%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL024-2 : 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 : n005.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 12:33:50 PM UTC 2026
% Result : Unsatisfiable 4.57s 1.68s
% Output : Refutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 25
% Syntax : Number of formulae : 144 ( 144 unt; 12 def)
% Number of atoms : 144 ( 143 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 : 163 ( 163 !; 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(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
composition(meet(sk1,converse(sk2)),sk3) != join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),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,
composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3) != join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3)),
inference(definition_unfolding,[],[f24,f6,f6,f6,f6]) ).
fof(f30,definition,
sF0 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f31,plain,
complement(sk1) = sF0,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF1 = converse(sk2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f33,plain,
converse(sk2) = sF1,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF2 = complement(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f35,plain,
complement(sF1) = sF2,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF3 = join(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f37,plain,
join(sF0,sF2) = sF3,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f39,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF5 = composition(sF4,sk3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f41,plain,
composition(sF4,sk3) = 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(sF4,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f51,plain,
composition(sF4,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,f39,f37,f35,f33,f31,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(f113,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f56,f15]) ).
fof(f114,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f113,f55]) ).
fof(f127,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f56,f1]) ).
fof(f157,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f160,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(f167,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f160,f12]) ).
fof(f172,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f167,f11]) ).
fof(f176,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f172,f11]) ).
fof(f178,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f176,f12]) ).
fof(f184,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(f197,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f221,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f184,f15]) ).
fof(f237,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f221,f197]) ).
fof(f249,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f237,f55]) ).
fof(f279,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[],[f56,f55]) ).
fof(f281,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f279,f1]) ).
fof(f283,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(complement(X0),top))) = X0,
inference(forward_demodulation,[],[f281,f1]) ).
fof(f285,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f283,f1]) ).
fof(f287,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f285,f1]) ).
fof(f332,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f127,f15]) ).
fof(f335,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(superposition,[],[f184,f127]) ).
fof(f344,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(forward_demodulation,[],[f335,f1]) ).
fof(f345,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f332,f1]) ).
fof(f369,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f345,f1]) ).
fof(f382,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f369,f55]) ).
fof(f389,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f114,f382]) ).
fof(f399,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(X1,complement(X0)))),
inference(backward_demodulation,[],[f344,f389]) ).
fof(f400,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f382,f389]) ).
fof(f414,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f400]) ).
fof(f416,plain,
top = complement(zero),
inference(superposition,[],[f389,f55]) ).
fof(f418,plain,
sk2 = complement(sF6),
inference(superposition,[],[f389,f43]) ).
fof(f419,plain,
sk3 = complement(sF7),
inference(superposition,[],[f389,f45]) ).
fof(f424,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f56,f389]) ).
fof(f428,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f127,f389]) ).
fof(f456,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f424,f1]) ).
fof(f546,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,[],[f424,f428]) ).
fof(f549,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,[],[f546,f389]) ).
fof(f565,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,[],[f549,f197]) ).
fof(f578,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,[],[f565,f1]) ).
fof(f590,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f578,f389]) ).
fof(f600,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f590,f389]) ).
fof(f619,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(join(X0,X0)),complement(zero)))),
inference(superposition,[],[f456,f400]) ).
fof(f621,plain,
complement(sF7) = join(complement(sF8),complement(join(sF7,complement(sF6)))),
inference(superposition,[],[f456,f47]) ).
fof(f639,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,[],[f428,f456]) ).
fof(f648,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,[],[f639,f1]) ).
fof(f655,plain,
complement(sF7) = join(complement(sF8),complement(join(sF7,sk2))),
inference(forward_demodulation,[],[f621,f418]) ).
fof(f657,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f619,f1]) ).
fof(f666,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,[],[f648,f1]) ).
fof(f672,plain,
complement(sF7) = join(sF9,complement(join(sF7,sk2))),
inference(forward_demodulation,[],[f655,f49]) ).
fof(f674,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f657,f416]) ).
fof(f682,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,[],[f666,f2]) ).
fof(f687,plain,
sk3 = join(sF9,complement(join(sF7,sk2))),
inference(forward_demodulation,[],[f672,f419]) ).
fof(f689,plain,
! [X0] : complement(complement(join(X0,X0))) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f674,f389]) ).
fof(f696,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f682,f389]) ).
fof(f701,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f689,f389]) ).
fof(f708,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f696,f389]) ).
fof(f804,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f157,f8]) ).
fof(f818,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f804,f10]) ).
fof(f829,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f59,f818]) ).
fof(f838,plain,
one = converse(one),
inference(superposition,[],[f8,f818]) ).
fof(f839,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f818,f838]) ).
fof(f847,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f829,f839]) ).
fof(f852,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f249,f847]) ).
fof(f854,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f852,f389]) ).
fof(f858,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f414,f854]) ).
fof(f859,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(complement(X0),top))),
inference(backward_demodulation,[],[f701,f858]) ).
fof(f860,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f400,f858]) ).
fof(f862,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f860,f1]) ).
fof(f863,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(X0)))),
inference(forward_demodulation,[],[f859,f399]) ).
fof(f866,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(complement(X0))) = X0,
inference(backward_demodulation,[],[f287,f862]) ).
fof(f871,plain,
! [X0] : join(complement(complement(X0)),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f866,f1]) ).
fof(f873,plain,
! [X0] : join(X0,complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f871,f389]) ).
fof(f875,plain,
! [X0] : join(X0,X0) = X0,
inference(backward_demodulation,[],[f863,f873]) ).
fof(f944,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f875]) ).
fof(f946,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f197,f875]) ).
fof(f1087,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f944,f456]) ).
fof(f1122,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1087,f1]) ).
fof(f1136,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f600,f1122]) ).
fof(f1143,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f708,f1136]) ).
fof(f1147,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1143,f946]) ).
fof(f1165,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1147,f1]) ).
fof(f1370,plain,
join(sF7,complement(sF6)) = join(sF7,complement(sF8)),
inference(superposition,[],[f1165,f47]) ).
fof(f1403,plain,
join(sF7,complement(sF6)) = join(sF7,sF9),
inference(forward_demodulation,[],[f1370,f49]) ).
fof(f1429,plain,
join(sF7,sk2) = join(sF7,sF9),
inference(forward_demodulation,[],[f1403,f418]) ).
fof(f1450,plain,
sk3 = join(sF9,complement(join(sF7,sF9))),
inference(backward_demodulation,[],[f687,f1429]) ).
fof(f1462,plain,
sk3 = join(sF9,complement(sF7)),
inference(forward_demodulation,[],[f1450,f1165]) ).
fof(f1468,plain,
sk3 = join(sF9,sk3),
inference(forward_demodulation,[],[f1462,f419]) ).
fof(f1689,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f178]) ).
fof(f1704,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f1689,f10]) ).
fof(f1745,plain,
! [X0] : composition(sF4,join(X0,sk3)) = join(composition(sF4,X0),sF5),
inference(superposition,[],[f1704,f41]) ).
fof(f1772,plain,
! [X0] : join(sF5,composition(sF4,X0)) = composition(sF4,join(X0,sk3)),
inference(forward_demodulation,[],[f1745,f1]) ).
fof(f3126,plain,
composition(sF4,sk3) = join(sF5,composition(sF4,sF9)),
inference(superposition,[],[f1772,f1468]) ).
fof(f3145,plain,
composition(sF4,sk3) = join(sF5,sF10),
inference(forward_demodulation,[],[f3126,f51]) ).
fof(f3153,plain,
composition(sF4,sk3) = join(sF10,sF5),
inference(forward_demodulation,[],[f3145,f1]) ).
fof(f3156,plain,
composition(sF4,sk3) = sF11,
inference(forward_demodulation,[],[f3153,f53]) ).
fof(f3158,plain,
sF5 = sF11,
inference(forward_demodulation,[],[f3156,f41]) ).
fof(f3159,plain,
$false,
inference(forward_subsumption_resolution,[],[f3158,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL024-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 22:52:17 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 4.57/1.68 % (265711)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.57/1.68 % (265718)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4098656608:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.57/1.68 % (265720)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1749705857:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.57/1.68 % (265719)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2904645551:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.57/1.68 % (265717)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=2269951182:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.57/1.68 % (265716)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=230121555:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.57/1.68 % (265722)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=575743802:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.57/1.68 % (265721)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3333498044:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.57/1.68 % (265719)Instruction limit reached!
% 4.57/1.68 % (265719)------------------------------
% 4.57/1.68 % (265719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.68 % (265719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.68 % (265719)CaDiCaL version: 2.1.3
% 4.57/1.68 % (265719)Termination reason: Instruction limit
% 4.57/1.68 % (265719)Termination phase: Saturation
% 4.57/1.68 % (265719)Time elapsed: 0.084 s
% 4.57/1.68 % (265719)Peak memory usage: 89 MB
% 4.57/1.68 % (265719)Instructions burned: 137 (million)
% 4.57/1.68 % (265720)Instruction limit reached!
% 4.57/1.68 % (265720)------------------------------
% 4.57/1.68 % (265720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.68 % (265720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.68 % (265720)CaDiCaL version: 2.1.3
% 4.57/1.68 % (265720)Termination reason: Instruction limit
% 4.57/1.68 % (265720)Termination phase: Saturation
% 4.57/1.68 % (265720)Time elapsed: 0.108 s
% 4.57/1.68 % (265720)Peak memory usage: 89 MB
% 4.57/1.68 % (265720)Instructions burned: 181 (million)
% 4.57/1.68 % (265721)Instruction limit reached!
% 4.57/1.68 % (265721)------------------------------
% 4.57/1.68 % (265721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.68 % (265721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.68 % (265721)CaDiCaL version: 2.1.3
% 4.57/1.68 % (265721)Termination reason: Instruction limit
% 4.57/1.68 % (265721)Termination phase: Saturation
% 4.57/1.68 % (265721)Time elapsed: 0.169 s
% 4.57/1.68 % (265721)Peak memory usage: 91 MB
% 4.57/1.68 % (265721)Instructions burned: 259 (million)
% 4.57/1.68 % (265730)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=625331403:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.57/1.68 % (265731)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2604983395:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.57/1.68 % (265732)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3802017820:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 4.57/1.68 % (265732)Instruction limit reached!
% 4.57/1.68 % (265732)------------------------------
% 4.57/1.68 % (265732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.57/1.68 % (265732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.57/1.68 % (265732)CaDiCaL version: 2.1.3
% 4.57/1.68 % (265732)Termination reason: Instruction limit
% 4.57/1.68 % (265732)Termination phase: Saturation
% 4.57/1.68 % (265732)Time elapsed: 0.107 s
% 4.57/1.68 % (265732)Peak memory usage: 90 MB
% 4.57/1.68 % (265732)Instructions burned: 216 (million)
% 4.57/1.68 % (265718)First to succeed.
% 4.57/1.68 % (265718)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-265711"
% 4.57/1.68 % (265736)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=1788124227: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)
% 4.57/1.68 % (265718)Refutation found. Thanks to Tanya!
% 4.57/1.68 % SZS status Unsatisfiable for theBenchmark
% 4.57/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 6.36/1.77 % (265718)------------------------------
% 6.36/1.77 % (265718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/1.77 % (265718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.77 % (265718)CaDiCaL version: 2.1.3
% 6.36/1.77 % (265718)Termination reason: Refutation
% 6.36/1.77 % (265718)Time elapsed: 0.554 s
% 6.36/1.77 % (265718)Peak memory usage: 134 MB
% 6.36/1.77 % (265718)Instructions burned: 1503 (million)
% 6.36/1.77 % (265718)------------------------------
% 6.36/1.77 % (265718)------------------------------
% 6.36/1.77 % (265711)Success in time 0.829 s
% 6.36/1.77 % Vampire exiting
%------------------------------------------------------------------------------