%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL035+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:03:24 PM UTC 2026
% Result : Theorem 260.41s 38.71s
% Output : CNFRefutation 185.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 20
% Syntax : Number of formulae : 285 ( 280 unt; 5 def)
% Number of atoms : 290 ( 289 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 352 ( 346 !; 6 ?)
% 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(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
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] :
( composition(X0,top) = X0
=> composition(meet(X1,converse(X0)),meet(X0,X2)) = composition(X1,meet(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( composition(X0,top) = X0
=> composition(meet(X1,converse(X0)),meet(X0,X2)) = composition(X1,meet(X0,X2)) ),
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,X1,X2] :
( composition(meet(X1,converse(X0)),meet(X0,X2)) != composition(X1,meet(X0,X2))
& composition(X0,top) = X0 ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
? [X0] :
( ? [X1,X2] : composition(meet(X1,converse(X0)),meet(X0,X2)) != composition(X1,meet(X0,X2))
& composition(X0,top) = X0 ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
( composition(meet(sK1_skl,converse(sK0_skl)),meet(sK0_skl,sK2_skl)) != composition(sK1_skl,meet(sK0_skl,sK2_skl))
& composition(sK0_skl,top) = sK0_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)],[f36]) ).
fof(f38,plain,
composition(sK0_skl,top) = sK0_skl,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
composition(meet(sK1_skl,converse(sK0_skl)),meet(sK0_skl,sK2_skl)) != composition(sK1_skl,meet(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,definition,
sF2_fnc = converse(sK0_skl),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f41,definition,
sF1_fnc = meet(sK1_skl,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f42,definition,
sF3_fnc = meet(sK0_skl,sK2_skl),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f43,definition,
sF0_fnc = composition(sF1_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f44,definition,
sF4_fnc = composition(sK1_skl,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f45,plain,
sF0_fnc != sF4_fnc,
inference(definition_folding,[],[f39,f44,f43,f42,f41,f40]) ).
fof(f46,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f47,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f46]) ).
fof(f48,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f49,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f47]) ).
fof(f57,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f60,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f66,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f60]) ).
fof(f68,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f70,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(f72,plain,
! [X0,X1] : zero = meet(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f31]) ).
fof(f73,plain,
sF3_fnc = meet(sK2_skl,sK0_skl),
inference(backward_demodulation,[status(thm)],[f76,f42]) ).
fof(f76,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f68]) ).
fof(f78,plain,
! [X0,X1] : zero = complement(join(meet(X0,X1),complement(meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f70,f72]) ).
fof(f79,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f30,f78]) ).
fof(f82,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f79,f22]) ).
fof(f85,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f82]) ).
fof(f88,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(paramodulation,[status(thm)],[f20,f30]) ).
fof(f89,plain,
top = join(top,zero),
inference(paramodulation,[status(thm)],[f79,f30]) ).
fof(f90,plain,
! [X0,X1] : top = join(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f30]) ).
fof(f93,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f94,plain,
top = join(zero,top),
inference(forward_demodulation,[status(thm)],[f19,f89]) ).
fof(f95,plain,
! [X0,X1] : top = join(complement(X0),join(complement(X1),meet(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f90]) ).
fof(f97,plain,
! [X0] : join(zero,join(top,X0)) = join(top,X0),
inference(paramodulation,[status(thm)],[f94,f20]) ).
fof(f104,plain,
! [X0] : composition(sK1_skl,composition(sF3_fnc,X0)) = composition(sF4_fnc,X0),
inference(paramodulation,[status(thm)],[f44,f23]) ).
fof(f105,plain,
! [X0] : composition(sF1_fnc,composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f43,f23]) ).
fof(f107,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f122,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f124,plain,
! [X0] : converse(composition(sK0_skl,X0)) = composition(converse(X0),sF2_fnc),
inference(paramodulation,[status(thm)],[f40,f28]) ).
fof(f125,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f141,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f144,plain,
! [X0] : converse(join(sK0_skl,X0)) = join(sF2_fnc,converse(X0)),
inference(paramodulation,[status(thm)],[f40,f27]) ).
fof(f145,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f152,plain,
! [X0,X1] : converse(join(X0,X1)) = converse(join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f27,f141]) ).
fof(f203,plain,
! [X0] : join(zero,join(X0,top)) = join(top,X0),
inference(paramodulation,[status(thm)],[f19,f97]) ).
fof(f209,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X1,X2),composition(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f25]) ).
fof(f215,plain,
! [X0] : composition(join(sK0_skl,X0),top) = join(sK0_skl,composition(X0,top)),
inference(paramodulation,[status(thm)],[f38,f25]) ).
fof(f219,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(f222,plain,
! [X0] : composition(join(X0,sK0_skl),top) = join(composition(X0,top),sK0_skl),
inference(paramodulation,[status(thm)],[f38,f25]) ).
fof(f230,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = composition(join(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f25,f209]) ).
fof(f237,plain,
! [X0] : composition(join(X0,sK0_skl),top) = join(sK0_skl,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f19,f222]) ).
fof(f247,plain,
! [X0,X1] : composition(join(X0,sK1_skl),composition(sF3_fnc,X1)) = join(composition(X0,composition(sF3_fnc,X1)),composition(sF4_fnc,X1)),
inference(paramodulation,[status(thm)],[f104,f25]) ).
fof(f252,plain,
! [X0,X1] : composition(join(X0,sK1_skl),composition(sF3_fnc,X1)) = join(composition(sF4_fnc,X1),composition(X0,composition(sF3_fnc,X1))),
inference(forward_demodulation,[status(thm)],[f19,f247]) ).
fof(f253,plain,
! [X0,X1] : composition(join(X0,sK1_skl),composition(sF3_fnc,X1)) = composition(join(sF4_fnc,composition(X0,sF3_fnc)),X1),
inference(forward_demodulation,[status(thm)],[f219,f252]) ).
fof(f260,plain,
! [X0,X1] : composition(join(X0,sF1_fnc),composition(sF3_fnc,X1)) = join(composition(X0,composition(sF3_fnc,X1)),composition(sF0_fnc,X1)),
inference(paramodulation,[status(thm)],[f105,f25]) ).
fof(f265,plain,
! [X0,X1] : composition(join(X0,sF1_fnc),composition(sF3_fnc,X1)) = join(composition(sF0_fnc,X1),composition(X0,composition(sF3_fnc,X1))),
inference(forward_demodulation,[status(thm)],[f19,f260]) ).
fof(f266,plain,
! [X0,X1] : composition(join(X0,sF1_fnc),composition(sF3_fnc,X1)) = composition(join(sF0_fnc,composition(X0,sF3_fnc)),X1),
inference(forward_demodulation,[status(thm)],[f219,f265]) ).
fof(f316,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f30,f93]) ).
fof(f331,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(paramodulation,[status(thm)],[f79,f48]) ).
fof(f350,plain,
! [X0] : join(complement(one),composition(converse(X0),complement(X0))) = complement(one),
inference(paramodulation,[status(thm)],[f24,f48]) ).
fof(f353,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f79,f331]) ).
fof(f498,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(f511,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(f552,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,f498]) ).
fof(f575,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,f511]) ).
fof(f581,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f125]) ).
fof(f610,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f581]) ).
fof(f637,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f107,f610]) ).
fof(f638,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f610]) ).
fof(f641,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f610,f48]) ).
fof(f652,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f610,f25]) ).
fof(f662,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f610,f637]) ).
fof(f667,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f662,f641]) ).
fof(f691,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f638,f652]) ).
fof(f726,plain,
converse(join(sK0_skl,one)) = join(sF2_fnc,one),
inference(paramodulation,[status(thm)],[f638,f144]) ).
fof(f749,plain,
converse(join(one,sK0_skl)) = join(sF2_fnc,one),
inference(forward_demodulation,[status(thm)],[f152,f726]) ).
fof(f750,plain,
converse(join(one,sK0_skl)) = join(one,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f19,f749]) ).
fof(f771,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),complement(X1)))) = complement(join(complement(X0),complement(X1))),
inference(paramodulation,[status(thm)],[f22,f667]) ).
fof(f776,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f667,f22]) ).
fof(f777,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f667,f93]) ).
fof(f790,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = complement(join(complement(X0),complement(X1))),
inference(forward_demodulation,[status(thm)],[f22,f771]) ).
fof(f792,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f790]) ).
fof(f807,plain,
! [X0] : join(X0,top) = top,
inference(backward_demodulation,[status(thm)],[f808,f316]) ).
fof(f808,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f30,f777]) ).
fof(f827,plain,
! [X0] : join(zero,top) = join(top,X0),
inference(backward_demodulation,[status(thm)],[f807,f203]) ).
fof(f837,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[status(thm)],[f94,f827]) ).
fof(f861,plain,
! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(paramodulation,[status(thm)],[f31,f49]) ).
fof(f864,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f49]) ).
fof(f867,plain,
! [X0] : X0 = join(meet(X0,top),complement(top)),
inference(paramodulation,[status(thm)],[f807,f49]) ).
fof(f879,plain,
! [X0] : X0 = join(zero,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f22,f861]) ).
fof(f880,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f776,f879]) ).
fof(f881,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f864]) ).
fof(f886,plain,
! [X0] : X0 = join(complement(top),meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f19,f867]) ).
fof(f888,plain,
! [X0] : X0 = join(zero,meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f79,f886]) ).
fof(f931,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))),
inference(paramodulation,[status(thm)],[f22,f880]) ).
fof(f932,plain,
! [X0] : meet(complement(X0),top) = complement(X0),
inference(paramodulation,[status(thm)],[f880,f85]) ).
fof(f935,plain,
! [X0] : meet(top,complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f76,f932]) ).
fof(f951,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(paramodulation,[status(thm)],[f76,f888]) ).
fof(f976,plain,
! [X0,X1] : join(X0,top) = join(complement(X1),join(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f57]) ).
fof(f1041,plain,
! [X0,X1] : top = join(complement(X0),join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f807,f976]) ).
fof(f1042,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f57,f1041]) ).
fof(f1074,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(paramodulation,[status(thm)],[f935,f951]) ).
fof(f1083,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1074,f880]) ).
fof(f1084,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1074,f85]) ).
fof(f1085,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1074,f931]) ).
fof(f1102,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1105,f888]) ).
fof(f1105,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f1083,f1084]) ).
fof(f1130,plain,
! [X0] : X0 = meet(top,X0),
inference(backward_demodulation,[status(thm)],[f1102,f951]) ).
fof(f1134,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(backward_demodulation,[status(thm)],[f1102,f353]) ).
fof(f1173,plain,
! [X0] : X0 = join(X0,complement(join(complement(X0),top))),
inference(paramodulation,[status(thm)],[f1105,f49]) ).
fof(f1176,plain,
! [X0] : X0 = join(X0,complement(top)),
inference(forward_demodulation,[status(thm)],[f807,f1173]) ).
fof(f1177,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f79,f1176]) ).
fof(f1216,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X2,X1)),
inference(paramodulation,[status(thm)],[f57,f66]) ).
fof(f1235,plain,
! [X0,X1] : join(X0,top) = join(X1,join(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f30,f66]) ).
fof(f1299,plain,
! [X0,X1] : top = join(X0,join(X1,complement(X0))),
inference(forward_demodulation,[status(thm)],[f807,f1235]) ).
fof(f1522,plain,
! [X0,X1] : X0 = join(meet(X0,join(X1,complement(complement(X0)))),complement(top)),
inference(paramodulation,[status(thm)],[f1299,f49]) ).
fof(f1543,plain,
! [X0,X1] : X0 = join(complement(top),meet(X0,join(X1,complement(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f19,f1522]) ).
fof(f1544,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(X1,complement(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f79,f1543]) ).
fof(f1545,plain,
! [X0,X1] : X0 = meet(X0,join(X1,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f1102,f1544]) ).
fof(f1546,plain,
! [X0,X1] : X0 = meet(X0,join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1083,f1545]) ).
fof(f1574,plain,
! [X0,X1] : converse(X0) = meet(converse(X0),converse(join(X1,X0))),
inference(paramodulation,[status(thm)],[f27,f1546]) ).
fof(f1585,plain,
! [X0,X1] : X0 = meet(X0,join(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f1546]) ).
fof(f1634,plain,
! [X0,X1] : meet(X0,X1) = meet(meet(X0,X1),X0),
inference(paramodulation,[status(thm)],[f49,f1585]) ).
fof(f1636,plain,
! [X0] : sF2_fnc = meet(sF2_fnc,converse(join(sK0_skl,X0))),
inference(paramodulation,[status(thm)],[f144,f1585]) ).
fof(f1659,plain,
! [X0,X1] : meet(X0,X1) = meet(X0,meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f76,f1634]) ).
fof(f1668,plain,
meet(sK1_skl,sF2_fnc) = meet(sK1_skl,sF1_fnc),
inference(paramodulation,[status(thm)],[f41,f1659]) ).
fof(f1676,plain,
! [X0,X1] : meet(X0,X1) = meet(X0,meet(X1,X0)),
inference(paramodulation,[status(thm)],[f76,f1659]) ).
fof(f1684,plain,
sF1_fnc = meet(sK1_skl,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f41,f1668]) ).
fof(f1716,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(X1),meet(X0,X1))),complement(top)),
inference(paramodulation,[status(thm)],[f95,f49]) ).
fof(f1764,plain,
! [X0,X1] : X0 = join(complement(top),meet(X0,join(complement(X1),meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f19,f1716]) ).
fof(f1765,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(complement(X1),meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f79,f1764]) ).
fof(f1766,plain,
! [X0,X1] : X0 = meet(X0,join(complement(X1),meet(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1102,f1765]) ).
fof(f1792,plain,
meet(sK0_skl,sK2_skl) = meet(sK0_skl,sF3_fnc),
inference(paramodulation,[status(thm)],[f73,f1676]) ).
fof(f1816,plain,
meet(sK2_skl,sK0_skl) = meet(sK0_skl,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f76,f1792]) ).
fof(f1817,plain,
sF3_fnc = meet(sK0_skl,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f73,f1816]) ).
fof(f1854,plain,
sF2_fnc = meet(sF2_fnc,converse(top)),
inference(paramodulation,[status(thm)],[f88,f1636]) ).
fof(f1879,plain,
sF2_fnc = join(sF2_fnc,complement(join(complement(sF2_fnc),converse(top)))),
inference(paramodulation,[status(thm)],[f1854,f49]) ).
fof(f2157,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(zero)),
inference(paramodulation,[status(thm)],[f1177,f145]) ).
fof(f2164,plain,
! [X0] : converse(top) = join(X0,converse(top)),
inference(paramodulation,[status(thm)],[f807,f145]) ).
fof(f2202,plain,
! [X0] : X0 = join(X0,converse(zero)),
inference(forward_demodulation,[status(thm)],[f26,f2157]) ).
fof(f2204,plain,
sF2_fnc = join(sF2_fnc,complement(converse(top))),
inference(backward_demodulation,[status(thm)],[f2164,f1879]) ).
fof(f2236,plain,
zero = converse(zero),
inference(paramodulation,[status(thm)],[f1102,f2202]) ).
fof(f2340,plain,
top = join(converse(top),sF2_fnc),
inference(paramodulation,[status(thm)],[f2204,f1299]) ).
fof(f2352,plain,
top = join(sF2_fnc,converse(top)),
inference(forward_demodulation,[status(thm)],[f19,f2340]) ).
fof(f2353,plain,
top = converse(join(sK0_skl,top)),
inference(forward_demodulation,[status(thm)],[f144,f2352]) ).
fof(f2354,plain,
top = converse(join(top,sK0_skl)),
inference(forward_demodulation,[status(thm)],[f152,f2353]) ).
fof(f2365,plain,
top = converse(top),
inference(forward_demodulation,[status(thm)],[f837,f2354]) ).
fof(f2411,plain,
! [X0] : converse(composition(X0,top)) = composition(top,converse(X0)),
inference(paramodulation,[status(thm)],[f2365,f122]) ).
fof(f2412,plain,
converse(composition(sK0_skl,top)) = composition(top,sF2_fnc),
inference(paramodulation,[status(thm)],[f2365,f124]) ).
fof(f2439,plain,
converse(sK0_skl) = composition(top,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f38,f2412]) ).
fof(f2440,plain,
sF2_fnc = composition(top,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f40,f2439]) ).
fof(f2455,plain,
! [X0] : composition(top,composition(sF2_fnc,X0)) = composition(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f2440,f23]) ).
fof(f3530,plain,
! [X0,X1] : X0 = meet(X0,join(X1,meet(X0,complement(X1)))),
inference(paramodulation,[status(thm)],[f1083,f1766]) ).
fof(f3543,plain,
sK1_skl = meet(sK1_skl,join(complement(sF2_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f41,f1766]) ).
fof(f3579,plain,
sK1_skl = meet(sK1_skl,join(sF1_fnc,complement(sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f19,f3543]) ).
fof(f3759,plain,
! [X0,X1] : X0 = meet(X0,join(X1,meet(complement(X1),X0))),
inference(paramodulation,[status(thm)],[f76,f3530]) ).
fof(f3983,plain,
! [X0,X1] : top = join(X0,complement(meet(X0,X1))),
inference(paramodulation,[status(thm)],[f1085,f1042]) ).
fof(f4087,plain,
! [X0,X1] : top = complement(meet(X0,meet(complement(X0),X1))),
inference(paramodulation,[status(thm)],[f1085,f3983]) ).
fof(f4265,plain,
! [X0,X1] : meet(X0,meet(complement(X0),X1)) = complement(top),
inference(paramodulation,[status(thm)],[f4087,f1083]) ).
fof(f4308,plain,
! [X0,X1] : meet(X0,meet(complement(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f79,f4265]) ).
fof(f4383,plain,
! [X0,X1] : meet(X0,meet(X1,complement(X0))) = zero,
inference(paramodulation,[status(thm)],[f76,f4308]) ).
fof(f4426,plain,
! [X0,X1] : meet(complement(X0),meet(X1,X0)) = zero,
inference(paramodulation,[status(thm)],[f1083,f4383]) ).
fof(f4705,plain,
! [X0,X1] : meet(complement(join(X0,X1)),X1) = zero,
inference(paramodulation,[status(thm)],[f1546,f4426]) ).
fof(f4748,plain,
! [X0,X1] : meet(X0,complement(join(X1,X0))) = zero,
inference(forward_demodulation,[status(thm)],[f76,f4705]) ).
fof(f6524,plain,
composition(join(one,sF2_fnc),complement(composition(join(one,sK0_skl),top))) = zero,
inference(paramodulation,[status(thm)],[f750,f1134]) ).
fof(f6577,plain,
composition(join(one,sF2_fnc),complement(join(sK0_skl,composition(one,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f237,f6524]) ).
fof(f6578,plain,
composition(join(one,sF2_fnc),complement(join(sK0_skl,top))) = zero,
inference(forward_demodulation,[status(thm)],[f662,f6577]) ).
fof(f6579,plain,
composition(join(one,sF2_fnc),complement(top)) = zero,
inference(forward_demodulation,[status(thm)],[f807,f6578]) ).
fof(f6580,plain,
composition(join(one,sF2_fnc),zero) = zero,
inference(forward_demodulation,[status(thm)],[f79,f6579]) ).
fof(f6581,plain,
join(zero,composition(sF2_fnc,zero)) = zero,
inference(forward_demodulation,[status(thm)],[f691,f6580]) ).
fof(f6584,plain,
composition(sF2_fnc,zero) = zero,
inference(forward_demodulation,[status(thm)],[f1102,f6581]) ).
fof(f7134,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f76,f881]) ).
fof(f7146,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f76,f881]) ).
fof(f8239,plain,
! [X0] : join(X0,meet(top,X0)) = meet(top,X0),
inference(paramodulation,[status(thm)],[f1130,f792]) ).
fof(f8335,plain,
! [X0] : join(X0,X0) = meet(top,X0),
inference(forward_demodulation,[status(thm)],[f1130,f8239]) ).
fof(f8351,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1130,f8335]) ).
fof(f8615,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f8351,f66]) ).
fof(f8705,plain,
! [X0,X1] : join(meet(X0,complement(X1)),X0) = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f7134,f8615]) ).
fof(f8835,plain,
! [X0,X1] : join(X0,meet(X0,complement(X1))) = join(meet(X1,X0),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f8705]) ).
fof(f8836,plain,
! [X0,X1] : join(X0,meet(X0,complement(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f7134,f8835]) ).
fof(f8980,plain,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
inference(paramodulation,[status(thm)],[f1083,f8836]) ).
fof(f9055,plain,
join(sK0_skl,sF3_fnc) = sK0_skl,
inference(paramodulation,[status(thm)],[f1817,f8980]) ).
fof(f9060,plain,
join(sK1_skl,sF1_fnc) = sK1_skl,
inference(paramodulation,[status(thm)],[f1684,f8980]) ).
fof(f9080,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f76,f8980]) ).
fof(f9156,plain,
composition(sK0_skl,top) = join(sK0_skl,composition(sF3_fnc,top)),
inference(paramodulation,[status(thm)],[f9055,f215]) ).
fof(f9171,plain,
sK0_skl = join(sK0_skl,composition(sF3_fnc,top)),
inference(forward_demodulation,[status(thm)],[f38,f9156]) ).
fof(f9406,plain,
! [X0] : join(sK1_skl,join(sF1_fnc,X0)) = join(X0,sK1_skl),
inference(paramodulation,[status(thm)],[f9060,f57]) ).
fof(f10200,plain,
! [X0,X1] : join(join(X0,meet(complement(X0),X1)),X1) = join(X0,meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f3759,f9080]) ).
fof(f10312,plain,
! [X0,X1] : join(X0,join(meet(complement(X0),X1),X1)) = join(X0,meet(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f20,f10200]) ).
fof(f10313,plain,
! [X0,X1] : join(X0,join(X1,meet(complement(X0),X1))) = join(X0,meet(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f1216,f10312]) ).
fof(f10338,plain,
! [X0,X1] : join(X0,X1) = join(X0,meet(complement(X0),X1)),
inference(forward_demodulation,[status(thm)],[f9080,f10313]) ).
fof(f10557,plain,
meet(composition(sF3_fnc,top),complement(sK0_skl)) = zero,
inference(paramodulation,[status(thm)],[f9171,f4748]) ).
fof(f10573,plain,
meet(complement(sK0_skl),composition(sF3_fnc,top)) = zero,
inference(forward_demodulation,[status(thm)],[f76,f10557]) ).
fof(f11123,plain,
! [X0] : meet(composition(converse(X0),complement(X0)),complement(complement(one))) = zero,
inference(paramodulation,[status(thm)],[f350,f4748]) ).
fof(f11153,plain,
! [X0] : meet(complement(complement(one)),composition(converse(X0),complement(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f76,f11123]) ).
fof(f11154,plain,
! [X0] : meet(one,composition(converse(X0),complement(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f1083,f11153]) ).
fof(f21352,plain,
composition(top,zero) = composition(sF2_fnc,zero),
inference(paramodulation,[status(thm)],[f6584,f2455]) ).
fof(f21400,plain,
composition(top,zero) = zero,
inference(forward_demodulation,[status(thm)],[f6584,f21352]) ).
fof(f21624,plain,
! [X0] : composition(join(X0,top),zero) = join(composition(X0,zero),zero),
inference(paramodulation,[status(thm)],[f21400,f25]) ).
fof(f21825,plain,
! [X0] : composition(top,zero) = join(composition(X0,zero),zero),
inference(forward_demodulation,[status(thm)],[f807,f21624]) ).
fof(f21826,plain,
! [X0] : zero = join(composition(X0,zero),zero),
inference(forward_demodulation,[status(thm)],[f21400,f21825]) ).
fof(f21885,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[status(thm)],[f1177,f21826]) ).
fof(f22773,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(paramodulation,[status(thm)],[f21885,f125]) ).
fof(f22843,plain,
! [X0] : zero = composition(converse(zero),X0),
inference(forward_demodulation,[status(thm)],[f2236,f22773]) ).
fof(f22897,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[status(thm)],[f2236,f22843]) ).
fof(f26696,plain,
join(join(sF1_fnc,complement(sF2_fnc)),sK1_skl) = join(sF1_fnc,complement(sF2_fnc)),
inference(paramodulation,[status(thm)],[f3579,f9080]) ).
fof(f26716,plain,
join(sF1_fnc,join(complement(sF2_fnc),sK1_skl)) = join(sF1_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f20,f26696]) ).
fof(f26717,plain,
join(sK1_skl,join(sF1_fnc,complement(sF2_fnc))) = join(sF1_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f57,f26716]) ).
fof(f26718,plain,
join(complement(sF2_fnc),sK1_skl) = join(sF1_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f9406,f26717]) ).
fof(f26720,plain,
join(sK1_skl,complement(sF2_fnc)) = join(sF1_fnc,complement(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f19,f26718]) ).
fof(f52856,plain,
join(meet(composition(converse(sF3_fnc),complement(sK0_skl)),top),composition(meet(converse(sF3_fnc),composition(top,converse(complement(sK0_skl)))),zero)) = composition(meet(converse(sF3_fnc),composition(top,converse(complement(sK0_skl)))),meet(complement(sK0_skl),composition(sF3_fnc,top))),
inference(paramodulation,[status(thm)],[f10573,f575]) ).
fof(f52901,plain,
join(composition(converse(sF3_fnc),complement(sK0_skl)),composition(meet(converse(sF3_fnc),composition(top,converse(complement(sK0_skl)))),zero)) = composition(meet(converse(sF3_fnc),composition(top,converse(complement(sK0_skl)))),meet(complement(sK0_skl),composition(sF3_fnc,top))),
inference(forward_demodulation,[status(thm)],[f1105,f52856]) ).
fof(f52902,plain,
join(composition(converse(sF3_fnc),complement(sK0_skl)),zero) = composition(meet(converse(sF3_fnc),composition(top,converse(complement(sK0_skl)))),meet(complement(sK0_skl),composition(sF3_fnc,top))),
inference(forward_demodulation,[status(thm)],[f21885,f52901]) ).
fof(f52903,plain,
composition(converse(sF3_fnc),complement(sK0_skl)) = composition(meet(converse(sF3_fnc),composition(top,converse(complement(sK0_skl)))),meet(complement(sK0_skl),composition(sF3_fnc,top))),
inference(forward_demodulation,[status(thm)],[f1177,f52902]) ).
fof(f52904,plain,
composition(converse(sF3_fnc),complement(sK0_skl)) = composition(meet(converse(sF3_fnc),converse(composition(complement(sK0_skl),top))),meet(complement(sK0_skl),composition(sF3_fnc,top))),
inference(forward_demodulation,[status(thm)],[f2411,f52903]) ).
fof(f52905,plain,
composition(converse(sF3_fnc),complement(sK0_skl)) = composition(meet(converse(sF3_fnc),converse(composition(complement(sK0_skl),top))),zero),
inference(forward_demodulation,[status(thm)],[f10573,f52904]) ).
fof(f52906,plain,
composition(converse(sF3_fnc),complement(sK0_skl)) = zero,
inference(forward_demodulation,[status(thm)],[f21885,f52905]) ).
fof(f52984,plain,
converse(zero) = composition(converse(complement(sK0_skl)),sF3_fnc),
inference(paramodulation,[status(thm)],[f52906,f125]) ).
fof(f53042,plain,
zero = composition(converse(complement(sK0_skl)),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f2236,f52984]) ).
fof(f53187,plain,
! [X0] : composition(join(converse(complement(sK0_skl)),sF1_fnc),composition(sF3_fnc,X0)) = composition(join(sF0_fnc,zero),X0),
inference(paramodulation,[status(thm)],[f53042,f266]) ).
fof(f53188,plain,
! [X0] : composition(join(converse(complement(sK0_skl)),sK1_skl),composition(sF3_fnc,X0)) = composition(join(sF4_fnc,zero),X0),
inference(paramodulation,[status(thm)],[f53042,f253]) ).
fof(f53253,plain,
! [X0] : composition(join(sF1_fnc,converse(complement(sK0_skl))),composition(sF3_fnc,X0)) = composition(join(sF0_fnc,zero),X0),
inference(forward_demodulation,[status(thm)],[f230,f53187]) ).
fof(f53254,plain,
! [X0] : composition(join(sF1_fnc,converse(complement(sK0_skl))),composition(sF3_fnc,X0)) = composition(join(zero,sF0_fnc),X0),
inference(forward_demodulation,[status(thm)],[f230,f53253]) ).
fof(f53255,plain,
! [X0] : composition(join(sF1_fnc,converse(complement(sK0_skl))),composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f1102,f53254]) ).
fof(f53256,plain,
! [X0] : composition(join(sK1_skl,converse(complement(sK0_skl))),composition(sF3_fnc,X0)) = composition(join(sF4_fnc,zero),X0),
inference(forward_demodulation,[status(thm)],[f230,f53188]) ).
fof(f53257,plain,
! [X0] : composition(join(sK1_skl,converse(complement(sK0_skl))),composition(sF3_fnc,X0)) = composition(join(zero,sF4_fnc),X0),
inference(forward_demodulation,[status(thm)],[f230,f53256]) ).
fof(f53258,plain,
! [X0] : composition(join(sK1_skl,converse(complement(sK0_skl))),composition(sF3_fnc,X0)) = composition(sF4_fnc,X0),
inference(forward_demodulation,[status(thm)],[f1102,f53257]) ).
fof(f53568,plain,
! [X0] : join(meet(composition(one,converse(complement(X0))),converse(X0)),composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0))))) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(paramodulation,[status(thm)],[f11154,f552]) ).
fof(f53667,plain,
! [X0] : join(meet(converse(X0),composition(one,converse(complement(X0)))),composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0))))) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f76,f53568]) ).
fof(f53668,plain,
! [X0] : join(meet(converse(X0),converse(complement(X0))),composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0))))) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f662,f53667]) ).
fof(f53669,plain,
! [X0] : join(meet(converse(X0),converse(complement(X0))),zero) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f22897,f53668]) ).
fof(f53670,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = composition(meet(one,composition(converse(X0),complement(X0))),meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f1177,f53669]) ).
fof(f53671,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0)))),
inference(forward_demodulation,[status(thm)],[f11154,f53670]) ).
fof(f53672,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f22897,f53671]) ).
fof(f53863,plain,
! [X0] : meet(X0,converse(complement(converse(X0)))) = zero,
inference(paramodulation,[status(thm)],[f26,f53672]) ).
fof(f53905,plain,
! [X0] : converse(X0) = join(zero,meet(complement(converse(complement(X0))),converse(X0))),
inference(paramodulation,[status(thm)],[f53672,f7146]) ).
fof(f53972,plain,
! [X0] : converse(X0) = meet(complement(converse(complement(X0))),converse(X0)),
inference(forward_demodulation,[status(thm)],[f1102,f53905]) ).
fof(f53973,plain,
! [X0] : converse(X0) = meet(converse(X0),complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f76,f53972]) ).
fof(f54328,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = join(X0,zero),
inference(paramodulation,[status(thm)],[f53863,f10338]) ).
fof(f54396,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[status(thm)],[f1177,f54328]) ).
fof(f54543,plain,
! [X0] : converse(converse(complement(converse(complement(X0))))) = meet(converse(converse(complement(converse(complement(X0))))),converse(X0)),
inference(paramodulation,[status(thm)],[f54396,f1574]) ).
fof(f54621,plain,
! [X0] : complement(converse(complement(X0))) = meet(converse(converse(complement(converse(complement(X0))))),converse(X0)),
inference(forward_demodulation,[status(thm)],[f26,f54543]) ).
fof(f54622,plain,
! [X0] : complement(converse(complement(X0))) = meet(converse(X0),converse(converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f76,f54621]) ).
fof(f54623,plain,
! [X0] : complement(converse(complement(X0))) = meet(converse(X0),complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f26,f54622]) ).
fof(f54656,plain,
! [X0] : complement(converse(complement(X0))) = converse(X0),
inference(forward_demodulation,[status(thm)],[f53973,f54623]) ).
fof(f54928,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(paramodulation,[status(thm)],[f1083,f54656]) ).
fof(f55051,plain,
! [X0] : composition(join(sK1_skl,complement(converse(sK0_skl))),composition(sF3_fnc,X0)) = composition(sF4_fnc,X0),
inference(backward_demodulation,[status(thm)],[f54928,f53258]) ).
fof(f55052,plain,
! [X0] : composition(join(sF1_fnc,complement(converse(sK0_skl))),composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(backward_demodulation,[status(thm)],[f54928,f53255]) ).
fof(f55212,plain,
! [X0] : composition(join(sK1_skl,complement(sF2_fnc)),composition(sF3_fnc,X0)) = composition(sF4_fnc,X0),
inference(forward_demodulation,[status(thm)],[f40,f55051]) ).
fof(f55213,plain,
! [X0] : composition(join(sF1_fnc,complement(sF2_fnc)),composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f40,f55052]) ).
fof(f55214,plain,
! [X0] : composition(join(sK1_skl,complement(sF2_fnc)),composition(sF3_fnc,X0)) = composition(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f26720,f55213]) ).
fof(f55230,plain,
! [X0] : composition(sF4_fnc,X0) = composition(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f55212,f55214]) ).
fof(f55724,plain,
sF4_fnc = composition(sF0_fnc,one),
inference(paramodulation,[status(thm)],[f24,f55230]) ).
fof(f55793,plain,
sF4_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f24,f55724]) ).
fof(f55794,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f55793,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL035+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.61 % Computer : n017.cluster.edu
% 0.12/5.61 % Model : x86_64 x86_64
% 0.12/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.61 % Memory : 8046.5625MB
% 0.12/5.61 % OS : Linux 6.8.0-71-generic
% 0.12/5.61 % CPULimit : 300
% 0.12/5.61 % WCLimit : 300
% 0.12/5.61 % DateTime : Mon Sep 21 04:01:03 UTC 2026
% 0.12/5.62 % CPUTime :
% 0.12/5.62 % Drodi V4.1.1
% 260.41/38.71 % Refutation found
% 260.41/38.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 260.41/38.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 25.75/39.75 % Elapsed time: 34.121319 seconds
% 25.75/39.75 % CPU time: 263.627798 seconds
% 25.75/39.75 % Total memory used: 1.179 GB
% 25.75/39.75 % Net memory used: 1.134 GB
%------------------------------------------------------------------------------