%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP575-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:14:54 AM UTC 2026
% Result : Unsatisfiable 3.51s 1.51s
% Output : Refutation 5.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 5
% Syntax : Number of formulae : 134 ( 134 unt; 0 def)
% Number of atoms : 134 ( 133 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 278 ( 278 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f6,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f7,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[],[f6,f3]) ).
fof(f8,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[],[f6,f4]) ).
fof(f9,plain,
! [X0,X1] : identity = double_divide(double_divide(X1,X0),multiply(X0,X1)),
inference(superposition,[],[f4,f6]) ).
fof(f10,plain,
! [X0,X1] : multiply(identity,double_divide(X1,X0)) = inverse(multiply(X0,X1)),
inference(superposition,[],[f7,f6]) ).
fof(f11,plain,
! [X0] : multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[],[f7,f7]) ).
fof(f12,plain,
! [X0] : identity = double_divide(inverse(X0),multiply(identity,X0)),
inference(superposition,[],[f4,f7]) ).
fof(f26,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f1,f3]) ).
fof(f27,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f26,f3]) ).
fof(f28,plain,
! [X0] : identity = double_divide(multiply(identity,inverse(X0)),multiply(identity,multiply(identity,X0))),
inference(superposition,[],[f12,f11]) ).
fof(f81,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,inverse(X0)),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[],[f27,f3]) ).
fof(f82,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(X1,identity),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[],[f27,f4]) ).
fof(f84,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X1,X0),inverse(double_divide(X2,double_divide(double_divide(X0,double_divide(X3,X2)),inverse(X3)))))),inverse(identity)) = X1,
inference(superposition,[],[f27,f27]) ).
fof(f87,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X2,double_divide(double_divide(X3,double_divide(double_divide(X1,X0),X2)),multiply(X0,X1))),inverse(identity)) = X3,
inference(superposition,[],[f27,f6]) ).
fof(f93,plain,
! [X2,X0,X1] : inverse(X0) = multiply(inverse(identity),double_divide(X1,double_divide(double_divide(X0,double_divide(X2,X1)),inverse(X2)))),
inference(superposition,[],[f6,f27]) ).
fof(f96,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X1,X0),multiply(double_divide(double_divide(X0,double_divide(X3,X2)),inverse(X3)),X2))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f84,f6]) ).
fof(f98,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(inverse(X1),inverse(X0))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f82,f3]) ).
fof(f121,plain,
! [X0] : double_divide(double_divide(inverse(inverse(X0)),identity),inverse(identity)) = X0,
inference(superposition,[],[f98,f4]) ).
fof(f128,plain,
! [X0] : double_divide(inverse(inverse(inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[],[f121,f3]) ).
fof(f129,plain,
! [X0] : double_divide(multiply(identity,inverse(X0)),inverse(identity)) = X0,
inference(forward_demodulation,[],[f128,f7]) ).
fof(f174,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),inverse(identity)) = X0,
inference(superposition,[],[f81,f4]) ).
fof(f192,plain,
identity = double_divide(double_divide(identity,identity),inverse(identity)),
inference(superposition,[],[f174,f4]) ).
fof(f201,plain,
identity = double_divide(inverse(identity),inverse(identity)),
inference(forward_demodulation,[],[f192,f3]) ).
fof(f203,plain,
inverse(identity) = double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)),
inference(superposition,[],[f81,f201]) ).
fof(f210,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f203,f174]) ).
fof(f217,plain,
! [X0] : double_divide(multiply(identity,inverse(X0)),identity) = X0,
inference(superposition,[],[f129,f210]) ).
fof(f232,plain,
! [X0] : double_divide(double_divide(identity,double_divide(inverse(X0),identity)),identity) = X0,
inference(superposition,[],[f98,f210]) ).
fof(f240,plain,
! [X0] : inverse(double_divide(identity,double_divide(inverse(X0),identity))) = X0,
inference(forward_demodulation,[],[f232,f3]) ).
fof(f248,plain,
! [X0] : inverse(multiply(identity,inverse(X0))) = X0,
inference(forward_demodulation,[],[f217,f3]) ).
fof(f255,plain,
! [X0] : multiply(double_divide(inverse(X0),identity),identity) = X0,
inference(forward_demodulation,[],[f240,f6]) ).
fof(f260,plain,
! [X0] : multiply(identity,inverse(inverse(X0))) = X0,
inference(forward_demodulation,[],[f248,f11]) ).
fof(f266,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(forward_demodulation,[],[f255,f3]) ).
fof(f270,plain,
! [X0] : multiply(identity,multiply(identity,X0)) = X0,
inference(forward_demodulation,[],[f260,f7]) ).
fof(f272,plain,
! [X0] : multiply(multiply(identity,X0),identity) = X0,
inference(forward_demodulation,[],[f266,f7]) ).
fof(f309,plain,
! [X2,X0,X1] : inverse(X0) = multiply(identity,double_divide(X1,double_divide(double_divide(X0,double_divide(X2,X1)),inverse(X2)))),
inference(forward_demodulation,[],[f93,f210]) ).
fof(f310,plain,
! [X2,X0,X1] : inverse(X0) = inverse(multiply(double_divide(double_divide(X0,double_divide(X2,X1)),inverse(X2)),X1)),
inference(forward_demodulation,[],[f309,f10]) ).
fof(f315,plain,
! [X0] : identity = double_divide(multiply(identity,inverse(X0)),X0),
inference(superposition,[],[f28,f270]) ).
fof(f345,plain,
! [X0] : multiply(identity,X0) = multiply(X0,identity),
inference(superposition,[],[f272,f270]) ).
fof(f427,plain,
! [X2,X0,X1] : inverse(inverse(X0)) = multiply(identity,multiply(double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X1)),X2)),
inference(superposition,[],[f7,f310]) ).
fof(f437,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(inverse(X1),double_divide(inverse(X0),inverse(X1))),inverse(identity)) = multiply(double_divide(double_divide(X0,double_divide(X2,X3)),inverse(X2)),X3),
inference(superposition,[],[f98,f310]) ).
fof(f443,plain,
! [X2,X3,X0] : multiply(double_divide(double_divide(X0,double_divide(X2,X3)),inverse(X2)),X3) = X0,
inference(forward_demodulation,[],[f437,f98]) ).
fof(f449,plain,
! [X2,X0,X1] : multiply(identity,X0) = multiply(identity,multiply(double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X1)),X2)),
inference(forward_demodulation,[],[f427,f7]) ).
fof(f663,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X2,double_divide(double_divide(X3,double_divide(double_divide(X1,X0),X2)),multiply(X0,X1))),identity) = X3,
inference(forward_demodulation,[],[f87,f210]) ).
fof(f664,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X2,double_divide(double_divide(X3,double_divide(double_divide(X1,X0),X2)),multiply(X0,X1)))) = X3,
inference(forward_demodulation,[],[f663,f3]) ).
fof(f665,plain,
! [X2,X3,X0,X1] : multiply(double_divide(double_divide(X3,double_divide(double_divide(X1,X0),X2)),multiply(X0,X1)),X2) = X3,
inference(forward_demodulation,[],[f664,f6]) ).
fof(f773,plain,
! [X0,X1] : multiply(double_divide(double_divide(X1,X0),multiply(double_divide(identity,inverse(X0)),identity)),inverse(identity)) = X1,
inference(superposition,[],[f665,f174]) ).
fof(f789,plain,
! [X2,X0,X1] : multiply(double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X1)),X2)),inverse(identity)),X2) = X0,
inference(superposition,[],[f665,f8]) ).
fof(f803,plain,
! [X2,X0,X1] : multiply(double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X1)),X2)),identity),X2) = X0,
inference(forward_demodulation,[],[f789,f210]) ).
fof(f816,plain,
! [X0,X1] : multiply(double_divide(double_divide(X1,X0),multiply(double_divide(identity,inverse(X0)),identity)),identity) = X1,
inference(forward_demodulation,[],[f773,f210]) ).
fof(f837,plain,
! [X2,X0,X1] : multiply(inverse(double_divide(X0,double_divide(double_divide(X1,inverse(X1)),X2))),X2) = X0,
inference(forward_demodulation,[],[f803,f3]) ).
fof(f847,plain,
! [X0,X1] : multiply(identity,double_divide(double_divide(X1,X0),multiply(double_divide(identity,inverse(X0)),identity))) = X1,
inference(forward_demodulation,[],[f816,f345]) ).
fof(f863,plain,
! [X2,X0,X1] : multiply(multiply(double_divide(double_divide(X1,inverse(X1)),X2),X0),X2) = X0,
inference(forward_demodulation,[],[f837,f6]) ).
fof(f869,plain,
! [X0,X1] : inverse(multiply(multiply(double_divide(identity,inverse(X0)),identity),double_divide(X1,X0))) = X1,
inference(forward_demodulation,[],[f847,f10]) ).
fof(f881,plain,
! [X2,X0] : multiply(multiply(double_divide(identity,X2),X0),X2) = X0,
inference(forward_demodulation,[],[f863,f4]) ).
fof(f886,plain,
! [X0,X1] : inverse(multiply(multiply(identity,double_divide(identity,inverse(X0))),double_divide(X1,X0))) = X1,
inference(forward_demodulation,[],[f869,f345]) ).
fof(f895,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(X0),identity)),double_divide(X1,X0))) = X1,
inference(forward_demodulation,[],[f886,f10]) ).
fof(f899,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(identity,inverse(X0))),double_divide(X1,X0))) = X1,
inference(forward_demodulation,[],[f895,f345]) ).
fof(f901,plain,
! [X0,X1] : inverse(multiply(multiply(identity,inverse(inverse(X0))),double_divide(X1,X0))) = X1,
inference(forward_demodulation,[],[f899,f11]) ).
fof(f902,plain,
! [X0,X1] : inverse(multiply(multiply(identity,multiply(identity,X0)),double_divide(X1,X0))) = X1,
inference(forward_demodulation,[],[f901,f7]) ).
fof(f903,plain,
! [X0,X1] : inverse(multiply(X0,double_divide(X1,X0))) = X1,
inference(forward_demodulation,[],[f902,f270]) ).
fof(f931,plain,
! [X2,X0] : double_divide(double_divide(X0,double_divide(inverse(X2),X0)),inverse(identity)) = X2,
inference(superposition,[],[f98,f903]) ).
fof(f945,plain,
! [X2,X0] : double_divide(double_divide(X0,double_divide(inverse(X2),X0)),identity) = X2,
inference(forward_demodulation,[],[f931,f210]) ).
fof(f970,plain,
! [X2,X0] : inverse(double_divide(X0,double_divide(inverse(X2),X0))) = X2,
inference(forward_demodulation,[],[f945,f3]) ).
fof(f985,plain,
! [X2,X0] : multiply(double_divide(inverse(X2),X0),X0) = X2,
inference(forward_demodulation,[],[f970,f6]) ).
fof(f995,plain,
! [X0] : identity = multiply(double_divide(identity,X0),X0),
inference(superposition,[],[f985,f210]) ).
fof(f1125,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,X0),multiply(double_divide(double_divide(X0,double_divide(X3,X2)),inverse(X3)),X2))),identity) = X1,
inference(forward_demodulation,[],[f96,f210]) ).
fof(f1126,plain,
! [X2,X3,X0,X1] : inverse(double_divide(identity,double_divide(double_divide(X1,X0),multiply(double_divide(double_divide(X0,double_divide(X3,X2)),inverse(X3)),X2)))) = X1,
inference(forward_demodulation,[],[f1125,f3]) ).
fof(f1127,plain,
! [X2,X3,X0,X1] : multiply(double_divide(double_divide(X1,X0),multiply(double_divide(double_divide(X0,double_divide(X3,X2)),inverse(X3)),X2)),identity) = X1,
inference(forward_demodulation,[],[f1126,f6]) ).
fof(f1128,plain,
! [X2,X3,X0,X1] : multiply(identity,double_divide(double_divide(X1,X0),multiply(double_divide(double_divide(X0,double_divide(X3,X2)),inverse(X3)),X2))) = X1,
inference(forward_demodulation,[],[f1127,f345]) ).
fof(f1129,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(double_divide(double_divide(X0,double_divide(X3,X2)),inverse(X3)),X2),double_divide(X1,X0))) = X1,
inference(forward_demodulation,[],[f1128,f10]) ).
fof(f1322,plain,
! [X2,X3,X0,X1] : double_divide(X1,X0) = inverse(multiply(multiply(double_divide(double_divide(multiply(X0,X1),double_divide(X2,X3)),inverse(X2)),X3),identity)),
inference(superposition,[],[f1129,f9]) ).
fof(f1386,plain,
! [X2,X3,X0,X1] : double_divide(X1,X0) = inverse(multiply(identity,multiply(double_divide(double_divide(multiply(X0,X1),double_divide(X2,X3)),inverse(X2)),X3))),
inference(forward_demodulation,[],[f1322,f345]) ).
fof(f1422,plain,
! [X2,X3,X0,X1] : double_divide(X1,X0) = multiply(identity,inverse(multiply(double_divide(double_divide(multiply(X0,X1),double_divide(X2,X3)),inverse(X2)),X3))),
inference(forward_demodulation,[],[f1386,f11]) ).
fof(f1454,plain,
! [X0,X1] : double_divide(X1,X0) = multiply(identity,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f1422,f310]) ).
fof(f1693,plain,
! [X0] : multiply(identity,X0) = X0,
inference(superposition,[],[f881,f995]) ).
fof(f1731,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f1693,f345]) ).
fof(f1757,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(superposition,[],[f129,f1693]) ).
fof(f1782,plain,
! [X0] : double_divide(inverse(X0),identity) = X0,
inference(forward_demodulation,[],[f1757,f210]) ).
fof(f1796,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f1782,f3]) ).
fof(f1815,plain,
! [X0] : identity = double_divide(double_divide(identity,X0),X0),
inference(superposition,[],[f9,f1731]) ).
fof(f2023,plain,
! [X0] : double_divide(identity,X0) = inverse(multiply(X0,identity)),
inference(superposition,[],[f903,f1815]) ).
fof(f2031,plain,
! [X0] : double_divide(identity,inverse(X0)) = double_divide(double_divide(identity,double_divide(identity,inverse(X0))),inverse(identity)),
inference(superposition,[],[f81,f1815]) ).
fof(f2032,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(forward_demodulation,[],[f2031,f174]) ).
fof(f2038,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(forward_demodulation,[],[f2023,f1731]) ).
fof(f2204,plain,
! [X0,X1] : double_divide(X1,X0) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[],[f1454,f1693]) ).
fof(f2222,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,multiply(double_divide(identity,X1),X0)),
inference(superposition,[],[f2204,f881]) ).
fof(f2235,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(superposition,[],[f2204,f903]) ).
fof(f2316,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[],[f2222,f2038]) ).
fof(f2391,plain,
! [X0,X1] : inverse(X0) = multiply(X1,double_divide(X0,X1)),
inference(superposition,[],[f6,f2235]) ).
fof(f2488,plain,
! [X0,X1] : multiply(identity,inverse(double_divide(X0,X1))) = multiply(double_divide(identity,inverse(X0)),X1),
inference(superposition,[],[f443,f315]) ).
fof(f2534,plain,
! [X0,X1] : multiply(X0,X1) = multiply(identity,inverse(double_divide(X0,X1))),
inference(forward_demodulation,[],[f2488,f2032]) ).
fof(f2569,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(forward_demodulation,[],[f2534,f1693]) ).
fof(f2676,plain,
! [X0,X1] : double_divide(X0,double_divide(identity,X1)) = multiply(inverse(X0),X1),
inference(superposition,[],[f881,f2391]) ).
fof(f2702,plain,
! [X0,X1] : double_divide(X0,inverse(X1)) = multiply(inverse(X0),X1),
inference(forward_demodulation,[],[f2676,f2038]) ).
fof(f2781,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f2569,f6]) ).
fof(f2814,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(multiply(X0,X1)),
inference(superposition,[],[f1796,f2569]) ).
fof(f2984,plain,
multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3)),
inference(superposition,[],[f5,f2781]) ).
fof(f3261,plain,
! [X0,X1] : double_divide(X1,X0) = double_divide(X0,X1),
inference(superposition,[],[f2814,f2204]) ).
fof(f5285,plain,
! [X0,X1] : inverse(X1) = double_divide(inverse(X0),multiply(multiply(identity,X0),X1)),
inference(superposition,[],[f2316,f7]) ).
fof(f5314,plain,
! [X0,X1] : inverse(multiply(multiply(inverse(X1),X0),inverse(X0))) = X1,
inference(superposition,[],[f903,f2316]) ).
fof(f5345,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[],[f5314,f2204]) ).
fof(f5366,plain,
! [X0,X1] : inverse(X1) = double_divide(inverse(X0),multiply(X0,X1)),
inference(forward_demodulation,[],[f5285,f1693]) ).
fof(f5445,plain,
! [X0,X1] : inverse(X0) = double_divide(inverse(X1),multiply(multiply(identity,X0),X1)),
inference(superposition,[],[f5345,f7]) ).
fof(f5517,plain,
! [X0,X1] : inverse(X0) = double_divide(inverse(X1),multiply(X0,X1)),
inference(forward_demodulation,[],[f5445,f1693]) ).
fof(f5599,plain,
! [X0,X1] : inverse(double_divide(X0,X1)) = double_divide(inverse(X1),inverse(X0)),
inference(superposition,[],[f5366,f2391]) ).
fof(f5708,plain,
! [X0,X1] : multiply(X1,X0) = double_divide(inverse(X1),inverse(X0)),
inference(forward_demodulation,[],[f5599,f6]) ).
fof(f5825,plain,
! [X0,X1] : double_divide(inverse(X1),X0) = inverse(double_divide(inverse(X0),X1)),
inference(superposition,[],[f5517,f985]) ).
fof(f5915,plain,
! [X0,X1] : double_divide(inverse(X1),X0) = multiply(X1,inverse(X0)),
inference(forward_demodulation,[],[f5825,f6]) ).
fof(f8749,plain,
! [X2,X0,X1] : multiply(identity,X0) = multiply(double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X1)),X2),
inference(forward_demodulation,[],[f449,f1693]) ).
fof(f8750,plain,
! [X2,X0,X1] : multiply(identity,X0) = multiply(X2,double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X1))),
inference(forward_demodulation,[],[f8749,f2781]) ).
fof(f8751,plain,
! [X2,X0,X1] : multiply(identity,X0) = multiply(X2,double_divide(inverse(X1),double_divide(X0,double_divide(X1,X2)))),
inference(forward_demodulation,[],[f8750,f3261]) ).
fof(f8752,plain,
! [X2,X0,X1] : multiply(X2,double_divide(inverse(X1),double_divide(X0,double_divide(X1,X2)))) = X0,
inference(forward_demodulation,[],[f8751,f1693]) ).
fof(f8777,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),double_divide(inverse(double_divide(X1,X0)),double_divide(X2,identity))) = X2,
inference(superposition,[],[f8752,f9]) ).
fof(f8780,plain,
! [X2,X0,X1] : multiply(X1,double_divide(inverse(double_divide(X0,X1)),double_divide(X2,X0))) = X2,
inference(superposition,[],[f8752,f2235]) ).
fof(f8921,plain,
! [X2,X0,X1] : multiply(X1,double_divide(multiply(X1,X0),double_divide(X2,X0))) = X2,
inference(forward_demodulation,[],[f8780,f6]) ).
fof(f8924,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),double_divide(inverse(double_divide(X1,X0)),inverse(X2))) = X2,
inference(forward_demodulation,[],[f8777,f3]) ).
fof(f8998,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = X2,
inference(forward_demodulation,[],[f8924,f5708]) ).
fof(f11167,plain,
! [X2,X0,X1] : multiply(multiply(inverse(X1),double_divide(X0,double_divide(X1,X2))),X0) = X2,
inference(superposition,[],[f8998,f443]) ).
fof(f11225,plain,
! [X2,X0,X1] : multiply(X0,multiply(inverse(X1),double_divide(X0,double_divide(X1,X2)))) = X2,
inference(forward_demodulation,[],[f11167,f2781]) ).
fof(f11315,plain,
! [X2,X0,X1] : multiply(X0,double_divide(X1,inverse(double_divide(X0,double_divide(X1,X2))))) = X2,
inference(forward_demodulation,[],[f11225,f2702]) ).
fof(f11391,plain,
! [X2,X0,X1] : multiply(X0,double_divide(X1,multiply(double_divide(X1,X2),X0))) = X2,
inference(forward_demodulation,[],[f11315,f6]) ).
fof(f11569,plain,
! [X2,X0,X1] : multiply(X0,X1) = double_divide(X2,multiply(double_divide(X2,X0),double_divide(identity,X1))),
inference(superposition,[],[f881,f11391]) ).
fof(f11606,plain,
! [X2,X0,X1] : multiply(X0,X1) = double_divide(X2,multiply(double_divide(X2,X0),inverse(X1))),
inference(forward_demodulation,[],[f11569,f2038]) ).
fof(f11701,plain,
! [X2,X0,X1] : multiply(X0,X1) = double_divide(X2,double_divide(inverse(double_divide(X2,X0)),X1)),
inference(forward_demodulation,[],[f11606,f5915]) ).
fof(f11772,plain,
! [X2,X0,X1] : multiply(X0,X1) = double_divide(X2,double_divide(multiply(X0,X2),X1)),
inference(forward_demodulation,[],[f11701,f6]) ).
fof(f13229,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(X0,multiply(X2,X1)),
inference(superposition,[],[f8921,f11772]) ).
fof(f17297,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(c3,b3)),
inference(superposition,[],[f2984,f13229]) ).
fof(f17298,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[],[f17297,f2781]) ).
fof(f17299,plain,
$false,
inference(trivial_inequality_removal,[],[f17298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP575-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:07:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.51/1.51 % (3768432)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.51/1.51 % (3768468)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2319894358:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.51/1.51 % (3768470)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=837743610:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.51/1.51 % (3768472)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1952955966:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.51/1.51 % (3768474)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4276329990:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.51/1.51 % (3768469)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2732017009:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.51/1.51 % (3768471)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=47290556:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.51/1.51 % (3768473)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=752384951:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.51/1.51 % (3768471)Instruction limit reached!
% 3.51/1.51 % (3768471)------------------------------
% 3.51/1.51 % (3768471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.51 % (3768471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.51 % (3768471)CaDiCaL version: 2.1.3
% 3.51/1.51 % (3768471)Termination reason: Instruction limit
% 3.51/1.51 % (3768471)Termination phase: Saturation
% 3.51/1.51 % (3768471)Time elapsed: 0.084 s
% 3.51/1.51 % (3768471)Peak memory usage: 88 MB
% 3.51/1.51 % (3768471)Instructions burned: 137 (million)
% 3.51/1.51 % (3768472)Instruction limit reached!
% 3.51/1.51 % (3768472)------------------------------
% 3.51/1.51 % (3768472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.51 % (3768472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.51 % (3768472)CaDiCaL version: 2.1.3
% 3.51/1.51 % (3768472)Termination reason: Instruction limit
% 3.51/1.51 % (3768472)Termination phase: Saturation
% 3.51/1.51 % (3768472)Time elapsed: 0.095 s
% 3.51/1.51 % (3768472)Peak memory usage: 90 MB
% 3.51/1.51 % (3768472)Instructions burned: 182 (million)
% 3.51/1.51 % (3768473)Instruction limit reached!
% 3.51/1.51 % (3768473)------------------------------
% 3.51/1.51 % (3768473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.51 % (3768473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.51 % (3768473)CaDiCaL version: 2.1.3
% 3.51/1.51 % (3768473)Termination reason: Instruction limit
% 3.51/1.51 % (3768473)Termination phase: Saturation
% 3.51/1.51 % (3768473)Time elapsed: 0.156 s
% 3.51/1.51 % (3768473)Peak memory usage: 90 MB
% 3.51/1.51 % (3768473)Instructions burned: 259 (million)
% 3.51/1.51 % (3768483)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2500919928:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.51/1.51 % (3768482)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3006757674:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.51/1.51 % (3768474)First to succeed.
% 3.51/1.51 % (3768474)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3768432"
% 3.51/1.51 % (3768484)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2668086836:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 3.51/1.51 % (3768484)Instruction limit reached!
% 3.51/1.51 % (3768484)------------------------------
% 3.51/1.51 % (3768484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.51 % (3768484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.51 % (3768484)CaDiCaL version: 2.1.3
% 3.51/1.51 % (3768484)Termination reason: Instruction limit
% 3.51/1.51 % (3768484)Termination phase: Saturation
% 3.51/1.51 % (3768484)Time elapsed: 0.121 s
% 3.51/1.51 % (3768484)Peak memory usage: 90 MB
% 3.51/1.51 % (3768484)Instructions burned: 216 (million)
% 3.51/1.51 % (3768474)Refutation found. Thanks to Tanya!
% 3.51/1.51 % SZS status Unsatisfiable for theBenchmark
% 3.51/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 5.27/1.70 % (3768474)------------------------------
% 5.27/1.70 % (3768474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.70 % (3768474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.70 % (3768474)CaDiCaL version: 2.1.3
% 5.27/1.70 % (3768474)Termination reason: Refutation
% 5.27/1.70 % (3768474)Time elapsed: 0.243 s
% 5.27/1.70 % (3768474)Peak memory usage: 92 MB
% 5.27/1.70 % (3768474)Instructions burned: 428 (million)
% 5.27/1.70 % (3768474)------------------------------
% 5.27/1.70 % (3768474)------------------------------
% 5.27/1.70 % (3768432)Success in time 0.647 s
% 5.27/1.70 % Vampire exiting
%------------------------------------------------------------------------------