%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL050-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Thu Sep 24 02:03:29 PM UTC 2026
% Result : Unsatisfiable 2.01s 1.37s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 18
% Syntax : Number of formulae : 218 ( 218 unt; 4 def)
% Number of atoms : 218 ( 217 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 214 ( 214 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : join(A,B) = join(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : composition(A,composition(B,C)) = composition(composition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : composition(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : converse(converse(A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : top = join(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : zero = meet(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f29,definition,
sF1_fnc = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f30,definition,
sF0_fnc = complement(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f31,definition,
sF3_fnc = complement(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f32,definition,
sF2_fnc = composition(sF3_fnc,top),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f33,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f28,f32,f31,f30,f29]) ).
fof(f34,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f15,f17]) ).
fof(f35,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f18,f34]) ).
fof(f36,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f15,f25]) ).
fof(f37,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f30,f31]) ).
fof(f38,plain,
sF2_fnc = composition(sF0_fnc,top),
inference(forward_demodulation,[status(thm)],[f37,f32]) ).
fof(f39,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f15,f35]) ).
fof(f40,plain,
top = join(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f30,f26]) ).
fof(f41,plain,
top = join(sF0_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f15,f40]) ).
fof(f44,plain,
! [X0] : composition(sk1,composition(top,X0)) = composition(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f29,f19]) ).
fof(f54,plain,
! [X0] : sF1_fnc = join(meet(sF1_fnc,X0),complement(join(sF0_fnc,X0))),
inference(paramodulation,[status(thm)],[f30,f39]) ).
fof(f73,plain,
! [X0] : composition(join(sF0_fnc,X0),top) = join(sF2_fnc,composition(X0,top)),
inference(paramodulation,[status(thm)],[f38,f21]) ).
fof(f78,plain,
! [X0] : composition(join(X0,sF0_fnc),top) = join(composition(X0,top),sF2_fnc),
inference(paramodulation,[status(thm)],[f38,f21]) ).
fof(f80,plain,
! [X0] : composition(join(X0,sk1),top) = join(composition(X0,top),sF1_fnc),
inference(paramodulation,[status(thm)],[f29,f21]) ).
fof(f87,plain,
! [X0] : composition(join(X0,sF0_fnc),top) = join(sF2_fnc,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f15,f78]) ).
fof(f92,plain,
! [X0] : composition(join(X0,sk1),top) = join(sF1_fnc,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f15,f80]) ).
fof(f100,plain,
composition(join(sF0_fnc,sF0_fnc),top) = join(sF2_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f38,f73]) ).
fof(f148,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f19]) ).
fof(f155,plain,
zero = meet(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f30,f27]) ).
fof(f192,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X1,X2),composition(X0,X2)),
inference(paramodulation,[status(thm)],[f21,f15]) ).
fof(f201,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(X1,complement(X0)))),
inference(paramodulation,[status(thm)],[f15,f39]) ).
fof(f209,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f214,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f22,f24]) ).
fof(f228,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f26,f18]) ).
fof(f229,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f15,f18]) ).
fof(f235,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f39]) ).
fof(f238,plain,
! [X0,X1,X2] : join(complement(X0),complement(X1)) = join(meet(join(complement(X0),complement(X1)),X2),complement(join(meet(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f18,f39]) ).
fof(f245,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f27,f228]) ).
fof(f247,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f15,f235]) ).
fof(f249,plain,
! [X0,X1,X2] : join(complement(X0),complement(X1)) = join(complement(join(meet(X0,X1),X2)),meet(join(complement(X0),complement(X1)),X2)),
inference(forward_demodulation,[status(thm)],[f15,f238]) ).
fof(f251,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f245,f18]) ).
fof(f252,plain,
! [X0] : meet(top,X0) = complement(join(zero,complement(X0))),
inference(paramodulation,[status(thm)],[f245,f18]) ).
fof(f255,plain,
top = join(top,zero),
inference(paramodulation,[status(thm)],[f245,f26]) ).
fof(f256,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f15,f251]) ).
fof(f257,plain,
top = join(zero,top),
inference(forward_demodulation,[status(thm)],[f15,f255]) ).
fof(f277,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f296,plain,
! [X0] : join(sF0_fnc,join(sF1_fnc,X0)) = join(top,X0),
inference(paramodulation,[status(thm)],[f41,f16]) ).
fof(f297,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f26,f16]) ).
fof(f309,plain,
! [X0] : join(sF0_fnc,composition(converse(X0),complement(composition(X0,sF1_fnc)))) = complement(sF1_fnc),
inference(paramodulation,[status(thm)],[f30,f36]) ).
fof(f323,plain,
! [X0] : join(sF0_fnc,composition(converse(X0),complement(composition(X0,sF1_fnc)))) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f30,f309]) ).
fof(f440,plain,
meet(top,top) = complement(join(zero,zero)),
inference(paramodulation,[status(thm)],[f245,f256]) ).
fof(f542,plain,
! [X0] : meet(top,X0) = meet(X0,top),
inference(paramodulation,[status(thm)],[f256,f252]) ).
fof(f551,plain,
! [X0,X1] : meet(top,join(complement(X0),complement(X1))) = complement(join(zero,meet(X0,X1))),
inference(paramodulation,[status(thm)],[f18,f252]) ).
fof(f593,plain,
! [X0] : top = join(meet(X0,top),meet(top,complement(X0))),
inference(paramodulation,[status(thm)],[f542,f247]) ).
fof(f598,plain,
! [X0] : X0 = join(meet(top,X0),complement(join(complement(X0),top))),
inference(paramodulation,[status(thm)],[f542,f39]) ).
fof(f603,plain,
! [X0] : X0 = join(meet(top,X0),complement(join(top,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f15,f598]) ).
fof(f636,plain,
! [X0] : join(sF0_fnc,composition(join(X0,sk1),top)) = join(top,composition(X0,top)),
inference(paramodulation,[status(thm)],[f92,f296]) ).
fof(f640,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = composition(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f192]) ).
fof(f752,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f20,f214]) ).
fof(f771,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f22,f752]) ).
fof(f783,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f148,f771]) ).
fof(f784,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f20,f771]) ).
fof(f785,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f771,f36]) ).
fof(f794,plain,
composition(join(converse(one),sF0_fnc),top) = join(sF2_fnc,top),
inference(paramodulation,[status(thm)],[f771,f87]) ).
fof(f797,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(composition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f771,f192]) ).
fof(f798,plain,
! [X0,X1] : composition(join(X0,converse(one)),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f771,f192]) ).
fof(f810,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f771,f783]) ).
fof(f812,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f810,f785]) ).
fof(f823,plain,
composition(join(sF0_fnc,converse(one)),top) = join(sF2_fnc,top),
inference(forward_demodulation,[status(thm)],[f640,f794]) ).
fof(f824,plain,
composition(join(sF0_fnc,one),top) = join(sF2_fnc,top),
inference(forward_demodulation,[status(thm)],[f784,f823]) ).
fof(f825,plain,
composition(join(one,sF0_fnc),top) = join(sF2_fnc,top),
inference(forward_demodulation,[status(thm)],[f640,f824]) ).
fof(f826,plain,
composition(join(one,sF0_fnc),top) = join(top,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f15,f825]) ).
fof(f833,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(composition(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f784,f797]) ).
fof(f834,plain,
! [X0] : join(sF0_fnc,composition(join(X0,sk1),top)) = composition(join(one,X0),top),
inference(backward_demodulation,[status(thm)],[f836,f636]) ).
fof(f836,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f15,f833]) ).
fof(f837,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f784,f798]) ).
fof(f910,plain,
join(zero,complement(top)) = complement(top),
inference(paramodulation,[status(thm)],[f245,f812]) ).
fof(f911,plain,
join(meet(top,top),complement(join(zero,zero))) = complement(join(zero,zero)),
inference(paramodulation,[status(thm)],[f440,f812]) ).
fof(f917,plain,
join(sF0_fnc,complement(sF1_fnc)) = complement(sF1_fnc),
inference(paramodulation,[status(thm)],[f30,f812]) ).
fof(f919,plain,
join(complement(join(zero,zero)),meet(top,top)) = complement(join(zero,zero)),
inference(paramodulation,[status(thm)],[f440,f812]) ).
fof(f927,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f812,f39]) ).
fof(f929,plain,
join(zero,zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f245,f910]) ).
fof(f936,plain,
join(zero,zero) = zero,
inference(forward_demodulation,[status(thm)],[f245,f929]) ).
fof(f937,plain,
join(meet(top,top),meet(top,top)) = complement(join(zero,zero)),
inference(forward_demodulation,[status(thm)],[f440,f911]) ).
fof(f938,plain,
join(meet(top,top),meet(top,top)) = meet(top,top),
inference(forward_demodulation,[status(thm)],[f440,f937]) ).
fof(f953,plain,
join(sF0_fnc,sF0_fnc) = complement(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f30,f917]) ).
fof(f960,plain,
composition(sF0_fnc,top) = join(sF2_fnc,sF2_fnc),
inference(backward_demodulation,[status(thm)],[f961,f100]) ).
fof(f961,plain,
join(sF0_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f30,f953]) ).
fof(f965,plain,
join(meet(top,top),complement(join(zero,zero))) = complement(join(zero,zero)),
inference(forward_demodulation,[status(thm)],[f15,f919]) ).
fof(f966,plain,
join(meet(top,top),meet(top,top)) = complement(join(zero,zero)),
inference(forward_demodulation,[status(thm)],[f440,f965]) ).
fof(f967,plain,
meet(top,top) = complement(join(zero,zero)),
inference(forward_demodulation,[status(thm)],[f938,f966]) ).
fof(f968,plain,
meet(top,top) = complement(zero),
inference(forward_demodulation,[status(thm)],[f936,f967]) ).
fof(f992,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f15,f927]) ).
fof(f993,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f27,f992]) ).
fof(f994,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f15,f993]) ).
fof(f1013,plain,
sF2_fnc = join(sF2_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f38,f960]) ).
fof(f1020,plain,
! [X0] : join(sF2_fnc,join(sF2_fnc,X0)) = join(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f1013,f16]) ).
fof(f1021,plain,
sF1_fnc = join(meet(sF1_fnc,sF0_fnc),complement(sF0_fnc)),
inference(paramodulation,[status(thm)],[f961,f54]) ).
fof(f1023,plain,
sF1_fnc = join(complement(sF0_fnc),meet(sF1_fnc,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f15,f1021]) ).
fof(f1024,plain,
sF1_fnc = join(complement(sF0_fnc),zero),
inference(forward_demodulation,[status(thm)],[f155,f1023]) ).
fof(f1025,plain,
sF1_fnc = join(zero,complement(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f15,f1024]) ).
fof(f1091,plain,
! [X0] : meet(top,complement(X0)) = complement(X0),
inference(paramodulation,[status(thm)],[f994,f252]) ).
fof(f1102,plain,
! [X0] : top = join(meet(X0,top),complement(X0)),
inference(backward_demodulation,[status(thm)],[f1091,f593]) ).
fof(f1106,plain,
! [X0] : top = join(complement(X0),meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f15,f1102]) ).
fof(f1112,plain,
! [X0,X1] : meet(top,meet(X0,X1)) = complement(join(complement(X0),complement(X1))),
inference(paramodulation,[status(thm)],[f18,f1091]) ).
fof(f1133,plain,
! [X0,X1] : meet(top,meet(X0,X1)) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f18,f1112]) ).
fof(f1154,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f201]) ).
fof(f1185,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f15,f1154]) ).
fof(f1371,plain,
join(sF2_fnc,top) = join(sF2_fnc,complement(sF2_fnc)),
inference(paramodulation,[status(thm)],[f26,f1020]) ).
fof(f1381,plain,
join(top,sF2_fnc) = join(sF2_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f15,f1371]) ).
fof(f1382,plain,
composition(join(one,sF0_fnc),top) = top,
inference(backward_demodulation,[status(thm)],[f1383,f826]) ).
fof(f1383,plain,
join(top,sF2_fnc) = top,
inference(forward_demodulation,[status(thm)],[f26,f1381]) ).
fof(f1484,plain,
! [X0] : composition(join(join(one,sF0_fnc),X0),top) = join(composition(X0,top),top),
inference(paramodulation,[status(thm)],[f1382,f192]) ).
fof(f1508,plain,
! [X0] : composition(join(one,join(sF0_fnc,X0)),top) = join(composition(X0,top),top),
inference(forward_demodulation,[status(thm)],[f16,f1484]) ).
fof(f1509,plain,
! [X0] : composition(join(one,join(sF0_fnc,X0)),top) = join(top,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f15,f1508]) ).
fof(f1510,plain,
! [X0] : composition(join(one,join(sF0_fnc,X0)),top) = composition(join(X0,one),top),
inference(forward_demodulation,[status(thm)],[f837,f1509]) ).
fof(f1540,plain,
! [X0] : X0 = join(meet(X0,meet(X0,top)),complement(top)),
inference(paramodulation,[status(thm)],[f1106,f39]) ).
fof(f1553,plain,
! [X0] : X0 = join(complement(top),meet(X0,meet(X0,top))),
inference(forward_demodulation,[status(thm)],[f15,f1540]) ).
fof(f1554,plain,
! [X0] : X0 = join(zero,meet(X0,meet(X0,top))),
inference(forward_demodulation,[status(thm)],[f245,f1553]) ).
fof(f1558,plain,
! [X0] : X0 = join(zero,meet(X0,meet(top,X0))),
inference(paramodulation,[status(thm)],[f542,f1554]) ).
fof(f1804,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(meet(X0,X1),top)),meet(top,join(complement(X0),complement(X1)))),
inference(paramodulation,[status(thm)],[f542,f249]) ).
fof(f1900,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(top,meet(X0,X1))),meet(top,join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f15,f1804]) ).
fof(f1901,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(top,meet(X0,X1))),complement(join(zero,meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f551,f1900]) ).
fof(f1902,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(zero,meet(X0,X1))),complement(join(top,meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f1901]) ).
fof(f2292,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f812,f297]) ).
fof(f2296,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f26,f297]) ).
fof(f2300,plain,
! [X0] : join(top,join(zero,X0)) = join(top,X0),
inference(paramodulation,[status(thm)],[f245,f297]) ).
fof(f2314,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))),
inference(paramodulation,[status(thm)],[f297,f39]) ).
fof(f2326,plain,
! [X0] : X0 = join(meet(top,X0),complement(top)),
inference(backward_demodulation,[status(thm)],[f2327,f603]) ).
fof(f2327,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f26,f2292]) ).
fof(f2336,plain,
! [X0] : join(X0,top) = top,
inference(forward_demodulation,[status(thm)],[f2327,f2296]) ).
fof(f2337,plain,
! [X0] : join(zero,join(X0,top)) = join(top,X0),
inference(forward_demodulation,[status(thm)],[f277,f2300]) ).
fof(f2338,plain,
! [X0] : join(zero,top) = join(top,X0),
inference(forward_demodulation,[status(thm)],[f2336,f2337]) ).
fof(f2344,plain,
! [X0] : join(sF0_fnc,join(sF1_fnc,X0)) = top,
inference(backward_demodulation,[status(thm)],[f2367,f296]) ).
fof(f2347,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(zero,meet(X0,X1))),complement(top)),
inference(backward_demodulation,[status(thm)],[f2367,f1902]) ).
fof(f2367,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[status(thm)],[f257,f2338]) ).
fof(f2397,plain,
! [X0,X1] : X0 = join(complement(join(top,X1)),meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f15,f2314]) ).
fof(f2398,plain,
! [X0,X1] : X0 = join(complement(top),meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f2367,f2397]) ).
fof(f2399,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f245,f2398]) ).
fof(f2414,plain,
! [X0] : X0 = join(complement(top),meet(top,X0)),
inference(forward_demodulation,[status(thm)],[f15,f2326]) ).
fof(f2417,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(forward_demodulation,[status(thm)],[f245,f2414]) ).
fof(f2422,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(top),complement(join(zero,meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f2347]) ).
fof(f2423,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(join(zero,meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f245,f2422]) ).
fof(f2502,plain,
meet(top,top) = top,
inference(paramodulation,[status(thm)],[f1558,f2417]) ).
fof(f2507,plain,
! [X0,X1] : meet(X0,X1) = join(zero,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f1133,f2417]) ).
fof(f2508,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(paramodulation,[status(thm)],[f1091,f2417]) ).
fof(f2521,plain,
top = complement(zero),
inference(backward_demodulation,[status(thm)],[f2502,f968]) ).
fof(f2523,plain,
! [X0] : X0 = meet(top,X0),
inference(backward_demodulation,[status(thm)],[f2507,f2417]) ).
fof(f2526,plain,
! [X0] : X0 = meet(X0,meet(top,X0)),
inference(backward_demodulation,[status(thm)],[f2507,f1558]) ).
fof(f2547,plain,
! [X0,X1] : X0 = meet(X0,join(complement(complement(X0)),X1)),
inference(backward_demodulation,[status(thm)],[f2507,f2399]) ).
fof(f2550,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))),
inference(backward_demodulation,[status(thm)],[f2507,f2423]) ).
fof(f2553,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f2508,f994]) ).
fof(f2554,plain,
sF1_fnc = complement(sF0_fnc),
inference(backward_demodulation,[status(thm)],[f2508,f1025]) ).
fof(f2647,plain,
! [X0] : X0 = meet(X0,X0),
inference(forward_demodulation,[status(thm)],[f2523,f2526]) ).
fof(f2723,plain,
! [X0,X1] : meet(X0,X1) = complement(complement(meet(X1,X0))),
inference(backward_demodulation,[status(thm)],[f2724,f229]) ).
fof(f2724,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f2508,f2550]) ).
fof(f2727,plain,
! [X0,X1] : X0 = meet(X0,join(X0,X1)),
inference(backward_demodulation,[status(thm)],[f2553,f2547]) ).
fof(f2900,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f2553,f2723]) ).
fof(f2917,plain,
! [X0] : X0 = join(X0,meet(X0,complement(X0))),
inference(paramodulation,[status(thm)],[f2647,f1185]) ).
fof(f2949,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f27,f2917]) ).
fof(f3024,plain,
! [X0] : X0 = join(zero,X0),
inference(paramodulation,[status(thm)],[f15,f2949]) ).
fof(f3029,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(zero)),
inference(paramodulation,[status(thm)],[f2949,f209]) ).
fof(f3047,plain,
! [X0] : X0 = join(X0,converse(zero)),
inference(forward_demodulation,[status(thm)],[f22,f3029]) ).
fof(f3714,plain,
! [X0] : join(sF0_fnc,composition(join(X0,sk1),top)) = top,
inference(paramodulation,[status(thm)],[f92,f2344]) ).
fof(f3733,plain,
! [X0] : top = composition(join(one,X0),top),
inference(backward_demodulation,[status(thm)],[f3714,f834]) ).
fof(f3745,plain,
! [X0] : top = composition(join(X0,one),top),
inference(backward_demodulation,[status(thm)],[f3733,f1510]) ).
fof(f3750,plain,
top = composition(top,top),
inference(paramodulation,[status(thm)],[f2367,f3745]) ).
fof(f3890,plain,
composition(sk1,top) = composition(sF1_fnc,top),
inference(paramodulation,[status(thm)],[f3750,f44]) ).
fof(f3908,plain,
sF1_fnc = composition(sF1_fnc,top),
inference(forward_demodulation,[status(thm)],[f29,f3890]) ).
fof(f3950,plain,
composition(join(sF1_fnc,sF0_fnc),top) = join(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f3908,f87]) ).
fof(f3959,plain,
join(complement(top),composition(converse(sF1_fnc),complement(sF1_fnc))) = complement(top),
inference(paramodulation,[status(thm)],[f3908,f36]) ).
fof(f3967,plain,
composition(join(sF0_fnc,sF1_fnc),top) = join(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f640,f3950]) ).
fof(f3968,plain,
composition(top,top) = join(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f41,f3967]) ).
fof(f3969,plain,
top = join(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3750,f3968]) ).
fof(f3971,plain,
top = join(sF1_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f15,f3969]) ).
fof(f3985,plain,
join(zero,composition(converse(sF1_fnc),complement(sF1_fnc))) = complement(top),
inference(forward_demodulation,[status(thm)],[f245,f3959]) ).
fof(f3986,plain,
composition(converse(sF1_fnc),complement(sF1_fnc)) = complement(top),
inference(forward_demodulation,[status(thm)],[f3024,f3985]) ).
fof(f3987,plain,
composition(converse(sF1_fnc),sF0_fnc) = complement(top),
inference(forward_demodulation,[status(thm)],[f30,f3986]) ).
fof(f3988,plain,
composition(converse(sF1_fnc),sF0_fnc) = zero,
inference(forward_demodulation,[status(thm)],[f245,f3987]) ).
fof(f4049,plain,
zero = converse(zero),
inference(paramodulation,[status(thm)],[f3024,f3047]) ).
fof(f4143,plain,
converse(zero) = composition(converse(sF0_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f3988,f214]) ).
fof(f4157,plain,
zero = composition(converse(sF0_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f4049,f4143]) ).
fof(f4212,plain,
join(sF0_fnc,composition(converse(converse(sF0_fnc)),complement(zero))) = sF0_fnc,
inference(paramodulation,[status(thm)],[f4157,f323]) ).
fof(f4227,plain,
join(sF0_fnc,composition(sF0_fnc,complement(zero))) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f22,f4212]) ).
fof(f4228,plain,
join(sF0_fnc,composition(sF0_fnc,top)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f2521,f4227]) ).
fof(f4229,plain,
join(sF0_fnc,sF2_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f38,f4228]) ).
fof(f4588,plain,
! [X0,X1] : X0 = meet(X0,join(X1,X0)),
inference(paramodulation,[status(thm)],[f15,f2727]) ).
fof(f4654,plain,
sF2_fnc = meet(sF2_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f4229,f4588]) ).
fof(f4688,plain,
sF2_fnc = meet(sF0_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f2900,f4654]) ).
fof(f4707,plain,
sF0_fnc = join(sF2_fnc,complement(join(sF2_fnc,complement(sF0_fnc)))),
inference(paramodulation,[status(thm)],[f4688,f201]) ).
fof(f4723,plain,
sF0_fnc = join(sF2_fnc,complement(join(sF2_fnc,sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f2554,f4707]) ).
fof(f4724,plain,
sF0_fnc = join(sF2_fnc,complement(join(sF1_fnc,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f15,f4723]) ).
fof(f4725,plain,
sF0_fnc = join(sF2_fnc,complement(top)),
inference(forward_demodulation,[status(thm)],[f3971,f4724]) ).
fof(f4726,plain,
sF0_fnc = join(sF2_fnc,zero),
inference(forward_demodulation,[status(thm)],[f245,f4725]) ).
fof(f4727,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f2949,f4726]) ).
fof(f4728,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4727,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL050-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n003.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Mon Sep 21 04:10:30 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.44 % Drodi V4.1.1
% 2.01/1.37 % Refutation found
% 2.01/1.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.01/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.54/1.43 % Elapsed time: 0.983052 seconds
% 0.54/1.43 % CPU time: 7.104576 seconds
% 0.54/1.43 % Total memory used: 83.689 MB
% 0.54/1.43 % Net memory used: 80.763 MB
%------------------------------------------------------------------------------