%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL044+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 : n018.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 02:03:27 PM UTC 2026
% Result : Theorem 18.97s 7.92s
% Output : CNFRefutation 18.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 14
% Syntax : Number of formulae : 151 ( 147 unt; 0 def)
% Number of atoms : 155 ( 154 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 216 ( 213 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [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))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1,X2] :
( join(composition(complement(X0),X1),complement(X2)) = complement(X2)
=> join(composition(X2,converse(X1)),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( join(composition(complement(X0),X1),complement(X2)) = complement(X2)
=> join(composition(X2,converse(X1)),X0) = X0 ),
inference(negated_conjecture,[status(cth)],[f17]) ).
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(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,X1,X2] :
( join(composition(X2,converse(X1)),X0) != X0
& join(composition(complement(X0),X1),complement(X2)) = complement(X2) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
( join(composition(sK2_skl,converse(sK1_skl)),sK0_skl) != sK0_skl
& join(composition(complement(sK0_skl),sK1_skl),complement(sK2_skl)) = complement(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl)],[f35]) ).
fof(f37,plain,
join(composition(complement(sK0_skl),sK1_skl),complement(sK2_skl)) = complement(sK2_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
join(composition(sK2_skl,converse(sK1_skl)),sK0_skl) != sK0_skl,
inference(cnf_transformation,[status(thm)],[f36]) ).
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,
join(complement(sK2_skl),composition(complement(sK0_skl),sK1_skl)) = complement(sK2_skl),
inference(forward_demodulation,[status(thm)],[f19,f37]) ).
fof(f47,plain,
join(sK0_skl,composition(sK2_skl,converse(sK1_skl))) != sK0_skl,
inference(forward_demodulation,[status(thm)],[f19,f38]) ).
fof(f48,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f44]) ).
fof(f57,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f63,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f57]) ).
fof(f67,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f71,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f77,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f71]) ).
fof(f84,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f103,plain,
! [X0,X1] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f267,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f48]) ).
fof(f273,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f267]) ).
fof(f276,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f63,f273]) ).
fof(f278,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f63,f273]) ).
fof(f286,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f63,f276]) ).
fof(f338,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f84]) ).
fof(f344,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f338]) ).
fof(f348,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f344]) ).
fof(f349,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f344,f45]) ).
fof(f355,plain,
! [X0,X1] : composition(join(X0,converse(one)),X1) = join(composition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f344,f25]) ).
fof(f356,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f344,f25]) ).
fof(f358,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f348,f344]) ).
fof(f362,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(composition(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f348,f355]) ).
fof(f364,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f362]) ).
fof(f365,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f348,f356]) ).
fof(f366,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f358,f349]) ).
fof(f381,plain,
! [X0] : converse(join(X0,one)) = join(converse(X0),one),
inference(paramodulation,[status(thm)],[f348,f103]) ).
fof(f392,plain,
! [X0] : converse(join(X0,one)) = join(one,converse(X0)),
inference(forward_demodulation,[status(thm)],[f19,f381]) ).
fof(f399,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f31,f278]) ).
fof(f400,plain,
! [X0] : X0 = join(meet(X0,X0),zero),
inference(paramodulation,[status(thm)],[f31,f276]) ).
fof(f402,plain,
! [X0] : X0 = join(zero,meet(complement(complement(X0)),X0)),
inference(paramodulation,[status(thm)],[f31,f278]) ).
fof(f407,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f19,f399]) ).
fof(f408,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f63,f407]) ).
fof(f409,plain,
! [X0] : X0 = join(zero,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f19,f400]) ).
fof(f411,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f63,f402]) ).
fof(f415,plain,
! [X0] : X0 = complement(complement(X0)),
inference(forward_demodulation,[status(thm)],[f408,f411]) ).
fof(f420,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f415]) ).
fof(f427,plain,
! [X0,X1] : meet(X0,complement(X1)) = complement(join(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f415,f22]) ).
fof(f431,plain,
! [X0] : complement(meet(X0,X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f420,f366]) ).
fof(f460,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f431,f415]) ).
fof(f468,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f471,f409]) ).
fof(f471,plain,
! [X0] : meet(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f415,f460]) ).
fof(f490,plain,
! [X0] : X0 = join(X0,meet(complement(X0),X0)),
inference(paramodulation,[status(thm)],[f471,f278]) ).
fof(f504,plain,
! [X0] : X0 = join(X0,meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f63,f490]) ).
fof(f505,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f31,f504]) ).
fof(f508,plain,
complement(zero) = top,
inference(paramodulation,[status(thm)],[f30,f468]) ).
fof(f512,plain,
! [X0] : converse(converse(X0)) = join(converse(zero),X0),
inference(paramodulation,[status(thm)],[f468,f103]) ).
fof(f518,plain,
! [X0] : X0 = join(converse(zero),X0),
inference(forward_demodulation,[status(thm)],[f26,f512]) ).
fof(f520,plain,
zero = complement(top),
inference(paramodulation,[status(thm)],[f508,f415]) ).
fof(f532,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(paramodulation,[status(thm)],[f520,f45]) ).
fof(f536,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = complement(top),
inference(forward_demodulation,[status(thm)],[f468,f532]) ).
fof(f537,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(forward_demodulation,[status(thm)],[f520,f536]) ).
fof(f562,plain,
zero = converse(zero),
inference(paramodulation,[status(thm)],[f505,f518]) ).
fof(f647,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(f704,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,f647]) ).
fof(f1222,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f420]) ).
fof(f1226,plain,
! [X0] : join(top,complement(X0)) = complement(meet(zero,X0)),
inference(paramodulation,[status(thm)],[f508,f420]) ).
fof(f1227,plain,
! [X0,X1] : join(X0,complement(X1)) = complement(meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f415,f420]) ).
fof(f1229,plain,
! [X0] : join(complement(X0),zero) = complement(meet(X0,top)),
inference(paramodulation,[status(thm)],[f520,f420]) ).
fof(f1242,plain,
! [X0,X1] : complement(meet(X0,X1)) = complement(meet(X1,X0)),
inference(forward_demodulation,[status(thm)],[f420,f1222]) ).
fof(f1250,plain,
! [X0] : complement(X0) = complement(meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f505,f1229]) ).
fof(f1266,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f1250,f415]) ).
fof(f1289,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f415,f1266]) ).
fof(f1316,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X2,X1)),
inference(paramodulation,[status(thm)],[f67,f77]) ).
fof(f1673,plain,
! [X0,X1] : top = join(meet(X0,X1),complement(meet(X1,X0))),
inference(paramodulation,[status(thm)],[f1242,f30]) ).
fof(f1882,plain,
meet(sK2_skl,complement(composition(complement(sK0_skl),sK1_skl))) = complement(complement(sK2_skl)),
inference(paramodulation,[status(thm)],[f46,f427]) ).
fof(f1902,plain,
! [X0] : meet(zero,complement(X0)) = complement(join(top,X0)),
inference(paramodulation,[status(thm)],[f508,f427]) ).
fof(f1920,plain,
meet(sK2_skl,complement(composition(complement(sK0_skl),sK1_skl))) = sK2_skl,
inference(forward_demodulation,[status(thm)],[f415,f1882]) ).
fof(f2018,plain,
! [X0] : composition(join(one,converse(X0)),complement(composition(join(X0,one),top))) = zero,
inference(paramodulation,[status(thm)],[f392,f537]) ).
fof(f2038,plain,
! [X0] : composition(join(one,converse(X0)),complement(join(top,composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f364,f2018]) ).
fof(f2039,plain,
! [X0] : composition(join(one,converse(X0)),meet(zero,complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f1902,f2038]) ).
fof(f3056,plain,
! [X0] : zero = meet(meet(zero,X0),join(top,complement(X0))),
inference(paramodulation,[status(thm)],[f1226,f31]) ).
fof(f3101,plain,
! [X0] : join(X0,complement(complement(X0))) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f471,f1227]) ).
fof(f3139,plain,
! [X0] : join(X0,X0) = complement(complement(X0)),
inference(forward_demodulation,[status(thm)],[f415,f3101]) ).
fof(f3148,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f415,f3139]) ).
fof(f3210,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f3148,f77]) ).
fof(f3265,plain,
! [X0,X1] : join(meet(complement(X0),X1),X1) = join(meet(X0,X1),meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f286,f3210]) ).
fof(f3290,plain,
! [X0] : join(complement(X0),top) = join(X0,complement(X0)),
inference(paramodulation,[status(thm)],[f30,f3210]) ).
fof(f3326,plain,
! [X0,X1] : join(X0,meet(complement(X1),X0)) = join(meet(X1,X0),meet(complement(X1),X0)),
inference(forward_demodulation,[status(thm)],[f19,f3265]) ).
fof(f3327,plain,
! [X0,X1] : join(X0,meet(complement(X1),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f286,f3326]) ).
fof(f3380,plain,
! [X0] : join(top,complement(X0)) = join(X0,complement(X0)),
inference(forward_demodulation,[status(thm)],[f19,f3290]) ).
fof(f3389,plain,
! [X0] : zero = meet(meet(zero,X0),top),
inference(backward_demodulation,[status(thm)],[f3393,f3056]) ).
fof(f3393,plain,
! [X0] : join(top,complement(X0)) = top,
inference(forward_demodulation,[status(thm)],[f30,f3380]) ).
fof(f3443,plain,
! [X0] : composition(join(one,converse(X0)),zero) = zero,
inference(backward_demodulation,[status(thm)],[f3470,f2039]) ).
fof(f3470,plain,
! [X0] : zero = meet(zero,X0),
inference(forward_demodulation,[status(thm)],[f1289,f3389]) ).
fof(f3490,plain,
! [X0] : join(zero,composition(converse(X0),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f365,f3443]) ).
fof(f3498,plain,
! [X0] : composition(converse(X0),zero) = zero,
inference(forward_demodulation,[status(thm)],[f468,f3490]) ).
fof(f3996,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(paramodulation,[status(thm)],[f3498,f84]) ).
fof(f4040,plain,
! [X0] : zero = composition(converse(zero),X0),
inference(forward_demodulation,[status(thm)],[f562,f3996]) ).
fof(f4062,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[status(thm)],[f562,f4040]) ).
fof(f4274,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f415,f3327]) ).
fof(f4331,plain,
! [X0,X1,X2] : join(X0,join(X1,meet(X2,X0))) = join(X1,X0),
inference(paramodulation,[status(thm)],[f4274,f77]) ).
fof(f4333,plain,
! [X0,X1,X2] : join(X0,join(meet(X1,X0),X2)) = join(X2,X0),
inference(paramodulation,[status(thm)],[f4274,f67]) ).
fof(f6342,plain,
! [X0,X1] : top = join(meet(X0,complement(X1)),join(X1,complement(X0))),
inference(paramodulation,[status(thm)],[f1227,f1673]) ).
fof(f6421,plain,
! [X0,X1] : top = join(X0,join(meet(X1,complement(X0)),complement(X1))),
inference(forward_demodulation,[status(thm)],[f77,f6342]) ).
fof(f6422,plain,
! [X0,X1] : top = join(X0,join(complement(X1),meet(X1,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f1316,f6421]) ).
fof(f7216,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(X0,X1),complement(X0)),
inference(paramodulation,[status(thm)],[f276,f4331]) ).
fof(f7295,plain,
! [X0,X1] : top = join(X0,join(complement(X1),complement(X0))),
inference(backward_demodulation,[status(thm)],[f7296,f6422]) ).
fof(f7296,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f7216]) ).
fof(f7360,plain,
! [X0,X1] : top = join(X0,complement(meet(X1,X0))),
inference(forward_demodulation,[status(thm)],[f420,f7295]) ).
fof(f7684,plain,
! [X0,X1] : meet(X0,complement(complement(meet(X1,complement(X0))))) = complement(top),
inference(paramodulation,[status(thm)],[f7360,f427]) ).
fof(f7748,plain,
! [X0,X1] : meet(X0,meet(X1,complement(X0))) = complement(top),
inference(forward_demodulation,[status(thm)],[f415,f7684]) ).
fof(f7749,plain,
! [X0,X1] : meet(X0,meet(X1,complement(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f520,f7748]) ).
fof(f7776,plain,
meet(composition(complement(sK0_skl),sK1_skl),sK2_skl) = zero,
inference(paramodulation,[status(thm)],[f1920,f7749]) ).
fof(f7824,plain,
meet(sK2_skl,composition(complement(sK0_skl),sK1_skl)) = zero,
inference(forward_demodulation,[status(thm)],[f63,f7776]) ).
fof(f8962,plain,
! [X0,X1] : join(X0,X1) = join(meet(complement(X0),X1),X0),
inference(paramodulation,[status(thm)],[f278,f4333]) ).
fof(f9073,plain,
! [X0,X1] : join(X0,X1) = join(X0,meet(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f19,f8962]) ).
fof(f18649,plain,
join(meet(composition(sK2_skl,converse(sK1_skl)),complement(sK0_skl)),composition(zero,meet(converse(sK1_skl),composition(converse(sK2_skl),complement(sK0_skl))))) = composition(meet(sK2_skl,composition(complement(sK0_skl),sK1_skl)),meet(converse(sK1_skl),composition(converse(sK2_skl),complement(sK0_skl)))),
inference(paramodulation,[status(thm)],[f7824,f704]) ).
fof(f18822,plain,
join(meet(complement(sK0_skl),composition(sK2_skl,converse(sK1_skl))),composition(zero,meet(converse(sK1_skl),composition(converse(sK2_skl),complement(sK0_skl))))) = composition(meet(sK2_skl,composition(complement(sK0_skl),sK1_skl)),meet(converse(sK1_skl),composition(converse(sK2_skl),complement(sK0_skl)))),
inference(forward_demodulation,[status(thm)],[f63,f18649]) ).
fof(f18823,plain,
join(meet(complement(sK0_skl),composition(sK2_skl,converse(sK1_skl))),zero) = composition(meet(sK2_skl,composition(complement(sK0_skl),sK1_skl)),meet(converse(sK1_skl),composition(converse(sK2_skl),complement(sK0_skl)))),
inference(forward_demodulation,[status(thm)],[f4062,f18822]) ).
fof(f18824,plain,
meet(complement(sK0_skl),composition(sK2_skl,converse(sK1_skl))) = composition(meet(sK2_skl,composition(complement(sK0_skl),sK1_skl)),meet(converse(sK1_skl),composition(converse(sK2_skl),complement(sK0_skl)))),
inference(forward_demodulation,[status(thm)],[f505,f18823]) ).
fof(f18825,plain,
meet(complement(sK0_skl),composition(sK2_skl,converse(sK1_skl))) = composition(zero,meet(converse(sK1_skl),composition(converse(sK2_skl),complement(sK0_skl)))),
inference(forward_demodulation,[status(thm)],[f7824,f18824]) ).
fof(f18826,plain,
meet(complement(sK0_skl),composition(sK2_skl,converse(sK1_skl))) = zero,
inference(forward_demodulation,[status(thm)],[f4062,f18825]) ).
fof(f19055,plain,
join(sK0_skl,composition(sK2_skl,converse(sK1_skl))) = join(sK0_skl,zero),
inference(paramodulation,[status(thm)],[f18826,f9073]) ).
fof(f19095,plain,
join(sK0_skl,composition(sK2_skl,converse(sK1_skl))) = sK0_skl,
inference(forward_demodulation,[status(thm)],[f505,f19055]) ).
fof(f19096,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f19095,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL044+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n018.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Mon Sep 21 04:10:34 UTC 2026
% 0.18/5.47 % CPUTime :
% 0.18/5.48 % Drodi V4.1.1
% 18.97/7.92 % Refutation found
% 18.97/7.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.97/7.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.08/8.02 % Elapsed time: 2.534257 seconds
% 1.08/8.02 % CPU time: 19.550379 seconds
% 1.08/8.02 % Total memory used: 205.058 MB
% 1.08/8.02 % Net memory used: 200.944 MB
%------------------------------------------------------------------------------