TSTP Solution File: GRP544-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP544-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 0.95s 1.08s
% Output : Proof 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP544-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n019.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 : Mon Jun 13 12:10:54 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.95/1.08 % SZS status Unsatisfiable
% 0.95/1.08 % SZS output start Proof
% 0.95/1.08 The input problem is unsatisfiable because
% 0.95/1.08
% 0.95/1.08 [1] the following set of Horn clauses is unsatisfiable:
% 0.95/1.08
% 0.95/1.08 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B
% 0.95/1.08 multiply(A, B) = divide(A, divide(identity, B))
% 0.95/1.08 inverse(A) = divide(identity, A)
% 0.95/1.08 identity = divide(A, A)
% 0.95/1.08 multiply(a, b) = multiply(b, a) ==> \bottom
% 0.95/1.08
% 0.95/1.08 This holds because
% 0.95/1.08
% 0.95/1.08 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.95/1.08
% 0.95/1.08 E:
% 0.95/1.08 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B
% 0.95/1.08 f1(multiply(a, b)) = true__
% 0.95/1.08 f1(multiply(b, a)) = false__
% 0.95/1.08 identity = divide(A, A)
% 0.95/1.08 inverse(A) = divide(identity, A)
% 0.95/1.08 multiply(A, B) = divide(A, divide(identity, B))
% 0.95/1.08 G:
% 0.95/1.08 true__ = false__
% 0.95/1.08
% 0.95/1.08 This holds because
% 0.95/1.08
% 0.95/1.08 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.95/1.08
% 0.95/1.08 divide(X0, inverse(Y1)) = divide(Y1, inverse(X0))
% 0.95/1.08 divide(inverse(X1), inverse(X0)) = divide(X0, X1)
% 0.95/1.08 divide(A, A) -> identity
% 0.95/1.08 divide(X0, divide(inverse(Y1), inverse(X0))) -> Y1
% 0.95/1.08 divide(Y0, divide(X0, inverse(Y0))) -> inverse(X0)
% 0.95/1.08 divide(Y0, divide(Y0, Y1)) -> Y1
% 0.95/1.08 divide(Y1, identity) -> Y1
% 0.95/1.08 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) -> B
% 0.95/1.08 divide(identity, A) -> inverse(A)
% 0.95/1.08 divide(inverse(X0), divide(inverse(X0), Y1)) -> Y1
% 0.95/1.08 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1)
% 0.95/1.08 divide(inverse(X1), divide(inverse(Y1), X1)) -> Y1
% 0.95/1.08 divide(inverse(Y0), divide(X0, Y0)) -> inverse(X0)
% 0.95/1.08 divide(inverse(Y0), identity) -> inverse(Y0)
% 0.95/1.08 divide(inverse(Y2), divide(X0, inverse(divide(inverse(X0), Y2)))) -> identity
% 0.95/1.08 divide(inverse(Y2), divide(inverse(Y0), inverse(divide(Y0, Y2)))) -> identity
% 0.95/1.08 divide(inverse(divide(X1, identity)), divide(X0, X1)) -> inverse(X0)
% 0.95/1.08 divide(inverse(divide(divide(divide(Y0, Y1), Y2), Y0)), Y2) -> Y1
% 0.95/1.08 divide(inverse(divide(divide(inverse(Y1), Y2), identity)), Y2) -> Y1
% 0.95/1.08 divide(inverse(divide(inverse(Y2), Y1)), Y2) -> Y1
% 0.95/1.08 divide(inverse(inverse(Y0)), divide(Y0, Y1)) -> Y1
% 0.95/1.08 divide(inverse(inverse(Y1)), identity) -> Y1
% 0.95/1.08 divide(inverse(inverse(inverse(divide(inverse(Y1), X1)))), X1) -> Y1
% 0.95/1.08 divide(inverse(inverse(inverse(inverse(X0)))), X1) -> divide(X0, X1)
% 0.95/1.08 f1(divide(a, inverse(b))) -> true__
% 0.95/1.08 f1(divide(b, inverse(a))) -> false__
% 0.95/1.08 f1(multiply(a, b)) -> true__
% 0.95/1.08 f1(multiply(b, a)) -> false__
% 0.95/1.08 inverse(divide(inverse(Y0), inverse(divide(Y0, Y1)))) -> Y1
% 0.95/1.08 inverse(divide(inverse(Y1), identity)) -> Y1
% 0.95/1.08 inverse(identity) -> identity
% 0.95/1.08 inverse(inverse(Y1)) -> Y1
% 0.95/1.08 multiply(A, B) -> divide(A, divide(identity, B))
% 0.95/1.08 true__ -> false__
% 0.95/1.08 with the LPO induced by
% 0.95/1.08 a > b > f1 > multiply > divide > identity > inverse > true__ > false__
% 0.95/1.08
% 0.95/1.08 % SZS output end Proof
% 0.95/1.08
%------------------------------------------------------------------------------