%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP119-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:12:38 AM UTC 2026
% Result : Unsatisfiable 2.42s 1.60s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of formulae : 83 ( 83 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 116 ( 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,X2))),multiply(X2,multiply(X2,X2)))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
multiply(identity,identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom2) ).
fof(f3,plain,
identity = multiply(identity,identity),
inference(reorient_equations,[],[f2]) ).
fof(f4,negated_conjecture,
multiply(a,multiply(a,multiply(a,a))) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order4) ).
fof(f5,plain,
identity != multiply(a,multiply(a,multiply(a,a))),
inference(reorient_equations,[],[f4]) ).
fof(f6,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,X1))),multiply(X1,multiply(X1,X1)))) = X0,
inference(superposition,[],[f1,f3]) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),multiply(identity,identity))),
inference(superposition,[],[f1,f3]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),multiply(X0,X2))) = multiply(X1,multiply(multiply(X1,X0),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))),
inference(superposition,[],[f1,f1]) ).
fof(f10,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),multiply(identity,identity))) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),identity)) = X1,
inference(forward_demodulation,[],[f10,f3]) ).
fof(f12,plain,
! [X0] : identity = multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity)),
inference(forward_demodulation,[],[f7,f3]) ).
fof(f21,plain,
! [X0] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity)) = X0,
inference(superposition,[],[f11,f3]) ).
fof(f30,plain,
! [X0] : multiply(identity,multiply(identity,multiply(X0,identity))) = multiply(identity,multiply(multiply(identity,X0),identity)),
inference(superposition,[],[f21,f21]) ).
fof(f38,plain,
! [X0] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity))),
inference(superposition,[],[f30,f30]) ).
fof(f45,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity))) = X0,
inference(superposition,[],[f21,f30]) ).
fof(f54,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))) = X0,
inference(forward_demodulation,[],[f45,f30]) ).
fof(f61,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity))) = X0,
inference(forward_demodulation,[],[f38,f21]) ).
fof(f97,plain,
! [X0] : multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity))))) = X0,
inference(superposition,[],[f6,f12]) ).
fof(f115,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity))))) = X0,
inference(forward_demodulation,[],[f97,f3]) ).
fof(f121,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity))))) = X0,
inference(forward_demodulation,[],[f115,f3]) ).
fof(f135,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = multiply(multiply(identity,X0),identity),
inference(superposition,[],[f21,f61]) ).
fof(f219,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),multiply(identity,X0))) = multiply(identity,multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))))),
inference(superposition,[],[f9,f3]) ).
fof(f236,plain,
! [X2,X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))),multiply(X2,multiply(X2,X2)))) = X1,
inference(superposition,[],[f1,f9]) ).
fof(f237,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),identity)) = X1,
inference(superposition,[],[f11,f9]) ).
fof(f245,plain,
! [X0,X1] : multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(superposition,[],[f6,f9]) ).
fof(f254,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(forward_demodulation,[],[f245,f3]) ).
fof(f255,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),identity)) = X1,
inference(forward_demodulation,[],[f237,f3]) ).
fof(f263,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))))) = multiply(identity,multiply(identity,multiply(identity,X0))),
inference(forward_demodulation,[],[f219,f3]) ).
fof(f275,plain,
! [X0,X1] : multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(forward_demodulation,[],[f254,f3]) ).
fof(f276,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(identity,identity)))),identity)) = X1,
inference(forward_demodulation,[],[f255,f3]) ).
fof(f294,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,identity))),identity)) = X1,
inference(forward_demodulation,[],[f276,f3]) ).
fof(f305,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),identity)),identity)) = X1,
inference(forward_demodulation,[],[f294,f3]) ).
fof(f325,plain,
! [X0] : multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity) = multiply(multiply(X0,X0),multiply(multiply(X0,multiply(identity,identity)),identity)),
inference(superposition,[],[f305,f12]) ).
fof(f347,plain,
! [X0] : multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity) = multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),
inference(forward_demodulation,[],[f325,f3]) ).
fof(f379,plain,
! [X0,X1] : multiply(X0,identity) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1)),identity)),
inference(superposition,[],[f135,f275]) ).
fof(f390,plain,
! [X0,X1] : multiply(X0,identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1),identity))),
inference(forward_demodulation,[],[f379,f30]) ).
fof(f407,plain,
! [X0] : identity = multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))),
inference(superposition,[],[f12,f347]) ).
fof(f470,plain,
! [X0] : identity = multiply(multiply(identity,X0),multiply(multiply(multiply(identity,X0),multiply(identity,X0)),multiply(multiply(identity,multiply(X0,identity)),identity))),
inference(superposition,[],[f407,f135]) ).
fof(f496,plain,
! [X0] : identity = multiply(multiply(identity,X0),multiply(multiply(multiply(identity,X0),multiply(identity,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f470,f135]) ).
fof(f1107,plain,
! [X0,X1] : multiply(identity,multiply(multiply(X0,identity),identity)) = multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1),
inference(superposition,[],[f21,f390]) ).
fof(f2714,plain,
! [X0] : multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0))))) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,X0))),identity)),identity)),
inference(superposition,[],[f305,f263]) ).
fof(f2719,plain,
! [X0] : multiply(identity,multiply(identity,X0)) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0))))),
inference(forward_demodulation,[],[f2714,f305]) ).
fof(f2789,plain,
! [X0] : multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,X0)),identity)),identity)),
inference(superposition,[],[f305,f2719]) ).
fof(f2794,plain,
! [X0] : multiply(identity,X0) = multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))),
inference(forward_demodulation,[],[f2789,f305]) ).
fof(f2832,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X1,multiply(X0,multiply(X0,X0))))),multiply(identity,X0))) = X1,
inference(superposition,[],[f6,f2794]) ).
fof(f3076,plain,
! [X0,X1] : multiply(identity,multiply(identity,multiply(X0,X1))) = multiply(identity,multiply(multiply(identity,X0),multiply(identity,X1))),
inference(superposition,[],[f2832,f6]) ).
fof(f3367,plain,
! [X0,X1] : multiply(multiply(identity,X0),multiply(identity,X1)) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,X1))),identity)),identity)),
inference(superposition,[],[f305,f3076]) ).
fof(f3372,plain,
! [X0,X1] : multiply(identity,multiply(X0,X1)) = multiply(multiply(identity,X0),multiply(identity,X1)),
inference(forward_demodulation,[],[f3367,f305]) ).
fof(f3567,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),X1)) = multiply(X0,multiply(identity,X1)),
inference(superposition,[],[f3372,f54]) ).
fof(f4726,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(multiply(identity,multiply(X0,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))))))),multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(superposition,[],[f1107,f3567]) ).
fof(f4747,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(identity,multiply(multiply(X0,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))))),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4726,f3372]) ).
fof(f4796,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(identity,multiply(multiply(X0,multiply(X0,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))))),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4747,f3567]) ).
fof(f4838,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4796,f54]) ).
fof(f4862,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,identity))) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4838,f30]) ).
fof(f4878,plain,
! [X0] : multiply(identity,multiply(identity,identity)) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4862,f3]) ).
fof(f4888,plain,
! [X0] : multiply(identity,identity) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4878,f3]) ).
fof(f4896,plain,
! [X0] : identity = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4888,f3]) ).
fof(f5218,plain,
! [X0] : identity = multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),identity),identity)))),
inference(superposition,[],[f496,f4896]) ).
fof(f5246,plain,
! [X0] : identity = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),identity),identity)))),
inference(forward_demodulation,[],[f5218,f3076]) ).
fof(f5276,plain,
! [X0] : identity = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(forward_demodulation,[],[f5246,f54]) ).
fof(f5338,plain,
! [X0] : identity = multiply(multiply(identity,X0),multiply(identity,multiply(multiply(multiply(X0,multiply(X0,X0)),identity),identity))),
inference(superposition,[],[f5276,f2794]) ).
fof(f5379,plain,
! [X0] : identity = multiply(identity,multiply(X0,multiply(multiply(multiply(X0,multiply(X0,X0)),identity),identity))),
inference(forward_demodulation,[],[f5338,f3372]) ).
fof(f5419,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))) = X0,
inference(forward_demodulation,[],[f121,f347]) ).
fof(f5442,plain,
! [X0] : identity = multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(multiply(X0,multiply(multiply(multiply(X0,multiply(X0,X0)),identity),identity)),identity),identity)))),
inference(superposition,[],[f496,f5379]) ).
fof(f5486,plain,
! [X0] : identity = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X0,multiply(multiply(multiply(X0,multiply(X0,X0)),identity),identity)),identity),identity)))),
inference(forward_demodulation,[],[f5442,f3076]) ).
fof(f5523,plain,
! [X0] : identity = multiply(X0,multiply(multiply(multiply(X0,multiply(X0,X0)),identity),identity)),
inference(forward_demodulation,[],[f5486,f54]) ).
fof(f5953,plain,
! [X2,X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,X2))),multiply(X2,multiply(X2,X2)))) = X1,
inference(forward_demodulation,[],[f236,f2794]) ).
fof(f6535,plain,
! [X0,X1] : multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),X0)) = multiply(X1,multiply(multiply(X1,identity),multiply(multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))))),multiply(multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))))))))),
inference(superposition,[],[f9,f5419]) ).
fof(f6548,plain,
! [X0,X1] : multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),X0)) = multiply(X1,multiply(multiply(X1,identity),multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))))),
inference(forward_demodulation,[],[f6535,f2794]) ).
fof(f6584,plain,
! [X0,X1] : multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),X0)) = multiply(X1,multiply(multiply(X1,identity),X0)),
inference(forward_demodulation,[],[f6548,f5419]) ).
fof(f7189,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,X1),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(X0,multiply(multiply(X0,identity),multiply(X1,X2))),
inference(superposition,[],[f9,f6584]) ).
fof(f7247,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,X1),multiply(identity,X2))) = multiply(X0,multiply(multiply(X0,identity),multiply(X1,X2))),
inference(forward_demodulation,[],[f7189,f2794]) ).
fof(f9387,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,identity),multiply(X1,X2)) = multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,X2))),multiply(identity,X3))),multiply(X3,multiply(X3,X3)))),
inference(superposition,[],[f5953,f7247]) ).
fof(f9447,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),multiply(identity,X2)) = multiply(multiply(X0,identity),multiply(X1,X2)),
inference(forward_demodulation,[],[f9387,f5953]) ).
fof(f10031,plain,
! [X0] : identity = multiply(multiply(X0,identity),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))),
inference(superposition,[],[f9447,f5276]) ).
fof(f11387,plain,
! [X0] : multiply(X0,identity) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))),
inference(superposition,[],[f6,f10031]) ).
fof(f11405,plain,
! [X0] : multiply(X0,identity) = multiply(identity,multiply(multiply(identity,identity),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))),
inference(forward_demodulation,[],[f11387,f3]) ).
fof(f11430,plain,
! [X0] : multiply(X0,identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))),
inference(forward_demodulation,[],[f11405,f3]) ).
fof(f11452,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f11430,f5419]) ).
fof(f11698,plain,
! [X0] : identity = multiply(X0,multiply(multiply(X0,multiply(X0,X0)),identity)),
inference(superposition,[],[f5523,f11452]) ).
fof(f11719,plain,
! [X0] : identity = multiply(X0,multiply(X0,multiply(X0,X0))),
inference(forward_demodulation,[],[f11698,f11452]) ).
fof(f12148,plain,
identity != identity,
inference(superposition,[],[f5,f11719]) ).
fof(f12149,plain,
$false,
inference(trivial_inequality_removal,[],[f12148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP119-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:19:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 2.42/1.60 % (3247123)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.42/1.60 % (3247201)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=1849944660:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 2.42/1.60 % (3247199)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=1950658360:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 2.42/1.60 % (3247210)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1055495549:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 2.42/1.60 % (3247207)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3152649959:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 2.42/1.60 % (3247205)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3677001431:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 2.42/1.60 % (3247203)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2820543437:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 2.42/1.60 % (3247208)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3493228797:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 2.42/1.60 % (3247205)Instruction limit reached!
% 2.42/1.60 % (3247205)------------------------------
% 2.42/1.60 % (3247205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.60 % (3247205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.60 % (3247205)CaDiCaL version: 2.1.3
% 2.42/1.60 % (3247205)Termination reason: Instruction limit
% 2.42/1.60 % (3247205)Termination phase: Saturation
% 2.42/1.60 % (3247205)Time elapsed: 0.079 s
% 2.42/1.60 % (3247205)Peak memory usage: 89 MB
% 2.42/1.60 % (3247205)Instructions burned: 137 (million)
% 2.42/1.60 % (3247207)Instruction limit reached!
% 2.42/1.60 % (3247207)------------------------------
% 2.42/1.60 % (3247207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.60 % (3247207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.60 % (3247207)CaDiCaL version: 2.1.3
% 2.42/1.60 % (3247207)Termination reason: Instruction limit
% 2.42/1.60 % (3247207)Termination phase: Saturation
% 2.42/1.60 % (3247207)Time elapsed: 0.097 s
% 2.42/1.60 % (3247207)Peak memory usage: 89 MB
% 2.42/1.60 % (3247207)Instructions burned: 182 (million)
% 2.42/1.60 % (3247208)Instruction limit reached!
% 2.42/1.60 % (3247208)------------------------------
% 2.42/1.60 % (3247208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.60 % (3247208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.60 % (3247208)CaDiCaL version: 2.1.3
% 2.42/1.60 % (3247208)Termination reason: Instruction limit
% 2.42/1.60 % (3247208)Termination phase: Saturation
% 2.42/1.60 % (3247208)Time elapsed: 0.145 s
% 2.42/1.60 % (3247208)Peak memory usage: 91 MB
% 2.42/1.60 % (3247208)Instructions burned: 257 (million)
% 2.42/1.60 % (3247222)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2004033790:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 2.42/1.60 % (3247223)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1397883594:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 2.42/1.60 % (3247210)First to succeed.
% 2.42/1.60 % (3247210)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3247123"
% 2.42/1.60 % (3247233)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=217621837:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 2.42/1.60 % (3247233)Instruction limit reached!
% 2.42/1.60 % (3247233)------------------------------
% 2.42/1.60 % (3247233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.60 % (3247233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.60 % (3247233)CaDiCaL version: 2.1.3
% 2.42/1.60 % (3247233)Termination reason: Instruction limit
% 2.42/1.60 % (3247233)Termination phase: Saturation
% 2.42/1.60 % (3247233)Time elapsed: 0.113 s
% 2.42/1.60 % (3247233)Peak memory usage: 89 MB
% 2.42/1.60 % (3247233)Instructions burned: 215 (million)
% 2.42/1.60 % (3247210)Refutation found. Thanks to Tanya!
% 2.42/1.60 % SZS status Unsatisfiable for theBenchmark
% 2.42/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.80 % (3247210)------------------------------
% 0.19/1.80 % (3247210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.80 % (3247210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.80 % (3247210)CaDiCaL version: 2.1.3
% 0.19/1.80 % (3247210)Termination reason: Refutation
% 0.19/1.80 % (3247210)Time elapsed: 0.277 s
% 0.19/1.80 % (3247210)Peak memory usage: 92 MB
% 0.19/1.80 % (3247210)Instructions burned: 515 (million)
% 0.19/1.80 % (3247210)------------------------------
% 0.19/1.80 % (3247210)------------------------------
% 0.19/1.80 % (3247123)Success in time 0.655 s
% 0.19/1.80 % Vampire exiting
%------------------------------------------------------------------------------