%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL050-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:03:30 PM UTC 2026
% Result : Unsatisfiable 25.76s 3.83s
% Output : CNFRefutation 25.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 19
% Syntax : Number of formulae : 248 ( 248 unt; 4 def)
% Number of atoms : 248 ( 247 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 : 7 ( 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 : 272 ( 272 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : join(A,B) = join(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : composition(A,composition(B,C)) = composition(composition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : composition(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : converse(converse(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : top = join(A,complement(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : zero = meet(A,complement(A)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,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(f34,plain,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF1_fnc = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f36,definition,
sF0_fnc = complement(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f37,definition,
sF3_fnc = complement(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f38,definition,
sF2_fnc = composition(sF3_fnc,top),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f39,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f34,f38,f37,f36,f35]) ).
fof(f40,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f18,f20]) ).
fof(f41,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f21,f40]) ).
fof(f42,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f18,f28]) ).
fof(f43,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f36,f37]) ).
fof(f44,plain,
sF2_fnc = composition(sF0_fnc,top),
inference(forward_demodulation,[status(thm)],[f43,f38]) ).
fof(f45,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f18,f41]) ).
fof(f52,plain,
! [X0,X1] : top = join(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f29]) ).
fof(f54,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f29,f21]) ).
fof(f55,plain,
! [X0,X1] : top = join(complement(X0),join(complement(X1),meet(X0,X1))),
inference(forward_demodulation,[status(thm)],[f19,f52]) ).
fof(f57,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f30,f54]) ).
fof(f70,plain,
! [X0] : composition(sF0_fnc,composition(top,X0)) = composition(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f44,f22]) ).
fof(f95,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(paramodulation,[status(thm)],[f57,f42]) ).
fof(f101,plain,
join(complement(top),composition(converse(sF0_fnc),complement(sF2_fnc))) = complement(top),
inference(paramodulation,[status(thm)],[f44,f42]) ).
fof(f103,plain,
join(complement(top),composition(converse(sk1),complement(sF1_fnc))) = complement(top),
inference(paramodulation,[status(thm)],[f35,f42]) ).
fof(f104,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f57,f95]) ).
fof(f108,plain,
join(zero,composition(converse(sF0_fnc),complement(sF2_fnc))) = complement(top),
inference(forward_demodulation,[status(thm)],[f57,f101]) ).
fof(f109,plain,
join(zero,composition(converse(sF0_fnc),complement(sF2_fnc))) = zero,
inference(forward_demodulation,[status(thm)],[f57,f108]) ).
fof(f110,plain,
join(zero,composition(converse(sk1),complement(sF1_fnc))) = complement(top),
inference(forward_demodulation,[status(thm)],[f57,f103]) ).
fof(f111,plain,
join(zero,composition(converse(sk1),sF0_fnc)) = complement(top),
inference(forward_demodulation,[status(thm)],[f36,f110]) ).
fof(f112,plain,
join(zero,composition(converse(sk1),sF0_fnc)) = zero,
inference(forward_demodulation,[status(thm)],[f57,f111]) ).
fof(f117,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f45]) ).
fof(f119,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f29,f45]) ).
fof(f128,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f18,f117]) ).
fof(f130,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f18,f119]) ).
fof(f131,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f57,f130]) ).
fof(f140,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f22]) ).
fof(f149,plain,
! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(paramodulation,[status(thm)],[f30,f45]) ).
fof(f151,plain,
! [X0] : X0 = join(zero,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f21,f149]) ).
fof(f159,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f18,f21]) ).
fof(f167,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f21,f159]) ).
fof(f191,plain,
top = join(zero,meet(top,complement(zero))),
inference(paramodulation,[status(thm)],[f57,f131]) ).
fof(f194,plain,
sF1_fnc = join(zero,meet(sF1_fnc,complement(sF0_fnc))),
inference(paramodulation,[status(thm)],[f36,f131]) ).
fof(f196,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f197,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f198,plain,
! [X0,X1] : join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = complement(converse(X0)),
inference(paramodulation,[status(thm)],[f27,f42]) ).
fof(f200,plain,
! [X0,X1] : join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))) = complement(converse(X0)),
inference(forward_demodulation,[status(thm)],[f25,f198]) ).
fof(f204,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f167,f128]) ).
fof(f207,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f167,f128]) ).
fof(f209,plain,
! [X0] : X0 = join(meet(X0,top),meet(X0,zero)),
inference(paramodulation,[status(thm)],[f57,f128]) ).
fof(f212,plain,
! [X0] : X0 = join(meet(X0,sF1_fnc),meet(X0,sF0_fnc)),
inference(paramodulation,[status(thm)],[f36,f128]) ).
fof(f217,plain,
! [X0] : X0 = join(meet(X0,sF0_fnc),meet(X0,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f18,f212]) ).
fof(f221,plain,
! [X0] : X0 = join(meet(X0,top),meet(zero,X0)),
inference(paramodulation,[status(thm)],[f167,f209]) ).
fof(f224,plain,
! [X0] : X0 = join(meet(sF0_fnc,X0),meet(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f167,f217]) ).
fof(f227,plain,
! [X0] : X0 = join(meet(X0,sF0_fnc),meet(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f167,f217]) ).
fof(f235,plain,
complement(zero) = join(meet(complement(zero),top),zero),
inference(paramodulation,[status(thm)],[f30,f221]) ).
fof(f241,plain,
complement(zero) = join(zero,meet(complement(zero),top)),
inference(forward_demodulation,[status(thm)],[f18,f235]) ).
fof(f242,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(forward_demodulation,[status(thm)],[f167,f241]) ).
fof(f244,plain,
complement(zero) = top,
inference(forward_demodulation,[status(thm)],[f191,f242]) ).
fof(f246,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f259,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f29,f19]) ).
fof(f260,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f267,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f19,f260]) ).
fof(f276,plain,
! [X0] : composition(join(sk1,X0),top) = join(sF1_fnc,composition(X0,top)),
inference(paramodulation,[status(thm)],[f35,f24]) ).
fof(f310,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f322,plain,
! [X0] : X0 = join(meet(sF0_fnc,X0),meet(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f167,f227]) ).
fof(f356,plain,
complement(sF0_fnc) = join(zero,meet(complement(sF0_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f30,f224]) ).
fof(f366,plain,
complement(sF0_fnc) = join(zero,meet(sF1_fnc,complement(sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f167,f356]) ).
fof(f369,plain,
complement(sF0_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f194,f366]) ).
fof(f415,plain,
! [X0] : zero = join(meet(zero,X0),complement(join(top,X0))),
inference(paramodulation,[status(thm)],[f244,f45]) ).
fof(f549,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f30,f207]) ).
fof(f565,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f18,f549]) ).
fof(f566,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f167,f565]) ).
fof(f570,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f131,f566]) ).
fof(f578,plain,
! [X0,X1] : complement(meet(X0,X1)) = join(complement(X0),complement(X1)),
inference(paramodulation,[status(thm)],[f21,f570]) ).
fof(f588,plain,
! [X0,X1] : meet(X0,complement(X1)) = complement(join(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f570,f21]) ).
fof(f589,plain,
! [X0,X1] : meet(complement(X0),X1) = complement(join(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f570,f21]) ).
fof(f797,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f23,f197]) ).
fof(f814,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f25,f797]) ).
fof(f829,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f140,f814]) ).
fof(f830,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f23,f814]) ).
fof(f833,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f814,f42]) ).
fof(f843,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f814,f24]) ).
fof(f850,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f814,f829]) ).
fof(f854,plain,
! [X0] : complement(meet(X0,composition(one,X0))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f578,f833]) ).
fof(f855,plain,
! [X0] : complement(meet(X0,X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f850,f854]) ).
fof(f871,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f830,f843]) ).
fof(f880,plain,
! [X0] : converse(join(one,X0)) = join(one,converse(X0)),
inference(paramodulation,[status(thm)],[f830,f26]) ).
fof(f923,plain,
! [X0] : complement(complement(X0)) = meet(X0,X0),
inference(paramodulation,[status(thm)],[f855,f570]) ).
fof(f934,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f941,f151]) ).
fof(f941,plain,
! [X0] : X0 = meet(X0,X0),
inference(forward_demodulation,[status(thm)],[f570,f923]) ).
fof(f960,plain,
composition(converse(sk1),sF0_fnc) = zero,
inference(backward_demodulation,[status(thm)],[f934,f112]) ).
fof(f979,plain,
composition(converse(sF0_fnc),complement(sF2_fnc)) = zero,
inference(backward_demodulation,[status(thm)],[f934,f109]) ).
fof(f980,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(backward_demodulation,[status(thm)],[f934,f104]) ).
fof(f1004,plain,
! [X0] : X0 = join(X0,zero),
inference(paramodulation,[status(thm)],[f18,f934]) ).
fof(f1052,plain,
! [X0] : top = join(complement(X0),join(complement(X0),X0)),
inference(paramodulation,[status(thm)],[f941,f55]) ).
fof(f1112,plain,
! [X0] : top = join(complement(X0),join(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f246,f1052]) ).
fof(f1113,plain,
! [X0] : top = join(X0,join(complement(X0),complement(X0))),
inference(forward_demodulation,[status(thm)],[f267,f1112]) ).
fof(f1114,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f259,f1113]) ).
fof(f1124,plain,
! [X0,X1,X2] : join(meet(converse(composition(X0,X1)),X2),composition(meet(converse(X1),composition(X2,converse(converse(X0)))),meet(converse(X0),composition(converse(converse(X1)),X2)))) = composition(meet(converse(X1),composition(X2,converse(converse(X0)))),meet(converse(X0),composition(converse(converse(X1)),X2))),
inference(paramodulation,[status(thm)],[f27,f31]) ).
fof(f1130,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1))),
inference(paramodulation,[status(thm)],[f23,f31]) ).
fof(f1135,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),converse(X2)),composition(meet(X0,converse(composition(X1,X2))),meet(X1,composition(converse(X0),converse(X2))))) = composition(meet(X0,composition(converse(X2),converse(X1))),meet(X1,composition(converse(X0),converse(X2)))),
inference(paramodulation,[status(thm)],[f27,f31]) ).
fof(f1158,plain,
! [X0,X1,X2] : join(meet(converse(composition(X0,X1)),X2),composition(meet(converse(X1),composition(X2,X0)),meet(converse(X0),composition(converse(converse(X1)),X2)))) = composition(meet(converse(X1),composition(X2,converse(converse(X0)))),meet(converse(X0),composition(converse(converse(X1)),X2))),
inference(forward_demodulation,[status(thm)],[f25,f1124]) ).
fof(f1159,plain,
! [X0,X1,X2] : join(meet(converse(composition(X0,X1)),X2),composition(meet(converse(X1),composition(X2,X0)),meet(converse(X0),composition(X1,X2)))) = composition(meet(converse(X1),composition(X2,converse(converse(X0)))),meet(converse(X0),composition(converse(converse(X1)),X2))),
inference(forward_demodulation,[status(thm)],[f25,f1158]) ).
fof(f1160,plain,
! [X0,X1,X2] : join(meet(converse(composition(X0,X1)),X2),composition(meet(converse(X1),composition(X2,X0)),meet(converse(X0),composition(X1,X2)))) = composition(meet(converse(X1),composition(X2,X0)),meet(converse(X0),composition(converse(converse(X1)),X2))),
inference(forward_demodulation,[status(thm)],[f25,f1159]) ).
fof(f1161,plain,
! [X0,X1,X2] : join(meet(converse(composition(X0,X1)),X2),composition(meet(converse(X1),composition(X2,X0)),meet(converse(X0),composition(X1,X2)))) = composition(meet(converse(X1),composition(X2,X0)),meet(converse(X0),composition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f25,f1160]) ).
fof(f1162,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,composition(X1,one)),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f830,f1130]) ).
fof(f1163,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,X1),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f23,f1162]) ).
fof(f1164,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,X1),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,composition(X1,one)),meet(one,composition(converse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f830,f1163]) ).
fof(f1165,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,X1),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,X1),meet(one,composition(converse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f23,f1164]) ).
fof(f1179,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),converse(X2)),composition(meet(X0,converse(composition(X1,X2))),meet(X1,converse(composition(X2,X0))))) = composition(meet(X0,composition(converse(X2),converse(X1))),meet(X1,composition(converse(X0),converse(X2)))),
inference(forward_demodulation,[status(thm)],[f27,f1135]) ).
fof(f1180,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),converse(X2)),composition(meet(X0,converse(composition(X1,X2))),meet(X1,converse(composition(X2,X0))))) = composition(meet(X0,converse(composition(X1,X2))),meet(X1,composition(converse(X0),converse(X2)))),
inference(forward_demodulation,[status(thm)],[f27,f1179]) ).
fof(f1181,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),converse(X2)),composition(meet(X0,converse(composition(X1,X2))),meet(X1,converse(composition(X2,X0))))) = composition(meet(X0,converse(composition(X1,X2))),meet(X1,converse(composition(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f27,f1180]) ).
fof(f1359,plain,
! [X0] : top = join(top,X0),
inference(paramodulation,[status(thm)],[f570,f1114]) ).
fof(f1380,plain,
! [X0] : zero = join(meet(zero,X0),complement(top)),
inference(backward_demodulation,[status(thm)],[f1359,f415]) ).
fof(f1390,plain,
! [X0] : zero = join(complement(top),meet(zero,X0)),
inference(forward_demodulation,[status(thm)],[f18,f1380]) ).
fof(f1391,plain,
! [X0] : zero = join(zero,meet(zero,X0)),
inference(forward_demodulation,[status(thm)],[f57,f1390]) ).
fof(f1400,plain,
! [X0] : zero = meet(zero,X0),
inference(forward_demodulation,[status(thm)],[f934,f1391]) ).
fof(f1435,plain,
! [X0] : top = join(X0,top),
inference(paramodulation,[status(thm)],[f18,f1359]) ).
fof(f1563,plain,
! [X0] : zero = meet(X0,zero),
inference(paramodulation,[status(thm)],[f167,f1400]) ).
fof(f1698,plain,
join(complement(converse(converse(sF0_fnc))),composition(complement(sF2_fnc),complement(converse(zero)))) = complement(converse(converse(sF0_fnc))),
inference(paramodulation,[status(thm)],[f979,f200]) ).
fof(f1699,plain,
join(complement(converse(converse(sk1))),composition(sF0_fnc,complement(converse(zero)))) = complement(converse(converse(sk1))),
inference(paramodulation,[status(thm)],[f960,f200]) ).
fof(f1724,plain,
join(complement(sF0_fnc),composition(complement(sF2_fnc),complement(converse(zero)))) = complement(converse(converse(sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f25,f1698]) ).
fof(f1725,plain,
join(sF1_fnc,composition(complement(sF2_fnc),complement(converse(zero)))) = complement(converse(converse(sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f369,f1724]) ).
fof(f1726,plain,
join(sF1_fnc,composition(complement(sF2_fnc),complement(converse(zero)))) = complement(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f25,f1725]) ).
fof(f1727,plain,
join(sF1_fnc,composition(complement(sF2_fnc),complement(converse(zero)))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f369,f1726]) ).
fof(f1728,plain,
join(complement(sk1),composition(sF0_fnc,complement(converse(zero)))) = complement(converse(converse(sk1))),
inference(forward_demodulation,[status(thm)],[f25,f1699]) ).
fof(f1729,plain,
join(complement(sk1),composition(sF0_fnc,complement(converse(zero)))) = complement(sk1),
inference(forward_demodulation,[status(thm)],[f25,f1728]) ).
fof(f1943,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(zero)),
inference(paramodulation,[status(thm)],[f1004,f310]) ).
fof(f1969,plain,
! [X0] : X0 = join(X0,converse(zero)),
inference(forward_demodulation,[status(thm)],[f25,f1943]) ).
fof(f1984,plain,
zero = converse(zero),
inference(paramodulation,[status(thm)],[f934,f1969]) ).
fof(f2007,plain,
join(complement(sk1),composition(sF0_fnc,complement(zero))) = complement(sk1),
inference(backward_demodulation,[status(thm)],[f1984,f1729]) ).
fof(f2008,plain,
join(sF1_fnc,composition(complement(sF2_fnc),complement(zero))) = sF1_fnc,
inference(backward_demodulation,[status(thm)],[f1984,f1727]) ).
fof(f2030,plain,
join(complement(sk1),composition(sF0_fnc,top)) = complement(sk1),
inference(forward_demodulation,[status(thm)],[f244,f2007]) ).
fof(f2031,plain,
join(complement(sk1),sF2_fnc) = complement(sk1),
inference(forward_demodulation,[status(thm)],[f44,f2030]) ).
fof(f2032,plain,
join(sF2_fnc,complement(sk1)) = complement(sk1),
inference(forward_demodulation,[status(thm)],[f18,f2031]) ).
fof(f2033,plain,
join(sF1_fnc,composition(complement(sF2_fnc),top)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f244,f2008]) ).
fof(f2275,plain,
! [X0,X1] : complement(meet(X0,complement(X1))) = join(complement(X0),X1),
inference(paramodulation,[status(thm)],[f570,f578]) ).
fof(f2427,plain,
! [X0,X1] : meet(complement(X0),complement(X1)) = complement(join(X0,X1)),
inference(paramodulation,[status(thm)],[f570,f588]) ).
fof(f2480,plain,
meet(complement(sF2_fnc),sk1) = complement(complement(sk1)),
inference(paramodulation,[status(thm)],[f2032,f589]) ).
fof(f2519,plain,
meet(sk1,complement(sF2_fnc)) = complement(complement(sk1)),
inference(forward_demodulation,[status(thm)],[f167,f2480]) ).
fof(f2520,plain,
meet(sk1,complement(sF2_fnc)) = sk1,
inference(forward_demodulation,[status(thm)],[f570,f2519]) ).
fof(f2947,plain,
! [X0,X1] : join(X0,top) = join(X1,join(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f29,f267]) ).
fof(f3050,plain,
! [X0,X1] : top = join(X0,join(X1,complement(X0))),
inference(forward_demodulation,[status(thm)],[f1435,f2947]) ).
fof(f3871,plain,
! [X0,X1] : top = join(X0,complement(meet(X1,X0))),
inference(paramodulation,[status(thm)],[f578,f3050]) ).
fof(f3986,plain,
! [X0,X1] : meet(X0,complement(complement(meet(X1,complement(X0))))) = complement(top),
inference(paramodulation,[status(thm)],[f3871,f588]) ).
fof(f4017,plain,
! [X0,X1] : meet(X0,meet(X1,complement(X0))) = complement(top),
inference(forward_demodulation,[status(thm)],[f570,f3986]) ).
fof(f4019,plain,
! [X0,X1] : meet(X0,meet(X1,complement(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f57,f4017]) ).
fof(f4165,plain,
! [X0,X1] : X0 = join(zero,meet(complement(meet(X1,complement(X0))),X0)),
inference(paramodulation,[status(thm)],[f4019,f207]) ).
fof(f4207,plain,
! [X0,X1] : X0 = meet(complement(meet(X1,complement(X0))),X0),
inference(forward_demodulation,[status(thm)],[f934,f4165]) ).
fof(f4208,plain,
! [X0,X1] : X0 = meet(X0,complement(meet(X1,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f167,f4207]) ).
fof(f4209,plain,
! [X0,X1] : X0 = meet(X0,join(complement(X1),X0)),
inference(forward_demodulation,[status(thm)],[f2275,f4208]) ).
fof(f4220,plain,
! [X0,X1] : complement(X0) = meet(complement(X0),complement(meet(X1,X0))),
inference(paramodulation,[status(thm)],[f578,f4209]) ).
fof(f4270,plain,
! [X0,X1] : complement(X0) = complement(join(X0,meet(X1,X0))),
inference(forward_demodulation,[status(thm)],[f2427,f4220]) ).
fof(f6294,plain,
! [X0,X1] : complement(complement(X0)) = join(X0,meet(X1,X0)),
inference(paramodulation,[status(thm)],[f4270,f570]) ).
fof(f6374,plain,
! [X0,X1] : X0 = join(X0,meet(X1,X0)),
inference(forward_demodulation,[status(thm)],[f570,f6294]) ).
fof(f6401,plain,
complement(sF2_fnc) = join(complement(sF2_fnc),sk1),
inference(paramodulation,[status(thm)],[f2520,f6374]) ).
fof(f6443,plain,
complement(sF2_fnc) = join(sk1,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f18,f6401]) ).
fof(f7781,plain,
composition(complement(sF2_fnc),top) = join(sF1_fnc,composition(complement(sF2_fnc),top)),
inference(paramodulation,[status(thm)],[f6443,f276]) ).
fof(f7801,plain,
composition(complement(sF2_fnc),top) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f2033,f7781]) ).
fof(f7834,plain,
join(complement(top),composition(converse(complement(sF2_fnc)),complement(sF1_fnc))) = complement(top),
inference(paramodulation,[status(thm)],[f7801,f42]) ).
fof(f7870,plain,
join(zero,composition(converse(complement(sF2_fnc)),complement(sF1_fnc))) = complement(top),
inference(forward_demodulation,[status(thm)],[f57,f7834]) ).
fof(f7871,plain,
composition(converse(complement(sF2_fnc)),complement(sF1_fnc)) = complement(top),
inference(forward_demodulation,[status(thm)],[f934,f7870]) ).
fof(f7872,plain,
composition(converse(complement(sF2_fnc)),sF0_fnc) = complement(top),
inference(forward_demodulation,[status(thm)],[f36,f7871]) ).
fof(f7874,plain,
composition(converse(complement(sF2_fnc)),sF0_fnc) = zero,
inference(forward_demodulation,[status(thm)],[f57,f7872]) ).
fof(f8434,plain,
! [X0] : composition(join(one,converse(X0)),complement(composition(join(one,X0),top))) = zero,
inference(paramodulation,[status(thm)],[f880,f980]) ).
fof(f8478,plain,
! [X0] : composition(join(one,converse(X0)),complement(join(top,composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f871,f8434]) ).
fof(f8479,plain,
! [X0] : composition(join(one,converse(X0)),complement(top)) = zero,
inference(forward_demodulation,[status(thm)],[f1359,f8478]) ).
fof(f8480,plain,
! [X0] : composition(join(one,converse(X0)),zero) = zero,
inference(forward_demodulation,[status(thm)],[f57,f8479]) ).
fof(f8481,plain,
! [X0] : join(zero,composition(converse(X0),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f871,f8480]) ).
fof(f8486,plain,
! [X0] : composition(converse(X0),zero) = zero,
inference(forward_demodulation,[status(thm)],[f934,f8481]) ).
fof(f9690,plain,
! [X0,X1] : composition(composition(X0,converse(X1)),zero) = zero,
inference(paramodulation,[status(thm)],[f196,f8486]) ).
fof(f9696,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(paramodulation,[status(thm)],[f8486,f197]) ).
fof(f9723,plain,
! [X0,X1] : composition(X0,composition(converse(X1),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f22,f9690]) ).
fof(f9754,plain,
! [X0] : composition(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f8486,f9723]) ).
fof(f9772,plain,
! [X0] : zero = composition(converse(zero),X0),
inference(forward_demodulation,[status(thm)],[f1984,f9696]) ).
fof(f9801,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[status(thm)],[f1984,f9772]) ).
fof(f13726,plain,
! [X0] : join(meet(converse(composition(X0,converse(sk1))),sF0_fnc),composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),zero))) = composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),composition(converse(sk1),sF0_fnc))),
inference(paramodulation,[status(thm)],[f960,f1161]) ).
fof(f14157,plain,
! [X0] : join(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),zero))) = composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),composition(converse(sk1),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f167,f13726]) ).
fof(f14158,plain,
! [X0] : join(meet(sF0_fnc,composition(sk1,converse(X0))),composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),zero))) = composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),composition(converse(sk1),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f196,f14157]) ).
fof(f14159,plain,
! [X0] : join(meet(sF0_fnc,composition(sk1,converse(X0))),composition(meet(sk1,composition(sF0_fnc,X0)),meet(converse(X0),zero))) = composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),composition(converse(sk1),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f25,f14158]) ).
fof(f14160,plain,
! [X0] : join(meet(sF0_fnc,composition(sk1,converse(X0))),composition(meet(sk1,composition(sF0_fnc,X0)),zero)) = composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),composition(converse(sk1),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f1563,f14159]) ).
fof(f14161,plain,
! [X0] : join(meet(sF0_fnc,composition(sk1,converse(X0))),zero) = composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),composition(converse(sk1),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f9754,f14160]) ).
fof(f14162,plain,
! [X0] : meet(sF0_fnc,composition(sk1,converse(X0))) = composition(meet(converse(converse(sk1)),composition(sF0_fnc,X0)),meet(converse(X0),composition(converse(sk1),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f1004,f14161]) ).
fof(f14163,plain,
! [X0] : meet(sF0_fnc,composition(sk1,converse(X0))) = composition(meet(sk1,composition(sF0_fnc,X0)),meet(converse(X0),composition(converse(sk1),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f25,f14162]) ).
fof(f14164,plain,
! [X0] : meet(sF0_fnc,composition(sk1,converse(X0))) = composition(meet(sk1,composition(sF0_fnc,X0)),meet(converse(X0),zero)),
inference(forward_demodulation,[status(thm)],[f960,f14163]) ).
fof(f14165,plain,
! [X0] : meet(sF0_fnc,composition(sk1,converse(X0))) = composition(meet(sk1,composition(sF0_fnc,X0)),zero),
inference(forward_demodulation,[status(thm)],[f1563,f14164]) ).
fof(f14166,plain,
! [X0] : meet(sF0_fnc,composition(sk1,converse(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f9754,f14165]) ).
fof(f14302,plain,
join(meet(complement(sF2_fnc),sF0_fnc),composition(meet(complement(sF2_fnc),sF0_fnc),meet(one,zero))) = composition(meet(complement(sF2_fnc),sF0_fnc),meet(one,composition(converse(complement(sF2_fnc)),sF0_fnc))),
inference(paramodulation,[status(thm)],[f7874,f1165]) ).
fof(f14487,plain,
join(meet(sF0_fnc,complement(sF2_fnc)),composition(meet(complement(sF2_fnc),sF0_fnc),meet(one,zero))) = composition(meet(complement(sF2_fnc),sF0_fnc),meet(one,composition(converse(complement(sF2_fnc)),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f167,f14302]) ).
fof(f14488,plain,
join(meet(sF0_fnc,complement(sF2_fnc)),composition(meet(sF0_fnc,complement(sF2_fnc)),meet(one,zero))) = composition(meet(complement(sF2_fnc),sF0_fnc),meet(one,composition(converse(complement(sF2_fnc)),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f167,f14487]) ).
fof(f14489,plain,
join(meet(sF0_fnc,complement(sF2_fnc)),composition(meet(sF0_fnc,complement(sF2_fnc)),zero)) = composition(meet(complement(sF2_fnc),sF0_fnc),meet(one,composition(converse(complement(sF2_fnc)),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f1563,f14488]) ).
fof(f14490,plain,
join(meet(sF0_fnc,complement(sF2_fnc)),zero) = composition(meet(complement(sF2_fnc),sF0_fnc),meet(one,composition(converse(complement(sF2_fnc)),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f9754,f14489]) ).
fof(f14491,plain,
meet(sF0_fnc,complement(sF2_fnc)) = composition(meet(complement(sF2_fnc),sF0_fnc),meet(one,composition(converse(complement(sF2_fnc)),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f1004,f14490]) ).
fof(f14492,plain,
meet(sF0_fnc,complement(sF2_fnc)) = composition(meet(sF0_fnc,complement(sF2_fnc)),meet(one,composition(converse(complement(sF2_fnc)),sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f167,f14491]) ).
fof(f14493,plain,
meet(sF0_fnc,complement(sF2_fnc)) = composition(meet(sF0_fnc,complement(sF2_fnc)),meet(one,zero)),
inference(forward_demodulation,[status(thm)],[f7874,f14492]) ).
fof(f14494,plain,
meet(sF0_fnc,complement(sF2_fnc)) = composition(meet(sF0_fnc,complement(sF2_fnc)),zero),
inference(forward_demodulation,[status(thm)],[f1563,f14493]) ).
fof(f14495,plain,
meet(sF0_fnc,complement(sF2_fnc)) = zero,
inference(forward_demodulation,[status(thm)],[f9754,f14494]) ).
fof(f14665,plain,
! [X0] : join(meet(composition(sF0_fnc,X0),converse(converse(sk1))),composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(zero)))) = composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(paramodulation,[status(thm)],[f960,f1181]) ).
fof(f15107,plain,
! [X0] : join(meet(composition(sF0_fnc,X0),sk1),composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(zero)))) = composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f25,f14665]) ).
fof(f15108,plain,
! [X0] : join(meet(sk1,composition(sF0_fnc,X0)),composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(zero)))) = composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f167,f15107]) ).
fof(f15109,plain,
! [X0] : join(meet(sk1,composition(sF0_fnc,X0)),composition(meet(sF0_fnc,composition(sk1,converse(X0))),meet(X0,converse(zero)))) = composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f196,f15108]) ).
fof(f15110,plain,
! [X0] : join(meet(sk1,composition(sF0_fnc,X0)),composition(zero,meet(X0,converse(zero)))) = composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f14166,f15109]) ).
fof(f15111,plain,
! [X0] : join(meet(sk1,composition(sF0_fnc,X0)),zero) = composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f9801,f15110]) ).
fof(f15112,plain,
! [X0] : meet(sk1,composition(sF0_fnc,X0)) = composition(meet(sF0_fnc,converse(composition(X0,converse(sk1)))),meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f1004,f15111]) ).
fof(f15113,plain,
! [X0] : meet(sk1,composition(sF0_fnc,X0)) = composition(meet(sF0_fnc,composition(sk1,converse(X0))),meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f196,f15112]) ).
fof(f15114,plain,
! [X0] : meet(sk1,composition(sF0_fnc,X0)) = composition(zero,meet(X0,converse(composition(converse(sk1),sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f14166,f15113]) ).
fof(f15115,plain,
! [X0] : meet(sk1,composition(sF0_fnc,X0)) = zero,
inference(forward_demodulation,[status(thm)],[f9801,f15114]) ).
fof(f15358,plain,
sF0_fnc = join(meet(sF2_fnc,sF0_fnc),zero),
inference(paramodulation,[status(thm)],[f14495,f204]) ).
fof(f15389,plain,
sF0_fnc = meet(sF2_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f1004,f15358]) ).
fof(f15390,plain,
sF0_fnc = meet(sF0_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f167,f15389]) ).
fof(f15524,plain,
sF2_fnc = join(sF0_fnc,meet(sF1_fnc,sF2_fnc)),
inference(paramodulation,[status(thm)],[f15390,f322]) ).
fof(f15700,plain,
! [X0] : meet(sk1,composition(sF2_fnc,X0)) = zero,
inference(paramodulation,[status(thm)],[f70,f15115]) ).
fof(f15766,plain,
! [X0] : join(meet(composition(sk1,X0),sF2_fnc),composition(zero,meet(X0,composition(converse(sk1),sF2_fnc)))) = composition(meet(sk1,composition(sF2_fnc,converse(X0))),meet(X0,composition(converse(sk1),sF2_fnc))),
inference(paramodulation,[status(thm)],[f15700,f31]) ).
fof(f15789,plain,
! [X0] : join(meet(sF2_fnc,composition(sk1,X0)),composition(zero,meet(X0,composition(converse(sk1),sF2_fnc)))) = composition(meet(sk1,composition(sF2_fnc,converse(X0))),meet(X0,composition(converse(sk1),sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f167,f15766]) ).
fof(f15790,plain,
! [X0] : join(meet(sF2_fnc,composition(sk1,X0)),zero) = composition(meet(sk1,composition(sF2_fnc,converse(X0))),meet(X0,composition(converse(sk1),sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f9801,f15789]) ).
fof(f15791,plain,
! [X0] : meet(sF2_fnc,composition(sk1,X0)) = composition(meet(sk1,composition(sF2_fnc,converse(X0))),meet(X0,composition(converse(sk1),sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f1004,f15790]) ).
fof(f15792,plain,
! [X0] : meet(sF2_fnc,composition(sk1,X0)) = composition(zero,meet(X0,composition(converse(sk1),sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f15700,f15791]) ).
fof(f15793,plain,
! [X0] : meet(sF2_fnc,composition(sk1,X0)) = zero,
inference(forward_demodulation,[status(thm)],[f9801,f15792]) ).
fof(f15872,plain,
meet(sF2_fnc,sF1_fnc) = zero,
inference(paramodulation,[status(thm)],[f35,f15793]) ).
fof(f15897,plain,
sF2_fnc = join(sF0_fnc,zero),
inference(backward_demodulation,[status(thm)],[f15898,f15524]) ).
fof(f15898,plain,
meet(sF1_fnc,sF2_fnc) = zero,
inference(forward_demodulation,[status(thm)],[f167,f15872]) ).
fof(f15934,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f1004,f15897]) ).
fof(f15935,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f15934,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL050-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n014.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 04:08:49 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.45 % Drodi V4.1.1
% 25.76/3.83 % Refutation found
% 25.76/3.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 25.76/3.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 25.76/3.95 % Elapsed time: 3.494123 seconds
% 25.76/3.95 % CPU time: 27.329813 seconds
% 25.76/3.95 % Total memory used: 290.203 MB
% 25.76/3.95 % Net memory used: 285.206 MB
%------------------------------------------------------------------------------