TSTP Solution File: SET169+3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:34:11 EDT 2023
% Result : Theorem 150.37s 19.26s
% Output : CNFRefutation 150.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 130 ( 21 unt; 0 def)
% Number of atoms : 332 ( 27 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 324 ( 122 ~; 148 |; 29 &)
% ( 24 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 18 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 153 (; 146 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C,D] :
( ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f12,plain,
( ! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ! [B,C,D] :
( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f16,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
( ! [B,C,D] :
( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ! [B,C,D] :
( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
( ! [B,C] :
( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ! [B,C] :
( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( X0 != X1
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f27,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f28,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f29,plain,
! [B,C] :
( ( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f31,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_0(C,B),B)
& ~ member(sk0_0(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f36,plain,
! [B,C] :
( ( B != C
| ! [D] :
( ( ~ member(D,B)
| member(D,C) )
& ( member(D,B)
| ~ member(D,C) ) ) )
& ( B = C
| ? [D] :
( ( ~ member(D,B)
| ~ member(D,C) )
& ( member(D,B)
| member(D,C) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f37,plain,
( ! [B,C] :
( B != C
| ( ! [D] :
( ~ member(D,B)
| member(D,C) )
& ! [D] :
( member(D,B)
| ~ member(D,C) ) ) )
& ! [B,C] :
( B = C
| ? [D] :
( ( ~ member(D,B)
| ~ member(D,C) )
& ( member(D,B)
| member(D,C) ) ) ) ),
inference(miniscoping,[status(esa)],[f36]) ).
fof(f38,plain,
( ! [B,C] :
( B != C
| ( ! [D] :
( ~ member(D,B)
| member(D,C) )
& ! [D] :
( member(D,B)
| ~ member(D,C) ) ) )
& ! [B,C] :
( B = C
| ( ( ~ member(sk0_1(C,B),B)
| ~ member(sk0_1(C,B),C) )
& ( member(sk0_1(C,B),B)
| member(sk0_1(C,B),C) ) ) ) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sk0_1(X1,X0),X0)
| ~ member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f42,plain,
! [X0,X1] :
( X0 = X1
| member(sk0_1(X1,X0),X0)
| member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f43,plain,
? [B,C,D] : intersection(B,union(C,D)) != union(intersection(B,C),intersection(B,D)),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f44,plain,
intersection(sk0_2,union(sk0_3,sk0_4)) != union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)),
inference(skolemization,[status(esa)],[f43]) ).
fof(f45,plain,
intersection(sk0_2,union(sk0_3,sk0_4)) != union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f23]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ member(X0,union(intersection(X1,X2),X3))
| member(X0,X3) ),
inference(resolution,[status(thm)],[f18,f13]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ member(X0,union(X2,intersection(X3,X1)))
| member(X0,X2) ),
inference(resolution,[status(thm)],[f19,f13]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,intersection(X1,union(X2,X3)))
| member(X0,X2)
| member(X0,X3) ),
inference(resolution,[status(thm)],[f19,f13]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,union(X3,intersection(X1,X2))) ),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f162,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,union(intersection(X1,X2),X3)) ),
inference(resolution,[status(thm)],[f20,f14]) ).
fof(f187,plain,
! [X0,X1,X2,X3] :
( member(X0,intersection(X1,union(X2,X3)))
| ~ member(X0,X1)
| ~ member(X0,X3) ),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( member(X0,intersection(X1,union(X2,X3)))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(resolution,[status(thm)],[f20,f14]) ).
fof(f231,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),intersection(X2,X1)) ),
inference(resolution,[status(thm)],[f34,f19]) ).
fof(f239,plain,
! [X0,X1] :
( subset(intersection(X0,X1),X1)
| subset(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f231,f33]) ).
fof(f240,plain,
! [X0,X1] : subset(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(esa)],[f239]) ).
fof(f252,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(paramodulation,[status(thm)],[f27,f240]) ).
fof(f321,plain,
( spl0_4
<=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f322,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f323,plain,
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
| spl0_4 ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,plain,
( spl0_5
<=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f325,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4)))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f326,plain,
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4)))
| spl0_5 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,plain,
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
| ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4))) ),
inference(resolution,[status(thm)],[f41,f45]) ).
fof(f328,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f327,f321,f324]) ).
fof(f355,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
| member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4))) ),
inference(resolution,[status(thm)],[f42,f45]) ).
fof(f356,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f355,f321,f324]) ).
fof(f412,plain,
( spl0_6
<=> union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = intersection(sk0_2,union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f413,plain,
( union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = intersection(sk0_2,union(sk0_3,sk0_4))
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f417,plain,
( spl0_7
<=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f419,plain,
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
| spl0_7 ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f470,plain,
! [X0] :
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,X0))
| spl0_7 ),
inference(resolution,[status(thm)],[f419,f18]) ).
fof(f547,plain,
( union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = intersection(sk0_2,union(sk0_3,sk0_4))
| member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
| spl0_7 ),
inference(resolution,[status(thm)],[f470,f42]) ).
fof(f548,plain,
( spl0_6
| spl0_4
| spl0_7 ),
inference(split_clause,[status(thm)],[f547,f412,f321,f417]) ).
fof(f590,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f413,f45]) ).
fof(f591,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f756,plain,
( spl0_12
<=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f956,plain,
( spl0_13
<=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f957,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_3))
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f956]) ).
fof(f959,plain,
( spl0_14
<=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f960,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_4))
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f959]) ).
fof(f3401,plain,
( spl0_31
<=> intersection(sk0_2,union(sk0_3,sk0_4)) = intersection(sk0_2,union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f3403,plain,
( intersection(sk0_2,union(sk0_3,sk0_4)) != intersection(sk0_2,union(sk0_3,sk0_4))
| spl0_31 ),
inference(component_clause,[status(thm)],[f3401]) ).
fof(f5527,plain,
( spl0_107
<=> subset(sk0_2,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f5529,plain,
( ~ subset(sk0_2,sk0_2)
| spl0_107 ),
inference(component_clause,[status(thm)],[f5527]) ).
fof(f5551,plain,
( $false
| spl0_107 ),
inference(forward_subsumption_resolution,[status(thm)],[f5529,f46]) ).
fof(f5552,plain,
spl0_107,
inference(contradiction_clause,[status(thm)],[f5551]) ).
fof(f6059,plain,
( spl0_127
<=> subset(intersection(union(sk0_3,sk0_4),sk0_2),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f6061,plain,
( ~ subset(intersection(union(sk0_3,sk0_4),sk0_2),sk0_2)
| spl0_127 ),
inference(component_clause,[status(thm)],[f6059]) ).
fof(f6098,plain,
( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),sk0_2)
| spl0_127 ),
inference(forward_demodulation,[status(thm)],[f27,f6061]) ).
fof(f6099,plain,
( $false
| spl0_127 ),
inference(forward_subsumption_resolution,[status(thm)],[f6098,f252]) ).
fof(f6100,plain,
spl0_127,
inference(contradiction_clause,[status(thm)],[f6099]) ).
fof(f7533,plain,
( spl0_155
<=> subset(intersection(sk0_2,union(sk0_3,sk0_4)),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f7535,plain,
( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),sk0_2)
| spl0_155 ),
inference(component_clause,[status(thm)],[f7533]) ).
fof(f7560,plain,
( $false
| spl0_155 ),
inference(forward_subsumption_resolution,[status(thm)],[f7535,f252]) ).
fof(f7561,plain,
spl0_155,
inference(contradiction_clause,[status(thm)],[f7560]) ).
fof(f7737,plain,
( spl0_158
<=> subset(union(sk0_3,sk0_4),union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f7739,plain,
( ~ subset(union(sk0_3,sk0_4),union(sk0_3,sk0_4))
| spl0_158 ),
inference(component_clause,[status(thm)],[f7737]) ).
fof(f7765,plain,
( $false
| spl0_158 ),
inference(forward_subsumption_resolution,[status(thm)],[f7739,f46]) ).
fof(f7766,plain,
spl0_158,
inference(contradiction_clause,[status(thm)],[f7765]) ).
fof(f7838,plain,
( spl0_162
<=> subset(intersection(union(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f7840,plain,
( ~ subset(intersection(union(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4))
| spl0_162 ),
inference(component_clause,[status(thm)],[f7838]) ).
fof(f7877,plain,
( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),union(sk0_3,sk0_4))
| spl0_162 ),
inference(forward_demodulation,[status(thm)],[f27,f7840]) ).
fof(f7878,plain,
( $false
| spl0_162 ),
inference(forward_subsumption_resolution,[status(thm)],[f7877,f240]) ).
fof(f7879,plain,
spl0_162,
inference(contradiction_clause,[status(thm)],[f7878]) ).
fof(f8612,plain,
( spl0_175
<=> subset(intersection(sk0_2,sk0_2),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f8614,plain,
( ~ subset(intersection(sk0_2,sk0_2),sk0_2)
| spl0_175 ),
inference(component_clause,[status(thm)],[f8612]) ).
fof(f8635,plain,
( $false
| spl0_175 ),
inference(forward_subsumption_resolution,[status(thm)],[f8614,f252]) ).
fof(f8636,plain,
spl0_175,
inference(contradiction_clause,[status(thm)],[f8635]) ).
fof(f11162,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
| member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_4))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f322,f77]) ).
fof(f11163,plain,
( spl0_7
| spl0_14
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f11162,f417,f959,f321]) ).
fof(f13048,plain,
( spl0_209
<=> subset(intersection(sk0_2,union(sk0_3,sk0_4)),intersection(sk0_2,union(sk0_3,sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f13050,plain,
( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),intersection(sk0_2,union(sk0_3,sk0_4)))
| spl0_209 ),
inference(component_clause,[status(thm)],[f13048]) ).
fof(f13165,plain,
( $false
| spl0_209 ),
inference(forward_subsumption_resolution,[status(thm)],[f13050,f46]) ).
fof(f13166,plain,
spl0_209,
inference(contradiction_clause,[status(thm)],[f13165]) ).
fof(f13922,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4)
| member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_3))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f87,f322]) ).
fof(f13923,plain,
( spl0_12
| spl0_13
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f13922,f756,f956,f321]) ).
fof(f14449,plain,
( spl0_227
<=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f14877,plain,
( spl0_231
<=> subset(intersection(sk0_2,union(sk0_3,sk0_4)),union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f14879,plain,
( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),union(sk0_3,sk0_4))
| spl0_231 ),
inference(component_clause,[status(thm)],[f14877]) ).
fof(f14904,plain,
( $false
| spl0_231 ),
inference(forward_subsumption_resolution,[status(thm)],[f14879,f240]) ).
fof(f14905,plain,
spl0_231,
inference(contradiction_clause,[status(thm)],[f14904]) ).
fof(f21730,plain,
( $false
| spl0_31 ),
inference(trivial_equality_resolution,[status(esa)],[f3403]) ).
fof(f21731,plain,
spl0_31,
inference(contradiction_clause,[status(thm)],[f21730]) ).
fof(f24046,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3)
| member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f325,f92]) ).
fof(f24047,plain,
( spl0_227
| spl0_12
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f24046,f14449,f756,f324]) ).
fof(f24419,plain,
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
| ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3)
| spl0_4 ),
inference(resolution,[status(thm)],[f323,f162]) ).
fof(f24420,plain,
( ~ spl0_7
| ~ spl0_227
| spl0_4 ),
inference(split_clause,[status(thm)],[f24419,f417,f14449,f321]) ).
fof(f24421,plain,
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
| ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4)
| spl0_4 ),
inference(resolution,[status(thm)],[f323,f161]) ).
fof(f24422,plain,
( ~ spl0_7
| ~ spl0_12
| spl0_4 ),
inference(split_clause,[status(thm)],[f24421,f417,f756,f321]) ).
fof(f40469,plain,
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
| ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4)
| spl0_5 ),
inference(resolution,[status(thm)],[f187,f326]) ).
fof(f40470,plain,
( ~ spl0_7
| ~ spl0_12
| spl0_5 ),
inference(split_clause,[status(thm)],[f40469,f417,f756,f324]) ).
fof(f46299,plain,
( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
| ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3)
| spl0_5 ),
inference(resolution,[status(thm)],[f188,f326]) ).
fof(f46300,plain,
( ~ spl0_7
| ~ spl0_227
| spl0_5 ),
inference(split_clause,[status(thm)],[f46299,f417,f14449,f324]) ).
fof(f51485,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f960,f18]) ).
fof(f51486,plain,
( spl0_7
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f51485,f417,f959]) ).
fof(f51609,plain,
( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f957,f19]) ).
fof(f51610,plain,
( spl0_227
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f51609,f14449,f956]) ).
fof(f51718,plain,
$false,
inference(sat_refutation,[status(thm)],[f328,f356,f548,f591,f5552,f6100,f7561,f7766,f7879,f8636,f11163,f13166,f13923,f14905,f21731,f24047,f24420,f24422,f40470,f46300,f51486,f51610]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 10:26:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 150.37/19.26 % Refutation found
% 150.37/19.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 150.37/19.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 152.38/19.60 % Elapsed time: 19.210346 seconds
% 152.38/19.60 % CPU time: 151.767248 seconds
% 152.38/19.60 % Memory used: 1.217 GB
%------------------------------------------------------------------------------