TSTP Solution File: GRP188-2 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP188-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n023.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 10:53:58 EDT 2022
% Result : Unsatisfiable 1.88s 2.05s
% Output : Proof 1.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP188-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.13 % Command : moca.sh %s
% 0.13/0.35 % Computer : n023.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 05:05:36 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.88/2.05 % SZS status Unsatisfiable
% 1.88/2.05 % SZS output start Proof
% 1.88/2.05 The input problem is unsatisfiable because
% 1.88/2.05
% 1.88/2.05 [1] the following set of Horn clauses is unsatisfiable:
% 1.88/2.05
% 1.88/2.05 multiply(identity, X) = X
% 1.88/2.05 multiply(inverse(X), X) = identity
% 1.88/2.05 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 1.88/2.05 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 1.88/2.05 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 1.88/2.05 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 1.88/2.05 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 1.88/2.05 least_upper_bound(X, X) = X
% 1.88/2.05 greatest_lower_bound(X, X) = X
% 1.88/2.05 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 1.88/2.05 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 1.88/2.05 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 1.88/2.05 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 1.88/2.05 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 1.88/2.05 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 1.88/2.05 inverse(identity) = identity
% 1.88/2.05 inverse(inverse(X)) = X
% 1.88/2.05 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X))
% 1.88/2.05 least_upper_bound(b, least_upper_bound(a, b)) = least_upper_bound(a, b) ==> \bottom
% 1.88/2.05
% 1.88/2.05 This holds because
% 1.88/2.05
% 1.88/2.05 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.88/2.05
% 1.88/2.05 E:
% 1.88/2.05 f1(least_upper_bound(a, b)) = false__
% 1.88/2.05 f1(least_upper_bound(b, least_upper_bound(a, b))) = true__
% 1.88/2.05 greatest_lower_bound(X, X) = X
% 1.88/2.05 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 1.88/2.05 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 1.88/2.05 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 1.88/2.05 inverse(identity) = identity
% 1.88/2.05 inverse(inverse(X)) = X
% 1.88/2.05 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X))
% 1.88/2.05 least_upper_bound(X, X) = X
% 1.88/2.05 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 1.88/2.05 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 1.88/2.05 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 1.88/2.05 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 1.88/2.05 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 1.88/2.05 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 1.88/2.05 multiply(identity, X) = X
% 1.88/2.05 multiply(inverse(X), X) = identity
% 1.88/2.05 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 1.88/2.05 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 1.88/2.05 G:
% 1.88/2.05 true__ = false__
% 1.88/2.05
% 1.88/2.05 This holds because
% 1.88/2.05
% 1.88/2.05 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.88/2.05
% 1.88/2.05 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 1.88/2.05 greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y2)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 1.88/2.05 greatest_lower_bound(Y2, greatest_lower_bound(Y0, Y1)) = greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y2))
% 1.88/2.05 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 1.88/2.06 f1(least_upper_bound(a, b)) -> false__
% 1.88/2.06 f1(least_upper_bound(b, least_upper_bound(a, b))) -> true__
% 1.88/2.06 greatest_lower_bound(X, X) -> X
% 1.88/2.06 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X
% 1.88/2.06 greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y0)) -> greatest_lower_bound(Y0, Y1)
% 1.88/2.06 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0
% 1.88/2.06 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2)
% 1.88/2.06 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 1.88/2.06 greatest_lower_bound(inverse(greatest_lower_bound(Y0, identity)), multiply(Y0, inverse(greatest_lower_bound(Y0, identity)))) -> identity
% 1.88/2.06 greatest_lower_bound(multiply(inverse(greatest_lower_bound(Y1, Y2)), Y1), multiply(inverse(greatest_lower_bound(Y1, Y2)), Y2)) -> identity
% 1.88/2.06 inverse(identity) -> identity
% 1.88/2.06 inverse(inverse(X)) -> X
% 1.88/2.06 inverse(multiply(X, Y)) -> multiply(inverse(Y), inverse(X))
% 1.88/2.06 least_upper_bound(X, X) -> X
% 1.88/2.06 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X
% 1.88/2.06 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0
% 1.88/2.06 least_upper_bound(Y0, least_upper_bound(Y1, Y0)) -> least_upper_bound(Y0, Y1)
% 1.88/2.06 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2)
% 1.88/2.06 least_upper_bound(inverse(least_upper_bound(Y0, identity)), multiply(Y0, inverse(least_upper_bound(Y0, identity)))) -> identity
% 1.88/2.06 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z))
% 1.88/2.06 least_upper_bound(multiply(inverse(least_upper_bound(Y1, Y2)), Y1), multiply(inverse(least_upper_bound(Y1, Y2)), Y2)) -> identity
% 1.88/2.06 multiply(X, greatest_lower_bound(Y, Z)) -> greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 1.88/2.06 multiply(X, least_upper_bound(Y, Z)) -> least_upper_bound(multiply(X, Y), multiply(X, Z))
% 1.88/2.06 multiply(X0, identity) -> X0
% 1.88/2.06 multiply(X0, inverse(X0)) -> identity
% 1.88/2.06 multiply(X0, multiply(inverse(X0), Y1)) -> Y1
% 1.88/2.06 multiply(greatest_lower_bound(Y, Z), X) -> greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 1.88/2.06 multiply(greatest_lower_bound(Y0, identity), Y1) -> greatest_lower_bound(Y1, multiply(Y0, Y1))
% 1.88/2.06 multiply(identity, X) -> X
% 1.88/2.06 multiply(inverse(X), X) -> identity
% 1.88/2.06 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2
% 1.88/2.06 multiply(least_upper_bound(Y, Z), X) -> least_upper_bound(multiply(Y, X), multiply(Z, X))
% 1.88/2.06 multiply(least_upper_bound(Y0, identity), Y1) -> least_upper_bound(Y1, multiply(Y0, Y1))
% 1.88/2.06 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z))
% 1.88/2.06 true__ -> false__
% 1.88/2.06 with the LPO induced by
% 1.88/2.06 b > a > f1 > inverse > multiply > greatest_lower_bound > least_upper_bound > identity > true__ > false__
% 1.88/2.06
% 1.88/2.06 % SZS output end Proof
% 1.88/2.06
%------------------------------------------------------------------------------