%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL019+2 : 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 : n026.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 12:33:47 PM UTC 2026
% Result : Theorem 10.87s 2.44s
% Output : Refutation 11.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 20
% Syntax : Number of formulae : 153 ( 148 unt; 7 def)
% Number of atoms : 163 ( 162 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 155 ( 151 !; 4 ?)
% 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] :
( ( composition(X0,top) = X0
& composition(X1,top) = X1 )
=> composition(meet(X0,X1),top) = meet(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( composition(X0,top) = X0
& composition(X1,top) = X1 )
=> composition(meet(X0,X1),top) = meet(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( meet(X0,X1) != composition(meet(X0,X1),top)
& composition(X0,top) = X0
& composition(X1,top) = X1 ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( meet(X0,X1) != composition(meet(X0,X1),top)
& composition(X0,top) = X0
& composition(X1,top) = X1 ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( meet(sK0,sK1) != composition(meet(sK0,sK1),top)
& sK0 = composition(sK0,top)
& sK1 = composition(sK1,top) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
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(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f28,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f29,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f30,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f31,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f32,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f33,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f34,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
sK1 = composition(sK1,top),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
sK0 = composition(sK0,top),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
meet(sK0,sK1) != composition(meet(sK0,sK1),top),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f34,f25]) ).
fof(f45,plain,
complement(join(complement(sK0),complement(sK1))) != composition(complement(join(complement(sK0),complement(sK1))),top),
inference(definition_unfolding,[],[f40,f25,f25]) ).
fof(f46,definition,
sF2 = complement(sK0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f47,plain,
complement(sK0) = sF2,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF3 = complement(sK1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f49,plain,
complement(sK1) = sF3,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF4 = join(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f51,plain,
join(sF2,sF3) = sF4,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f53,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f52]) ).
fof(f54,definition,
sF6 = composition(sF5,top),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f55,plain,
composition(sF5,top) = sF6,
inference(reorient_equations,[],[f54]) ).
fof(f56,plain,
sF5 != sF6,
inference(definition_folding,[],[f45,f55,f53,f51,f49,f47,f53,f51,f49,f47]) ).
fof(f57,definition,
sF7 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f58,plain,
composition(sK0,top) = sF7,
inference(reorient_equations,[],[f57]) ).
fof(f59,plain,
sK0 = sF7,
inference(definition_folding,[],[f39,f58]) ).
fof(f60,definition,
sF8 = composition(sK1,top),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f61,plain,
composition(sK1,top) = sF8,
inference(reorient_equations,[],[f60]) ).
fof(f62,plain,
sK1 = sF8,
inference(definition_folding,[],[f38,f61]) ).
fof(f63,plain,
sK0 = composition(sK0,top),
inference(forward_demodulation,[],[f58,f59]) ).
fof(f64,plain,
sK1 = composition(sK1,top),
inference(forward_demodulation,[],[f61,f62]) ).
fof(f81,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f31,f29]) ).
fof(f83,plain,
! [X0] : composition(join(sK1,X0),top) = join(sK1,composition(X0,top)),
inference(superposition,[],[f28,f64]) ).
fof(f84,plain,
! [X0] : composition(join(sK0,X0),top) = join(sK0,composition(X0,top)),
inference(superposition,[],[f28,f63]) ).
fof(f85,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f28,f31]) ).
fof(f101,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f24,f22]) ).
fof(f102,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f24,f22]) ).
fof(f175,plain,
zero = complement(top),
inference(superposition,[],[f41,f33]) ).
fof(f211,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f85,f31]) ).
fof(f220,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f211,f30]) ).
fof(f223,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f220,f30]) ).
fof(f225,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f223,f31]) ).
fof(f274,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f23,f33]) ).
fof(f275,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f23,f24]) ).
fof(f282,plain,
! [X0] : join(sF2,join(sF3,X0)) = join(sF4,X0),
inference(superposition,[],[f23,f51]) ).
fof(f297,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f81,f27]) ).
fof(f311,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f297,f29]) ).
fof(f326,plain,
one = converse(one),
inference(superposition,[],[f27,f311]) ).
fof(f337,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f311,f326]) ).
fof(f352,plain,
! [X0] : complement(X0) = join(composition(converse(one),complement(X0)),complement(X0)),
inference(superposition,[],[f32,f337]) ).
fof(f357,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f352,f311]) ).
fof(f463,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f29,f225]) ).
fof(f476,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f463,f29]) ).
fof(f511,plain,
! [X0,X1] : composition(X0,join(one,X1)) = join(X0,composition(X0,X1)),
inference(superposition,[],[f476,f27]) ).
fof(f527,plain,
! [X0] : composition(sF5,join(X0,top)) = join(composition(sF5,X0),sF6),
inference(superposition,[],[f476,f55]) ).
fof(f626,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(superposition,[],[f275,f357]) ).
fof(f635,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f626,f24]) ).
fof(f664,plain,
! [X0,X1] : join(X1,complement(join(top,X0))) = X1,
inference(superposition,[],[f635,f274]) ).
fof(f672,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f635,f41]) ).
fof(f679,plain,
! [X0,X1] : join(complement(complement(X0)),complement(join(complement(X0),join(complement(complement(X0)),X1)))) = X0,
inference(superposition,[],[f24,f635]) ).
fof(f694,plain,
! [X0,X1] : join(complement(complement(X0)),complement(join(top,X1))) = X0,
inference(forward_demodulation,[],[f679,f274]) ).
fof(f707,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f694,f664]) ).
fof(f713,plain,
top = complement(zero),
inference(superposition,[],[f707,f175]) ).
fof(f714,plain,
sK0 = complement(sF2),
inference(superposition,[],[f707,f47]) ).
fof(f715,plain,
sK1 = complement(sF3),
inference(superposition,[],[f707,f49]) ).
fof(f716,plain,
sF4 = complement(sF5),
inference(superposition,[],[f707,f53]) ).
fof(f726,plain,
! [X0,X1] : complement(X0) = join(complement(join(complement(X1),X0)),complement(join(X0,X1))),
inference(superposition,[],[f102,f707]) ).
fof(f732,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f357,f707]) ).
fof(f733,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f635,f707]) ).
fof(f801,plain,
! [X0] : complement(complement(complement(X0))) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(superposition,[],[f726,f33]) ).
fof(f832,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(complement(X0)),complement(join(join(X0,X1),complement(join(complement(X1),X0))))),
inference(superposition,[],[f101,f726]) ).
fof(f837,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(complement(complement(join(X0,X1))),complement(join(complement(X1),X0)))),complement(complement(X0))),
inference(superposition,[],[f102,f726]) ).
fof(f850,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(complement(complement(join(X0,X1))),complement(join(complement(X1),X0)))),X0),
inference(forward_demodulation,[],[f837,f707]) ).
fof(f855,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(complement(X0)),complement(join(X0,join(X1,complement(join(complement(X1),X0)))))),
inference(forward_demodulation,[],[f832,f23]) ).
fof(f873,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,X0))),
inference(forward_demodulation,[],[f801,f707]) ).
fof(f885,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(join(X0,X1),complement(join(complement(X1),X0)))),X0),
inference(forward_demodulation,[],[f850,f707]) ).
fof(f888,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f855,f635]) ).
fof(f894,plain,
! [X0] : complement(X0) = join(complement(top),complement(X0)),
inference(forward_demodulation,[],[f873,f732]) ).
fof(f899,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(X0,join(X1,complement(join(complement(X1),X0))))),X0),
inference(forward_demodulation,[],[f885,f23]) ).
fof(f900,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f888,f707]) ).
fof(f905,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f894,f175]) ).
fof(f906,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(join(X0,X1)),X0),
inference(forward_demodulation,[],[f899,f635]) ).
fof(f911,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f900,f22]) ).
fof(f1031,plain,
! [X0] : complement(zero) = join(complement(join(complement(complement(X0)),zero)),complement(complement(X0))),
inference(superposition,[],[f726,f905]) ).
fof(f1033,plain,
! [X0] : complement(zero) = join(complement(zero),complement(complement(X0))),
inference(forward_demodulation,[],[f1031,f906]) ).
fof(f1039,plain,
! [X0] : complement(zero) = join(complement(zero),X0),
inference(forward_demodulation,[],[f1033,f707]) ).
fof(f1040,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[],[f1039,f713]) ).
fof(f1049,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f22,f1040]) ).
fof(f1069,plain,
! [X0,X1] : join(complement(X1),complement(join(X0,X1))) = join(complement(join(X0,X1)),complement(join(complement(X0),X1))),
inference(superposition,[],[f911,f911]) ).
fof(f1107,plain,
! [X0,X1] : complement(X1) = join(complement(join(complement(complement(join(X0,X1))),X1)),complement(join(complement(X0),X1))),
inference(superposition,[],[f726,f911]) ).
fof(f1113,plain,
! [X0,X1] : complement(X1) = join(complement(join(join(X0,X1),X1)),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f1107,f707]) ).
fof(f1144,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,join(X1,X1))),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f1113,f23]) ).
fof(f1162,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f1144,f732]) ).
fof(f1172,plain,
! [X0,X1] : complement(X1) = join(complement(X1),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1162,f1069]) ).
fof(f1214,plain,
complement(sF3) = join(complement(sF3),complement(sF4)),
inference(superposition,[],[f1172,f51]) ).
fof(f1251,plain,
complement(sF3) = join(complement(sF3),sF5),
inference(forward_demodulation,[],[f1214,f53]) ).
fof(f1273,plain,
sK1 = join(sK1,sF5),
inference(forward_demodulation,[],[f1251,f715]) ).
fof(f1412,plain,
complement(sF2) = join(complement(sF2),complement(sF4)),
inference(superposition,[],[f733,f51]) ).
fof(f1451,plain,
complement(sF2) = join(complement(sF2),sF5),
inference(forward_demodulation,[],[f1412,f53]) ).
fof(f1473,plain,
sK0 = join(sK0,sF5),
inference(forward_demodulation,[],[f1451,f714]) ).
fof(f1557,plain,
composition(sK1,top) = join(sK1,composition(sF5,top)),
inference(superposition,[],[f83,f1273]) ).
fof(f1567,plain,
composition(sK1,top) = join(sK1,sF6),
inference(forward_demodulation,[],[f1557,f55]) ).
fof(f1571,plain,
sK1 = join(sK1,sF6),
inference(forward_demodulation,[],[f1567,f64]) ).
fof(f1578,plain,
join(sK1,complement(sK1)) = join(complement(sF6),sK1),
inference(superposition,[],[f900,f1571]) ).
fof(f1582,plain,
top = join(complement(sF6),sK1),
inference(forward_demodulation,[],[f1578,f33]) ).
fof(f2563,plain,
composition(sK0,top) = join(sK0,composition(sF5,top)),
inference(superposition,[],[f84,f1473]) ).
fof(f2576,plain,
composition(sK0,top) = join(sK0,sF6),
inference(forward_demodulation,[],[f2563,f55]) ).
fof(f2580,plain,
sK0 = join(sK0,sF6),
inference(forward_demodulation,[],[f2576,f63]) ).
fof(f2591,plain,
join(sK0,complement(sK0)) = join(complement(sF6),sK0),
inference(superposition,[],[f900,f2580]) ).
fof(f2597,plain,
top = join(complement(sF6),sK0),
inference(forward_demodulation,[],[f2591,f33]) ).
fof(f3768,plain,
join(complement(sK1),complement(sF6)) = join(complement(sF6),complement(top)),
inference(superposition,[],[f900,f1582]) ).
fof(f3775,plain,
join(complement(sK1),complement(sF6)) = join(complement(sF6),zero),
inference(forward_demodulation,[],[f3768,f175]) ).
fof(f3791,plain,
complement(sF6) = join(complement(sK1),complement(sF6)),
inference(forward_demodulation,[],[f3775,f672]) ).
fof(f3802,plain,
complement(sF6) = join(sF3,complement(sF6)),
inference(forward_demodulation,[],[f3791,f49]) ).
fof(f4526,plain,
! [X0] : composition(X0,top) = join(X0,composition(X0,top)),
inference(superposition,[],[f511,f1049]) ).
fof(f4998,plain,
join(complement(sF6),complement(top)) = join(complement(sK0),complement(sF6)),
inference(superposition,[],[f900,f2597]) ).
fof(f5009,plain,
join(complement(sF6),complement(top)) = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f4998,f47]) ).
fof(f5029,plain,
join(complement(sF6),zero) = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f5009,f175]) ).
fof(f5040,plain,
complement(sF6) = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f5029,f672]) ).
fof(f8535,plain,
join(sF5,composition(sF5,top)) = join(composition(sF5,one),sF6),
inference(superposition,[],[f511,f527]) ).
fof(f8556,plain,
join(sF5,composition(sF5,top)) = join(sF5,sF6),
inference(forward_demodulation,[],[f8535,f27]) ).
fof(f8584,plain,
composition(sF5,top) = join(sF5,sF6),
inference(forward_demodulation,[],[f8556,f4526]) ).
fof(f8599,plain,
sF6 = join(sF5,sF6),
inference(forward_demodulation,[],[f8584,f55]) ).
fof(f8623,plain,
complement(sF5) = join(complement(sF5),complement(sF6)),
inference(superposition,[],[f733,f8599]) ).
fof(f8633,plain,
sF4 = join(sF4,complement(sF6)),
inference(forward_demodulation,[],[f8623,f716]) ).
fof(f10736,plain,
join(sF2,complement(sF6)) = join(sF4,complement(sF6)),
inference(superposition,[],[f282,f3802]) ).
fof(f10796,plain,
sF4 = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f10736,f8633]) ).
fof(f10819,plain,
sF4 = complement(sF6),
inference(forward_demodulation,[],[f10796,f5040]) ).
fof(f10866,plain,
complement(sF4) = sF6,
inference(superposition,[],[f707,f10819]) ).
fof(f10883,plain,
sF5 = sF6,
inference(forward_demodulation,[],[f10866,f53]) ).
fof(f10906,plain,
$false,
inference(forward_subsumption_resolution,[],[f10883,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL019+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:54:42 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 10.87/2.44 % (3298680)Detected formulas, will run a generic FOF schedule.
% 10.87/2.44 % (3298687)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=3631823964:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.87/2.44 % (3298691)dis-21_1_sil=8000:lcm=predicate:random_seed=2384541205: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)
% 10.87/2.44 % (3298689)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1203998030:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.87/2.44 % (3298685)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=4189638675:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.87/2.44 % (3298688)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1235310929:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.87/2.44 % (3298686)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=2298870449:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.87/2.44 % (3298691)Refutation not found, incomplete strategy
% 10.87/2.44 % (3298691)------------------------------
% 10.87/2.44 % (3298691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298691)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298691)Termination reason: Refutation not found, incomplete strategy
% 10.87/2.44 % (3298691)Time elapsed: 0.002 s
% 10.87/2.44 % (3298691)Peak memory usage: 88 MB
% 10.87/2.44 % (3298691)Instructions burned: 1 (million)
% 10.87/2.44 % (3298690)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=601757501:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.87/2.44 % (3298688)Instruction limit reached!
% 10.87/2.44 % (3298688)------------------------------
% 10.87/2.44 % (3298688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298688)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298688)Termination reason: Instruction limit
% 10.87/2.44 % (3298688)Termination phase: Saturation
% 10.87/2.44 % (3298688)Time elapsed: 0.061 s
% 10.87/2.44 % (3298688)Peak memory usage: 89 MB
% 10.87/2.44 % (3298688)Instructions burned: 109 (million)
% 10.87/2.44 % (3298689)Instruction limit reached!
% 10.87/2.44 % (3298689)------------------------------
% 10.87/2.44 % (3298689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298689)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298689)Termination reason: Instruction limit
% 10.87/2.44 % (3298689)Termination phase: Saturation
% 10.87/2.44 % (3298689)Time elapsed: 0.068 s
% 10.87/2.44 % (3298689)Peak memory usage: 89 MB
% 10.87/2.44 % (3298689)Instructions burned: 120 (million)
% 10.87/2.44 % (3298690)Instruction limit reached!
% 10.87/2.44 % (3298690)------------------------------
% 10.87/2.44 % (3298690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298690)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298690)Termination reason: Instruction limit
% 10.87/2.44 % (3298690)Termination phase: Saturation
% 10.87/2.44 % (3298690)Time elapsed: 0.083 s
% 10.87/2.44 % (3298690)Peak memory usage: 90 MB
% 10.87/2.44 % (3298690)Instructions burned: 140 (million)
% 10.87/2.44 % (3298700)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2859526474:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.87/2.44 % (3298699)lrs+10_1_sil=8000:sp=occurrence:random_seed=981620833:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.87/2.44 % (3298701)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3209696446:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.87/2.44 % (3298691)------------------------------
% 10.87/2.44 % (3298691)------------------------------
% 10.87/2.44 % (3298700)Instruction limit reached!
% 10.87/2.44 % (3298700)------------------------------
% 10.87/2.44 % (3298700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298700)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298700)Termination reason: Instruction limit
% 10.87/2.44 % (3298700)Termination phase: Saturation
% 10.87/2.44 % (3298700)Time elapsed: 0.085 s
% 10.87/2.44 % (3298700)Peak memory usage: 91 MB
% 10.87/2.44 % (3298700)Instructions burned: 157 (million)
% 10.87/2.44 % (3298699)Instruction limit reached!
% 10.87/2.44 % (3298699)------------------------------
% 10.87/2.44 % (3298699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298699)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298699)Termination reason: Instruction limit
% 10.87/2.44 % (3298699)Termination phase: Saturation
% 10.87/2.44 % (3298699)Time elapsed: 0.169 s
% 10.87/2.44 % (3298699)Peak memory usage: 92 MB
% 10.87/2.44 % (3298699)Instructions burned: 286 (million)
% 10.87/2.44 % (3298705)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=2452955708:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 10.87/2.44 % (3298706)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1665266737:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.87/2.44 % (3298701)Instruction limit reached!
% 10.87/2.44 % (3298701)------------------------------
% 10.87/2.44 % (3298701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298701)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298701)Termination reason: Instruction limit
% 10.87/2.44 % (3298701)Termination phase: Saturation
% 10.87/2.44 % (3298701)Time elapsed: 0.192 s
% 10.87/2.44 % (3298701)Peak memory usage: 92 MB
% 10.87/2.44 % (3298701)Instructions burned: 326 (million)
% 10.87/2.44 % (3298707)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3206524504:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.87/2.44 % (3298710)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=46096369:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 10.87/2.44 % (3298705)Instruction limit reached!
% 10.87/2.44 % (3298705)------------------------------
% 10.87/2.44 % (3298705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298705)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298705)Termination reason: Instruction limit
% 10.87/2.44 % (3298705)Termination phase: Saturation
% 10.87/2.44 % (3298705)Time elapsed: 0.157 s
% 10.87/2.44 % (3298705)Peak memory usage: 91 MB
% 10.87/2.44 % (3298705)Instructions burned: 248 (million)
% 10.87/2.44 % (3298706)Instruction limit reached!
% 10.87/2.44 % (3298706)------------------------------
% 10.87/2.44 % (3298706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298706)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298706)Termination reason: Instruction limit
% 10.87/2.44 % (3298706)Termination phase: Saturation
% 10.87/2.44 % (3298706)Time elapsed: 0.176 s
% 10.87/2.44 % (3298706)Peak memory usage: 92 MB
% 10.87/2.44 % (3298706)Instructions burned: 295 (million)
% 10.87/2.44 % (3298710)Instruction limit reached!
% 10.87/2.44 % (3298710)------------------------------
% 10.87/2.44 % (3298710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298710)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298710)Termination reason: Instruction limit
% 10.87/2.44 % (3298710)Termination phase: Saturation
% 10.87/2.44 % (3298710)Time elapsed: 0.070 s
% 10.87/2.44 % (3298710)Peak memory usage: 90 MB
% 10.87/2.44 % (3298710)Instructions burned: 113 (million)
% 10.87/2.44 % (3298713)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3111888616:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 10.87/2.44 % (3298713)Refutation not found, incomplete strategy
% 10.87/2.44 % (3298713)------------------------------
% 10.87/2.44 % (3298713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298713)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298713)Termination reason: Refutation not found, incomplete strategy
% 10.87/2.44 % (3298713)Time elapsed: 0.001 s
% 10.87/2.44 % (3298713)Peak memory usage: 87 MB
% 10.87/2.44 % (3298713)Instructions burned: 1 (million)
% 10.87/2.44 % (3298714)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2509029048:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 10.87/2.44 % (3298715)lrs+10_1_sil=8000:sp=occurrence:random_seed=2546627907:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.87/2.44 % (3298714)Instruction limit reached!
% 10.87/2.44 % (3298714)------------------------------
% 10.87/2.44 % (3298714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298714)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298714)Termination reason: Instruction limit
% 10.87/2.44 % (3298714)Termination phase: Saturation
% 10.87/2.44 % (3298714)Time elapsed: 0.059 s
% 10.87/2.44 % (3298714)Peak memory usage: 89 MB
% 10.87/2.44 % (3298714)Instructions burned: 114 (million)
% 10.87/2.44 % (3298719)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3501338667:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 10.87/2.44 % (3298713)------------------------------
% 10.87/2.44 % (3298713)------------------------------
% 10.87/2.44 % (3298721)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2517409791:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 10.87/2.44 % (3298719)Instruction limit reached!
% 10.87/2.44 % (3298719)------------------------------
% 10.87/2.44 % (3298719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298719)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298719)Termination reason: Instruction limit
% 10.87/2.44 % (3298719)Termination phase: Saturation
% 10.87/2.44 % (3298719)Time elapsed: 0.215 s
% 10.87/2.44 % (3298719)Peak memory usage: 93 MB
% 10.87/2.44 % (3298719)Instructions burned: 438 (million)
% 10.87/2.44 % (3298685)First to succeed.
% 10.87/2.44 % (3298685)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3298680"
% 10.87/2.44 % (3298723)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=520977628:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 10.87/2.44 % (3298723)Refutation not found, incomplete strategy
% 10.87/2.44 % (3298723)------------------------------
% 10.87/2.44 % (3298723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298723)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298723)Termination reason: Refutation not found, incomplete strategy
% 10.87/2.44 % (3298723)Time elapsed: 0.002 s
% 10.87/2.44 % (3298723)Peak memory usage: 89 MB
% 10.87/2.44 % (3298723)Instructions burned: 2 (million)
% 10.87/2.44 % (3298715)Instruction limit reached!
% 10.87/2.44 % (3298715)------------------------------
% 10.87/2.44 % (3298715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.87/2.44 % (3298715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.87/2.44 % (3298715)CaDiCaL version: 2.1.3
% 10.87/2.44 % (3298715)Termination reason: Instruction limit
% 10.87/2.44 % (3298715)Termination phase: Saturation
% 10.87/2.44 % (3298715)Time elapsed: 0.528 s
% 10.87/2.44 % (3298715)Peak memory usage: 99 MB
% 10.87/2.44 % (3298715)Instructions burned: 908 (million)
% 10.87/2.44 % (3298725)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1340050908:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 10.87/2.44 % (3298685)Refutation found. Thanks to Tanya!
% 10.87/2.44 % SZS status Theorem for theBenchmark
% 10.87/2.44 % SZS output start Proof for theBenchmark
% See solution above
% 11.76/2.63 % (3298685)------------------------------
% 11.76/2.63 % (3298685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.76/2.63 % (3298685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.76/2.63 % (3298685)CaDiCaL version: 2.1.3
% 11.76/2.63 % (3298685)Termination reason: Refutation
% 11.76/2.63 % (3298685)Time elapsed: 1.169 s
% 11.76/2.63 % (3298685)Peak memory usage: 137 MB
% 11.76/2.63 % (3298685)Instructions burned: 1856 (million)
% 11.76/2.63 % (3298685)------------------------------
% 11.76/2.63 % (3298685)------------------------------
% 11.76/2.63 % (3298680)Success in time 1.574 s
% 11.76/2.63 % Vampire exiting
%------------------------------------------------------------------------------