.26 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.11/1.26
% 1.11/1.26 divide(X0, inverse(Y1)) = divide(Y1, inverse(X0))
% 1.11/1.26 divide(X0, inverse(Y1)) = divide(Y1, inverse(inverse(inverse(X0))))
% 1.11/1.26 divide(inverse(Y0), X0) = divide(inverse(X0), Y0)
% 1.11/1.26 divide(inverse(Y0), X0) = divide(inverse(inverse(inverse(X0))), Y0)
% 1.11/1.26 divide(inverse(Y0), inverse(Y1)) = divide(Y1, Y0)
% 1.11/1.26 divide(A, A) -> identity
% 1.11/1.26 divide(X0, divide(inverse(Y1), inverse(X0))) -> Y1
% 1.11/1.26 divide(Y0, divide(Y0, Y1)) -> Y1
% 1.11/1.26 divide(Y1, identity) -> inverse(inverse(Y1))
% 1.11/1.26 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) -> C
% 1.11/1.26 divide(identity, A) -> inverse(A)
% 1.11/1.26 divide(inverse(X0), divide(inverse(X0), Y1)) -> Y1
% 1.11/1.26 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1)
% 1.11/1.26 divide(inverse(Y0), divide(X0, Y0)) -> inverse(X0)
% 1.11/1.26 divide(inverse(Y0), divide(divide(divide(Y1, Y0), Y2), Y1)) -> Y2
% 1.11/1.26 divide(inverse(Y0), divide(divide(inverse(Y0), Y2), identity)) -> Y2
% 1.11/1.26 divide(inverse(Y0), divide(inverse(Y2), Y0)) -> Y2
% 1.11/1.26 divide(inverse(Y0), identity) -> inverse(Y0)
% 1.11/1.26 divide(inverse(inverse(X1)), divide(X1, Y1)) -> Y1
% 1.11/1.26 divide(inverse(inverse(X1)), inverse(inverse(X0))) -> divide(X1, X0)
% 1.11/1.26 divide(inverse(inverse(Y1)), identity) -> Y1
% 1.11/1.26 f1(a2) -> false__
% 1.11/1.26 f1(inverse(inverse(a2))) -> true__
% 1.11/1.26 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 1.11/1.26 inverse(divide(X0, inverse(divide(inverse(X0), Y1)))) -> Y1
% 1.11/1.26 inverse(divide(divide(divide(Y1, identity), Y2), Y1)) -> Y2
% 1.11/1.26 inverse(divide(inverse(Y0), inverse(divide(inverse(inverse(Y0)), Y1)))) -> Y1
% 1.11/1.26 inverse(divide(inverse(Y1), identity)) -> Y1
% 1.11/1.26 inverse(identity) -> identity
% 1.11/1.26 inverse(inverse(Y0)) -> Y0
% 1.11/1.26 inverse(inverse(inverse(Y0))) -> inverse(Y0)
% 1.11/1.26 inverse(inverse(inverse(inverse(Y1)))) -> Y1
% 1.11/1.26 multiply(A, B) -> divide(A, divide(identity, B))
% 1.11/1.26 true__ -> false__
% 1.11/1.26 with the LPO induced by
% 1.11/1.26 b2 > a2 > f1 > multiply > divide > identity > inverse > true__ > false__
% 1.11/1.26
% 1.11/1.26 % SZS output end Proof
% 1.11/1.26
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