%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL035-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:03:24 PM UTC 2026
% Result : Unsatisfiable 151.27s 19.57s
% Output : CNFRefutation 138.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 21
% Syntax : Number of formulae : 282 ( 282 unt; 5 def)
% Number of atoms : 282 ( 281 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 340 ( 340 !; 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,axiom,
! [A,B,C] : join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
composition(meet(sk2,converse(sk1)),meet(sk1,sk3)) != composition(sk2,meet(sk1,sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
composition(sk1,top) = sk1,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
composition(meet(sk2,converse(sk1)),meet(sk1,sk3)) != composition(sk2,meet(sk1,sk3)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f37,definition,
sF2_fnc = converse(sk1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f38,definition,
sF1_fnc = meet(sk2,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f39,definition,
sF3_fnc = meet(sk1,sk3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f40,definition,
sF0_fnc = composition(sF1_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f41,definition,
sF4_fnc = composition(sk2,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f42,plain,
sF0_fnc != sF4_fnc,
inference(definition_folding,[],[f36,f41,f40,f39,f38,f37]) ).
fof(f43,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f44,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f43]) ).
fof(f45,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f46,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f44]) ).
fof(f54,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f57,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f63,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f57]) ).
fof(f65,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f67,plain,
! [X0,X1,X2] : meet(join(complement(X0),complement(X1)),X2) = complement(join(meet(X0,X1),complement(X2))),
inference(paramodulation,[status(thm)],[f22,f22]) ).
fof(f69,plain,
! [X0,X1] : zero = meet(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f31]) ).
fof(f70,plain,
sF3_fnc = meet(sk3,sk1),
inference(backward_demodulation,[status(thm)],[f73,f39]) ).
fof(f73,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f65]) ).
fof(f75,plain,
! [X0,X1] : zero = complement(join(meet(X0,X1),complement(meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f67,f69]) ).
fof(f76,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f30,f75]) ).
fof(f79,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f76,f22]) ).
fof(f82,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f79]) ).
fof(f85,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(paramodulation,[status(thm)],[f20,f30]) ).
fof(f86,plain,
top = join(top,zero),
inference(paramodulation,[status(thm)],[f76,f30]) ).
fof(f87,plain,
! [X0,X1] : top = join(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f30]) ).
fof(f90,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f91,plain,
top = join(zero,top),
inference(forward_demodulation,[status(thm)],[f19,f86]) ).
fof(f92,plain,
! [X0,X1] : top = join(complement(X0),join(complement(X1),meet(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f87]) ).
fof(f94,plain,
! [X0] : join(zero,join(top,X0)) = join(top,X0),
inference(paramodulation,[status(thm)],[f91,f20]) ).
fof(f101,plain,
! [X0] : composition(sk2,composition(sF3_fnc,X0)) = composition(sF4_fnc,X0),
inference(paramodulation,[status(thm)],[f41,f23]) ).
fof(f102,plain,
! [X0] : composition(sF1_fnc,composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f40,f23]) ).
fof(f104,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f119,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f121,plain,
! [X0] : converse(composition(sk1,X0)) = composition(converse(X0),sF2_fnc),
inference(paramodulation,[status(thm)],[f37,f28]) ).
fof(f122,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f138,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f141,plain,
! [X0] : converse(join(sk1,X0)) = join(sF2_fnc,converse(X0)),
inference(paramodulation,[status(thm)],[f37,f27]) ).
fof(f142,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f149,plain,
! [X0,X1] : converse(join(X0,X1)) = converse(join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f27,f138]) ).
fof(f200,plain,
! [X0] : join(zero,join(X0,top)) = join(top,X0),
inference(paramodulation,[status(thm)],[f19,f94]) ).
fof(f206,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X1,X2),composition(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f25]) ).
fof(f212,plain,
! [X0] : composition(join(sk1,X0),top) = join(sk1,composition(X0,top)),
inference(paramodulation,[status(thm)],[f35,f25]) ).
fof(f216,plain,
! [X0,X1,X2,X3] : composition(join(X0,composition(X1,X2)),X3) = join(composition(X0,X3),composition(X1,composition(X2,X3))),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f219,plain,
! [X0] : composition(join(X0,sk1),top) = join(composition(X0,top),sk1),
inference(paramodulation,[status(thm)],[f35,f25]) ).
fof(f227,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = composition(join(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f25,f206]) ).
fof(f234,plain,
! [X0] : composition(join(X0,sk1),top) = join(sk1,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f19,f219]) ).
fof(f244,plain,
! [X0,X1] : composition(join(X0,sk2),composition(sF3_fnc,X1)) = join(composition(X0,composition(sF3_fnc,X1)),composition(sF4_fnc,X1)),
inference(paramodulation,[status(thm)],[f101,f25]) ).
fof(f249,plain,
! [X0,X1] : composition(join(X0,sk2),composition(sF3_fnc,X1)) = join(composition(sF4_fnc,X1),composition(X0,composition(sF3_fnc,X1))),
inference(forward_demodulation,[status(thm)],[f19,f244]) ).
fof(f250,plain,
! [X0,X1] : composition(join(X0,sk2),composition(sF3_fnc,X1)) = composition(join(sF4_fnc,composition(X0,sF3_fnc)),X1),
inference(forward_demodulation,[status(thm)],[f216,f249]) ).
fof(f257,plain,
! [X0,X1] : composition(join(X0,sF1_fnc),composition(sF3_fnc,X1)) = join(composition(X0,composition(sF3_fnc,X1)),composition(sF0_fnc,X1)),
inference(paramodulation,[status(thm)],[f102,f25]) ).
fof(f262,plain,
! [X0,X1] : composition(join(X0,sF1_fnc),composition(sF3_fnc,X1)) = join(composition(sF0_fnc,X1),composition(X0,composition(sF3_fnc,X1))),
inference(forward_demodulation,[status(thm)],[f19,f257]) ).
fof(f263,plain,
! [X0,X1] : composition(join(X0,sF1_fnc),composition(sF3_fnc,X1)) = composition(join(sF0_fnc,composition(X0,sF3_fnc)),X1),
inference(forward_demodulation,[status(thm)],[f216,f262]) ).
fof(f313,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f30,f90]) ).
fof(f328,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(paramodulation,[status(thm)],[f76,f45]) ).
fof(f347,plain,
! [X0] : join(complement(one),composition(converse(X0),complement(X0))) = complement(one),
inference(paramodulation,[status(thm)],[f24,f45]) ).
fof(f350,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f76,f328]) ).
fof(f495,plain,
! [X0,X1,X2] : join(meet(composition(X0,converse(X1)),X2),composition(meet(X0,composition(X2,X1)),meet(converse(X1),composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(converse(X1)))),meet(converse(X1),composition(converse(X0),X2))),
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f508,plain,
! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(converse(converse(X0)),X2))),
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f549,plain,
! [X0,X1,X2] : join(meet(composition(X0,converse(X1)),X2),composition(meet(X0,composition(X2,X1)),meet(converse(X1),composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,X1)),meet(converse(X1),composition(converse(X0),X2))),
inference(forward_demodulation,[status(thm)],[f26,f495]) ).
fof(f572,plain,
! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f26,f508]) ).
fof(f578,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f122]) ).
fof(f607,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f578]) ).
fof(f634,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f104,f607]) ).
fof(f635,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f607]) ).
fof(f638,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f607,f45]) ).
fof(f649,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f607,f25]) ).
fof(f659,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f607,f634]) ).
fof(f664,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f659,f638]) ).
fof(f688,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f635,f649]) ).
fof(f723,plain,
converse(join(sk1,one)) = join(sF2_fnc,one),
inference(paramodulation,[status(thm)],[f635,f141]) ).
fof(f746,plain,
converse(join(one,sk1)) = join(sF2_fnc,one),
inference(forward_demodulation,[status(thm)],[f149,f723]) ).
fof(f747,plain,
converse(join(one,sk1)) = join(one,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f19,f746]) ).
fof(f768,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),complement(X1)))) = complement(join(complement(X0),complement(X1))),
inference(paramodulation,[status(thm)],[f22,f664]) ).
fof(f773,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f664,f22]) ).
fof(f774,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f664,f90]) ).
fof(f787,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = complement(join(complement(X0),complement(X1))),
inference(forward_demodulation,[status(thm)],[f22,f768]) ).
fof(f789,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f787]) ).
fof(f804,plain,
! [X0] : join(X0,top) = top,
inference(backward_demodulation,[status(thm)],[f805,f313]) ).
fof(f805,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f30,f774]) ).
fof(f824,plain,
! [X0] : join(zero,top) = join(top,X0),
inference(backward_demodulation,[status(thm)],[f804,f200]) ).
fof(f834,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[status(thm)],[f91,f824]) ).
fof(f858,plain,
! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(paramodulation,[status(thm)],[f31,f46]) ).
fof(f861,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f46]) ).
fof(f864,plain,
! [X0] : X0 = join(meet(X0,top),complement(top)),
inference(paramodulation,[status(thm)],[f804,f46]) ).
fof(f876,plain,
! [X0] : X0 = join(zero,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f22,f858]) ).
fof(f877,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f773,f876]) ).
fof(f878,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f861]) ).
fof(f883,plain,
! [X0] : X0 = join(complement(top),meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f19,f864]) ).
fof(f885,plain,
! [X0] : X0 = join(zero,meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f76,f883]) ).
fof(f928,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))),
inference(paramodulation,[status(thm)],[f22,f877]) ).
fof(f929,plain,
! [X0] : meet(complement(X0),top) = complement(X0),
inference(paramodulation,[status(thm)],[f877,f82]) ).
fof(f932,plain,
! [X0] : meet(top,complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f73,f929]) ).
fof(f948,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(paramodulation,[status(thm)],[f73,f885]) ).
fof(f973,plain,
! [X0,X1] : join(X0,top) = join(complement(X1),join(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f54]) ).
fof(f1038,plain,
! [X0,X1] : top = join(complement(X0),join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f804,f973]) ).
fof(f1039,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f54,f1038]) ).
fof(f1071,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(paramodulation,[status(thm)],[f932,f948]) ).
fof(f1080,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1071,f877]) ).
fof(f1081,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1071,f82]) ).
fof(f1082,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1071,f928]) ).
fof(f1099,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1102,f885]) ).
fof(f1102,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f1080,f1081]) ).
fof(f1127,plain,
! [X0] : X0 = meet(top,X0),
inference(backward_demodulation,[status(thm)],[f1099,f948]) ).
fof(f1131,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(backward_demodulation,[status(thm)],[f1099,f350]) ).
fof(f1170,plain,
! [X0] : X0 = join(X0,complement(join(complement(X0),top))),
inference(paramodulation,[status(thm)],[f1102,f46]) ).
fof(f1173,plain,
! [X0] : X0 = join(X0,complement(top)),
inference(forward_demodulation,[status(thm)],[f804,f1170]) ).
fof(f1174,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f76,f1173]) ).
fof(f1213,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X2,X1)),
inference(paramodulation,[status(thm)],[f54,f63]) ).
fof(f1232,plain,
! [X0,X1] : join(X0,top) = join(X1,join(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f30,f63]) ).
fof(f1296,plain,
! [X0,X1] : top = join(X0,join(X1,complement(X0))),
inference(forward_demodulation,[status(thm)],[f804,f1232]) ).
fof(f1519,plain,
! [X0,X1] : X0 = join(meet(X0,join(X1,complement(complement(X0)))),complement(top)),
inference(paramodulation,[status(thm)],[f1296,f46]) ).
fof(f1540,plain,
! [X0,X1] : X0 = join(complement(top),meet(X0,join(X1,complement(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f19,f1519]) ).
fof(f1541,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(X1,complement(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f76,f1540]) ).
fof(f1542,plain,
! [X0,X1] : X0 = meet(X0,join(X1,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f1099,f1541]) ).
fof(f1543,plain,
! [X0,X1] : X0 = meet(X0,join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1080,f1542]) ).
fof(f1571,plain,
! [X0,X1] : converse(X0) = meet(converse(X0),converse(join(X1,X0))),
inference(paramodulation,[status(thm)],[f27,f1543]) ).
fof(f1582,plain,
! [X0,X1] : X0 = meet(X0,join(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f1543]) ).
fof(f1631,plain,
! [X0,X1] : meet(X0,X1) = meet(meet(X0,X1),X0),
inference(paramodulation,[status(thm)],[f46,f1582]) ).
fof(f1633,plain,
! [X0] : sF2_fnc = meet(sF2_fnc,converse(join(sk1,X0))),
inference(paramodulation,[status(thm)],[f141,f1582]) ).
fof(f1656,plain,
! [X0,X1] : meet(X0,X1) = meet(X0,meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f73,f1631]) ).
fof(f1665,plain,
meet(sk2,sF2_fnc) = meet(sk2,sF1_fnc),
inference(paramodulation,[status(thm)],[f38,f1656]) ).
fof(f1673,plain,
! [X0,X1] : meet(X0,X1) = meet(X0,meet(X1,X0)),
inference(paramodulation,[status(thm)],[f73,f1656]) ).
fof(f1681,plain,
sF1_fnc = meet(sk2,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f38,f1665]) ).
fof(f1713,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(X1),meet(X0,X1))),complement(top)),
inference(paramodulation,[status(thm)],[f92,f46]) ).
fof(f1761,plain,
! [X0,X1] : X0 = join(complement(top),meet(X0,join(complement(X1),meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f19,f1713]) ).
fof(f1762,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(complement(X1),meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f76,f1761]) ).
fof(f1763,plain,
! [X0,X1] : X0 = meet(X0,join(complement(X1),meet(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1099,f1762]) ).
fof(f1789,plain,
meet(sk1,sk3) = meet(sk1,sF3_fnc),
inference(paramodulation,[status(thm)],[f70,f1673]) ).
fof(f1813,plain,
meet(sk3,sk1) = meet(sk1,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f73,f1789]) ).
fof(f1814,plain,
sF3_fnc = meet(sk1,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f70,f1813]) ).
fof(f1851,plain,
sF2_fnc = meet(sF2_fnc,converse(top)),
inference(paramodulation,[status(thm)],[f85,f1633]) ).
fof(f1876,plain,
sF2_fnc = join(sF2_fnc,complement(join(complement(sF2_fnc),converse(top)))),
inference(paramodulation,[status(thm)],[f1851,f46]) ).
fof(f2154,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(zero)),
inference(paramodulation,[status(thm)],[f1174,f142]) ).
fof(f2161,plain,
! [X0] : converse(top) = join(X0,converse(top)),
inference(paramodulation,[status(thm)],[f804,f142]) ).
fof(f2199,plain,
! [X0] : X0 = join(X0,converse(zero)),
inference(forward_demodulation,[status(thm)],[f26,f2154]) ).
fof(f2201,plain,
sF2_fnc = join(sF2_fnc,complement(converse(top))),
inference(backward_demodulation,[status(thm)],[f2161,f1876]) ).
fof(f2233,plain,
zero = converse(zero),
inference(paramodulation,[status(thm)],[f1099,f2199]) ).
fof(f2337,plain,
top = join(converse(top),sF2_fnc),
inference(paramodulation,[status(thm)],[f2201,f1296]) ).
fof(f2349,plain,
top = join(sF2_fnc,converse(top)),
inference(forward_demodulation,[status(thm)],[f19,f2337]) ).
fof(f2350,plain,
top = converse(join(sk1,top)),
inference(forward_demodulation,[status(thm)],[f141,f2349]) ).
fof(f2351,plain,
top = converse(join(top,sk1)),
inference(forward_demodulation,[status(thm)],[f149,f2350]) ).
fof(f2362,plain,
top = converse(top),
inference(forward_demodulation,[status(thm)],[f834,f2351]) ).
fof(f2408,plain,
! [X0] : converse(composition(X0,top)) = composition(top,converse(X0)),
inference(paramodulation,[status(thm)],[f2362,f119]) ).
fof(f2409,plain,
converse(composition(sk1,top)) = composition(top,sF2_fnc),
inference(paramodulation,[status(thm)],[f2362,f121]) ).
fof(f2436,plain,
converse(sk1) = composition(top,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f35,f2409]) ).
fof(f2437,plain,
sF2_fnc = composition(top,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f37,f2436]) ).
fof(f2452,plain,
! [X0] : composition(top,composition(sF2_fnc,X0)) = composition(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f2437,f23]) ).
fof(f3527,plain,
! [X0,X1] : X0 = meet(X0,join(X1,meet(X0,complement(X1)))),
inference(paramodulation,[status(thm)],[f1080,f1763]) ).
fof(f3540,plain,
sk2 = meet(sk2,join(complement(sF2_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f38,f1763]) ).
fof(f3576,plain,
sk2 = meet(sk2,join(sF1_fnc,complement(sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f19,f3540]) ).
fof(f3756,plain,
! [X0,X1] : X0 = meet(X0,join(X1,meet(complement(X1),X0))),
inference(paramodulation,[status(thm)],[f73,f3527]) ).
fof(f3980,plain,
! [X0,X1] : top = join(X0,complement(meet(X0,X1))),
inference(paramodulation,[status(thm)],[f1082,f1039]) ).
fof(f4084,plain,
! [X0,X1] : top = complement(meet(X0,meet(complement(X0),X1))),
inference(paramodulation,[status(thm)],[f1082,f3980]) ).
fof(f4262,plain,
! [X0,X1] : meet(X0,meet(complement(X0),X1)) = complement(top),
inference(paramodulation,[status(thm)],[f4084,f1080]) ).
fof(f4305,plain,
! [X0,X1] : meet(X0,meet(complement(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f76,f4262]) ).
fof(f4380,plain,
! [X0,X1] : meet(X0,meet(X1,complement(X0))) = zero,
inference(paramodulation,[status(thm)],[f73,f4305]) ).
fof(f4423,plain,
! [X0,X1] : meet(complement(X0),meet(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f1080,f4380]) ).
fof(f4702,plain,
! [X0,X1] : meet(complement(join(X0,X1)),X1) = zero,
inference(paramodulation,[status(thm)],[f1543,f4423]) ).
fof(f4745,plain,
! [X0,X1] : meet(X0,complement(join(X1,X0))) = zero,
inference(forward_demodulation,[status(thm)],[f73,f4702]) ).
fof(f6521,plain,
composition(join(one,sF2_fnc),complement(composition(join(one,sk1),top))) = zero,
inference(paramodulation,[status(thm)],[f747,f1131]) ).
fof(f6574,plain,
composition(join(one,sF2_fnc),complement(join(sk1,composition(one,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f234,f6521]) ).
fof(f6575,plain,
composition(join(one,sF2_fnc),complement(join(sk1,top))) = zero,
inference(forward_demodulation,[status(thm)],[f659,f6574]) ).
fof(f6576,plain,
composition(join(one,sF2_fnc),complement(top)) = zero,
inference(forward_demodulation,[status(thm)],[f804,f6575]) ).
fof(f6577,plain,
composition(join(one,sF2_fnc),zero) = zero,
inference(forward_demodulation,[status(thm)],[f76,f6576]) ).
fof(f6578,plain,
join(zero,composition(sF2_fnc,zero)) = zero,
inference(forward_demodulation,[status(thm)],[f688,f6577]) ).
fof(f6581,plain,
composition(sF2_fnc,zero) = zero,
inference(forward_demodulation,[status(thm)],[f1099,f6578]) ).
fof(f7131,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f73,f878]) ).
fof(f7143,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f73,f878]) ).
fof(f8236,plain,
! [X0] : join(X0,meet(top,X0)) = meet(top,X0),
inference(paramodulation,[status(thm)],[f1127,f789]) ).
fof(f8332,plain,
! [X0] : join(X0,X0) = meet(top,X0),
inference(forward_demodulation,[status(thm)],[f1127,f8236]) ).
fof(f8348,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1127,f8332]) ).
fof(f8612,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f8348,f63]) ).
fof(f8702,plain,
! [X0,X1] : join(meet(X0,complement(X1)),X0) = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f7131,f8612]) ).
fof(f8832,plain,
! [X0,X1] : join(X0,meet(X0,complement(X1))) = join(meet(X1,X0),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f8702]) ).
fof(f8833,plain,
! [X0,X1] : join(X0,meet(X0,complement(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f7131,f8832]) ).
fof(f8977,plain,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
inference(paramodulation,[status(thm)],[f1080,f8833]) ).
fof(f9052,plain,
join(sk1,sF3_fnc) = sk1,
inference(paramodulation,[status(thm)],[f1814,f8977]) ).
fof(f9057,plain,
join(sk2,sF1_fnc) = sk2,
inference(paramodulation,[status(thm)],[f1681,f8977]) ).
fof(f9077,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f73,f8977]) ).
fof(f9153,plain,
composition(sk1,top) = join(sk1,composition(sF3_fnc,top)),
inference(paramodulation,[status(thm)],[f9052,f212]) ).
fof(f9168,plain,
sk1 = join(sk1,composition(sF3_fnc,top)),
inference(forward_demodulation,[status(thm)],[f35,f9153]) ).
fof(f9403,plain,
! [X0] : join(sk2,join(sF1_fnc,X0)) = join(X0,sk2),
inference(paramodulation,[status(thm)],[f9057,f54]) ).
fof(f10197,plain,
! [X0,X1] : join(join(X0,meet(complement(X0),X1)),X1) = join(X0,meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f3756,f9077]) ).
fof(f10309,plain,
! [X0,X1] : join(X0,join(meet(complement(X0),X1),X1)) = join(X0,meet(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f20,f10197]) ).
fof(f10310,plain,
! [X0,X1] : join(X0,join(X1,meet(complement(X0),X1))) = join(X0,meet(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1213,f10309]) ).
fof(f10335,plain,
! [X0,X1] : join(X0,X1) = join(X0,meet(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f9077,f10310]) ).
fof(f10554,plain,
meet(composition(sF3_fnc,top),complement(sk1)) = zero,
inference(paramodulation,[status(thm)],[f9168,f4745]) ).
fof(f10570,plain,
meet(complement(sk1),composition(sF3_fnc,top)) = zero,
inference(forward_demodulation,[status(thm)],[f73,f10554]) ).
fof(f11120,plain,
! [X0] : meet(composition(converse(X0),complement(X0)),complement(complement(one))) = zero,
inference(paramodulation,[status(thm)],[f347,f4745]) ).
fof(f11150,plain,
! [X0] : meet(complement(complement(one)),composition(converse(X0),complement(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f73,f11120]) ).
fof(f11151,plain,
! [X0] : meet(one,composition(converse(X0),complement(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f1080,f11150]) ).
fof(f21349,plain,
composition(top,zero) = composition(sF2_fnc,zero),
inference(paramodulation,[status(thm)],[f6581,f2452]) ).
fof(f21397,plain,
composition(top,zero) = zero,
inference(forward_demodulation,[status(thm)],[f6581,f21349]) ).
fof(f21621,plain,
! [X0] : composition(join(X0,top),zero) = join(composition(X0,zero),zero),
inference(paramodulation,[status(thm)],[f21397,f25]) ).
fof(f21822,plain,
! [X0] : composition(top,zero) = join(composition(X0,zero),zero),
inference(forward_demodulation,[status(thm)],[f804,f21621]) ).
fof(f21823,plain,
! [X0] : zero = join(composition(X0,zero),zero),
inference(forward_demodulation,[status(thm)],[f21397,f21822]) ).
fof(f21882,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[status(thm)],[f1174,f21823]) ).
fof(f22770,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(paramodulation,[status(thm)],[f21882,f122]) ).
fof(f22840,plain,
! [X0] : zero = composition(converse(zero),X0),
inference(forward_demodulation,[status(thm)],[f2233,f22770]) ).
fof(f22894,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[status(thm)],[f2233,f22840]) ).
fof(f26693,plain,
join(join(sF1_fnc,complement(sF2_fnc)),sk2) = join(sF1_fnc,complement(sF2_fnc)),
inference(paramodulation,[status(thm)],[f3576,f9077]) ).
fof(f26713,plain,
join(sF1_fnc,join(complement(sF2_fnc),sk2)) = join(sF1_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f20,f26693]) ).
fof(f26714,plain,
join(sk2,join(sF1_fnc,complement(sF2_fnc))) = join(sF1_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f54,f26713]) ).
fof(f26715,plain,
join(complement(sF2_fnc),sk2) = join(sF1_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f9403,f26714]) ).
fof(f26717,plain,
join(sk2,complement(sF2_fnc)) = join(sF1_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f19,f26715]) ).
fof(f52987,plain,
join(meet(composition(converse(sF3_fnc),complement(sk1)),top),composition(meet(converse(sF3_fnc),composition(top,converse(complement(sk1)))),zero)) = composition(meet(converse(sF3_fnc),composition(top,converse(complement(sk1)))),meet(complement(sk1),composition(sF3_fnc,top))),
inference(paramodulation,[status(thm)],[f10570,f572]) ).
fof(f53032,plain,
join(composition(converse(sF3_fnc),complement(sk1)),composition(meet(converse(sF3_fnc),composition(top,converse(complement(sk1)))),zero)) = composition(meet(converse(sF3_fnc),composition(top,converse(complement(sk1)))),meet(complement(sk1),composition(sF3_fnc,top))),
inference(forward_demodulation,[status(thm)],[f1102,f52987]) ).
fof(f53033,plain,
join(composition(converse(sF3_fnc),complement(sk1)),zero) = composition(meet(converse(sF3_fnc),composition(top,converse(complement(sk1)))),meet(complement(sk1),composition(sF3_fnc,top))),
inference(forward_demodulation,[status(thm)],[f21882,f53032]) ).
fof(f53034,plain,
composition(converse(sF3_fnc),complement(sk1)) = composition(meet(converse(sF3_fnc),composition(top,converse(complement(sk1)))),meet(complement(sk1),composition(sF3_fnc,top))),
inference(forward_demodulation,[status(thm)],[f1174,f53033]) ).
fof(f53035,plain,
composition(converse(sF3_fnc),complement(sk1)) = composition(meet(converse(sF3_fnc),converse(composition(complement(sk1),top))),meet(complement(sk1),composition(sF3_fnc,top))),
inference(forward_demodulation,[status(thm)],[f2408,f53034]) ).
fof(f53036,plain,
composition(converse(sF3_fnc),complement(sk1)) = composition(meet(converse(sF3_fnc),converse(composition(complement(sk1),top))),zero),
inference(forward_demodulation,[status(thm)],[f10570,f53035]) ).
fof(f53037,plain,
composition(converse(sF3_fnc),complement(sk1)) = zero,
inference(forward_demodulation,[status(thm)],[f21882,f53036]) ).
fof(f53119,plain,
converse(zero) = composition(converse(complement(sk1)),sF3_fnc),
inference(paramodulation,[status(thm)],[f53037,f122]) ).
fof(f53177,plain,
zero = composition(converse(complement(sk1)),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f2233,f53119]) ).
fof(f53323,plain,
! [X0] : composition(join(converse(complement(sk1)),sF1_fnc),composition(sF3_fnc,X0)) = composition(join(sF0_fnc,zero),X0),
inference(paramodulation,[status(thm)],[f53177,f263]) ).
fof(f53324,plain,
! [X0] : composition(join(converse(complement(sk1)),sk2),composition(sF3_fnc,X0)) = composition(join(sF4_fnc,zero),X0),
inference(paramodulation,[status(thm)],[f53177,f250]) ).
fof(f53389,plain,
! [X0] : composition(join(sF1_fnc,converse(complement(sk1))),composition(sF3_fnc,X0)) = composition(join(sF0_fnc,zero),X0),
inference(forward_demodulation,[status(thm)],[f227,f53323]) ).
fof(f53390,plain,
! [X0] : composition(join(sF1_fnc,converse(complement(sk1))),composition(sF3_fnc,X0)) = composition(join(zero,sF0_fnc),X0),
inference(forward_demodulation,[status(thm)],[f227,f53389]) ).
fof(f53391,plain,
! [X0] : composition(join(sF1_fnc,converse(complement(sk1))),composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f1099,f53390]) ).
fof(f53392,plain,
! [X0] : composition(join(sk2,converse(complement(sk1))),composition(sF3_fnc,X0)) = composition(join(sF4_fnc,zero),X0),
inference(forward_demodulation,[status(thm)],[f227,f53324]) ).
fof(f53393,plain,
! [X0] : composition(join(sk2,converse(complement(sk1))),composition(sF3_fnc,X0)) = composition(join(zero,sF4_fnc),X0),
inference(forward_demodulation,[status(thm)],[f227,f53392]) ).
fof(f53394,plain,
! [X0] : composition(join(sk2,converse(complement(sk1))),composition(sF3_fnc,X0)) = composition(sF4_fnc,X0),
inference(forward_demodulation,[status(thm)],[f1099,f53393]) ).
fof(f53704,plain,
! [X0] : join(meet(composition(one,converse(complement(X0))),converse(X0)),composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0))))) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(paramodulation,[status(thm)],[f11151,f549]) ).
fof(f53806,plain,
! [X0] : join(meet(converse(X0),composition(one,converse(complement(X0)))),composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0))))) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f73,f53704]) ).
fof(f53807,plain,
! [X0] : join(meet(converse(X0),converse(complement(X0))),composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0))))) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f659,f53806]) ).
fof(f53808,plain,
! [X0] : join(meet(converse(X0),converse(complement(X0))),zero) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f22894,f53807]) ).
fof(f53809,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f1174,f53808]) ).
fof(f53810,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f11151,f53809]) ).
fof(f53811,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f22894,f53810]) ).
fof(f54002,plain,
! [X0] : meet(X0,converse(complement(converse(X0)))) = zero,
inference(paramodulation,[status(thm)],[f26,f53811]) ).
fof(f54044,plain,
! [X0] : converse(X0) = join(zero,meet(complement(converse(complement(X0))),converse(X0))),
inference(paramodulation,[status(thm)],[f53811,f7143]) ).
fof(f54111,plain,
! [X0] : converse(X0) = meet(complement(converse(complement(X0))),converse(X0)),
inference(forward_demodulation,[status(thm)],[f1099,f54044]) ).
fof(f54112,plain,
! [X0] : converse(X0) = meet(converse(X0),complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f73,f54111]) ).
fof(f54467,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = join(X0,zero),
inference(paramodulation,[status(thm)],[f54002,f10335]) ).
fof(f54535,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[status(thm)],[f1174,f54467]) ).
fof(f54682,plain,
! [X0] : converse(converse(complement(converse(complement(X0))))) = meet(converse(converse(complement(converse(complement(X0))))),converse(X0)),
inference(paramodulation,[status(thm)],[f54535,f1571]) ).
fof(f54766,plain,
! [X0] : complement(converse(complement(X0))) = meet(converse(converse(complement(converse(complement(X0))))),converse(X0)),
inference(forward_demodulation,[status(thm)],[f26,f54682]) ).
fof(f54767,plain,
! [X0] : complement(converse(complement(X0))) = meet(converse(X0),converse(converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f73,f54766]) ).
fof(f54768,plain,
! [X0] : complement(converse(complement(X0))) = meet(converse(X0),complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f26,f54767]) ).
fof(f54801,plain,
! [X0] : complement(converse(complement(X0))) = converse(X0),
inference(forward_demodulation,[status(thm)],[f54112,f54768]) ).
fof(f55074,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(paramodulation,[status(thm)],[f1080,f54801]) ).
fof(f55151,plain,
! [X0] : composition(join(sk2,complement(converse(sk1))),composition(sF3_fnc,X0)) = composition(sF4_fnc,X0),
inference(backward_demodulation,[status(thm)],[f55074,f53394]) ).
fof(f55152,plain,
! [X0] : composition(join(sF1_fnc,complement(converse(sk1))),composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(backward_demodulation,[status(thm)],[f55074,f53391]) ).
fof(f55330,plain,
! [X0] : composition(join(sk2,complement(sF2_fnc)),composition(sF3_fnc,X0)) = composition(sF4_fnc,X0),
inference(forward_demodulation,[status(thm)],[f37,f55151]) ).
fof(f55331,plain,
! [X0] : composition(join(sF1_fnc,complement(sF2_fnc)),composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f37,f55152]) ).
fof(f55332,plain,
! [X0] : composition(join(sk2,complement(sF2_fnc)),composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f26717,f55331]) ).
fof(f55346,plain,
! [X0] : composition(sF4_fnc,X0) = composition(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f55330,f55332]) ).
fof(f55908,plain,
sF4_fnc = composition(sF0_fnc,one),
inference(paramodulation,[status(thm)],[f24,f55346]) ).
fof(f55977,plain,
sF4_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f24,f55908]) ).
fof(f55978,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f55977,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL035-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:08:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 151.27/19.57 % Refutation found
% 151.27/19.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 151.27/19.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 62.03/19.80 % Elapsed time: 19.423635 seconds
% 62.03/19.80 % CPU time: 153.148278 seconds
% 62.03/19.80 % Total memory used: 821.945 MB
% 62.03/19.80 % Net memory used: 785.093 MB
%------------------------------------------------------------------------------