%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Unsatisfiable 17.64s 3.37s
% Output : Refutation 18.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 22
% Syntax : Number of formulae : 205 ( 205 unt; 7 def)
% Number of atoms : 205 ( 204 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 197 ( 197 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f8,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f23,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
composition(sk2,top) = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
sk2 = composition(sk2,top),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
composition(meet(sk1,sk2),top) != meet(sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_19) ).
fof(f28,plain,
meet(sk1,sk2) != composition(meet(sk1,sk2),top),
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f33,plain,
complement(join(complement(sk1),complement(sk2))) != composition(complement(join(complement(sk1),complement(sk2))),top),
inference(definition_unfolding,[],[f28,f6,f6]) ).
fof(f34,definition,
sF0 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f35,plain,
composition(sk1,top) = sF0,
inference(reorient_equations,[],[f34]) ).
fof(f36,plain,
sk1 = sF0,
inference(definition_folding,[],[f24,f35]) ).
fof(f37,definition,
sF1 = composition(sk2,top),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f38,plain,
composition(sk2,top) = sF1,
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
sk2 = sF1,
inference(definition_folding,[],[f26,f38]) ).
fof(f40,definition,
sF2 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f41,plain,
complement(sk1) = sF2,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF3 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f43,plain,
complement(sk2) = sF3,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF4 = join(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f45,plain,
join(sF2,sF3) = sF4,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f47,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF6 = composition(sF5,top),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f49,plain,
composition(sF5,top) = sF6,
inference(reorient_equations,[],[f48]) ).
fof(f50,plain,
sF5 != sF6,
inference(definition_folding,[],[f33,f49,f47,f45,f43,f41,f47,f45,f43,f41]) ).
fof(f51,plain,
zero = complement(top),
inference(backward_demodulation,[],[f29,f15]) ).
fof(f52,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f55,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f56,plain,
sk1 = composition(sk1,top),
inference(forward_demodulation,[],[f35,f36]) ).
fof(f57,plain,
sk2 = composition(sk2,top),
inference(forward_demodulation,[],[f38,f39]) ).
fof(f85,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f52,f15]) ).
fof(f86,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f85,f51]) ).
fof(f92,plain,
! [X0] : composition(join(sk2,X0),top) = join(sk2,composition(X0,top)),
inference(superposition,[],[f9,f57]) ).
fof(f93,plain,
! [X0] : composition(join(sk1,X0),top) = join(sk1,composition(X0,top)),
inference(superposition,[],[f9,f56]) ).
fof(f106,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f52,f1]) ).
fof(f129,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[],[f52,f51]) ).
fof(f131,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f129,f1]) ).
fof(f132,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(complement(X0),top))) = X0,
inference(forward_demodulation,[],[f131,f1]) ).
fof(f133,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f132,f1]) ).
fof(f134,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f133,f1]) ).
fof(f138,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f52]) ).
fof(f139,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f143,plain,
! [X0] : join(sF2,join(sF3,X0)) = join(sF4,X0),
inference(superposition,[],[f2,f45]) ).
fof(f149,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f155,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f158,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f165,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f158,f12]) ).
fof(f171,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f165,f11]) ).
fof(f174,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f171,f11]) ).
fof(f176,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f174,f12]) ).
fof(f193,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f138,f15]) ).
fof(f209,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f193,f149]) ).
fof(f219,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f209,f51]) ).
fof(f275,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f106,f15]) ).
fof(f278,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(superposition,[],[f138,f106]) ).
fof(f287,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(forward_demodulation,[],[f278,f1]) ).
fof(f288,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f275,f1]) ).
fof(f306,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f288,f1]) ).
fof(f316,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f306,f51]) ).
fof(f322,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f86,f316]) ).
fof(f332,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(X1,complement(X0)))),
inference(backward_demodulation,[],[f287,f322]) ).
fof(f333,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f316,f322]) ).
fof(f347,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f333]) ).
fof(f350,plain,
sk1 = complement(sF2),
inference(superposition,[],[f322,f41]) ).
fof(f351,plain,
sk2 = complement(sF3),
inference(superposition,[],[f322,f43]) ).
fof(f352,plain,
sF4 = complement(sF5),
inference(superposition,[],[f322,f47]) ).
fof(f354,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f52,f322]) ).
fof(f358,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f106,f322]) ).
fof(f382,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f354,f1]) ).
fof(f391,plain,
complement(sF2) = join(complement(sF4),complement(join(sF2,complement(sF3)))),
inference(superposition,[],[f354,f45]) ).
fof(f413,plain,
complement(sF2) = join(complement(sF4),complement(join(sF2,sk2))),
inference(forward_demodulation,[],[f391,f351]) ).
fof(f423,plain,
complement(sF2) = join(sF5,complement(join(sF2,sk2))),
inference(forward_demodulation,[],[f413,f47]) ).
fof(f429,plain,
sk1 = join(sF5,complement(join(sF2,sk2))),
inference(forward_demodulation,[],[f423,f350]) ).
fof(f451,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f176]) ).
fof(f462,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f451,f10]) ).
fof(f490,plain,
! [X0] : composition(sF5,join(top,X0)) = join(sF6,composition(sF5,X0)),
inference(superposition,[],[f462,f49]) ).
fof(f544,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0)))))),
inference(superposition,[],[f354,f358]) ).
fof(f547,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(complement(X1),X0)))),
inference(forward_demodulation,[],[f544,f322]) ).
fof(f561,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(join(X0,X1)),complement(X1))))),
inference(forward_demodulation,[],[f547,f149]) ).
fof(f573,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f561,f1]) ).
fof(f584,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f573,f322]) ).
fof(f593,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f584,f322]) ).
fof(f608,plain,
! [X0,X1] : join(top,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f139,f1]) ).
fof(f610,plain,
! [X0,X1] : join(top,complement(join(X0,complement(X1)))) = join(join(X0,X1),complement(X0)),
inference(superposition,[],[f139,f354]) ).
fof(f626,plain,
! [X0,X1] : join(top,complement(join(X0,complement(X1)))) = join(X0,join(X1,complement(X0))),
inference(forward_demodulation,[],[f610,f2]) ).
fof(f635,plain,
! [X0,X1] : join(top,X1) = join(top,complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f626,f608]) ).
fof(f680,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(join(X1,X0),X1)))),
inference(superposition,[],[f333,f149]) ).
fof(f703,plain,
! [X0,X1] : complement(join(X1,X0)) = join(zero,complement(join(X0,join(X1,join(X0,X1))))),
inference(forward_demodulation,[],[f680,f2]) ).
fof(f729,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f155,f8]) ).
fof(f747,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f729,f10]) ).
fof(f767,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f55,f747]) ).
fof(f768,plain,
one = converse(one),
inference(superposition,[],[f8,f747]) ).
fof(f772,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f747,f768]) ).
fof(f784,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f767,f772]) ).
fof(f791,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f219,f784]) ).
fof(f793,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f791,f322]) ).
fof(f796,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f347,f793]) ).
fof(f797,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f333,f796]) ).
fof(f799,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f797,f1]) ).
fof(f802,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(complement(X0))) = X0,
inference(backward_demodulation,[],[f134,f799]) ).
fof(f803,plain,
! [X0,X1] : complement(join(X1,X0)) = complement(join(X0,join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f703,f799]) ).
fof(f808,plain,
! [X0] : join(complement(complement(X0)),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f802,f1]) ).
fof(f810,plain,
! [X0] : join(X0,complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f808,f322]) ).
fof(f883,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(join(top,complement(complement(X0))))),
inference(superposition,[],[f139,f810]) ).
fof(f886,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(forward_demodulation,[],[f883,f635]) ).
fof(f897,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f886,f15]) ).
fof(f905,plain,
! [X0] : join(X0,complement(top)) = X0,
inference(backward_demodulation,[],[f810,f897]) ).
fof(f908,plain,
! [X1] : top = join(top,X1),
inference(backward_demodulation,[],[f635,f897]) ).
fof(f915,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f139,f908]) ).
fof(f916,plain,
! [X0] : composition(sF5,top) = join(sF6,composition(sF5,X0)),
inference(backward_demodulation,[],[f490,f908]) ).
fof(f934,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[],[f905,f51]) ).
fof(f950,plain,
! [X0] : sF6 = join(sF6,composition(sF5,X0)),
inference(forward_demodulation,[],[f916,f49]) ).
fof(f1028,plain,
sF6 = join(sF6,sF5),
inference(superposition,[],[f950,f8]) ).
fof(f1037,plain,
sF6 = join(sF5,sF6),
inference(forward_demodulation,[],[f1028,f1]) ).
fof(f1038,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f784,f322]) ).
fof(f1082,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f1038]) ).
fof(f1084,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f149,f1038]) ).
fof(f1090,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,join(X0,X1))),
inference(superposition,[],[f2,f1038]) ).
fof(f1096,plain,
! [X0,X1] : complement(join(X0,X1)) = complement(join(X1,X0)),
inference(backward_demodulation,[],[f803,f1090]) ).
fof(f1125,plain,
complement(sF5) = join(complement(sF6),complement(join(sF5,complement(sF6)))),
inference(superposition,[],[f354,f1037]) ).
fof(f1128,plain,
sF4 = join(complement(sF6),complement(join(sF5,complement(sF6)))),
inference(forward_demodulation,[],[f1125,f352]) ).
fof(f2447,plain,
join(sF2,sF3) = join(sF4,sF3),
inference(superposition,[],[f143,f1038]) ).
fof(f2481,plain,
join(sF2,sF3) = join(sF3,sF4),
inference(forward_demodulation,[],[f2447,f1]) ).
fof(f2490,plain,
sF4 = join(sF3,sF4),
inference(forward_demodulation,[],[f2481,f45]) ).
fof(f2576,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(join(complement(join(X0,complement(X1))),join(X1,X0))),complement(complement(X0))),
inference(superposition,[],[f358,f382]) ).
fof(f2584,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1082,f382]) ).
fof(f2585,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f2584,f1]) ).
fof(f2592,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X1,X0)))),
inference(forward_demodulation,[],[f2576,f1]) ).
fof(f2624,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f593,f2585]) ).
fof(f2631,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f2592,f1096]) ).
fof(f2658,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f2631,f2]) ).
fof(f2677,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,X1)))),
inference(forward_demodulation,[],[f2658,f2624]) ).
fof(f2692,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f2677,f1084]) ).
fof(f2702,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f2692,f322]) ).
fof(f2709,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f2702,f322]) ).
fof(f2735,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f2709,f1]) ).
fof(f2740,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(top)),
inference(superposition,[],[f2709,f915]) ).
fof(f2759,plain,
join(sF2,complement(sF3)) = join(sF2,complement(sF4)),
inference(superposition,[],[f2709,f45]) ).
fof(f2808,plain,
join(sF2,complement(sF3)) = join(sF2,sF5),
inference(forward_demodulation,[],[f2759,f47]) ).
fof(f2820,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,zero),
inference(forward_demodulation,[],[f2740,f51]) ).
fof(f2827,plain,
sF4 = join(complement(sF6),complement(sF5)),
inference(backward_demodulation,[],[f1128,f2735]) ).
fof(f2841,plain,
join(sF2,sk2) = join(sF2,sF5),
inference(forward_demodulation,[],[f2808,f351]) ).
fof(f2851,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f2820,f934]) ).
fof(f2857,plain,
sF4 = join(complement(sF5),complement(sF6)),
inference(forward_demodulation,[],[f2827,f1]) ).
fof(f2877,plain,
! [X0,X1] : join(X0,complement(join(X1,complement(X0)))) = X0,
inference(backward_demodulation,[],[f332,f2851]) ).
fof(f2887,plain,
sF4 = join(sF4,complement(sF6)),
inference(forward_demodulation,[],[f2857,f352]) ).
fof(f3027,plain,
! [X0] : sF5 = join(sF5,complement(join(X0,sF4))),
inference(superposition,[],[f2877,f352]) ).
fof(f3464,plain,
complement(sF3) = join(complement(sF4),complement(join(complement(sF4),sF3))),
inference(superposition,[],[f358,f2490]) ).
fof(f3469,plain,
complement(sF3) = join(complement(sF4),complement(sF3)),
inference(forward_demodulation,[],[f3464,f2709]) ).
fof(f3475,plain,
complement(sF3) = join(complement(sF3),complement(sF4)),
inference(forward_demodulation,[],[f3469,f1]) ).
fof(f3477,plain,
complement(sF3) = join(complement(sF3),sF5),
inference(forward_demodulation,[],[f3475,f47]) ).
fof(f3479,plain,
complement(sF3) = join(sF5,complement(sF3)),
inference(forward_demodulation,[],[f3477,f1]) ).
fof(f3481,plain,
sk2 = join(sF5,sk2),
inference(forward_demodulation,[],[f3479,f351]) ).
fof(f3483,plain,
sk2 = join(sk2,sF5),
inference(forward_demodulation,[],[f3481,f1]) ).
fof(f3545,plain,
composition(sk2,top) = join(sk2,composition(sF5,top)),
inference(superposition,[],[f92,f3483]) ).
fof(f3559,plain,
composition(sk2,top) = join(sk2,sF6),
inference(forward_demodulation,[],[f3545,f49]) ).
fof(f3562,plain,
sk2 = join(sk2,sF6),
inference(forward_demodulation,[],[f3559,f57]) ).
fof(f3574,plain,
complement(sF6) = join(complement(sk2),complement(join(sF6,complement(sk2)))),
inference(superposition,[],[f382,f3562]) ).
fof(f3578,plain,
complement(sF6) = join(complement(sk2),complement(sF6)),
inference(forward_demodulation,[],[f3574,f2735]) ).
fof(f3582,plain,
complement(sF6) = join(sF3,complement(sF6)),
inference(forward_demodulation,[],[f3578,f43]) ).
fof(f3583,plain,
join(sF4,complement(sF6)) = join(sF2,complement(sF6)),
inference(superposition,[],[f143,f3582]) ).
fof(f3604,plain,
sF4 = join(sF2,complement(sF6)),
inference(forward_demodulation,[],[f3583,f2887]) ).
fof(f3753,plain,
complement(complement(sF6)) = join(complement(sF4),complement(join(complement(sF6),complement(sF2)))),
inference(superposition,[],[f382,f3604]) ).
fof(f3755,plain,
join(sF2,complement(sF4)) = join(sF2,complement(complement(sF6))),
inference(superposition,[],[f2709,f3604]) ).
fof(f3758,plain,
join(sF2,complement(sF4)) = join(sF2,sF6),
inference(forward_demodulation,[],[f3755,f322]) ).
fof(f3759,plain,
complement(complement(sF6)) = join(complement(sF4),complement(join(complement(sF2),complement(sF6)))),
inference(forward_demodulation,[],[f3753,f1096]) ).
fof(f3768,plain,
join(sF2,sF5) = join(sF2,sF6),
inference(forward_demodulation,[],[f3758,f47]) ).
fof(f3769,plain,
complement(complement(sF6)) = join(complement(sF4),complement(join(sk1,complement(sF6)))),
inference(forward_demodulation,[],[f3759,f350]) ).
fof(f3776,plain,
join(sF2,sk2) = join(sF2,sF6),
inference(forward_demodulation,[],[f3768,f2841]) ).
fof(f3777,plain,
complement(complement(sF6)) = join(sF5,complement(join(sk1,complement(sF6)))),
inference(forward_demodulation,[],[f3769,f47]) ).
fof(f3783,plain,
sF6 = join(sF5,complement(join(sk1,complement(sF6)))),
inference(forward_demodulation,[],[f3777,f322]) ).
fof(f3796,plain,
complement(sF6) = join(complement(join(sF2,sk2)),complement(join(sF6,complement(sF2)))),
inference(superposition,[],[f382,f3776]) ).
fof(f3802,plain,
complement(sF6) = join(complement(join(sF2,sk2)),complement(join(sF6,sk1))),
inference(forward_demodulation,[],[f3796,f350]) ).
fof(f3810,plain,
complement(sF6) = join(complement(join(sF2,sk2)),complement(join(sk1,sF6))),
inference(forward_demodulation,[],[f3802,f1096]) ).
fof(f3993,plain,
join(sF5,complement(join(sF2,sk2))) = join(sF5,complement(sF2)),
inference(superposition,[],[f2735,f2841]) ).
fof(f3994,plain,
join(sF5,complement(join(sF2,sk2))) = join(sF5,sk1),
inference(forward_demodulation,[],[f3993,f350]) ).
fof(f4002,plain,
join(sF5,complement(join(sF2,sk2))) = join(sk1,sF5),
inference(forward_demodulation,[],[f3994,f1]) ).
fof(f4008,plain,
sk1 = join(sk1,sF5),
inference(forward_demodulation,[],[f4002,f429]) ).
fof(f4587,plain,
composition(sk1,top) = join(sk1,composition(sF5,top)),
inference(superposition,[],[f93,f4008]) ).
fof(f4601,plain,
composition(sk1,top) = join(sk1,sF6),
inference(forward_demodulation,[],[f4587,f49]) ).
fof(f4604,plain,
sk1 = join(sk1,sF6),
inference(forward_demodulation,[],[f4601,f56]) ).
fof(f4607,plain,
complement(sF6) = join(complement(join(sF2,sk2)),complement(sk1)),
inference(backward_demodulation,[],[f3810,f4604]) ).
fof(f4610,plain,
complement(sF6) = join(complement(sk1),complement(join(sF2,sk2))),
inference(forward_demodulation,[],[f4607,f1]) ).
fof(f4612,plain,
complement(sF6) = join(sF2,complement(join(sF2,sk2))),
inference(forward_demodulation,[],[f4610,f41]) ).
fof(f4613,plain,
complement(sF6) = join(sF2,complement(sk2)),
inference(forward_demodulation,[],[f4612,f2709]) ).
fof(f4614,plain,
join(sF2,sF3) = complement(sF6),
inference(forward_demodulation,[],[f4613,f43]) ).
fof(f4615,plain,
sF4 = complement(sF6),
inference(forward_demodulation,[],[f4614,f45]) ).
fof(f4633,plain,
sF6 = join(sF5,complement(join(sk1,sF4))),
inference(backward_demodulation,[],[f3783,f4615]) ).
fof(f4636,plain,
sF5 = sF6,
inference(forward_demodulation,[],[f4633,f3027]) ).
fof(f4639,plain,
$false,
inference(forward_subsumption_resolution,[],[f4636,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL019-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:52:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.64/3.37 % (1388686)Detected a unit-equality problem, will run specialized UEQ schedule.
% 17.64/3.37 % (1388763)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3233073643:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 17.64/3.37 % (1388769)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3605157492:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 17.64/3.37 % (1388762)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2773194449:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 17.64/3.37 % (1388770)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2618687566:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 17.64/3.37 % (1388766)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=500904823:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 17.64/3.37 % (1388765)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=236707662:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 17.64/3.37 % (1388768)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3374653202:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 17.64/3.37 % (1388766)Instruction limit reached!
% 17.64/3.37 % (1388766)------------------------------
% 17.64/3.37 % (1388766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.64/3.37 % (1388766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.64/3.37 % (1388766)CaDiCaL version: 2.1.3
% 17.64/3.37 % (1388766)Termination reason: Instruction limit
% 17.64/3.37 % (1388766)Termination phase: Saturation
% 17.64/3.37 % (1388766)Time elapsed: 0.138 s
% 17.64/3.37 % (1388766)Peak memory usage: 89 MB
% 17.64/3.37 % (1388766)Instructions burned: 137 (million)
% 17.64/3.37 % (1388768)Instruction limit reached!
% 17.64/3.37 % (1388768)------------------------------
% 17.64/3.37 % (1388768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.64/3.37 % (1388768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.64/3.37 % (1388768)CaDiCaL version: 2.1.3
% 17.64/3.37 % (1388768)Termination reason: Instruction limit
% 17.64/3.37 % (1388768)Termination phase: Saturation
% 17.64/3.37 % (1388768)Time elapsed: 0.177 s
% 17.64/3.37 % (1388768)Peak memory usage: 89 MB
% 17.64/3.37 % (1388768)Instructions burned: 182 (million)
% 17.64/3.37 % (1388769)Instruction limit reached!
% 17.64/3.37 % (1388769)------------------------------
% 17.64/3.37 % (1388769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.64/3.37 % (1388769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.64/3.37 % (1388769)CaDiCaL version: 2.1.3
% 17.64/3.37 % (1388769)Termination reason: Instruction limit
% 17.64/3.37 % (1388769)Termination phase: Saturation
% 17.64/3.37 % (1388769)Time elapsed: 0.272 s
% 17.64/3.37 % (1388769)Peak memory usage: 91 MB
% 17.64/3.37 % (1388769)Instructions burned: 258 (million)
% 17.64/3.37 % (1388809)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=225999331:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 17.64/3.37 % (1388811)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3208598676:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 17.64/3.37 % (1388813)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=868630589:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 17.64/3.37 % (1388813)Instruction limit reached!
% 17.64/3.37 % (1388813)------------------------------
% 17.64/3.37 % (1388813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.64/3.37 % (1388813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.64/3.37 % (1388813)CaDiCaL version: 2.1.3
% 17.64/3.37 % (1388813)Termination reason: Instruction limit
% 17.64/3.37 % (1388813)Termination phase: Saturation
% 17.64/3.37 % (1388813)Time elapsed: 0.199 s
% 17.64/3.37 % (1388813)Peak memory usage: 92 MB
% 17.64/3.37 % (1388813)Instructions burned: 215 (million)
% 17.64/3.37 % (1388823)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3921695705:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 17.64/3.37 % (1388770)Instruction limit reached!
% 17.64/3.37 % (1388770)------------------------------
% 17.64/3.37 % (1388770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.64/3.37 % (1388770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.64/3.37 % (1388770)CaDiCaL version: 2.1.3
% 17.64/3.37 % (1388770)Termination reason: Instruction limit
% 17.64/3.37 % (1388770)Termination phase: Saturation
% 17.64/3.37 % (1388770)Time elapsed: 1.089 s
% 17.64/3.37 % (1388770)Peak memory usage: 102 MB
% 17.64/3.37 % (1388770)Instructions burned: 1187 (million)
% 17.64/3.37 % (1388823)Instruction limit reached!
% 17.64/3.37 % (1388823)------------------------------
% 17.64/3.37 % (1388823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.64/3.37 % (1388823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.64/3.37 % (1388823)CaDiCaL version: 2.1.3
% 17.64/3.37 % (1388823)Termination reason: Instruction limit
% 17.64/3.37 % (1388823)Termination phase: Saturation
% 17.64/3.37 % (1388823)Time elapsed: 0.282 s
% 17.64/3.37 % (1388823)Peak memory usage: 90 MB
% 17.64/3.37 % (1388823)Instructions burned: 317 (million)
% 17.64/3.37 % (1388827)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=1022508553:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 17.64/3.37 % (1388832)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3428731738:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2984 on theBenchmark for (2984ds/2836Mi)
% 17.64/3.37 % (1388765)First to succeed.
% 17.64/3.37 % (1388765)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1388686"
% 17.64/3.37 % (1388765)Refutation found. Thanks to Tanya!
% 17.64/3.37 % SZS status Unsatisfiable for theBenchmark
% 17.64/3.37 % SZS output start Proof for theBenchmark
% See solution above
% 18.26/3.65 % (1388765)------------------------------
% 18.26/3.65 % (1388765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.26/3.65 % (1388765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.26/3.65 % (1388765)CaDiCaL version: 2.1.3
% 18.26/3.65 % (1388765)Termination reason: Refutation
% 18.26/3.65 % (1388765)Time elapsed: 1.809 s
% 18.26/3.65 % (1388765)Peak memory usage: 136 MB
% 18.26/3.65 % (1388765)Instructions burned: 1747 (million)
% 18.26/3.65 % (1388765)------------------------------
% 18.26/3.65 % (1388765)------------------------------
% 18.26/3.65 % (1388686)Success in time 2.506 s
% 18.26/3.65 % Vampire exiting
%------------------------------------------------------------------------------