%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL019+1 : 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 : n017.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 10.73s 2.54s
% Output : Refutation 11.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 20
% Syntax : Number of formulae : 161 ( 156 unt; 7 def)
% Number of atoms : 171 ( 170 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 : 170 ( 166 !; 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(f14,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(f15,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)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( meet(X0,X1) != composition(meet(X0,X1),top)
& composition(X0,top) = X0
& composition(X1,top) = X1 ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
? [X0,X1] :
( meet(X0,X1) != composition(meet(X0,X1),top)
& composition(X0,top) = X0
& composition(X1,top) = X1 ),
inference(flattening,[],[f16]) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
sK1 = composition(sK1,top),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
sK0 = composition(sK0,top),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
meet(sK0,sK1) != composition(meet(sK0,sK1),top),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f31,f22]) ).
fof(f36,plain,
complement(join(complement(sK0),complement(sK1))) != composition(complement(join(complement(sK0),complement(sK1))),top),
inference(definition_unfolding,[],[f34,f22,f22]) ).
fof(f37,definition,
sF2 = complement(sK0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f38,plain,
complement(sK0) = sF2,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF3 = complement(sK1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f40,plain,
complement(sK1) = sF3,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF4 = join(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f42,plain,
join(sF2,sF3) = sF4,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f44,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF6 = composition(sF5,top),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f46,plain,
composition(sF5,top) = sF6,
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
sF5 != sF6,
inference(definition_folding,[],[f36,f46,f44,f42,f40,f38,f44,f42,f40,f38]) ).
fof(f48,definition,
sF7 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f49,plain,
composition(sK0,top) = sF7,
inference(reorient_equations,[],[f48]) ).
fof(f50,plain,
sK0 = sF7,
inference(definition_folding,[],[f33,f49]) ).
fof(f51,definition,
sF8 = composition(sK1,top),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f52,plain,
composition(sK1,top) = sF8,
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
sK1 = sF8,
inference(definition_folding,[],[f32,f52]) ).
fof(f54,plain,
sK0 = composition(sK0,top),
inference(forward_demodulation,[],[f49,f50]) ).
fof(f55,plain,
sK1 = composition(sK1,top),
inference(forward_demodulation,[],[f52,f53]) ).
fof(f62,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f28,f26]) ).
fof(f64,plain,
! [X0] : composition(join(sK1,X0),top) = join(sK1,composition(X0,top)),
inference(superposition,[],[f25,f55]) ).
fof(f65,plain,
! [X0] : composition(join(sK0,X0),top) = join(sK0,composition(X0,top)),
inference(superposition,[],[f25,f54]) ).
fof(f66,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f25,f28]) ).
fof(f132,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f21,f19]) ).
fof(f139,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f21,f19]) ).
fof(f148,plain,
zero = complement(top),
inference(superposition,[],[f35,f30]) ).
fof(f167,plain,
top = join(top,zero),
inference(superposition,[],[f30,f148]) ).
fof(f177,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f62,f24]) ).
fof(f187,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f177,f26]) ).
fof(f200,plain,
one = converse(one),
inference(superposition,[],[f24,f187]) ).
fof(f205,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f187,f200]) ).
fof(f216,plain,
! [X0] : complement(X0) = join(composition(converse(one),complement(X0)),complement(X0)),
inference(superposition,[],[f29,f205]) ).
fof(f219,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f216,f187]) ).
fof(f233,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f66,f28]) ).
fof(f246,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f233,f27]) ).
fof(f256,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f246,f27]) ).
fof(f263,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f256,f28]) ).
fof(f286,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f26,f263]) ).
fof(f299,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f286,f26]) ).
fof(f333,plain,
! [X0] : composition(sF5,join(top,X0)) = join(sF6,composition(sF5,X0)),
inference(superposition,[],[f299,f46]) ).
fof(f342,plain,
! [X0] : composition(sF5,join(X0,top)) = join(composition(sF5,X0),sF6),
inference(superposition,[],[f299,f46]) ).
fof(f457,plain,
! [X0] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[],[f139,f30]) ).
fof(f473,plain,
! [X0] : join(complement(join(complement(X0),complement(X0))),zero) = X0,
inference(forward_demodulation,[],[f457,f148]) ).
fof(f479,plain,
! [X0] : join(complement(complement(X0)),zero) = X0,
inference(forward_demodulation,[],[f473,f219]) ).
fof(f481,plain,
! [X0,X1] : join(top,X1) = join(X0,join(complement(X0),X1)),
inference(superposition,[],[f20,f30]) ).
fof(f485,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f20,f21]) ).
fof(f493,plain,
! [X0] : join(sF2,join(sF3,X0)) = join(sF4,X0),
inference(superposition,[],[f20,f42]) ).
fof(f514,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[],[f481,f219]) ).
fof(f528,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f514,f30]) ).
fof(f543,plain,
! [X0] : join(complement(X0),X0) = join(top,zero),
inference(superposition,[],[f481,f479]) ).
fof(f548,plain,
! [X0] : top = join(complement(X0),X0),
inference(forward_demodulation,[],[f543,f167]) ).
fof(f634,plain,
! [X0,X1] : join(top,complement(join(complement(X0),X1))) = join(join(complement(X1),complement(X0)),X0),
inference(superposition,[],[f481,f132]) ).
fof(f640,plain,
! [X0,X1] : join(top,complement(join(complement(X0),X1))) = join(complement(X1),join(complement(X0),X0)),
inference(forward_demodulation,[],[f634,f20]) ).
fof(f648,plain,
! [X0,X1] : join(top,complement(join(complement(X0),X1))) = join(complement(X1),top),
inference(forward_demodulation,[],[f640,f548]) ).
fof(f651,plain,
! [X1] : top = join(complement(X1),top),
inference(forward_demodulation,[],[f648,f528]) ).
fof(f662,plain,
! [X0] : composition(sF5,top) = join(composition(sF5,complement(X0)),sF6),
inference(superposition,[],[f342,f651]) ).
fof(f670,plain,
! [X0] : sF6 = join(composition(sF5,complement(X0)),sF6),
inference(forward_demodulation,[],[f662,f46]) ).
fof(f731,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(superposition,[],[f485,f219]) ).
fof(f746,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f731,f21]) ).
fof(f795,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f746,f35]) ).
fof(f858,plain,
! [X0] : complement(complement(X0)) = X0,
inference(superposition,[],[f479,f795]) ).
fof(f881,plain,
sK0 = complement(sF2),
inference(superposition,[],[f858,f38]) ).
fof(f882,plain,
sK1 = complement(sF3),
inference(superposition,[],[f858,f40]) ).
fof(f883,plain,
sF4 = complement(sF5),
inference(superposition,[],[f858,f44]) ).
fof(f892,plain,
! [X0,X1] : complement(X0) = join(complement(join(complement(X1),X0)),complement(join(X0,X1))),
inference(superposition,[],[f132,f858]) ).
fof(f895,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f219,f858]) ).
fof(f902,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f746,f858]) ).
fof(f960,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(complement(X0)),complement(join(join(X0,X1),complement(join(complement(X1),X0))))),
inference(superposition,[],[f139,f892]) ).
fof(f978,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(complement(X0)),complement(join(X0,join(X1,complement(join(complement(X1),X0)))))),
inference(forward_demodulation,[],[f960,f20]) ).
fof(f1016,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f978,f746]) ).
fof(f1039,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1016,f858]) ).
fof(f1057,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f1039,f19]) ).
fof(f1061,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(complement(complement(join(X1,X0))),X1),
inference(superposition,[],[f1039,f1039]) ).
fof(f1069,plain,
! [X0,X1] : join(complement(complement(join(X0,X1))),complement(join(complement(X1),X0))) = join(complement(join(complement(X1),X0)),complement(complement(X0))),
inference(superposition,[],[f1039,f892]) ).
fof(f1119,plain,
! [X0,X1] : join(complement(complement(join(X0,X1))),complement(join(complement(X1),X0))) = join(complement(join(complement(X1),X0)),X0),
inference(forward_demodulation,[],[f1069,f858]) ).
fof(f1126,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(join(X1,X0),X1),
inference(forward_demodulation,[],[f1061,f858]) ).
fof(f1140,plain,
! [X0,X1] : join(join(X0,X1),complement(join(complement(X1),X0))) = join(complement(join(complement(X1),X0)),X0),
inference(forward_demodulation,[],[f1119,f858]) ).
fof(f1146,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(X1,join(X0,X1)),
inference(forward_demodulation,[],[f1126,f20]) ).
fof(f1153,plain,
! [X0,X1] : join(X0,join(X1,complement(join(complement(X1),X0)))) = join(complement(join(complement(X1),X0)),X0),
inference(forward_demodulation,[],[f1140,f20]) ).
fof(f1157,plain,
! [X0,X1] : join(complement(complement(X0)),X1) = join(X1,join(X0,X1)),
inference(forward_demodulation,[],[f1146,f1057]) ).
fof(f1161,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X1),X0)),X0),
inference(forward_demodulation,[],[f1153,f746]) ).
fof(f1164,plain,
! [X0,X1] : join(X0,X1) = join(X1,join(X0,X1)),
inference(forward_demodulation,[],[f1157,f858]) ).
fof(f1174,plain,
! [X0,X1] : join(complement(X1),complement(join(X0,X1))) = join(complement(join(X0,X1)),complement(join(complement(X0),X1))),
inference(superposition,[],[f1057,f1057]) ).
fof(f1198,plain,
! [X0,X1] : complement(X1) = join(complement(join(complement(complement(join(X0,X1))),X1)),complement(join(complement(X0),X1))),
inference(superposition,[],[f892,f1057]) ).
fof(f1228,plain,
! [X0,X1] : complement(X1) = join(complement(join(join(X0,X1),X1)),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f1198,f858]) ).
fof(f1251,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,join(X1,X1))),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f1228,f20]) ).
fof(f1264,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f1251,f895]) ).
fof(f1274,plain,
! [X0,X1] : complement(X1) = join(complement(X1),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1264,f1174]) ).
fof(f1312,plain,
complement(sF3) = join(complement(sF3),complement(sF4)),
inference(superposition,[],[f1274,f42]) ).
fof(f1345,plain,
complement(sF3) = join(complement(sF3),sF5),
inference(forward_demodulation,[],[f1312,f44]) ).
fof(f1369,plain,
sK1 = join(sK1,sF5),
inference(forward_demodulation,[],[f1345,f882]) ).
fof(f1545,plain,
composition(sK1,top) = join(sK1,composition(sF5,top)),
inference(superposition,[],[f64,f1369]) ).
fof(f1554,plain,
composition(sK1,top) = join(sK1,sF6),
inference(forward_demodulation,[],[f1545,f46]) ).
fof(f1558,plain,
sK1 = join(sK1,sF6),
inference(forward_demodulation,[],[f1554,f55]) ).
fof(f1564,plain,
join(sK1,complement(sK1)) = join(complement(sF6),sK1),
inference(superposition,[],[f1039,f1558]) ).
fof(f1568,plain,
top = join(complement(sF6),sK1),
inference(forward_demodulation,[],[f1564,f30]) ).
fof(f1608,plain,
complement(sF2) = join(complement(sF2),complement(sF4)),
inference(superposition,[],[f902,f42]) ).
fof(f1647,plain,
complement(sF2) = join(complement(sF2),sF5),
inference(forward_demodulation,[],[f1608,f44]) ).
fof(f1669,plain,
sK0 = join(sK0,sF5),
inference(forward_demodulation,[],[f1647,f881]) ).
fof(f2033,plain,
composition(sK0,top) = join(sK0,composition(sF5,top)),
inference(superposition,[],[f65,f1669]) ).
fof(f2045,plain,
composition(sK0,top) = join(sK0,sF6),
inference(forward_demodulation,[],[f2033,f46]) ).
fof(f2050,plain,
sK0 = join(sK0,sF6),
inference(forward_demodulation,[],[f2045,f54]) ).
fof(f2063,plain,
join(sK0,complement(sK0)) = join(complement(sF6),sK0),
inference(superposition,[],[f1039,f2050]) ).
fof(f2067,plain,
top = join(complement(sF6),sK0),
inference(forward_demodulation,[],[f2063,f30]) ).
fof(f2318,plain,
join(complement(sK1),complement(sF6)) = join(complement(sF6),complement(top)),
inference(superposition,[],[f1039,f1568]) ).
fof(f2323,plain,
join(complement(sK1),complement(sF6)) = join(complement(sF6),zero),
inference(forward_demodulation,[],[f2318,f148]) ).
fof(f2337,plain,
complement(sF6) = join(complement(sK1),complement(sF6)),
inference(forward_demodulation,[],[f2323,f795]) ).
fof(f2346,plain,
complement(sF6) = join(sF3,complement(sF6)),
inference(forward_demodulation,[],[f2337,f40]) ).
fof(f3117,plain,
join(complement(sF6),complement(top)) = join(complement(sK0),complement(sF6)),
inference(superposition,[],[f1039,f2067]) ).
fof(f3124,plain,
join(complement(sF6),complement(top)) = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f3117,f38]) ).
fof(f3138,plain,
join(complement(sF6),zero) = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f3124,f148]) ).
fof(f3147,plain,
complement(sF6) = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f3138,f795]) ).
fof(f6695,plain,
! [X0] : composition(sF5,join(top,X0)) = join(composition(sF5,complement(join(complement(X0),top))),sF6),
inference(superposition,[],[f342,f1161]) ).
fof(f6702,plain,
! [X0] : sF6 = composition(sF5,join(top,X0)),
inference(forward_demodulation,[],[f6695,f670]) ).
fof(f6802,plain,
! [X0] : sF6 = join(sF6,composition(sF5,X0)),
inference(forward_demodulation,[],[f6702,f333]) ).
fof(f8760,plain,
! [X0] : composition(sF5,join(X0,top)) = join(sF6,composition(sF5,join(X0,top))),
inference(superposition,[],[f333,f1164]) ).
fof(f8811,plain,
! [X0] : sF6 = composition(sF5,join(X0,top)),
inference(forward_demodulation,[],[f8760,f6802]) ).
fof(f8832,plain,
! [X0] : sF6 = join(composition(sF5,X0),sF6),
inference(forward_demodulation,[],[f8811,f342]) ).
fof(f8851,plain,
sF6 = join(sF5,sF6),
inference(superposition,[],[f8832,f24]) ).
fof(f8895,plain,
complement(sF5) = join(complement(sF5),complement(sF6)),
inference(superposition,[],[f902,f8851]) ).
fof(f8908,plain,
sF4 = join(sF4,complement(sF6)),
inference(forward_demodulation,[],[f8895,f883]) ).
fof(f10384,plain,
join(sF2,complement(sF6)) = join(sF4,complement(sF6)),
inference(superposition,[],[f493,f2346]) ).
fof(f10470,plain,
sF4 = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f10384,f8908]) ).
fof(f10490,plain,
sF4 = complement(sF6),
inference(forward_demodulation,[],[f10470,f3147]) ).
fof(f10530,plain,
complement(sF4) = sF6,
inference(superposition,[],[f858,f10490]) ).
fof(f10547,plain,
sF5 = sF6,
inference(forward_demodulation,[],[f10530,f44]) ).
fof(f10565,plain,
$false,
inference(forward_subsumption_resolution,[],[f10547,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL019+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 22:47:20 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 10.73/2.54 % (3036946)Detected formulas, will run a generic FOF schedule.
% 10.73/2.54 % (3036962)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=2110488464:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.73/2.54 % (3036960)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=4289108041:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.73/2.54 % (3036961)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=10946165:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.73/2.54 % (3036966)dis-21_1_sil=8000:lcm=predicate:random_seed=1706609612: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)
% 10.73/2.54 % (3036963)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2373549658:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.73/2.54 % (3036965)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1994484562:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.73/2.54 % (3036966)Refutation not found, incomplete strategy
% 10.73/2.54 % (3036966)------------------------------
% 10.73/2.54 % (3036966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036966)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036966)Termination reason: Refutation not found, incomplete strategy
% 10.73/2.54 % (3036966)Time elapsed: 0.001 s
% 10.73/2.54 % (3036966)Peak memory usage: 88 MB
% 10.73/2.54 % (3036966)Instructions burned: 1 (million)
% 10.73/2.54 % (3036964)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1365777848:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.73/2.54 % (3036963)Instruction limit reached!
% 10.73/2.54 % (3036963)------------------------------
% 10.73/2.54 % (3036963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036963)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036963)Termination reason: Instruction limit
% 10.73/2.54 % (3036963)Termination phase: Saturation
% 10.73/2.54 % (3036963)Time elapsed: 0.062 s
% 10.73/2.54 % (3036963)Peak memory usage: 90 MB
% 10.73/2.54 % (3036963)Instructions burned: 110 (million)
% 10.73/2.54 % (3036965)Instruction limit reached!
% 10.73/2.54 % (3036965)------------------------------
% 10.73/2.54 % (3036965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036965)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036965)Termination reason: Instruction limit
% 10.73/2.54 % (3036965)Termination phase: Saturation
% 10.73/2.54 % (3036965)Time elapsed: 0.082 s
% 10.73/2.54 % (3036965)Peak memory usage: 90 MB
% 10.73/2.54 % (3036965)Instructions burned: 139 (million)
% 10.73/2.54 % (3036964)Instruction limit reached!
% 10.73/2.54 % (3036964)------------------------------
% 10.73/2.54 % (3036964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036964)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036964)Termination reason: Instruction limit
% 10.73/2.54 % (3036964)Termination phase: Saturation
% 10.73/2.54 % (3036964)Time elapsed: 0.065 s
% 10.73/2.54 % (3036964)Peak memory usage: 88 MB
% 10.73/2.54 % (3036964)Instructions burned: 120 (million)
% 10.73/2.54 % (3036974)lrs+10_1_sil=8000:sp=occurrence:random_seed=3390980055:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.73/2.54 % (3036966)------------------------------
% 10.73/2.54 % (3036966)------------------------------
% 10.73/2.54 % (3036975)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1274871021:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.73/2.54 % (3036976)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1337094262:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.73/2.54 % (3036975)Instruction limit reached!
% 10.73/2.54 % (3036975)------------------------------
% 10.73/2.54 % (3036975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036975)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036975)Termination reason: Instruction limit
% 10.73/2.54 % (3036975)Termination phase: Saturation
% 10.73/2.54 % (3036975)Time elapsed: 0.092 s
% 10.73/2.54 % (3036975)Peak memory usage: 91 MB
% 10.73/2.54 % (3036975)Instructions burned: 159 (million)
% 10.73/2.54 % (3036974)Instruction limit reached!
% 10.73/2.54 % (3036974)------------------------------
% 10.73/2.54 % (3036974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036974)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036974)Termination reason: Instruction limit
% 10.73/2.54 % (3036974)Termination phase: Saturation
% 10.73/2.54 % (3036974)Time elapsed: 0.174 s
% 10.73/2.54 % (3036974)Peak memory usage: 92 MB
% 10.73/2.54 % (3036974)Instructions burned: 286 (million)
% 10.73/2.54 % (3036979)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=1292138203:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 10.73/2.54 % (3036976)Instruction limit reached!
% 10.73/2.54 % (3036976)------------------------------
% 10.73/2.54 % (3036976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036976)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036976)Termination reason: Instruction limit
% 10.73/2.54 % (3036976)Termination phase: Saturation
% 10.73/2.54 % (3036976)Time elapsed: 0.210 s
% 10.73/2.54 % (3036976)Peak memory usage: 92 MB
% 10.73/2.54 % (3036976)Instructions burned: 325 (million)
% 10.73/2.54 % (3036981)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=794156653:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 10.73/2.54 % (3036982)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4087848846:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.73/2.54 % (3036979)Instruction limit reached!
% 10.73/2.54 % (3036979)------------------------------
% 10.73/2.54 % (3036979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036979)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036979)Termination reason: Instruction limit
% 10.73/2.54 % (3036979)Termination phase: Saturation
% 10.73/2.54 % (3036979)Time elapsed: 0.148 s
% 10.73/2.54 % (3036979)Peak memory usage: 92 MB
% 10.73/2.54 % (3036979)Instructions burned: 248 (million)
% 10.73/2.54 % (3036985)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4109851510:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 10.73/2.54 % (3036981)Instruction limit reached!
% 10.73/2.54 % (3036981)------------------------------
% 10.73/2.54 % (3036981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036981)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036981)Termination reason: Instruction limit
% 10.73/2.54 % (3036981)Termination phase: Saturation
% 10.73/2.54 % (3036981)Time elapsed: 0.178 s
% 10.73/2.54 % (3036981)Peak memory usage: 92 MB
% 10.73/2.54 % (3036981)Instructions burned: 296 (million)
% 10.73/2.54 % (3037001)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2775509815:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 10.73/2.54 % (3037001)Refutation not found, incomplete strategy
% 10.73/2.54 % (3037001)------------------------------
% 10.73/2.54 % (3037001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3037001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3037001)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3037001)Termination reason: Refutation not found, incomplete strategy
% 10.73/2.54 % (3037001)Time elapsed: 0.001 s
% 10.73/2.54 % (3037001)Peak memory usage: 88 MB
% 10.73/2.54 % (3036985)Instruction limit reached!
% 10.73/2.54 % (3036985)------------------------------
% 10.73/2.54 % (3036985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3036985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3036985)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3036985)Termination reason: Instruction limit
% 10.73/2.54 % (3036985)Termination phase: Saturation
% 10.73/2.54 % (3036985)Time elapsed: 0.069 s
% 10.73/2.54 % (3036985)Peak memory usage: 90 MB
% 10.73/2.54 % (3036985)Instructions burned: 113 (million)
% 10.73/2.54 % (3037057)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2683233581:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 10.73/2.54 % (3037068)lrs+10_1_sil=8000:sp=occurrence:random_seed=4268573803:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 10.73/2.54 % (3037057)Instruction limit reached!
% 10.73/2.54 % (3037057)------------------------------
% 10.73/2.54 % (3037057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3037057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3037057)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3037057)Termination reason: Instruction limit
% 10.73/2.54 % (3037057)Termination phase: Saturation
% 10.73/2.54 % (3037057)Time elapsed: 0.064 s
% 10.73/2.54 % (3037057)Peak memory usage: 89 MB
% 10.73/2.54 % (3037057)Instructions burned: 116 (million)
% 10.73/2.54 % (3037001)------------------------------
% 10.73/2.54 % (3037001)------------------------------
% 10.73/2.54 % (3037145)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=553333857:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 10.73/2.54 % (3037148)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1750958215:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 10.73/2.54 % (3036960)First to succeed.
% 10.73/2.54 % (3036960)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3036946"
% 10.73/2.54 % (3037145)Instruction limit reached!
% 10.73/2.54 % (3037145)------------------------------
% 10.73/2.54 % (3037145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.54 % (3037145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.54 % (3037145)CaDiCaL version: 2.1.3
% 10.73/2.54 % (3037145)Termination reason: Instruction limit
% 10.73/2.54 % (3037145)Termination phase: Saturation
% 10.73/2.54 % (3037145)Time elapsed: 0.212 s
% 10.73/2.54 % (3037145)Peak memory usage: 92 MB
% 10.73/2.54 % (3037145)Instructions burned: 438 (million)
% 10.73/2.54 % (3036960)Refutation found. Thanks to Tanya!
% 10.73/2.54 % SZS status Theorem for theBenchmark
% 10.73/2.54 % SZS output start Proof for theBenchmark
% See solution above
% 11.73/2.74 % (3036960)------------------------------
% 11.73/2.74 % (3036960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.73/2.74 % (3036960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.73/2.74 % (3036960)CaDiCaL version: 2.1.3
% 11.73/2.74 % (3036960)Termination reason: Refutation
% 11.73/2.74 % (3036960)Time elapsed: 1.140 s
% 11.73/2.74 % (3036960)Peak memory usage: 136 MB
% 11.73/2.74 % (3036960)Instructions burned: 1794 (million)
% 11.73/2.74 % (3036960)------------------------------
% 11.73/2.74 % (3036960)------------------------------
% 11.73/2.74 % (3036946)Success in time 1.561 s
% 11.73/2.74 % Vampire exiting
%------------------------------------------------------------------------------