%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL042-2 : 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 02:03:26 PM UTC 2026
% Result : Unsatisfiable 13.39s 2.18s
% Output : CNFRefutation 13.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 16
% Syntax : Number of formulae : 191 ( 191 unt; 0 def)
% Number of atoms : 191 ( 190 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 273 ( 273 !; 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,
! [A] : meet(composition(sk1,A),composition(sk1,complement(A))) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
join(composition(converse(sk1),sk1),one) != one,
file('/export/starexec/sandbox/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,
! [X0] : meet(composition(sk1,X0),composition(sk1,complement(X0))) = zero,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
join(composition(converse(sk1),sk1),one) != one,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f42,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f41]) ).
fof(f43,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f44,plain,
join(one,composition(converse(sk1),sk1)) != one,
inference(forward_demodulation,[status(thm)],[f19,f36]) ).
fof(f45,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f42]) ).
fof(f47,plain,
meet(sk1,composition(sk1,complement(one))) = zero,
inference(paramodulation,[status(thm)],[f24,f35]) ).
fof(f52,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f53,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f54,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f56,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(f58,plain,
! [X0,X1] : zero = meet(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f31]) ).
fof(f62,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f54]) ).
fof(f64,plain,
! [X0,X1] : zero = complement(join(meet(X0,X1),complement(meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f56,f58]) ).
fof(f65,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f30,f64]) ).
fof(f76,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f90,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f93,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f99,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f93]) ).
fof(f107,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(f126,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f139,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f158,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(paramodulation,[status(thm)],[f30,f126]) ).
fof(f181,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f53]) ).
fof(f197,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f181]) ).
fof(f207,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f76,f197]) ).
fof(f208,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f197]) ).
fof(f215,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f197,f25]) ).
fof(f220,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f197,f207]) ).
fof(f227,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f208,f215]) ).
fof(f253,plain,
! [X0,X1] : join(X0,join(X1,complement(X0))) = join(top,X1),
inference(paramodulation,[status(thm)],[f19,f139]) ).
fof(f345,plain,
! [X0] : composition(join(one,one),X0) = join(X0,X0),
inference(paramodulation,[status(thm)],[f220,f227]) ).
fof(f367,plain,
! [X0] : join(complement(X0),composition(one,complement(composition(one,X0)))) = complement(X0),
inference(paramodulation,[status(thm)],[f208,f43]) ).
fof(f372,plain,
! [X0,X1] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(paramodulation,[status(thm)],[f26,f43]) ).
fof(f374,plain,
! [X0] : join(complement(X0),composition(converse(one),complement(X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f220,f43]) ).
fof(f376,plain,
! [X0,X1] : join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = complement(converse(X0)),
inference(paramodulation,[status(thm)],[f28,f43]) ).
fof(f381,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f220,f367]) ).
fof(f382,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f220,f381]) ).
fof(f388,plain,
! [X0] : composition(join(one,converse(one)),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f227,f374]) ).
fof(f389,plain,
! [X0] : composition(join(one,one),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f208,f388]) ).
fof(f390,plain,
! [X0,X1] : join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))) = complement(converse(X0)),
inference(forward_demodulation,[status(thm)],[f26,f376]) ).
fof(f405,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)],[f28,f32]) ).
fof(f421,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(f445,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)],[f28,f405]) ).
fof(f446,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)],[f28,f445]) ).
fof(f447,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)],[f28,f446]) ).
fof(f479,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,f421]) ).
fof(f485,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f45]) ).
fof(f489,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))),
inference(paramodulation,[status(thm)],[f139,f45]) ).
fof(f491,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f30,f45]) ).
fof(f495,plain,
! [X0,X1] : join(join(complement(X0),X1),X0) = join(top,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f45,f253]) ).
fof(f498,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f485]) ).
fof(f501,plain,
! [X0,X1] : X0 = join(complement(join(top,X1)),meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f19,f489]) ).
fof(f503,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f491]) ).
fof(f504,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f65,f503]) ).
fof(f507,plain,
! [X0,X1] : join(complement(X0),join(X1,X0)) = join(top,meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f495]) ).
fof(f508,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f90,f507]) ).
fof(f509,plain,
! [X0,X1] : join(top,X0) = join(top,meet(X1,X0)),
inference(forward_demodulation,[status(thm)],[f139,f508]) ).
fof(f613,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f382,f22]) ).
fof(f614,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f382,f45]) ).
fof(f615,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f382,f139]) ).
fof(f628,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f614]) ).
fof(f629,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f31,f628]) ).
fof(f630,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f629]) ).
fof(f632,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f30,f615]) ).
fof(f679,plain,
! [X0] : join(top,X0) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f613,f509]) ).
fof(f706,plain,
! [X0,X1] : X0 = join(complement(top),meet(X0,join(complement(complement(X0)),X1))),
inference(backward_demodulation,[status(thm)],[f715,f501]) ).
fof(f715,plain,
! [X0] : join(top,X0) = top,
inference(forward_demodulation,[status(thm)],[f632,f679]) ).
fof(f730,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f65,f706]) ).
fof(f739,plain,
converse(top) = top,
inference(paramodulation,[status(thm)],[f158,f715]) ).
fof(f780,plain,
! [X0] : converse(composition(top,X0)) = composition(converse(X0),top),
inference(paramodulation,[status(thm)],[f739,f53]) ).
fof(f782,plain,
! [X0] : converse(composition(X0,top)) = composition(top,converse(X0)),
inference(paramodulation,[status(thm)],[f739,f52]) ).
fof(f810,plain,
! [X0,X1] : meet(top,X0) = complement(join(meet(X1,complement(X1)),complement(X0))),
inference(paramodulation,[status(thm)],[f30,f56]) ).
fof(f833,plain,
! [X0] : meet(top,X0) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f31,f810]) ).
fof(f909,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f62,f498]) ).
fof(f914,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f62,f498]) ).
fof(f947,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f62,f909]) ).
fof(f983,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f31,f914]) ).
fof(f984,plain,
! [X0] : complement(X0) = join(meet(complement(X0),X0),complement(complement(complement(X0)))),
inference(paramodulation,[status(thm)],[f613,f914]) ).
fof(f1003,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f19,f983]) ).
fof(f1004,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f62,f1003]) ).
fof(f1006,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1019,f630]) ).
fof(f1014,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(X0,X1))),
inference(backward_demodulation,[status(thm)],[f1019,f730]) ).
fof(f1019,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f504,f1004]) ).
fof(f1020,plain,
! [X0] : complement(X0) = join(complement(complement(complement(X0))),meet(complement(X0),X0)),
inference(forward_demodulation,[status(thm)],[f19,f984]) ).
fof(f1021,plain,
! [X0] : complement(X0) = join(complement(X0),meet(complement(X0),X0)),
inference(forward_demodulation,[status(thm)],[f1019,f1020]) ).
fof(f1022,plain,
! [X0] : complement(X0) = join(complement(X0),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f62,f1021]) ).
fof(f1023,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(forward_demodulation,[status(thm)],[f31,f1022]) ).
fof(f1030,plain,
! [X0] : meet(top,X0) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1031,f833]) ).
fof(f1031,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[status(thm)],[f19,f1023]) ).
fof(f1089,plain,
! [X0,X1] : X0 = meet(X0,join(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1006,f1014]) ).
fof(f1098,plain,
! [X0] : meet(top,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1019,f1030]) ).
fof(f1153,plain,
complement(zero) = top,
inference(paramodulation,[status(thm)],[f30,f1006]) ).
fof(f1154,plain,
! [X0] : X0 = join(X0,zero),
inference(paramodulation,[status(thm)],[f19,f1006]) ).
fof(f1164,plain,
! [X0] : X0 = join(meet(zero,X0),meet(X0,top)),
inference(paramodulation,[status(thm)],[f1153,f909]) ).
fof(f1166,plain,
! [X0] : zero = join(meet(zero,X0),complement(join(top,X0))),
inference(paramodulation,[status(thm)],[f1153,f45]) ).
fof(f1174,plain,
! [X0] : zero = join(meet(zero,X0),complement(top)),
inference(forward_demodulation,[status(thm)],[f715,f1166]) ).
fof(f1175,plain,
! [X0] : zero = join(complement(top),meet(zero,X0)),
inference(forward_demodulation,[status(thm)],[f19,f1174]) ).
fof(f1176,plain,
! [X0] : zero = join(zero,meet(zero,X0)),
inference(forward_demodulation,[status(thm)],[f65,f1175]) ).
fof(f1177,plain,
! [X0] : X0 = join(zero,meet(X0,top)),
inference(backward_demodulation,[status(thm)],[f1178,f1164]) ).
fof(f1178,plain,
! [X0] : zero = meet(zero,X0),
inference(forward_demodulation,[status(thm)],[f1006,f1176]) ).
fof(f1183,plain,
! [X0] : X0 = meet(X0,top),
inference(forward_demodulation,[status(thm)],[f1006,f1177]) ).
fof(f1766,plain,
! [X0,X1] : X0 = meet(X0,composition(join(one,X1),X0)),
inference(paramodulation,[status(thm)],[f227,f1089]) ).
fof(f2208,plain,
! [X0] : X0 = meet(X0,composition(top,X0)),
inference(paramodulation,[status(thm)],[f30,f1766]) ).
fof(f2240,plain,
top = composition(top,top),
inference(paramodulation,[status(thm)],[f1098,f2208]) ).
fof(f2333,plain,
! [X0] : composition(join(one,one),X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f1019,f389]) ).
fof(f2347,plain,
! [X0] : X0 = join(X0,X0),
inference(backward_demodulation,[status(thm)],[f2348,f345]) ).
fof(f2348,plain,
! [X0] : composition(join(one,one),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1019,f2333]) ).
fof(f2398,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f2347,f99]) ).
fof(f3354,plain,
! [X0,X1] : join(meet(X0,complement(X1)),X0) = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f909,f2398]) ).
fof(f3411,plain,
! [X0,X1] : join(X0,meet(X0,complement(X1))) = join(meet(X1,X0),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f3354]) ).
fof(f3419,plain,
! [X0,X1] : join(X0,meet(X0,complement(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f909,f3411]) ).
fof(f3487,plain,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
inference(paramodulation,[status(thm)],[f1019,f3419]) ).
fof(f3568,plain,
! [X0,X1,X2] : join(X0,join(X1,meet(X0,X2))) = join(X1,X0),
inference(paramodulation,[status(thm)],[f3487,f99]) ).
fof(f7112,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(X0,X1),complement(X0)),
inference(paramodulation,[status(thm)],[f947,f3568]) ).
fof(f7201,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f7112]) ).
fof(f7822,plain,
! [X0] : join(zero,composition(X0,complement(composition(converse(X0),top)))) = complement(top),
inference(paramodulation,[status(thm)],[f65,f372]) ).
fof(f7865,plain,
! [X0] : composition(X0,complement(composition(converse(X0),top))) = complement(top),
inference(forward_demodulation,[status(thm)],[f1006,f7822]) ).
fof(f7866,plain,
! [X0] : composition(X0,complement(composition(converse(X0),top))) = zero,
inference(forward_demodulation,[status(thm)],[f65,f7865]) ).
fof(f12146,plain,
! [X0,X1] : join(complement(complement(X0)),X1) = join(X0,meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f1019,f7201]) ).
fof(f12251,plain,
! [X0,X1] : join(X0,X1) = join(X0,meet(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1019,f12146]) ).
fof(f17236,plain,
! [X0] : join(meet(composition(top,X0),converse(top)),composition(meet(top,converse(composition(X0,top))),meet(X0,converse(top)))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(paramodulation,[status(thm)],[f2240,f447]) ).
fof(f17458,plain,
! [X0] : join(meet(converse(top),composition(top,X0)),composition(meet(top,converse(composition(X0,top))),meet(X0,converse(top)))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f62,f17236]) ).
fof(f17459,plain,
! [X0] : join(meet(top,composition(top,X0)),composition(meet(top,converse(composition(X0,top))),meet(X0,converse(top)))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f739,f17458]) ).
fof(f17460,plain,
! [X0] : join(composition(top,X0),composition(meet(top,converse(composition(X0,top))),meet(X0,converse(top)))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f1098,f17459]) ).
fof(f17461,plain,
! [X0] : join(composition(top,X0),composition(converse(composition(X0,top)),meet(X0,converse(top)))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f1098,f17460]) ).
fof(f17462,plain,
! [X0] : join(composition(top,X0),composition(composition(top,converse(X0)),meet(X0,converse(top)))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f782,f17461]) ).
fof(f17463,plain,
! [X0] : join(composition(top,X0),composition(top,composition(converse(X0),meet(X0,converse(top))))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f23,f17462]) ).
fof(f17464,plain,
! [X0] : join(composition(top,X0),composition(top,composition(converse(X0),meet(X0,top)))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f739,f17463]) ).
fof(f17465,plain,
! [X0] : join(composition(top,X0),composition(top,composition(converse(X0),X0))) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f1183,f17464]) ).
fof(f17466,plain,
! [X0] : composition(join(top,composition(top,converse(X0))),X0) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f107,f17465]) ).
fof(f17467,plain,
! [X0] : composition(top,X0) = composition(meet(top,converse(composition(X0,top))),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f715,f17466]) ).
fof(f17468,plain,
! [X0] : composition(top,X0) = composition(converse(composition(X0,top)),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f1098,f17467]) ).
fof(f17469,plain,
! [X0] : composition(top,X0) = composition(composition(top,converse(X0)),meet(X0,converse(composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f782,f17468]) ).
fof(f17470,plain,
! [X0] : composition(top,X0) = composition(top,composition(converse(X0),meet(X0,converse(composition(top,top))))),
inference(forward_demodulation,[status(thm)],[f23,f17469]) ).
fof(f17471,plain,
! [X0] : composition(top,X0) = composition(top,composition(converse(X0),meet(X0,composition(converse(top),top)))),
inference(forward_demodulation,[status(thm)],[f780,f17470]) ).
fof(f17472,plain,
! [X0] : composition(top,X0) = composition(top,composition(converse(X0),meet(X0,composition(top,top)))),
inference(forward_demodulation,[status(thm)],[f739,f17471]) ).
fof(f17473,plain,
! [X0] : composition(top,X0) = composition(top,composition(converse(X0),meet(X0,top))),
inference(forward_demodulation,[status(thm)],[f2240,f17472]) ).
fof(f17474,plain,
! [X0] : composition(top,X0) = composition(top,composition(converse(X0),X0)),
inference(forward_demodulation,[status(thm)],[f1183,f17473]) ).
fof(f19031,plain,
! [X0] : join(complement(converse(top)),composition(composition(converse(X0),X0),complement(converse(composition(top,X0))))) = complement(converse(top)),
inference(paramodulation,[status(thm)],[f17474,f390]) ).
fof(f19191,plain,
! [X0] : join(complement(top),composition(composition(converse(X0),X0),complement(converse(composition(top,X0))))) = complement(converse(top)),
inference(forward_demodulation,[status(thm)],[f739,f19031]) ).
fof(f19192,plain,
! [X0] : join(zero,composition(composition(converse(X0),X0),complement(converse(composition(top,X0))))) = complement(converse(top)),
inference(forward_demodulation,[status(thm)],[f65,f19191]) ).
fof(f19193,plain,
! [X0] : composition(composition(converse(X0),X0),complement(converse(composition(top,X0)))) = complement(converse(top)),
inference(forward_demodulation,[status(thm)],[f1006,f19192]) ).
fof(f19194,plain,
! [X0] : composition(converse(X0),composition(X0,complement(converse(composition(top,X0))))) = complement(converse(top)),
inference(forward_demodulation,[status(thm)],[f23,f19193]) ).
fof(f19195,plain,
! [X0] : composition(converse(X0),composition(X0,complement(composition(converse(X0),top)))) = complement(converse(top)),
inference(forward_demodulation,[status(thm)],[f780,f19194]) ).
fof(f19196,plain,
! [X0] : composition(converse(X0),zero) = complement(converse(top)),
inference(forward_demodulation,[status(thm)],[f7866,f19195]) ).
fof(f19197,plain,
! [X0] : composition(converse(X0),zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f739,f19196]) ).
fof(f19231,plain,
! [X0] : composition(converse(X0),zero) = zero,
inference(forward_demodulation,[status(thm)],[f65,f19197]) ).
fof(f19374,plain,
! [X0,X1] : composition(composition(X0,converse(X1)),zero) = zero,
inference(paramodulation,[status(thm)],[f52,f19231]) ).
fof(f19418,plain,
! [X0,X1] : composition(X0,composition(converse(X1),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f23,f19374]) ).
fof(f19560,plain,
! [X0] : composition(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f19231,f19418]) ).
fof(f21208,plain,
join(meet(composition(converse(sk1),sk1),complement(one)),composition(meet(converse(sk1),composition(complement(one),converse(sk1))),zero)) = composition(meet(converse(sk1),composition(complement(one),converse(sk1))),meet(sk1,composition(sk1,complement(one)))),
inference(paramodulation,[status(thm)],[f47,f479]) ).
fof(f21391,plain,
join(meet(complement(one),composition(converse(sk1),sk1)),composition(meet(converse(sk1),composition(complement(one),converse(sk1))),zero)) = composition(meet(converse(sk1),composition(complement(one),converse(sk1))),meet(sk1,composition(sk1,complement(one)))),
inference(forward_demodulation,[status(thm)],[f62,f21208]) ).
fof(f21392,plain,
join(meet(complement(one),composition(converse(sk1),sk1)),zero) = composition(meet(converse(sk1),composition(complement(one),converse(sk1))),meet(sk1,composition(sk1,complement(one)))),
inference(forward_demodulation,[status(thm)],[f19560,f21391]) ).
fof(f21393,plain,
meet(complement(one),composition(converse(sk1),sk1)) = composition(meet(converse(sk1),composition(complement(one),converse(sk1))),meet(sk1,composition(sk1,complement(one)))),
inference(forward_demodulation,[status(thm)],[f1154,f21392]) ).
fof(f21394,plain,
meet(complement(one),composition(converse(sk1),sk1)) = composition(meet(converse(sk1),composition(complement(one),converse(sk1))),zero),
inference(forward_demodulation,[status(thm)],[f47,f21393]) ).
fof(f21395,plain,
meet(complement(one),composition(converse(sk1),sk1)) = zero,
inference(forward_demodulation,[status(thm)],[f19560,f21394]) ).
fof(f25403,plain,
join(one,composition(converse(sk1),sk1)) = join(one,zero),
inference(paramodulation,[status(thm)],[f21395,f12251]) ).
fof(f25455,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(forward_demodulation,[status(thm)],[f1154,f25403]) ).
fof(f25456,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f25455,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL042-2 : 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 04:05:51 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 13.39/2.18 % Refutation found
% 13.39/2.18 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.39/2.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.88/2.26 % Elapsed time: 1.879735 seconds
% 5.88/2.26 % CPU time: 14.407921 seconds
% 5.88/2.26 % Total memory used: 173.166 MB
% 5.88/2.26 % Net memory used: 170.113 MB
%------------------------------------------------------------------------------