%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL026+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:33:52 PM UTC 2026
% Result : Theorem 16.19s 3.16s
% Output : Refutation 17.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 15
% Syntax : Number of formulae : 146 ( 119 unt; 2 def)
% Number of atoms : 177 ( 149 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 31 ~; 23 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 190 ( 0 sgn 188 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f17,conjecture,
! [X0,X1] :
( join(X0,one) = one
=> ( join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1)
& join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( join(X0,one) = one
=> ( join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1)
& join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( ( composition(X0,X1) != join(meet(composition(X0,top),X1),composition(X0,X1))
| meet(composition(X0,top),X1) != join(composition(X0,X1),meet(composition(X0,top),X1)) )
& join(X0,one) = one ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( ( composition(sK0,sK1) != join(meet(composition(sK0,top),sK1),composition(sK0,sK1))
| meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1)) )
& one = join(sK0,one) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f19]) ).
fof(f21,plain,
one = join(sK0,one),
inference(cnf_transformation,[],[f20]) ).
fof(f22,plain,
( composition(sK0,sK1) != join(meet(composition(sK0,top),sK1),composition(sK0,sK1))
| meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f23,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f31,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f32,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f33,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f36,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f37,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f38,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
( composition(sK0,sK1) != join(complement(join(complement(composition(sK0,top)),complement(sK1))),composition(sK0,sK1))
| complement(join(complement(composition(sK0,top)),complement(sK1))) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1)))) ),
inference(definition_unfolding,[],[f22,f29,f29,f29]) ).
fof(f43,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f44,plain,
zero = complement(top),
inference(forward_demodulation,[],[f43,f35]) ).
fof(f45,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1))))
| complement(join(complement(composition(sK0,top)),complement(sK1))) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1)))) ),
inference(forward_demodulation,[],[f39,f24]) ).
fof(f46,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| complement(join(complement(composition(sK0,top)),complement(sK1))) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1)))) ),
inference(forward_demodulation,[],[f45,f24]) ).
fof(f47,plain,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top))))) ),
inference(forward_demodulation,[],[f46,f24]) ).
fof(f49,definition,
( spl2_1
<=> composition(sK0,sK1) = join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top))))) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f50,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| spl2_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl2_2
<=> complement(join(complement(sK1),complement(composition(sK0,top)))) = join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top))))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f53,plain,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| spl2_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f54,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f47,f52,f49]) ).
fof(f55,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f36,f37]) ).
fof(f64,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f38,f24]) ).
fof(f72,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f24,f38]) ).
fof(f77,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f64,f24]) ).
fof(f88,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f31,f37]) ).
fof(f90,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f32,f31]) ).
fof(f102,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f23,f38]) ).
fof(f109,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f24,f23]) ).
fof(f110,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f102,f109]) ).
fof(f210,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f38,f35]) ).
fof(f222,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(forward_demodulation,[],[f210,f44]) ).
fof(f230,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f88,f33]) ).
fof(f238,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f230,f37]) ).
fof(f247,plain,
one = converse(one),
inference(superposition,[],[f33,f238]) ).
fof(f258,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f90,f31]) ).
fof(f268,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f258,f36]) ).
fof(f275,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f268,f36]) ).
fof(f280,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f275,f31]) ).
fof(f296,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f37,f280]) ).
fof(f300,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f296,f37]) ).
fof(f325,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(one,X1)),
inference(superposition,[],[f300,f33]) ).
fof(f328,plain,
! [X0,X1] : join(composition(X0,X1),X0) = composition(X0,join(X1,one)),
inference(superposition,[],[f300,f33]) ).
fof(f341,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f328,f24]) ).
fof(f441,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f238,f247]) ).
fof(f487,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,sK0)),
inference(superposition,[],[f341,f21]) ).
fof(f521,plain,
! [X0] : join(X0,composition(X0,sK0)) = X0,
inference(forward_demodulation,[],[f487,f33]) ).
fof(f590,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(superposition,[],[f30,f238]) ).
fof(f604,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(forward_demodulation,[],[f590,f24]) ).
fof(f615,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f604,f441]) ).
fof(f632,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(X0,complement(join(complement(X0),complement(X1)))),
inference(superposition,[],[f110,f615]) ).
fof(f642,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f632,f72]) ).
fof(f668,plain,
! [X0] : join(X0,complement(top)) = X0,
inference(superposition,[],[f642,f35]) ).
fof(f669,plain,
! [X0] : join(X0,complement(complement(X0))) = X0,
inference(superposition,[],[f642,f642]) ).
fof(f676,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,X0),
inference(superposition,[],[f110,f642]) ).
fof(f689,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,X0),
inference(forward_demodulation,[],[f676,f24]) ).
fof(f693,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[],[f668,f44]) ).
fof(f934,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f24,f693]) ).
fof(f982,plain,
! [X0] : join(X0,zero) = join(complement(join(complement(X0),X0)),X0),
inference(superposition,[],[f110,f222]) ).
fof(f983,plain,
! [X0,X1] : join(X1,X0) = join(zero,join(complement(join(complement(X0),complement(X0))),X1)),
inference(superposition,[],[f109,f222]) ).
fof(f987,plain,
! [X0,X1] : join(X1,X0) = join(complement(join(complement(X0),complement(X0))),X1),
inference(forward_demodulation,[],[f983,f934]) ).
fof(f988,plain,
! [X0] : join(X0,zero) = join(X0,complement(join(complement(X0),X0))),
inference(forward_demodulation,[],[f982,f24]) ).
fof(f991,plain,
! [X0,X1] : join(X1,X0) = join(complement(complement(X0)),X1),
inference(forward_demodulation,[],[f987,f615]) ).
fof(f992,plain,
! [X0] : join(X0,X0) = join(X0,zero),
inference(forward_demodulation,[],[f988,f689]) ).
fof(f995,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[],[f992,f693]) ).
fof(f1005,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f23,f995]) ).
fof(f1084,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),complement(complement(X1))))),
inference(superposition,[],[f77,f991]) ).
fof(f1091,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(complement(X1))),
inference(superposition,[],[f24,f991]) ).
fof(f1111,plain,
! [X0] : complement(complement(X0)) = join(zero,X0),
inference(superposition,[],[f693,f991]) ).
fof(f1112,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f1111,f934]) ).
fof(f1134,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f1084,f1091]) ).
fof(f1194,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f77,f1112]) ).
fof(f1202,plain,
! [X0,X1] : join(X1,complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f642,f1112]) ).
fof(f1352,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f1202,f24]) ).
fof(f1445,plain,
! [X0,X1] : join(X1,X0) = join(complement(join(complement(X1),X0)),X0),
inference(superposition,[],[f110,f1352]) ).
fof(f1475,plain,
! [X0,X1] : join(X1,X0) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f1445,f24]) ).
fof(f1563,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(complement(join(complement(X1),X0)),join(X1,X0))),complement(complement(X0))),
inference(superposition,[],[f77,f1134]) ).
fof(f1588,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(complement(join(complement(X1),X0)),join(X1,X0))),X0),
inference(forward_demodulation,[],[f1563,f1091]) ).
fof(f1636,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(complement(join(complement(X1),X0)),join(X1,X0)))),
inference(forward_demodulation,[],[f1588,f24]) ).
fof(f1673,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(join(X1,X0),complement(join(complement(X1),X0))))),
inference(forward_demodulation,[],[f1636,f24]) ).
fof(f1703,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X1,join(X0,complement(join(complement(X1),X0)))))),
inference(forward_demodulation,[],[f1673,f23]) ).
fof(f1725,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X1,join(X1,X0)))),
inference(forward_demodulation,[],[f1703,f1475]) ).
fof(f1735,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f1725,f1005]) ).
fof(f1746,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f1735,f24]) ).
fof(f2690,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(composition(converse(X0),sK0))),
inference(superposition,[],[f55,f521]) ).
fof(f2706,plain,
! [X0] : converse(converse(X0)) = join(X0,composition(converse(sK0),X0)),
inference(forward_demodulation,[],[f2690,f88]) ).
fof(f2724,plain,
! [X0] : join(X0,composition(converse(sK0),X0)) = X0,
inference(forward_demodulation,[],[f2706,f37]) ).
fof(f2747,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,composition(converse(sK0),one))),
inference(superposition,[],[f325,f2724]) ).
fof(f2778,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,converse(sK0))),
inference(forward_demodulation,[],[f2747,f33]) ).
fof(f2793,plain,
! [X0] : join(X0,composition(X0,converse(sK0))) = X0,
inference(forward_demodulation,[],[f2778,f33]) ).
fof(f2836,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(composition(converse(X0),converse(sK0)))),
inference(superposition,[],[f55,f2793]) ).
fof(f2839,plain,
! [X0] : converse(converse(X0)) = join(X0,composition(converse(converse(sK0)),X0)),
inference(forward_demodulation,[],[f2836,f88]) ).
fof(f2866,plain,
! [X0] : converse(converse(X0)) = join(X0,composition(sK0,X0)),
inference(forward_demodulation,[],[f2839,f37]) ).
fof(f2883,plain,
! [X0] : join(X0,composition(sK0,X0)) = X0,
inference(forward_demodulation,[],[f2866,f37]) ).
fof(f2898,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(composition(sK0,X0),X1)),
inference(superposition,[],[f23,f2883]) ).
fof(f2911,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(complement(join(composition(sK0,complement(X0)),X0)),complement(complement(X0))),
inference(superposition,[],[f1194,f2883]) ).
fof(f2918,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(complement(join(composition(sK0,complement(X0)),X0)),X0),
inference(forward_demodulation,[],[f2911,f1091]) ).
fof(f2935,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(X0,complement(join(composition(sK0,complement(X0)),X0))),
inference(forward_demodulation,[],[f2918,f24]) ).
fof(f2944,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(complement(composition(sK0,complement(X0))),X0),
inference(forward_demodulation,[],[f2935,f1735]) ).
fof(f2948,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(X0,complement(composition(sK0,complement(X0)))),
inference(forward_demodulation,[],[f2944,f24]) ).
fof(f2957,plain,
! [X0,X1] : join(X0,composition(sK0,X1)) = join(X0,composition(sK0,join(X0,X1))),
inference(superposition,[],[f2898,f300]) ).
fof(f3081,plain,
! [X0] : join(X0,composition(sK0,complement(X0))) = join(X0,composition(sK0,top)),
inference(superposition,[],[f2957,f35]) ).
fof(f3436,plain,
! [X0] : join(complement(composition(sK0,complement(X0))),X0) = join(X0,complement(join(X0,composition(sK0,top)))),
inference(superposition,[],[f1746,f3081]) ).
fof(f3462,plain,
! [X0] : join(complement(composition(sK0,complement(X0))),X0) = join(complement(composition(sK0,top)),X0),
inference(forward_demodulation,[],[f3436,f1746]) ).
fof(f3482,plain,
! [X0] : join(X0,complement(composition(sK0,complement(X0)))) = join(complement(composition(sK0,top)),X0),
inference(forward_demodulation,[],[f3462,f24]) ).
fof(f3497,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(complement(composition(sK0,top)),X0),
inference(forward_demodulation,[],[f3482,f2948]) ).
fof(f4054,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(X0,complement(composition(sK0,top))),
inference(superposition,[],[f24,f3497]) ).
fof(f5438,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),complement(complement(composition(sK0,complement(complement(sK1))))))
| spl2_1 ),
inference(superposition,[],[f50,f4054]) ).
fof(f5508,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),composition(sK0,complement(complement(sK1))))
| spl2_1 ),
inference(forward_demodulation,[],[f5438,f1091]) ).
fof(f5543,plain,
( composition(sK0,sK1) != composition(sK0,join(sK1,complement(complement(sK1))))
| spl2_1 ),
inference(forward_demodulation,[],[f5508,f300]) ).
fof(f5564,plain,
( composition(sK0,sK1) != composition(sK0,sK1)
| spl2_1 ),
inference(forward_demodulation,[],[f5543,f669]) ).
fof(f5565,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[],[f5564]) ).
fof(f5566,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f5565]) ).
fof(f5597,plain,
( complement(complement(composition(sK0,complement(complement(sK1))))) != join(composition(sK0,sK1),complement(complement(composition(sK0,complement(complement(sK1))))))
| spl2_2 ),
inference(forward_demodulation,[],[f53,f4054]) ).
fof(f5598,plain,
( complement(complement(composition(sK0,complement(complement(sK1))))) != join(composition(sK0,sK1),composition(sK0,complement(complement(sK1))))
| spl2_2 ),
inference(forward_demodulation,[],[f5597,f1091]) ).
fof(f5599,plain,
( complement(complement(composition(sK0,complement(complement(sK1))))) != composition(sK0,join(sK1,complement(complement(sK1))))
| spl2_2 ),
inference(forward_demodulation,[],[f5598,f300]) ).
fof(f5600,plain,
( composition(sK0,sK1) != complement(complement(composition(sK0,complement(complement(sK1)))))
| spl2_2 ),
inference(forward_demodulation,[],[f5599,f669]) ).
fof(f5601,plain,
( composition(sK0,sK1) != composition(sK0,complement(complement(sK1)))
| spl2_2 ),
inference(forward_demodulation,[],[f5600,f1112]) ).
fof(f5602,plain,
( composition(sK0,sK1) != composition(sK0,sK1)
| spl2_2 ),
inference(forward_demodulation,[],[f5601,f1112]) ).
fof(f5603,plain,
( $false
| spl2_2 ),
inference(trivial_inequality_removal,[],[f5602]) ).
fof(f5604,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f5603]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f54]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f5566]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f5604]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f5605,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL026+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 22:55:09 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.19/3.16 % (2822009)Detected formulas, will run a generic FOF schedule.
% 16.19/3.16 % (2822037)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3990728328:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 16.19/3.16 % (2822036)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3847461091:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 16.19/3.16 % (2822033)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3975234342:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 16.19/3.16 % (2822032)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3557269125:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 16.19/3.16 % (2822034)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3276742453:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 16.19/3.16 % (2822038)dis-21_1_sil=8000:lcm=predicate:random_seed=4057597927:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 16.19/3.16 % (2822035)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=987252970:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 16.19/3.16 % (2822038)Refutation not found, incomplete strategy
% 16.19/3.16 % (2822038)------------------------------
% 16.19/3.16 % (2822038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822038)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822038)Termination reason: Refutation not found, incomplete strategy
% 16.19/3.16 % (2822038)Time elapsed: 0.003 s
% 16.19/3.16 % (2822038)Peak memory usage: 88 MB
% 16.19/3.16 % (2822038)Instructions burned: 1 (million)
% 16.19/3.16 % (2822037)Instruction limit reached!
% 16.19/3.16 % (2822037)------------------------------
% 16.19/3.16 % (2822037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822037)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822037)Termination reason: Instruction limit
% 16.19/3.16 % (2822037)Termination phase: Saturation
% 16.19/3.16 % (2822037)Time elapsed: 0.076 s
% 16.19/3.16 % (2822037)Peak memory usage: 90 MB
% 16.19/3.16 % (2822037)Instructions burned: 139 (million)
% 16.19/3.16 % (2822036)Instruction limit reached!
% 16.19/3.16 % (2822036)------------------------------
% 16.19/3.16 % (2822036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822036)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822036)Termination reason: Instruction limit
% 16.19/3.16 % (2822036)Termination phase: Saturation
% 16.19/3.16 % (2822036)Time elapsed: 0.114 s
% 16.19/3.16 % (2822036)Peak memory usage: 89 MB
% 16.19/3.16 % (2822036)Instructions burned: 119 (million)
% 16.19/3.16 % (2822035)Instruction limit reached!
% 16.19/3.16 % (2822035)------------------------------
% 16.19/3.16 % (2822035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822035)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822035)Termination reason: Instruction limit
% 16.19/3.16 % (2822035)Termination phase: Saturation
% 16.19/3.16 % (2822035)Time elapsed: 0.114 s
% 16.19/3.16 % (2822035)Peak memory usage: 90 MB
% 16.19/3.16 % (2822035)Instructions burned: 110 (million)
% 16.19/3.16 % (2822046)lrs+10_1_sil=8000:sp=occurrence:random_seed=2006249909:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 16.19/3.16 % (2822038)------------------------------
% 16.19/3.16 % (2822038)------------------------------
% 16.19/3.16 % (2822048)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3458003860:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 16.19/3.16 % (2822047)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2505318388:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 16.19/3.16 % (2822046)Instruction limit reached!
% 16.19/3.16 % (2822046)------------------------------
% 16.19/3.16 % (2822046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822046)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822046)Termination reason: Instruction limit
% 16.19/3.16 % (2822046)Termination phase: Saturation
% 16.19/3.16 % (2822046)Time elapsed: 0.155 s
% 16.19/3.16 % (2822046)Peak memory usage: 91 MB
% 16.19/3.16 % (2822046)Instructions burned: 286 (million)
% 16.19/3.16 % (2822047)Instruction limit reached!
% 16.19/3.16 % (2822047)------------------------------
% 16.19/3.16 % (2822047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822047)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822047)Termination reason: Instruction limit
% 16.19/3.16 % (2822047)Termination phase: Saturation
% 16.19/3.16 % (2822047)Time elapsed: 0.157 s
% 16.19/3.16 % (2822047)Peak memory usage: 90 MB
% 16.19/3.16 % (2822047)Instructions burned: 157 (million)
% 16.19/3.16 % (2822052)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1680112816:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 16.19/3.16 % (2822053)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1364518211:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 16.19/3.16 % (2822048)Instruction limit reached!
% 16.19/3.16 % (2822048)------------------------------
% 16.19/3.16 % (2822048)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822048)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822048)Termination reason: Instruction limit
% 16.19/3.16 % (2822048)Termination phase: Saturation
% 16.19/3.16 % (2822048)Time elapsed: 0.331 s
% 16.19/3.16 % (2822048)Peak memory usage: 92 MB
% 16.19/3.16 % (2822048)Instructions burned: 325 (million)
% 16.19/3.16 % (2822054)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=564106289:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 16.19/3.16 % (2822053)Instruction limit reached!
% 16.19/3.16 % (2822053)------------------------------
% 16.19/3.16 % (2822053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822053)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822053)Termination reason: Instruction limit
% 16.19/3.16 % (2822053)Termination phase: Saturation
% 16.19/3.16 % (2822053)Time elapsed: 0.158 s
% 16.19/3.16 % (2822053)Peak memory usage: 91 MB
% 16.19/3.16 % (2822053)Instructions burned: 295 (million)
% 16.19/3.16 % (2822052)Instruction limit reached!
% 16.19/3.16 % (2822052)------------------------------
% 16.19/3.16 % (2822052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822052)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822052)Termination reason: Instruction limit
% 16.19/3.16 % (2822052)Termination phase: Saturation
% 16.19/3.16 % (2822052)Time elapsed: 0.259 s
% 16.19/3.16 % (2822052)Peak memory usage: 91 MB
% 16.19/3.16 % (2822052)Instructions burned: 249 (million)
% 16.19/3.16 % (2822057)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1686210027:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 16.19/3.16 % (2822059)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3696849826:i=127:av=off:fsr=off:sup=off_2988 on theBenchmark for (2988ds/127Mi)
% 16.19/3.16 % (2822059)Refutation not found, incomplete strategy
% 16.19/3.16 % (2822059)------------------------------
% 16.19/3.16 % (2822059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822059)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822059)Termination reason: Refutation not found, incomplete strategy
% 16.19/3.16 % (2822059)Time elapsed: 0.001 s
% 16.19/3.16 % (2822059)Peak memory usage: 88 MB
% 16.19/3.16 % (2822059)Instructions burned: 1 (million)
% 16.19/3.16 % (2822057)Instruction limit reached!
% 16.19/3.16 % (2822057)------------------------------
% 16.19/3.16 % (2822057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822057)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822057)Termination reason: Instruction limit
% 16.19/3.16 % (2822057)Termination phase: Saturation
% 16.19/3.16 % (2822057)Time elapsed: 0.108 s
% 16.19/3.16 % (2822057)Peak memory usage: 89 MB
% 16.19/3.16 % (2822057)Instructions burned: 113 (million)
% 16.19/3.16 % (2822060)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3530809991:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2987 on theBenchmark for (2987ds/114Mi)
% 16.19/3.16 % (2822059)------------------------------
% 16.19/3.16 % (2822059)------------------------------
% 16.19/3.16 % (2822060)Instruction limit reached!
% 16.19/3.16 % (2822060)------------------------------
% 16.19/3.16 % (2822060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822060)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822060)Termination reason: Instruction limit
% 16.19/3.16 % (2822060)Termination phase: Saturation
% 16.19/3.16 % (2822060)Time elapsed: 0.107 s
% 16.19/3.16 % (2822060)Peak memory usage: 89 MB
% 16.19/3.16 % (2822060)Instructions burned: 114 (million)
% 16.19/3.16 % (2822063)lrs+10_1_sil=8000:sp=occurrence:random_seed=3381541856:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2985 on theBenchmark for (2985ds/907Mi)
% 16.19/3.16 % (2822033)First to succeed.
% 16.19/3.16 % (2822033)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2822009"
% 16.19/3.16 % (2822065)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3594270637:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 16.19/3.16 % (2822066)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3579972476:i=5202:ss=axioms:sgt=16_2983 on theBenchmark for (2983ds/5202Mi)
% 16.19/3.16 % (2822065)Instruction limit reached!
% 16.19/3.16 % (2822065)------------------------------
% 16.19/3.16 % (2822065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.19/3.16 % (2822065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.19/3.16 % (2822065)CaDiCaL version: 2.1.3
% 16.19/3.16 % (2822065)Termination reason: Instruction limit
% 16.19/3.16 % (2822065)Termination phase: Saturation
% 16.19/3.16 % (2822065)Time elapsed: 0.200 s
% 16.19/3.16 % (2822065)Peak memory usage: 90 MB
% 16.19/3.16 % (2822065)Instructions burned: 438 (million)
% 16.19/3.16 % (2822032)Also succeeded, but the first one will report.
% 16.19/3.16 % (2822033)Refutation found. Thanks to Tanya!
% 16.19/3.16 % SZS status Theorem for theBenchmark
% 16.19/3.16 % SZS output start Proof for theBenchmark
% See solution above
% 17.01/3.38 % (2822033)------------------------------
% 17.01/3.38 % (2822033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.01/3.38 % (2822033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.01/3.38 % (2822033)CaDiCaL version: 2.1.3
% 17.01/3.38 % (2822033)Termination reason: Refutation
% 17.01/3.38 % (2822033)Time elapsed: 1.605 s
% 17.01/3.38 % (2822033)Peak memory usage: 134 MB
% 17.01/3.38 % (2822033)Instructions burned: 1458 (million)
% 17.01/3.38 % (2822033)------------------------------
% 17.01/3.38 % (2822033)------------------------------
% 17.01/3.38 % (2822009)Success in time 2.343 s
% 17.01/3.38 % Vampire exiting
%------------------------------------------------------------------------------