%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 : Theorem 3.41s 0.86s
% Output : CNFRefutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 18
% Syntax : Number of formulae : 221 ( 221 unt; 4 def)
% Number of atoms : 221 ( 220 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 217 ( 216 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X0] : complement(composition(X0,top)) = composition(complement(composition(X0,top)),top),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0] : complement(composition(X0,top)) = composition(complement(composition(X0,top)),top),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
? [X0] : complement(composition(X0,top)) != composition(complement(composition(X0,top)),top),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,plain,
complement(composition(sK0_skl,top)) != composition(complement(composition(sK0_skl,top)),top),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f29]) ).
fof(f31,plain,
complement(composition(sK0_skl,top)) != composition(complement(composition(sK0_skl,top)),top),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,definition,
sF1_fnc = composition(sK0_skl,top),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f33,definition,
sF0_fnc = complement(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f34,definition,
sF3_fnc = complement(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f35,definition,
sF2_fnc = composition(sF3_fnc,top),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f36,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f31,f35,f34,f33,f32]) ).
fof(f37,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f16,f18]) ).
fof(f38,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f19,f37]) ).
fof(f39,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f16,f26]) ).
fof(f40,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f33,f34]) ).
fof(f41,plain,
sF2_fnc = composition(sF0_fnc,top),
inference(forward_demodulation,[status(thm)],[f40,f35]) ).
fof(f42,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f16,f38]) ).
fof(f43,plain,
top = join(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f33,f27]) ).
fof(f44,plain,
top = join(sF0_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f16,f43]) ).
fof(f47,plain,
! [X0] : composition(sK0_skl,composition(top,X0)) = composition(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f32,f20]) ).
fof(f57,plain,
! [X0] : sF1_fnc = join(meet(sF1_fnc,X0),complement(join(sF0_fnc,X0))),
inference(paramodulation,[status(thm)],[f33,f42]) ).
fof(f76,plain,
! [X0] : composition(join(sF0_fnc,X0),top) = join(sF2_fnc,composition(X0,top)),
inference(paramodulation,[status(thm)],[f41,f22]) ).
fof(f81,plain,
! [X0] : composition(join(X0,sF0_fnc),top) = join(composition(X0,top),sF2_fnc),
inference(paramodulation,[status(thm)],[f41,f22]) ).
fof(f83,plain,
! [X0] : composition(join(X0,sK0_skl),top) = join(composition(X0,top),sF1_fnc),
inference(paramodulation,[status(thm)],[f32,f22]) ).
fof(f90,plain,
! [X0] : composition(join(X0,sF0_fnc),top) = join(sF2_fnc,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f16,f81]) ).
fof(f95,plain,
! [X0] : composition(join(X0,sK0_skl),top) = join(sF1_fnc,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f16,f83]) ).
fof(f103,plain,
composition(join(sF0_fnc,sF0_fnc),top) = join(sF2_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f41,f76]) ).
fof(f151,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f20]) ).
fof(f158,plain,
zero = meet(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f33,f28]) ).
fof(f195,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X1,X2),composition(X0,X2)),
inference(paramodulation,[status(thm)],[f22,f16]) ).
fof(f204,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(X1,complement(X0)))),
inference(paramodulation,[status(thm)],[f16,f42]) ).
fof(f212,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f217,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f231,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f27,f19]) ).
fof(f232,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f238,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f42]) ).
fof(f241,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)],[f19,f42]) ).
fof(f248,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f28,f231]) ).
fof(f250,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f16,f238]) ).
fof(f252,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)],[f16,f241]) ).
fof(f254,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f248,f19]) ).
fof(f255,plain,
! [X0] : meet(top,X0) = complement(join(zero,complement(X0))),
inference(paramodulation,[status(thm)],[f248,f19]) ).
fof(f258,plain,
top = join(top,zero),
inference(paramodulation,[status(thm)],[f248,f27]) ).
fof(f259,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f16,f254]) ).
fof(f260,plain,
top = join(zero,top),
inference(forward_demodulation,[status(thm)],[f16,f258]) ).
fof(f280,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f299,plain,
! [X0] : join(sF0_fnc,join(sF1_fnc,X0)) = join(top,X0),
inference(paramodulation,[status(thm)],[f44,f17]) ).
fof(f300,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f27,f17]) ).
fof(f312,plain,
! [X0] : join(sF0_fnc,composition(converse(X0),complement(composition(X0,sF1_fnc)))) = complement(sF1_fnc),
inference(paramodulation,[status(thm)],[f33,f39]) ).
fof(f326,plain,
! [X0] : join(sF0_fnc,composition(converse(X0),complement(composition(X0,sF1_fnc)))) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f33,f312]) ).
fof(f443,plain,
meet(top,top) = complement(join(zero,zero)),
inference(paramodulation,[status(thm)],[f248,f259]) ).
fof(f545,plain,
! [X0] : meet(top,X0) = meet(X0,top),
inference(paramodulation,[status(thm)],[f259,f255]) ).
fof(f554,plain,
! [X0,X1] : meet(top,join(complement(X0),complement(X1))) = complement(join(zero,meet(X0,X1))),
inference(paramodulation,[status(thm)],[f19,f255]) ).
fof(f596,plain,
! [X0] : top = join(meet(X0,top),meet(top,complement(X0))),
inference(paramodulation,[status(thm)],[f545,f250]) ).
fof(f601,plain,
! [X0] : X0 = join(meet(top,X0),complement(join(complement(X0),top))),
inference(paramodulation,[status(thm)],[f545,f42]) ).
fof(f606,plain,
! [X0] : X0 = join(meet(top,X0),complement(join(top,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f16,f601]) ).
fof(f639,plain,
! [X0] : join(sF0_fnc,composition(join(X0,sK0_skl),top)) = join(top,composition(X0,top)),
inference(paramodulation,[status(thm)],[f95,f299]) ).
fof(f643,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = composition(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f22,f195]) ).
fof(f755,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f217]) ).
fof(f774,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f755]) ).
fof(f786,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f151,f774]) ).
fof(f787,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f21,f774]) ).
fof(f788,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f774,f39]) ).
fof(f797,plain,
composition(join(converse(one),sF0_fnc),top) = join(sF2_fnc,top),
inference(paramodulation,[status(thm)],[f774,f90]) ).
fof(f800,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(composition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f774,f195]) ).
fof(f801,plain,
! [X0,X1] : composition(join(X0,converse(one)),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f774,f195]) ).
fof(f813,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f774,f786]) ).
fof(f815,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f813,f788]) ).
fof(f825,plain,
composition(join(sF0_fnc,converse(one)),top) = join(sF2_fnc,top),
inference(forward_demodulation,[status(thm)],[f643,f797]) ).
fof(f826,plain,
composition(join(sF0_fnc,one),top) = join(sF2_fnc,top),
inference(forward_demodulation,[status(thm)],[f787,f825]) ).
fof(f827,plain,
composition(join(one,sF0_fnc),top) = join(sF2_fnc,top),
inference(forward_demodulation,[status(thm)],[f643,f826]) ).
fof(f828,plain,
composition(join(one,sF0_fnc),top) = join(top,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f16,f827]) ).
fof(f834,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(composition(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f787,f800]) ).
fof(f835,plain,
! [X0] : join(sF0_fnc,composition(join(X0,sK0_skl),top)) = composition(join(one,X0),top),
inference(backward_demodulation,[status(thm)],[f837,f639]) ).
fof(f837,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f16,f834]) ).
fof(f838,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f787,f801]) ).
fof(f911,plain,
join(zero,complement(top)) = complement(top),
inference(paramodulation,[status(thm)],[f248,f815]) ).
fof(f912,plain,
join(meet(top,top),complement(join(zero,zero))) = complement(join(zero,zero)),
inference(paramodulation,[status(thm)],[f443,f815]) ).
fof(f918,plain,
join(sF0_fnc,complement(sF1_fnc)) = complement(sF1_fnc),
inference(paramodulation,[status(thm)],[f33,f815]) ).
fof(f920,plain,
join(complement(join(zero,zero)),meet(top,top)) = complement(join(zero,zero)),
inference(paramodulation,[status(thm)],[f443,f815]) ).
fof(f928,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f815,f42]) ).
fof(f930,plain,
join(zero,zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f248,f911]) ).
fof(f937,plain,
join(zero,zero) = zero,
inference(forward_demodulation,[status(thm)],[f248,f930]) ).
fof(f938,plain,
join(meet(top,top),meet(top,top)) = complement(join(zero,zero)),
inference(forward_demodulation,[status(thm)],[f443,f912]) ).
fof(f939,plain,
join(meet(top,top),meet(top,top)) = meet(top,top),
inference(forward_demodulation,[status(thm)],[f443,f938]) ).
fof(f954,plain,
join(sF0_fnc,sF0_fnc) = complement(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f33,f918]) ).
fof(f961,plain,
composition(sF0_fnc,top) = join(sF2_fnc,sF2_fnc),
inference(backward_demodulation,[status(thm)],[f962,f103]) ).
fof(f962,plain,
join(sF0_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f33,f954]) ).
fof(f966,plain,
join(meet(top,top),complement(join(zero,zero))) = complement(join(zero,zero)),
inference(forward_demodulation,[status(thm)],[f16,f920]) ).
fof(f967,plain,
join(meet(top,top),meet(top,top)) = complement(join(zero,zero)),
inference(forward_demodulation,[status(thm)],[f443,f966]) ).
fof(f968,plain,
meet(top,top) = complement(join(zero,zero)),
inference(forward_demodulation,[status(thm)],[f939,f967]) ).
fof(f969,plain,
meet(top,top) = complement(zero),
inference(forward_demodulation,[status(thm)],[f937,f968]) ).
fof(f993,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f16,f928]) ).
fof(f994,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f28,f993]) ).
fof(f995,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f16,f994]) ).
fof(f1014,plain,
sF2_fnc = join(sF2_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f41,f961]) ).
fof(f1021,plain,
! [X0] : join(sF2_fnc,join(sF2_fnc,X0)) = join(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f1014,f17]) ).
fof(f1022,plain,
sF1_fnc = join(meet(sF1_fnc,sF0_fnc),complement(sF0_fnc)),
inference(paramodulation,[status(thm)],[f962,f57]) ).
fof(f1024,plain,
sF1_fnc = join(complement(sF0_fnc),meet(sF1_fnc,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f16,f1022]) ).
fof(f1025,plain,
sF1_fnc = join(complement(sF0_fnc),zero),
inference(forward_demodulation,[status(thm)],[f158,f1024]) ).
fof(f1026,plain,
sF1_fnc = join(zero,complement(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f16,f1025]) ).
fof(f1092,plain,
! [X0] : meet(top,complement(X0)) = complement(X0),
inference(paramodulation,[status(thm)],[f995,f255]) ).
fof(f1103,plain,
! [X0] : top = join(meet(X0,top),complement(X0)),
inference(backward_demodulation,[status(thm)],[f1092,f596]) ).
fof(f1107,plain,
! [X0] : top = join(complement(X0),meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f16,f1103]) ).
fof(f1113,plain,
! [X0,X1] : meet(top,meet(X0,X1)) = complement(join(complement(X0),complement(X1))),
inference(paramodulation,[status(thm)],[f19,f1092]) ).
fof(f1134,plain,
! [X0,X1] : meet(top,meet(X0,X1)) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f19,f1113]) ).
fof(f1155,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f204]) ).
fof(f1186,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f16,f1155]) ).
fof(f1372,plain,
join(sF2_fnc,top) = join(sF2_fnc,complement(sF2_fnc)),
inference(paramodulation,[status(thm)],[f27,f1021]) ).
fof(f1382,plain,
join(top,sF2_fnc) = join(sF2_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f16,f1372]) ).
fof(f1383,plain,
composition(join(one,sF0_fnc),top) = top,
inference(backward_demodulation,[status(thm)],[f1384,f828]) ).
fof(f1384,plain,
join(top,sF2_fnc) = top,
inference(forward_demodulation,[status(thm)],[f27,f1382]) ).
fof(f1485,plain,
! [X0] : composition(join(join(one,sF0_fnc),X0),top) = join(composition(X0,top),top),
inference(paramodulation,[status(thm)],[f1383,f195]) ).
fof(f1505,plain,
! [X0] : composition(join(one,join(sF0_fnc,X0)),top) = join(composition(X0,top),top),
inference(forward_demodulation,[status(thm)],[f17,f1485]) ).
fof(f1506,plain,
! [X0] : composition(join(one,join(sF0_fnc,X0)),top) = join(top,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f16,f1505]) ).
fof(f1507,plain,
! [X0] : composition(join(one,join(sF0_fnc,X0)),top) = composition(join(X0,one),top),
inference(forward_demodulation,[status(thm)],[f838,f1506]) ).
fof(f1538,plain,
! [X0] : X0 = join(meet(X0,meet(X0,top)),complement(top)),
inference(paramodulation,[status(thm)],[f1107,f42]) ).
fof(f1551,plain,
! [X0] : X0 = join(complement(top),meet(X0,meet(X0,top))),
inference(forward_demodulation,[status(thm)],[f16,f1538]) ).
fof(f1552,plain,
! [X0] : X0 = join(zero,meet(X0,meet(X0,top))),
inference(forward_demodulation,[status(thm)],[f248,f1551]) ).
fof(f1556,plain,
! [X0] : X0 = join(zero,meet(X0,meet(top,X0))),
inference(paramodulation,[status(thm)],[f545,f1552]) ).
fof(f1802,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)],[f545,f252]) ).
fof(f1898,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)],[f16,f1802]) ).
fof(f1899,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)],[f554,f1898]) ).
fof(f1900,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)],[f16,f1899]) ).
fof(f2290,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f815,f300]) ).
fof(f2294,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f27,f300]) ).
fof(f2298,plain,
! [X0] : join(top,join(zero,X0)) = join(top,X0),
inference(paramodulation,[status(thm)],[f248,f300]) ).
fof(f2312,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))),
inference(paramodulation,[status(thm)],[f300,f42]) ).
fof(f2324,plain,
! [X0] : X0 = join(meet(top,X0),complement(top)),
inference(backward_demodulation,[status(thm)],[f2325,f606]) ).
fof(f2325,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f27,f2290]) ).
fof(f2334,plain,
! [X0] : join(X0,top) = top,
inference(forward_demodulation,[status(thm)],[f2325,f2294]) ).
fof(f2335,plain,
! [X0] : join(zero,join(X0,top)) = join(top,X0),
inference(forward_demodulation,[status(thm)],[f280,f2298]) ).
fof(f2336,plain,
! [X0] : join(zero,top) = join(top,X0),
inference(forward_demodulation,[status(thm)],[f2334,f2335]) ).
fof(f2342,plain,
! [X0] : join(sF0_fnc,join(sF1_fnc,X0)) = top,
inference(backward_demodulation,[status(thm)],[f2364,f299]) ).
fof(f2345,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(zero,meet(X0,X1))),complement(top)),
inference(backward_demodulation,[status(thm)],[f2364,f1900]) ).
fof(f2364,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[status(thm)],[f260,f2336]) ).
fof(f2394,plain,
! [X0,X1] : X0 = join(complement(join(top,X1)),meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f16,f2312]) ).
fof(f2395,plain,
! [X0,X1] : X0 = join(complement(top),meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f2364,f2394]) ).
fof(f2396,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f248,f2395]) ).
fof(f2411,plain,
! [X0] : X0 = join(complement(top),meet(top,X0)),
inference(forward_demodulation,[status(thm)],[f16,f2324]) ).
fof(f2414,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(forward_demodulation,[status(thm)],[f248,f2411]) ).
fof(f2419,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(top),complement(join(zero,meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f16,f2345]) ).
fof(f2420,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(join(zero,meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f248,f2419]) ).
fof(f2499,plain,
meet(top,top) = top,
inference(paramodulation,[status(thm)],[f1556,f2414]) ).
fof(f2504,plain,
! [X0,X1] : meet(X0,X1) = join(zero,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f1134,f2414]) ).
fof(f2505,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(paramodulation,[status(thm)],[f1092,f2414]) ).
fof(f2518,plain,
top = complement(zero),
inference(backward_demodulation,[status(thm)],[f2499,f969]) ).
fof(f2520,plain,
! [X0] : X0 = meet(top,X0),
inference(backward_demodulation,[status(thm)],[f2504,f2414]) ).
fof(f2523,plain,
! [X0] : X0 = meet(X0,meet(top,X0)),
inference(backward_demodulation,[status(thm)],[f2504,f1556]) ).
fof(f2544,plain,
! [X0,X1] : X0 = meet(X0,join(complement(complement(X0)),X1)),
inference(backward_demodulation,[status(thm)],[f2504,f2396]) ).
fof(f2547,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))),
inference(backward_demodulation,[status(thm)],[f2504,f2420]) ).
fof(f2550,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f2505,f995]) ).
fof(f2551,plain,
sF1_fnc = complement(sF0_fnc),
inference(backward_demodulation,[status(thm)],[f2505,f1026]) ).
fof(f2644,plain,
! [X0] : X0 = meet(X0,X0),
inference(forward_demodulation,[status(thm)],[f2520,f2523]) ).
fof(f2720,plain,
! [X0,X1] : meet(X0,X1) = complement(complement(meet(X1,X0))),
inference(backward_demodulation,[status(thm)],[f2721,f232]) ).
fof(f2721,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f2505,f2547]) ).
fof(f2724,plain,
! [X0,X1] : X0 = meet(X0,join(X0,X1)),
inference(backward_demodulation,[status(thm)],[f2550,f2544]) ).
fof(f2897,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f2550,f2720]) ).
fof(f2914,plain,
! [X0] : X0 = join(X0,meet(X0,complement(X0))),
inference(paramodulation,[status(thm)],[f2644,f1186]) ).
fof(f2946,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f28,f2914]) ).
fof(f3021,plain,
! [X0] : X0 = join(zero,X0),
inference(paramodulation,[status(thm)],[f16,f2946]) ).
fof(f3026,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(zero)),
inference(paramodulation,[status(thm)],[f2946,f212]) ).
fof(f3044,plain,
! [X0] : X0 = join(X0,converse(zero)),
inference(forward_demodulation,[status(thm)],[f23,f3026]) ).
fof(f3711,plain,
! [X0] : join(sF0_fnc,composition(join(X0,sK0_skl),top)) = top,
inference(paramodulation,[status(thm)],[f95,f2342]) ).
fof(f3730,plain,
! [X0] : top = composition(join(one,X0),top),
inference(backward_demodulation,[status(thm)],[f3711,f835]) ).
fof(f3742,plain,
! [X0] : top = composition(join(X0,one),top),
inference(backward_demodulation,[status(thm)],[f3730,f1507]) ).
fof(f3746,plain,
top = composition(top,top),
inference(paramodulation,[status(thm)],[f2364,f3742]) ).
fof(f3886,plain,
composition(sK0_skl,top) = composition(sF1_fnc,top),
inference(paramodulation,[status(thm)],[f3746,f47]) ).
fof(f3904,plain,
sF1_fnc = composition(sF1_fnc,top),
inference(forward_demodulation,[status(thm)],[f32,f3886]) ).
fof(f3946,plain,
composition(join(sF1_fnc,sF0_fnc),top) = join(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f3904,f90]) ).
fof(f3955,plain,
join(complement(top),composition(converse(sF1_fnc),complement(sF1_fnc))) = complement(top),
inference(paramodulation,[status(thm)],[f3904,f39]) ).
fof(f3963,plain,
composition(join(sF0_fnc,sF1_fnc),top) = join(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f643,f3946]) ).
fof(f3964,plain,
composition(top,top) = join(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f44,f3963]) ).
fof(f3965,plain,
top = join(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3746,f3964]) ).
fof(f3967,plain,
top = join(sF1_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f16,f3965]) ).
fof(f3981,plain,
join(zero,composition(converse(sF1_fnc),complement(sF1_fnc))) = complement(top),
inference(forward_demodulation,[status(thm)],[f248,f3955]) ).
fof(f3982,plain,
composition(converse(sF1_fnc),complement(sF1_fnc)) = complement(top),
inference(forward_demodulation,[status(thm)],[f3021,f3981]) ).
fof(f3983,plain,
composition(converse(sF1_fnc),sF0_fnc) = complement(top),
inference(forward_demodulation,[status(thm)],[f33,f3982]) ).
fof(f3984,plain,
composition(converse(sF1_fnc),sF0_fnc) = zero,
inference(forward_demodulation,[status(thm)],[f248,f3983]) ).
fof(f4045,plain,
zero = converse(zero),
inference(paramodulation,[status(thm)],[f3021,f3044]) ).
fof(f4139,plain,
converse(zero) = composition(converse(sF0_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f3984,f217]) ).
fof(f4153,plain,
zero = composition(converse(sF0_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f4045,f4139]) ).
fof(f4208,plain,
join(sF0_fnc,composition(converse(converse(sF0_fnc)),complement(zero))) = sF0_fnc,
inference(paramodulation,[status(thm)],[f4153,f326]) ).
fof(f4223,plain,
join(sF0_fnc,composition(sF0_fnc,complement(zero))) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f23,f4208]) ).
fof(f4224,plain,
join(sF0_fnc,composition(sF0_fnc,top)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f2518,f4223]) ).
fof(f4225,plain,
join(sF0_fnc,sF2_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f41,f4224]) ).
fof(f4584,plain,
! [X0,X1] : X0 = meet(X0,join(X1,X0)),
inference(paramodulation,[status(thm)],[f16,f2724]) ).
fof(f4650,plain,
sF2_fnc = meet(sF2_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f4225,f4584]) ).
fof(f4684,plain,
sF2_fnc = meet(sF0_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f2897,f4650]) ).
fof(f4703,plain,
sF0_fnc = join(sF2_fnc,complement(join(sF2_fnc,complement(sF0_fnc)))),
inference(paramodulation,[status(thm)],[f4684,f204]) ).
fof(f4719,plain,
sF0_fnc = join(sF2_fnc,complement(join(sF2_fnc,sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f2551,f4703]) ).
fof(f4720,plain,
sF0_fnc = join(sF2_fnc,complement(join(sF1_fnc,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f16,f4719]) ).
fof(f4721,plain,
sF0_fnc = join(sF2_fnc,complement(top)),
inference(forward_demodulation,[status(thm)],[f3967,f4720]) ).
fof(f4722,plain,
sF0_fnc = join(sF2_fnc,zero),
inference(forward_demodulation,[status(thm)],[f248,f4721]) ).
fof(f4723,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f2946,f4722]) ).
fof(f4724,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4723,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:06:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 3.41/0.86 % Refutation found
% 3.41/0.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.41/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.41/0.88 % Elapsed time: 0.497397 seconds
% 3.41/0.88 % CPU time: 3.741641 seconds
% 3.41/0.88 % Total memory used: 74.085 MB
% 3.41/0.88 % Net memory used: 72.086 MB
%------------------------------------------------------------------------------