TSTP Solution File: GRP461-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP461-1 : TPTP v8.1.0. Released v2.6.0.
% 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 10:55:36 EDT 2022
% Result : Unsatisfiable 0.82s 0.97s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP461-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 09:18:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.82/0.97 % SZS status Unsatisfiable
% 0.82/0.97 % SZS output start Proof
% 0.82/0.97 The input problem is unsatisfiable because
% 0.82/0.97
% 0.82/0.97 [1] the following set of Horn clauses is unsatisfiable:
% 0.82/0.97
% 0.82/0.97 divide(A, divide(divide(divide(identity, B), C), divide(divide(divide(A, A), A), C))) = B
% 0.82/0.97 multiply(A, B) = divide(A, divide(identity, B))
% 0.82/0.97 inverse(A) = divide(identity, A)
% 0.82/0.97 identity = divide(A, A)
% 0.82/0.97 multiply(identity, a2) = a2 ==> \bottom
% 0.82/0.97
% 0.82/0.97 This holds because
% 0.82/0.97
% 0.82/0.97 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.82/0.97
% 0.82/0.97 E:
% 0.82/0.97 divide(A, divide(divide(divide(identity, B), C), divide(divide(divide(A, A), A), C))) = B
% 0.82/0.97 f1(a2) = false__
% 0.82/0.97 f1(multiply(identity, a2)) = true__
% 0.82/0.97 identity = divide(A, A)
% 0.82/0.97 inverse(A) = divide(identity, A)
% 0.82/0.97 multiply(A, B) = divide(A, divide(identity, B))
% 0.82/0.97 G:
% 0.82/0.97 true__ = false__
% 0.82/0.97
% 0.82/0.97 This holds because
% 0.82/0.97
% 0.82/0.97 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.82/0.97
% 0.82/0.97
% 0.82/0.97 divide(A, A) -> identity
% 0.82/0.97 divide(A, divide(divide(divide(identity, B), C), divide(divide(divide(A, A), A), C))) -> B
% 0.82/0.97 divide(Y0, divide(X0, inverse(Y0))) -> inverse(X0)
% 0.82/0.97 divide(Y0, divide(divide(inverse(Y1), Y2), divide(inverse(Y0), Y2))) -> Y1
% 0.82/0.97 divide(Y0, divide(divide(inverse(Y1), inverse(Y0)), identity)) -> Y1
% 0.82/0.97 divide(Y0, divide(inverse(Y1), inverse(Y0))) -> Y1
% 0.82/0.97 divide(Y0, divide(inverse(Y2), divide(inverse(Y0), Y2))) -> identity
% 0.82/0.97 divide(Y0, divide(inverse(inverse(Y0)), identity)) -> identity
% 0.82/0.97 divide(Y0, inverse(divide(inverse(Y0), X0))) -> inverse(inverse(inverse(X0)))
% 0.82/0.97 divide(Y0, inverse(divide(inverse(Y0), identity))) -> identity
% 0.82/0.97 divide(Y0, inverse(divide(inverse(Y0), inverse(Y1)))) -> Y1
% 0.82/0.97 divide(Y0, inverse(inverse(Y0))) -> identity
% 0.82/0.97 divide(Y1, identity) -> Y1
% 0.82/0.97 divide(divide(inverse(X0), X1), inverse(X1)) -> inverse(X0)
% 0.82/0.97 divide(identity, A) -> inverse(A)
% 0.82/0.97 divide(inverse(X0), divide(inverse(Y1), X0)) -> Y1
% 0.82/0.97 divide(inverse(X0), inverse(divide(X0, inverse(Y1)))) -> Y1
% 0.82/0.97 divide(inverse(Y0), inverse(divide(Y0, X0))) -> inverse(X0)
% 0.82/0.97 divide(inverse(inverse(X0)), X0) -> identity
% 0.82/0.97 divide(inverse(inverse(Y0)), inverse(X1)) -> divide(Y0, inverse(X1))
% 0.82/0.97 f1(a2) -> false__
% 0.82/0.97 f1(inverse(inverse(a2))) -> true__
% 0.82/0.97 f1(multiply(identity, a2)) -> true__
% 0.82/0.97 inverse(divide(X1, inverse(inverse(divide(inverse(inverse(Y0)), inverse(X1)))))) -> Y0
% 0.82/0.97 inverse(divide(divide(X0, Y1), inverse(Y1))) -> inverse(X0)
% 0.82/0.97 inverse(divide(divide(inverse(Y0), identity), identity)) -> Y0
% 0.82/0.97 inverse(divide(divide(inverse(Y0), inverse(X0)), X0)) -> Y0
% 0.82/0.97 inverse(divide(divide(inverse(Y1), Y2), inverse(Y2))) -> Y1
% 0.82/0.97 inverse(identity) -> identity
% 0.82/0.97 inverse(inverse(Y0)) -> Y0
% 0.82/0.97 inverse(inverse(inverse(X0))) -> inverse(X0)
% 0.82/0.97 inverse(inverse(inverse(inverse(Y1)))) -> Y1
% 0.82/0.97 multiply(A, B) -> divide(A, divide(identity, B))
% 0.82/0.97 true__ -> false__
% 0.82/0.97 with the LPO induced by
% 0.82/0.97 a2 > f1 > multiply > divide > identity > inverse > true__ > false__
% 0.82/0.97
% 0.82/0.97 % SZS output end Proof
% 0.82/0.97
%------------------------------------------------------------------------------