TSTP Solution File: SET199+4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET199+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 : Tue Apr 30 20:39:24 EDT 2024
% Result : Theorem 0.21s 0.52s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 87 ( 2 unt; 0 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 245 ( 85 ~; 123 |; 18 &)
% ( 17 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 13 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 85 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,X,Y] :
( ( subset(A,X)
& subset(A,Y) )
<=> subset(A,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,X,Y] :
( ( subset(A,X)
& subset(A,Y) )
<=> subset(A,intersection(X,Y)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f30,plain,
! [X,A,B] :
( ( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) )
& ( member(X,intersection(A,B))
| ~ member(X,A)
| ~ member(X,B) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f31,plain,
( ! [X,A,B] :
( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) )
& ! [X,A,B] :
( member(X,intersection(A,B))
| ~ member(X,A)
| ~ member(X,B) ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f68,plain,
? [A,X,Y] :
( ( subset(A,X)
& subset(A,Y) )
<~> subset(A,intersection(X,Y)) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
? [A,X,Y] :
( ( ( subset(A,X)
& subset(A,Y) )
| subset(A,intersection(X,Y)) )
& ( ~ subset(A,X)
| ~ subset(A,Y)
| ~ subset(A,intersection(X,Y)) ) ),
inference(NNF_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
( ( ( subset(sk0_3,sk0_4)
& subset(sk0_3,sk0_5) )
| subset(sk0_3,intersection(sk0_4,sk0_5)) )
& ( ~ subset(sk0_3,sk0_4)
| ~ subset(sk0_3,sk0_5)
| ~ subset(sk0_3,intersection(sk0_4,sk0_5)) ) ),
inference(skolemization,[status(esa)],[f69]) ).
fof(f71,plain,
( subset(sk0_3,sk0_4)
| subset(sk0_3,intersection(sk0_4,sk0_5)) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
( subset(sk0_3,sk0_5)
| subset(sk0_3,intersection(sk0_4,sk0_5)) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
( ~ subset(sk0_3,sk0_4)
| ~ subset(sk0_3,sk0_5)
| ~ subset(sk0_3,intersection(sk0_4,sk0_5)) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f74,plain,
( spl0_0
<=> subset(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f75,plain,
( subset(sk0_3,sk0_4)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( spl0_1
<=> subset(sk0_3,intersection(sk0_4,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f78,plain,
( subset(sk0_3,intersection(sk0_4,sk0_5))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f71,f74,f77]) ).
fof(f81,plain,
( spl0_2
<=> subset(sk0_3,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f82,plain,
( subset(sk0_3,sk0_5)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( spl0_2
| spl0_1 ),
inference(split_clause,[status(thm)],[f72,f81,f77]) ).
fof(f85,plain,
( ~ spl0_0
| ~ spl0_2
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f73,f74,f81,f77]) ).
fof(f92,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| member(sk0_0(X1,X0),intersection(X2,X0))
| ~ member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f19,f34]) ).
fof(f93,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f19,f18]) ).
fof(f114,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),intersection(X0,X0))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f92,f19]) ).
fof(f115,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),intersection(X0,X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( subset(X0,X1)
| subset(X0,X1)
| member(sk0_0(X1,X0),intersection(intersection(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f115,f92]) ).
fof(f117,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),intersection(intersection(X0,X0),X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f116]) ).
fof(f152,plain,
! [X0] :
( subset(X0,intersection(X0,X0))
| subset(X0,intersection(X0,X0)) ),
inference(resolution,[status(thm)],[f20,f115]) ).
fof(f153,plain,
! [X0] : subset(X0,intersection(X0,X0)),
inference(duplicate_literals_removal,[status(esa)],[f152]) ).
fof(f205,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(sk0_4,sk0_5))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f78,f93]) ).
fof(f210,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_5)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f205,f33]) ).
fof(f211,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_4)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f205,f32]) ).
fof(f214,plain,
( subset(sk0_3,sk0_5)
| subset(sk0_3,sk0_5)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f210,f20]) ).
fof(f215,plain,
( spl0_2
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f214,f81,f77]) ).
fof(f242,plain,
( subset(sk0_3,sk0_4)
| subset(sk0_3,sk0_4)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f211,f20]) ).
fof(f243,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f242,f74,f77]) ).
fof(f248,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_5)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f82,f93]) ).
fof(f251,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f75,f93]) ).
fof(f263,plain,
! [X0] :
( subset(sk0_3,X0)
| subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(sk0_5,sk0_3))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f248,f92]) ).
fof(f264,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(sk0_5,sk0_3))
| ~ spl0_2 ),
inference(duplicate_literals_removal,[status(esa)],[f263]) ).
fof(f265,plain,
! [X0,X1] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(X1,sk0_5))
| ~ member(sk0_0(X0,sk0_3),X1)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f248,f34]) ).
fof(f266,plain,
! [X0,X1] :
( subset(sk0_3,X0)
| ~ subset(sk0_5,X1)
| member(sk0_0(X0,sk0_3),X1)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f248,f18]) ).
fof(f291,plain,
( spl0_3
<=> subset(sk0_3,intersection(sk0_5,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f294,plain,
( subset(sk0_3,intersection(sk0_5,sk0_3))
| subset(sk0_3,intersection(sk0_5,sk0_3))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f264,f20]) ).
fof(f295,plain,
( spl0_3
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f294,f291,f81]) ).
fof(f296,plain,
! [X0] :
( subset(sk0_3,X0)
| subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(intersection(sk0_5,sk0_3),sk0_3))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f264,f92]) ).
fof(f297,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(intersection(sk0_5,sk0_3),sk0_3))
| ~ spl0_2 ),
inference(duplicate_literals_removal,[status(esa)],[f296]) ).
fof(f305,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),intersection(sk0_5,sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f266,f153]) ).
fof(f323,plain,
( spl0_5
<=> subset(sk0_3,intersection(sk0_5,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f326,plain,
( subset(sk0_3,intersection(sk0_5,sk0_5))
| subset(sk0_3,intersection(sk0_5,sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f305,f20]) ).
fof(f327,plain,
( spl0_5
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f326,f323,f81]) ).
fof(f349,plain,
( spl0_7
<=> subset(sk0_3,intersection(intersection(sk0_5,sk0_3),sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f352,plain,
( subset(sk0_3,intersection(intersection(sk0_5,sk0_3),sk0_3))
| subset(sk0_3,intersection(intersection(sk0_5,sk0_3),sk0_3))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f297,f20]) ).
fof(f353,plain,
( spl0_7
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f352,f349,f81]) ).
fof(f369,plain,
! [X0] :
( subset(sk0_3,intersection(X0,sk0_5))
| ~ member(sk0_0(intersection(X0,sk0_5),sk0_3),X0)
| subset(sk0_3,intersection(X0,sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f265,f20]) ).
fof(f370,plain,
! [X0] :
( subset(sk0_3,intersection(X0,sk0_5))
| ~ member(sk0_0(intersection(X0,sk0_5),sk0_3),X0)
| ~ spl0_2 ),
inference(duplicate_literals_removal,[status(esa)],[f369]) ).
fof(f629,plain,
( spl0_8
<=> subset(sk0_3,intersection(intersection(intersection(sk0_5,sk0_3),sk0_3),sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f632,plain,
( subset(sk0_3,intersection(intersection(intersection(sk0_5,sk0_3),sk0_3),sk0_5))
| subset(sk0_3,intersection(intersection(intersection(sk0_5,sk0_3),sk0_3),sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f370,f297]) ).
fof(f633,plain,
( spl0_8
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f632,f629,f81]) ).
fof(f644,plain,
( spl0_11
<=> subset(sk0_3,intersection(intersection(sk0_5,sk0_5),sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f647,plain,
( subset(sk0_3,intersection(intersection(sk0_5,sk0_5),sk0_5))
| subset(sk0_3,intersection(intersection(sk0_5,sk0_5),sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f370,f305]) ).
fof(f648,plain,
( spl0_11
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f647,f644,f81]) ).
fof(f649,plain,
( spl0_12
<=> subset(sk0_3,intersection(intersection(sk0_5,sk0_3),sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f652,plain,
( subset(sk0_3,intersection(intersection(sk0_5,sk0_3),sk0_5))
| subset(sk0_3,intersection(intersection(sk0_5,sk0_3),sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f370,f264]) ).
fof(f653,plain,
( spl0_12
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f652,f649,f81]) ).
fof(f658,plain,
( subset(sk0_3,intersection(sk0_4,sk0_5))
| subset(sk0_3,intersection(sk0_4,sk0_5))
| ~ spl0_2
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f370,f251]) ).
fof(f659,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f658,f77,f81,f74]) ).
fof(f662,plain,
( spl0_13
<=> subset(sk0_3,intersection(intersection(intersection(sk0_3,sk0_3),sk0_3),sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f665,plain,
( subset(sk0_3,intersection(intersection(intersection(sk0_3,sk0_3),sk0_3),sk0_5))
| subset(sk0_3,intersection(intersection(intersection(sk0_3,sk0_3),sk0_3),sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f370,f117]) ).
fof(f666,plain,
( spl0_13
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f665,f662,f81]) ).
fof(f667,plain,
( spl0_14
<=> subset(sk0_3,intersection(intersection(sk0_3,sk0_3),sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f670,plain,
( subset(sk0_3,intersection(intersection(sk0_3,sk0_3),sk0_5))
| subset(sk0_3,intersection(intersection(sk0_3,sk0_3),sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f370,f115]) ).
fof(f671,plain,
( spl0_14
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f670,f667,f81]) ).
fof(f672,plain,
( spl0_15
<=> subset(sk0_3,intersection(sk0_3,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f675,plain,
( subset(sk0_3,intersection(sk0_3,sk0_5))
| subset(sk0_3,intersection(sk0_3,sk0_5))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f370,f19]) ).
fof(f676,plain,
( spl0_15
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f675,f672,f81]) ).
fof(f684,plain,
$false,
inference(sat_refutation,[status(thm)],[f80,f84,f85,f215,f243,f295,f327,f353,f633,f648,f653,f659,f666,f671,f676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET199+4 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 22:07:10 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.36 % Drodi V3.6.0
% 0.21/0.52 % Refutation found
% 0.21/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.54 % Elapsed time: 0.185537 seconds
% 0.21/0.54 % CPU time: 1.357864 seconds
% 0.21/0.54 % Total memory used: 66.985 MB
% 0.21/0.54 % Net memory used: 65.934 MB
%------------------------------------------------------------------------------