%------------------------------------------------------------------------------
% 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/sandbox2/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 02:03:26 PM UTC 2026
% Result : Theorem 30.31s 4.38s
% Output : CNFRefutation 30.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 18
% Syntax : Number of formulae : 143 ( 139 unt; 3 def)
% Number of atoms : 147 ( 146 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 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 : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 180 ( 179 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
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(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] :
( join(composition(converse(X0),X0),one) != one
& ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
( join(composition(converse(sK0_skl),sK0_skl),one) != one
& ! [X1] : meet(composition(sK0_skl,X1),composition(sK0_skl,complement(X1))) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f35]) ).
fof(f37,plain,
! [X0] : meet(composition(sK0_skl,X0),composition(sK0_skl,complement(X0))) = zero,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
join(composition(converse(sK0_skl),sK0_skl),one) != one,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,definition,
sF2_fnc = converse(sK0_skl),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f40,definition,
sF1_fnc = composition(sF2_fnc,sK0_skl),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f41,definition,
sF0_fnc = join(sF1_fnc,one),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f42,plain,
sF0_fnc != one,
inference(definition_folding,[],[f38,f41,f40,f39]) ).
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,
sF0_fnc = join(one,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f19,f41]) ).
fof(f47,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f44]) ).
fof(f52,plain,
meet(sK0_skl,composition(sK0_skl,complement(one))) = zero,
inference(paramodulation,[status(thm)],[f24,f37]) ).
fof(f54,plain,
converse(sF2_fnc) = sK0_skl,
inference(paramodulation,[status(thm)],[f39,f26]) ).
fof(f56,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f64,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f56]) ).
fof(f77,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f139,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(paramodulation,[status(thm)],[f20,f30]) ).
fof(f142,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f30,f22]) ).
fof(f143,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f145,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f31,f142]) ).
fof(f161,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f164,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f172,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f235,plain,
! [X0,X1] : join(X0,join(X1,complement(X0))) = join(top,X1),
inference(paramodulation,[status(thm)],[f19,f143]) ).
fof(f321,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(paramodulation,[status(thm)],[f145,f45]) ).
fof(f339,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f145,f321]) ).
fof(f357,plain,
! [X0] : join(meet(sF1_fnc,X0),composition(meet(sF2_fnc,composition(X0,converse(sK0_skl))),meet(sK0_skl,composition(converse(sF2_fnc),X0)))) = composition(meet(sF2_fnc,composition(X0,converse(sK0_skl))),meet(sK0_skl,composition(converse(sF2_fnc),X0))),
inference(paramodulation,[status(thm)],[f40,f32]) ).
fof(f398,plain,
! [X0] : join(meet(sF1_fnc,X0),composition(meet(sF2_fnc,composition(X0,sF2_fnc)),meet(sK0_skl,composition(converse(sF2_fnc),X0)))) = composition(meet(sF2_fnc,composition(X0,converse(sK0_skl))),meet(sK0_skl,composition(converse(sF2_fnc),X0))),
inference(forward_demodulation,[status(thm)],[f39,f357]) ).
fof(f399,plain,
! [X0] : join(meet(sF1_fnc,X0),composition(meet(sF2_fnc,composition(X0,sF2_fnc)),meet(sK0_skl,composition(sK0_skl,X0)))) = composition(meet(sF2_fnc,composition(X0,converse(sK0_skl))),meet(sK0_skl,composition(converse(sF2_fnc),X0))),
inference(forward_demodulation,[status(thm)],[f54,f398]) ).
fof(f400,plain,
! [X0] : join(meet(sF1_fnc,X0),composition(meet(sF2_fnc,composition(X0,sF2_fnc)),meet(sK0_skl,composition(sK0_skl,X0)))) = composition(meet(sF2_fnc,composition(X0,sF2_fnc)),meet(sK0_skl,composition(converse(sF2_fnc),X0))),
inference(forward_demodulation,[status(thm)],[f39,f399]) ).
fof(f401,plain,
! [X0] : join(meet(sF1_fnc,X0),composition(meet(sF2_fnc,composition(X0,sF2_fnc)),meet(sK0_skl,composition(sK0_skl,X0)))) = composition(meet(sF2_fnc,composition(X0,sF2_fnc)),meet(sK0_skl,composition(sK0_skl,X0))),
inference(forward_demodulation,[status(thm)],[f54,f400]) ).
fof(f433,plain,
! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(paramodulation,[status(thm)],[f31,f47]) ).
fof(f436,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f47]) ).
fof(f438,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))),
inference(paramodulation,[status(thm)],[f143,f47]) ).
fof(f439,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f30,f47]) ).
fof(f450,plain,
! [X0] : X0 = join(zero,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f22,f433]) ).
fof(f451,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f436]) ).
fof(f453,plain,
! [X0,X1] : X0 = join(complement(join(top,X1)),meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f19,f438]) ).
fof(f454,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f439]) ).
fof(f455,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f145,f454]) ).
fof(f587,plain,
top = join(zero,meet(top,complement(zero))),
inference(paramodulation,[status(thm)],[f145,f455]) ).
fof(f598,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f64,f451]) ).
fof(f601,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f64,f451]) ).
fof(f603,plain,
! [X0] : X0 = join(meet(X0,top),meet(X0,zero)),
inference(paramodulation,[status(thm)],[f145,f451]) ).
fof(f613,plain,
! [X0] : X0 = join(meet(X0,top),meet(zero,X0)),
inference(paramodulation,[status(thm)],[f64,f603]) ).
fof(f622,plain,
complement(zero) = join(meet(complement(zero),top),zero),
inference(paramodulation,[status(thm)],[f31,f613]) ).
fof(f631,plain,
complement(zero) = join(zero,meet(complement(zero),top)),
inference(forward_demodulation,[status(thm)],[f19,f622]) ).
fof(f632,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(forward_demodulation,[status(thm)],[f64,f631]) ).
fof(f636,plain,
complement(zero) = top,
inference(forward_demodulation,[status(thm)],[f587,f632]) ).
fof(f881,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f31,f601]) ).
fof(f898,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f19,f881]) ).
fof(f899,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f64,f898]) ).
fof(f903,plain,
! [X0,X1] : X0 = join(complement(join(top,X1)),meet(X0,join(X0,X1))),
inference(backward_demodulation,[status(thm)],[f907,f453]) ).
fof(f907,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f455,f899]) ).
fof(f916,plain,
! [X0,X1] : complement(meet(X0,X1)) = join(complement(X0),complement(X1)),
inference(paramodulation,[status(thm)],[f22,f907]) ).
fof(f929,plain,
! [X0,X1] : meet(X0,complement(X1)) = complement(join(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f907,f22]) ).
fof(f1157,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f164]) ).
fof(f1193,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f1157]) ).
fof(f1223,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f77,f1193]) ).
fof(f1224,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f1193]) ).
fof(f1225,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f1193,f45]) ).
fof(f1238,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f1193,f25]) ).
fof(f1250,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1193,f1223]) ).
fof(f1255,plain,
! [X0] : complement(meet(X0,composition(one,X0))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f916,f1225]) ).
fof(f1256,plain,
! [X0] : complement(meet(X0,X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f1250,f1255]) ).
fof(f1285,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1224,f1238]) ).
fof(f1304,plain,
! [X0] : converse(join(one,X0)) = join(one,converse(X0)),
inference(paramodulation,[status(thm)],[f1224,f27]) ).
fof(f1355,plain,
! [X0] : complement(complement(X0)) = meet(X0,X0),
inference(paramodulation,[status(thm)],[f1256,f907]) ).
fof(f1367,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1371,f450]) ).
fof(f1371,plain,
! [X0] : X0 = meet(X0,X0),
inference(forward_demodulation,[status(thm)],[f907,f1355]) ).
fof(f1398,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(backward_demodulation,[status(thm)],[f1367,f339]) ).
fof(f1434,plain,
! [X0] : X0 = join(X0,zero),
inference(paramodulation,[status(thm)],[f19,f1367]) ).
fof(f2805,plain,
! [X0,X1] : complement(meet(complement(X0),X1)) = join(X0,complement(X1)),
inference(paramodulation,[status(thm)],[f907,f916]) ).
fof(f2904,plain,
! [X0] : meet(zero,complement(X0)) = complement(join(top,X0)),
inference(paramodulation,[status(thm)],[f636,f929]) ).
fof(f2943,plain,
! [X0,X1] : X0 = join(meet(zero,complement(X1)),meet(X0,join(X0,X1))),
inference(backward_demodulation,[status(thm)],[f2904,f903]) ).
fof(f3910,plain,
! [X0] : composition(join(one,converse(X0)),complement(composition(join(one,X0),top))) = zero,
inference(paramodulation,[status(thm)],[f1304,f1398]) ).
fof(f3959,plain,
! [X0] : composition(join(one,converse(X0)),complement(join(top,composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f1285,f3910]) ).
fof(f3960,plain,
! [X0] : composition(join(one,converse(X0)),meet(zero,complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f2904,f3959]) ).
fof(f4914,plain,
! [X0] : complement(complement(X0)) = join(X0,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f1371,f2805]) ).
fof(f4955,plain,
! [X0] : X0 = join(X0,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f907,f4914]) ).
fof(f4968,plain,
! [X0] : X0 = join(X0,X0),
inference(forward_demodulation,[status(thm)],[f907,f4955]) ).
fof(f5045,plain,
! [X0] : top = join(X0,join(X0,complement(X0))),
inference(paramodulation,[status(thm)],[f4968,f139]) ).
fof(f5156,plain,
! [X0] : meet(zero,complement(X0)) = complement(top),
inference(backward_demodulation,[status(thm)],[f5163,f2904]) ).
fof(f5163,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[status(thm)],[f235,f5045]) ).
fof(f5222,plain,
! [X0] : composition(join(one,converse(X0)),zero) = zero,
inference(backward_demodulation,[status(thm)],[f5229,f3960]) ).
fof(f5227,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(X0,X1))),
inference(backward_demodulation,[status(thm)],[f5229,f2943]) ).
fof(f5229,plain,
! [X0] : meet(zero,complement(X0)) = zero,
inference(forward_demodulation,[status(thm)],[f145,f5156]) ).
fof(f5245,plain,
! [X0] : join(zero,composition(converse(X0),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f1285,f5222]) ).
fof(f5246,plain,
! [X0] : composition(converse(X0),zero) = zero,
inference(forward_demodulation,[status(thm)],[f1367,f5245]) ).
fof(f5249,plain,
! [X0,X1] : X0 = meet(X0,join(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1367,f5227]) ).
fof(f5484,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(zero)),
inference(paramodulation,[status(thm)],[f1434,f172]) ).
fof(f5575,plain,
! [X0] : X0 = join(X0,converse(zero)),
inference(forward_demodulation,[status(thm)],[f26,f5484]) ).
fof(f6246,plain,
zero = converse(zero),
inference(paramodulation,[status(thm)],[f1367,f5575]) ).
fof(f6327,plain,
! [X0] : converse(composition(zero,X0)) = composition(converse(X0),zero),
inference(paramodulation,[status(thm)],[f6246,f164]) ).
fof(f6344,plain,
! [X0] : converse(composition(zero,X0)) = zero,
inference(forward_demodulation,[status(thm)],[f5246,f6327]) ).
fof(f6360,plain,
! [X0] : composition(X0,converse(zero)) = zero,
inference(paramodulation,[status(thm)],[f161,f6344]) ).
fof(f6411,plain,
! [X0] : composition(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f6246,f6360]) ).
fof(f6748,plain,
! [X0,X1] : complement(complement(X0)) = join(X0,complement(join(complement(X0),X1))),
inference(paramodulation,[status(thm)],[f5249,f2805]) ).
fof(f6763,plain,
! [X0,X1] : X0 = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f907,f6748]) ).
fof(f6764,plain,
! [X0,X1] : X0 = join(X0,meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f929,f6763]) ).
fof(f7282,plain,
! [X0,X1] : X0 = join(X0,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f907,f6764]) ).
fof(f8497,plain,
join(meet(sF1_fnc,complement(one)),composition(meet(sF2_fnc,composition(complement(one),sF2_fnc)),zero)) = composition(meet(sF2_fnc,composition(complement(one),sF2_fnc)),meet(sK0_skl,composition(sK0_skl,complement(one)))),
inference(paramodulation,[status(thm)],[f52,f401]) ).
fof(f8526,plain,
join(meet(sF1_fnc,complement(one)),zero) = composition(meet(sF2_fnc,composition(complement(one),sF2_fnc)),meet(sK0_skl,composition(sK0_skl,complement(one)))),
inference(forward_demodulation,[status(thm)],[f6411,f8497]) ).
fof(f8527,plain,
meet(sF1_fnc,complement(one)) = composition(meet(sF2_fnc,composition(complement(one),sF2_fnc)),meet(sK0_skl,composition(sK0_skl,complement(one)))),
inference(forward_demodulation,[status(thm)],[f1434,f8526]) ).
fof(f8528,plain,
meet(sF1_fnc,complement(one)) = composition(meet(sF2_fnc,composition(complement(one),sF2_fnc)),zero),
inference(forward_demodulation,[status(thm)],[f52,f8527]) ).
fof(f8529,plain,
meet(sF1_fnc,complement(one)) = zero,
inference(forward_demodulation,[status(thm)],[f6411,f8528]) ).
fof(f8553,plain,
sF1_fnc = join(meet(one,sF1_fnc),zero),
inference(paramodulation,[status(thm)],[f8529,f598]) ).
fof(f8563,plain,
sF1_fnc = meet(one,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1434,f8553]) ).
fof(f8591,plain,
one = join(one,sF1_fnc),
inference(paramodulation,[status(thm)],[f8563,f7282]) ).
fof(f8598,plain,
one = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f46,f8591]) ).
fof(f8599,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8598,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL042+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 % Computer : n018.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Mon Sep 21 04:09:58 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.49 % Drodi V4.1.1
% 30.31/4.38 % Refutation found
% 30.31/4.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 30.31/4.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.75/4.49 % Elapsed time: 3.993355 seconds
% 11.75/4.49 % CPU time: 31.040934 seconds
% 11.75/4.49 % Total memory used: 324.129 MB
% 11.75/4.49 % Net memory used: 316.957 MB
%------------------------------------------------------------------------------