%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL032-2 : 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 : n016.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 12:33:58 PM UTC 2026
% Result : Unsatisfiable 7.18s 1.91s
% Output : Refutation 9.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 25
% Syntax : Number of formulae : 200 ( 200 unt; 12 def)
% Number of atoms : 200 ( 199 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 : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 172 ( 172 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
fof(f23,negated_conjecture,
join(composition(sk1,meet(sk2,sk3)),meet(composition(sk1,sk2),composition(sk1,sk3))) != meet(composition(sk1,sk2),composition(sk1,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
meet(composition(sk1,sk2),composition(sk1,sk3)) != join(composition(sk1,meet(sk2,sk3)),meet(composition(sk1,sk2),composition(sk1,sk3))),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f29,plain,
complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))) != join(composition(sk1,complement(join(complement(sk2),complement(sk3)))),complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3))))),
inference(definition_unfolding,[],[f24,f6,f6,f6]) ).
fof(f30,definition,
sF0 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f31,plain,
composition(sk1,sk2) = sF0,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF1 = complement(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f33,plain,
complement(sF0) = sF1,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF2 = composition(sk1,sk3),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f35,plain,
composition(sk1,sk3) = sF2,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f37,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF4 = join(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f39,plain,
join(sF1,sF3) = sF4,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f41,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF6 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f43,plain,
complement(sk2) = sF6,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF7 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f45,plain,
complement(sk3) = sF7,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF8 = join(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f47,plain,
join(sF6,sF7) = sF8,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f49,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF10 = composition(sk1,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f51,plain,
composition(sk1,sF9) = sF10,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF11 = join(sF10,sF5),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f53,plain,
join(sF10,sF5) = sF11,
inference(reorient_equations,[],[f52]) ).
fof(f54,plain,
sF5 != sF11,
inference(definition_folding,[],[f29,f53,f41,f39,f37,f35,f33,f31,f51,f49,f47,f45,f43,f41,f39,f37,f35,f33,f31]) ).
fof(f55,plain,
zero = complement(top),
inference(backward_demodulation,[],[f25,f15]) ).
fof(f56,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f59,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f111,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f56,f1]) ).
fof(f135,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f56,f15]) ).
fof(f136,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f135,f55]) ).
fof(f156,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f56]) ).
fof(f160,plain,
! [X0] : join(sF1,join(sF3,X0)) = join(sF4,X0),
inference(superposition,[],[f2,f39]) ).
fof(f167,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f192,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f156,f15]) ).
fof(f208,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f192,f167]) ).
fof(f220,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f208,f55]) ).
fof(f245,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f247,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(f255,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f247,f12]) ).
fof(f261,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f255,f11]) ).
fof(f264,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f261,f11]) ).
fof(f266,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f264,f12]) ).
fof(f279,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f266]) ).
fof(f290,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f279,f10]) ).
fof(f312,plain,
! [X0] : composition(sk1,join(X0,sk3)) = join(composition(sk1,X0),sF2),
inference(superposition,[],[f290,f35]) ).
fof(f313,plain,
! [X0] : composition(sk1,join(X0,sk2)) = join(composition(sk1,X0),sF0),
inference(superposition,[],[f290,f31]) ).
fof(f324,plain,
! [X0] : join(sF0,composition(sk1,X0)) = composition(sk1,join(X0,sk2)),
inference(forward_demodulation,[],[f313,f1]) ).
fof(f325,plain,
! [X0] : join(sF2,composition(sk1,X0)) = composition(sk1,join(X0,sk3)),
inference(forward_demodulation,[],[f312,f1]) ).
fof(f432,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[],[f56,f55]) ).
fof(f434,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f432,f1]) ).
fof(f436,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(complement(X0),top))) = X0,
inference(forward_demodulation,[],[f434,f1]) ).
fof(f438,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f436,f1]) ).
fof(f440,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f438,f1]) ).
fof(f467,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f111,f15]) ).
fof(f470,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(superposition,[],[f156,f111]) ).
fof(f482,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(forward_demodulation,[],[f470,f1]) ).
fof(f483,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f467,f1]) ).
fof(f507,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f483,f1]) ).
fof(f520,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f507,f55]) ).
fof(f529,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f136,f520]) ).
fof(f539,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(X1,complement(X0)))),
inference(backward_demodulation,[],[f482,f529]) ).
fof(f540,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f520,f529]) ).
fof(f559,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f540]) ).
fof(f563,plain,
top = complement(zero),
inference(superposition,[],[f529,f55]) ).
fof(f564,plain,
sk2 = complement(sF6),
inference(superposition,[],[f529,f43]) ).
fof(f565,plain,
sk3 = complement(sF7),
inference(superposition,[],[f529,f45]) ).
fof(f566,plain,
sF0 = complement(sF1),
inference(superposition,[],[f529,f33]) ).
fof(f567,plain,
sF2 = complement(sF3),
inference(superposition,[],[f529,f37]) ).
fof(f568,plain,
sF4 = complement(sF5),
inference(superposition,[],[f529,f41]) ).
fof(f571,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f56,f529]) ).
fof(f575,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f111,f529]) ).
fof(f604,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f571,f1]) ).
fof(f617,plain,
complement(sF6) = join(complement(sF8),complement(join(sF6,complement(sF7)))),
inference(superposition,[],[f571,f47]) ).
fof(f645,plain,
complement(sF6) = join(complement(sF8),complement(join(sF6,sk3))),
inference(forward_demodulation,[],[f617,f565]) ).
fof(f659,plain,
complement(sF6) = join(sF9,complement(join(sF6,sk3))),
inference(forward_demodulation,[],[f645,f49]) ).
fof(f666,plain,
sk2 = join(sF9,complement(join(sF6,sk3))),
inference(forward_demodulation,[],[f659,f564]) ).
fof(f711,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,[],[f571,f575]) ).
fof(f712,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,[],[f711,f529]) ).
fof(f735,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,[],[f712,f167]) ).
fof(f750,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,[],[f735,f1]) ).
fof(f763,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f750,f529]) ).
fof(f773,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f763,f529]) ).
fof(f795,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(join(X0,X0)),complement(zero)))),
inference(superposition,[],[f604,f540]) ).
fof(f796,plain,
complement(sF3) = join(complement(sF4),complement(join(sF3,complement(sF1)))),
inference(superposition,[],[f604,f39]) ).
fof(f797,plain,
complement(sF7) = join(complement(sF8),complement(join(sF7,complement(sF6)))),
inference(superposition,[],[f604,f47]) ).
fof(f815,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,[],[f575,f604]) ).
fof(f827,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,[],[f815,f1]) ).
fof(f835,plain,
complement(sF7) = join(complement(sF8),complement(join(sF7,sk2))),
inference(forward_demodulation,[],[f797,f564]) ).
fof(f836,plain,
complement(sF3) = join(complement(sF4),complement(join(sF3,sF0))),
inference(forward_demodulation,[],[f796,f566]) ).
fof(f837,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f795,f1]) ).
fof(f849,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,[],[f827,f1]) ).
fof(f855,plain,
complement(sF7) = join(sF9,complement(join(sF7,sk2))),
inference(forward_demodulation,[],[f835,f49]) ).
fof(f856,plain,
complement(sF3) = join(complement(sF4),complement(join(sF0,sF3))),
inference(forward_demodulation,[],[f836,f1]) ).
fof(f857,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f837,f563]) ).
fof(f865,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,[],[f849,f2]) ).
fof(f870,plain,
sk3 = join(sF9,complement(join(sF7,sk2))),
inference(forward_demodulation,[],[f855,f565]) ).
fof(f871,plain,
complement(sF3) = join(sF5,complement(join(sF0,sF3))),
inference(forward_demodulation,[],[f856,f41]) ).
fof(f872,plain,
! [X0] : complement(complement(join(X0,X0))) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f857,f529]) ).
fof(f879,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f865,f529]) ).
fof(f884,plain,
sF2 = join(sF5,complement(join(sF0,sF3))),
inference(forward_demodulation,[],[f871,f567]) ).
fof(f885,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f872,f529]) ).
fof(f892,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f879,f529]) ).
fof(f1146,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f245,f8]) ).
fof(f1164,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1146,f10]) ).
fof(f1181,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f59,f1164]) ).
fof(f1195,plain,
one = converse(one),
inference(superposition,[],[f8,f1164]) ).
fof(f1200,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1164,f1195]) ).
fof(f1213,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1181,f1200]) ).
fof(f1225,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f220,f1213]) ).
fof(f1230,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f1225,f529]) ).
fof(f1235,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f559,f1230]) ).
fof(f1238,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(complement(X0),top))),
inference(backward_demodulation,[],[f885,f1235]) ).
fof(f1239,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f540,f1235]) ).
fof(f1241,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f1239,f1]) ).
fof(f1242,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(X0)))),
inference(forward_demodulation,[],[f1238,f539]) ).
fof(f1245,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(complement(X0))) = X0,
inference(backward_demodulation,[],[f440,f1241]) ).
fof(f1255,plain,
! [X0] : join(complement(complement(X0)),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f1245,f1]) ).
fof(f1258,plain,
! [X0] : join(X0,complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f1255,f529]) ).
fof(f1261,plain,
! [X0] : join(X0,X0) = X0,
inference(backward_demodulation,[],[f1242,f1258]) ).
fof(f1354,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f1261]) ).
fof(f1356,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f167,f1261]) ).
fof(f1481,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(X0)),
inference(superposition,[],[f1354,f575]) ).
fof(f1482,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1354,f604]) ).
fof(f1523,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1482,f1]) ).
fof(f1524,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1481,f1]) ).
fof(f1538,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f773,f1523]) ).
fof(f1545,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f892,f1538]) ).
fof(f1550,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1545,f1356]) ).
fof(f1568,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1550,f1]) ).
fof(f1584,plain,
join(sF6,complement(sF7)) = join(sF6,complement(sF8)),
inference(superposition,[],[f1550,f47]) ).
fof(f1619,plain,
join(sF6,complement(sF7)) = join(sF6,sF9),
inference(forward_demodulation,[],[f1584,f49]) ).
fof(f1641,plain,
join(sF6,sk3) = join(sF6,sF9),
inference(forward_demodulation,[],[f1619,f565]) ).
fof(f1662,plain,
sk2 = join(sF9,complement(join(sF6,sF9))),
inference(backward_demodulation,[],[f666,f1641]) ).
fof(f1677,plain,
sk2 = join(sF9,complement(sF6)),
inference(forward_demodulation,[],[f1662,f1568]) ).
fof(f1686,plain,
sk2 = join(sF9,sk2),
inference(forward_demodulation,[],[f1677,f564]) ).
fof(f1695,plain,
composition(sk1,sk2) = join(sF0,composition(sk1,sF9)),
inference(superposition,[],[f324,f1686]) ).
fof(f1706,plain,
composition(sk1,sk2) = join(sF0,sF10),
inference(forward_demodulation,[],[f1695,f51]) ).
fof(f1709,plain,
sF0 = join(sF0,sF10),
inference(forward_demodulation,[],[f1706,f31]) ).
fof(f1716,plain,
! [X0] : join(sF0,X0) = join(sF0,join(sF10,X0)),
inference(superposition,[],[f2,f1709]) ).
fof(f1747,plain,
join(sF3,complement(sF1)) = join(sF3,complement(sF4)),
inference(superposition,[],[f1568,f39]) ).
fof(f1748,plain,
join(sF7,complement(sF6)) = join(sF7,complement(sF8)),
inference(superposition,[],[f1568,f47]) ).
fof(f1785,plain,
join(sF7,complement(sF6)) = join(sF7,sF9),
inference(forward_demodulation,[],[f1748,f49]) ).
fof(f1786,plain,
join(sF3,complement(sF1)) = join(sF3,sF5),
inference(forward_demodulation,[],[f1747,f41]) ).
fof(f1810,plain,
join(sF7,sk2) = join(sF7,sF9),
inference(forward_demodulation,[],[f1785,f564]) ).
fof(f1811,plain,
join(sF3,sF0) = join(sF3,sF5),
inference(forward_demodulation,[],[f1786,f566]) ).
fof(f1831,plain,
sk3 = join(sF9,complement(join(sF7,sF9))),
inference(backward_demodulation,[],[f870,f1810]) ).
fof(f1832,plain,
join(sF0,sF3) = join(sF3,sF5),
inference(forward_demodulation,[],[f1811,f1]) ).
fof(f1843,plain,
sk3 = join(sF9,complement(sF7)),
inference(forward_demodulation,[],[f1831,f1568]) ).
fof(f1849,plain,
sk3 = join(sF9,sk3),
inference(forward_demodulation,[],[f1843,f565]) ).
fof(f1872,plain,
composition(sk1,sk3) = join(sF2,composition(sk1,sF9)),
inference(superposition,[],[f325,f1849]) ).
fof(f1885,plain,
composition(sk1,sk3) = join(sF2,sF10),
inference(forward_demodulation,[],[f1872,f51]) ).
fof(f1889,plain,
sF2 = join(sF2,sF10),
inference(forward_demodulation,[],[f1885,f35]) ).
fof(f1897,plain,
! [X0] : join(sF2,X0) = join(sF2,join(sF10,X0)),
inference(superposition,[],[f2,f1889]) ).
fof(f2061,plain,
join(sF5,complement(join(sF0,sF3))) = join(sF5,complement(sF3)),
inference(superposition,[],[f1568,f1832]) ).
fof(f2062,plain,
join(sF5,complement(join(sF0,sF3))) = join(sF5,sF2),
inference(forward_demodulation,[],[f2061,f567]) ).
fof(f2069,plain,
join(sF5,complement(join(sF0,sF3))) = join(sF2,sF5),
inference(forward_demodulation,[],[f2062,f1]) ).
fof(f2074,plain,
sF2 = join(sF2,sF5),
inference(forward_demodulation,[],[f2069,f884]) ).
fof(f2546,plain,
complement(sF1) = join(complement(sF1),complement(sF4)),
inference(superposition,[],[f1524,f39]) ).
fof(f2591,plain,
complement(sF1) = join(complement(sF1),sF5),
inference(forward_demodulation,[],[f2546,f41]) ).
fof(f2614,plain,
complement(sF1) = join(sF5,complement(sF1)),
inference(forward_demodulation,[],[f2591,f1]) ).
fof(f2632,plain,
sF0 = join(sF5,sF0),
inference(forward_demodulation,[],[f2614,f566]) ).
fof(f2644,plain,
sF0 = join(sF0,sF5),
inference(forward_demodulation,[],[f2632,f1]) ).
fof(f3230,plain,
complement(sF5) = join(complement(sF5),complement(sF11)),
inference(superposition,[],[f1523,f53]) ).
fof(f3261,plain,
sF4 = join(sF4,complement(sF11)),
inference(forward_demodulation,[],[f3230,f568]) ).
fof(f6971,plain,
join(sF2,sF5) = join(sF2,sF11),
inference(superposition,[],[f1897,f53]) ).
fof(f7041,plain,
sF2 = join(sF2,sF11),
inference(forward_demodulation,[],[f6971,f2074]) ).
fof(f7080,plain,
complement(sF11) = join(complement(sF11),complement(sF2)),
inference(superposition,[],[f1523,f7041]) ).
fof(f7087,plain,
complement(sF11) = join(complement(sF2),complement(sF11)),
inference(forward_demodulation,[],[f7080,f1]) ).
fof(f7095,plain,
complement(sF11) = join(sF3,complement(sF11)),
inference(forward_demodulation,[],[f7087,f37]) ).
fof(f7100,plain,
join(sF4,complement(sF11)) = join(sF1,complement(sF11)),
inference(superposition,[],[f160,f7095]) ).
fof(f7130,plain,
sF4 = join(sF1,complement(sF11)),
inference(forward_demodulation,[],[f7100,f3261]) ).
fof(f7228,plain,
join(sF0,sF5) = join(sF0,sF11),
inference(superposition,[],[f1716,f53]) ).
fof(f7298,plain,
sF0 = join(sF0,sF11),
inference(forward_demodulation,[],[f7228,f2644]) ).
fof(f7335,plain,
complement(sF11) = join(complement(sF11),complement(sF0)),
inference(superposition,[],[f1523,f7298]) ).
fof(f7342,plain,
complement(sF11) = join(complement(sF0),complement(sF11)),
inference(forward_demodulation,[],[f7335,f1]) ).
fof(f7350,plain,
complement(sF11) = join(sF1,complement(sF11)),
inference(forward_demodulation,[],[f7342,f33]) ).
fof(f7354,plain,
sF4 = complement(sF11),
inference(forward_demodulation,[],[f7350,f7130]) ).
fof(f7388,plain,
complement(sF4) = sF11,
inference(superposition,[],[f529,f7354]) ).
fof(f7403,plain,
sF5 = sF11,
inference(forward_demodulation,[],[f7388,f41]) ).
fof(f7410,plain,
$false,
inference(forward_subsumption_resolution,[],[f7403,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL032-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:59:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 7.18/1.91 % (3084908)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.18/1.91 % (3084918)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=473093828:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.18/1.91 % (3084913)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=859536938:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.18/1.91 % (3084919)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2362192427:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.18/1.91 % (3084916)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=323997002:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.18/1.91 % (3084914)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=463518237:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.18/1.91 % (3084915)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3966279354:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.18/1.91 % (3084917)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=185170158:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.18/1.91 % (3084916)Instruction limit reached!
% 7.18/1.91 % (3084916)------------------------------
% 7.18/1.91 % (3084916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.18/1.91 % (3084916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.91 % (3084916)CaDiCaL version: 2.1.3
% 7.18/1.91 % (3084916)Termination reason: Instruction limit
% 7.18/1.91 % (3084916)Termination phase: Saturation
% 7.18/1.91 % (3084916)Time elapsed: 0.083 s
% 7.18/1.91 % (3084916)Peak memory usage: 89 MB
% 7.18/1.91 % (3084916)Instructions burned: 137 (million)
% 7.18/1.91 % (3084918)Instruction limit reached!
% 7.18/1.91 % (3084918)------------------------------
% 7.18/1.91 % (3084918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.18/1.91 % (3084918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.91 % (3084918)CaDiCaL version: 2.1.3
% 7.18/1.91 % (3084918)Termination reason: Instruction limit
% 7.18/1.91 % (3084918)Termination phase: Saturation
% 7.18/1.91 % (3084918)Time elapsed: 0.098 s
% 7.18/1.91 % (3084918)Peak memory usage: 91 MB
% 7.18/1.91 % (3084918)Instructions burned: 259 (million)
% 7.18/1.91 % (3084917)Instruction limit reached!
% 7.18/1.91 % (3084917)------------------------------
% 7.18/1.91 % (3084917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.18/1.91 % (3084917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.91 % (3084917)CaDiCaL version: 2.1.3
% 7.18/1.91 % (3084917)Termination reason: Instruction limit
% 7.18/1.91 % (3084917)Termination phase: Saturation
% 7.18/1.91 % (3084917)Time elapsed: 0.104 s
% 7.18/1.91 % (3084917)Peak memory usage: 89 MB
% 7.18/1.91 % (3084917)Instructions burned: 181 (million)
% 7.18/1.91 % (3084928)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3592920010:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 7.18/1.91 % (3084927)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2655627349:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 7.18/1.91 % (3084929)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=26269356:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 7.18/1.91 % (3084929)Instruction limit reached!
% 7.18/1.91 % (3084929)------------------------------
% 7.18/1.91 % (3084929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.18/1.91 % (3084929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.91 % (3084929)CaDiCaL version: 2.1.3
% 7.18/1.91 % (3084929)Termination reason: Instruction limit
% 7.18/1.91 % (3084929)Termination phase: Saturation
% 7.18/1.91 % (3084929)Time elapsed: 0.113 s
% 7.18/1.91 % (3084929)Peak memory usage: 89 MB
% 7.18/1.91 % (3084929)Instructions burned: 215 (million)
% 7.18/1.91 % (3084933)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=1181561090:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 7.18/1.91 % (3084919)Instruction limit reached!
% 7.18/1.91 % (3084919)------------------------------
% 7.18/1.91 % (3084919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.18/1.91 % (3084919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.91 % (3084919)CaDiCaL version: 2.1.3
% 7.18/1.91 % (3084919)Termination reason: Instruction limit
% 7.18/1.91 % (3084919)Termination phase: Saturation
% 7.18/1.91 % (3084919)Time elapsed: 0.666 s
% 7.18/1.91 % (3084919)Peak memory usage: 101 MB
% 7.18/1.91 % (3084919)Instructions burned: 1188 (million)
% 7.18/1.91 % (3084933)Instruction limit reached!
% 7.18/1.91 % (3084933)------------------------------
% 7.18/1.91 % (3084933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.18/1.91 % (3084933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.91 % (3084933)CaDiCaL version: 2.1.3
% 7.18/1.91 % (3084933)Termination reason: Instruction limit
% 7.18/1.91 % (3084933)Termination phase: Saturation
% 7.18/1.91 % (3084933)Time elapsed: 0.189 s
% 7.18/1.91 % (3084933)Peak memory usage: 92 MB
% 7.18/1.91 % (3084933)Instructions burned: 317 (million)
% 7.18/1.91 % (3084935)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=2657431231:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 7.18/1.91 % (3084936)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=651638557:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 7.18/1.91 % (3084915)First to succeed.
% 7.18/1.91 % (3084915)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3084908"
% 7.18/1.91 % (3084915)Refutation found. Thanks to Tanya!
% 7.18/1.91 % SZS status Unsatisfiable for theBenchmark
% 7.18/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 9.57/2.11 % (3084915)------------------------------
% 9.57/2.11 % (3084915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.57/2.11 % (3084915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.57/2.11 % (3084915)CaDiCaL version: 2.1.3
% 9.57/2.11 % (3084915)Termination reason: Refutation
% 9.57/2.11 % (3084915)Time elapsed: 0.973 s
% 9.57/2.11 % (3084915)Peak memory usage: 139 MB
% 9.57/2.11 % (3084915)Instructions burned: 2152 (million)
% 9.57/2.11 % (3084915)------------------------------
% 9.57/2.11 % (3084915)------------------------------
% 9.57/2.11 % (3084908)Success in time 1.303 s
% 9.57/2.11 % Vampire exiting
%------------------------------------------------------------------------------