TSTP Solution File: SET010-1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET010-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 12:33:29 EDT 2023
% Result : Unsatisfiable 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 92 ( 12 unt; 0 def)
% Number of atoms : 226 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 252 ( 118 ~; 127 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 102 (; 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| member(g(Set1,Set2,Union),Set1)
| member(g(Set1,Set2,Union),Set2)
| member(g(Set1,Set2,Union),Union) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Set1,Set2,Union] :
( ~ member(g(Set1,Set2,Union),Set1)
| ~ member(g(Set1,Set2,Union),Union)
| union(Set1,Set2,Union) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Set1,Set2,Union] :
( ~ member(g(Set1,Set2,Union),Set2)
| ~ member(g(Set1,Set2,Union),Union)
| union(Set1,Set2,Union) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Set1,Set2,Intersection,Element] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Set1,Set2,Intersection,Element] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Set1,Set2,Intersection,Element] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Set2)
| ~ member(Element,Set1)
| member(Element,Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [Set1,Set2,Difference,Element] :
( ~ difference(Set1,Set2,Difference)
| ~ member(Element,Difference)
| member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Element,Set1,Set2,A_set] :
( ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ difference(A_set,Set1,Set2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Element,Set1,Set2,Difference] :
( ~ member(Element,Set1)
| ~ difference(Set1,Set2,Difference)
| member(Element,Difference)
| member(Element,Set2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
difference(c,a,cDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
difference(c,b,cDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
difference(c,aIb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,plain,
! [X0,X1,X2] :
( union(X0,X1,X2)
| member(g(X0,X1,X2),X0)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(g(X0,X1,X2),X0)
| ~ member(g(X0,X1,X2),X2)
| union(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ member(g(X0,X1,X2),X1)
| ~ member(g(X0,X1,X2),X2)
| union(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f46,plain,
! [Set1,Element] :
( ! [Intersection] :
( ! [Set2] : ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection) )
| member(Element,Set1) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
! [Set2,Element] :
( ! [Intersection] :
( ! [Set1] : ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection) )
| member(Element,Set2) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
! [Intersection,Element] :
( ! [Set1] :
( ! [Set2] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Set2) )
| ~ member(Element,Set1) )
| member(Element,Intersection) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| member(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f55,plain,
! [Set1,Element] :
( ! [Difference] :
( ! [Set2] : ~ difference(Set1,Set2,Difference)
| ~ member(Element,Difference) )
| member(Element,Set1) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ~ difference(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f57,plain,
! [Set1,Set2] :
( ! [Element] :
( ~ member(Element,Set1)
| ~ member(Element,Set2) )
| ! [A_set] : ~ difference(A_set,Set1,Set2) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ difference(X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f59,plain,
! [Element,Set2] :
( ! [Difference] :
( ! [Set1] :
( ~ member(Element,Set1)
| ~ difference(Set1,Set2,Difference) )
| member(Element,Difference) )
| member(Element,Set2) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ difference(X1,X2,X3)
| member(X0,X3)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f64,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f65,plain,
difference(c,a,cDa),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f66,plain,
difference(c,b,cDb),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f67,plain,
difference(c,aIb,cD_aIb),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f68,plain,
~ union(cDa,cDb,cD_aIb),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f69,plain,
( spl0_0
<=> member(g(cDa,cDb,cD_aIb),cDa) ),
introduced(split_symbol_definition) ).
fof(f70,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f71,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDa)
| spl0_0 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( spl0_1
<=> member(g(cDa,cDb,cD_aIb),cD_aIb) ),
introduced(split_symbol_definition) ).
fof(f73,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDa)
| ~ member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolution,[status(thm)],[f44,f68]) ).
fof(f76,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f75,f69,f72]) ).
fof(f161,plain,
( spl0_2
<=> member(g(cDa,cDb,cD_aIb),cDb) ),
introduced(split_symbol_definition) ).
fof(f162,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( spl0_3
<=> union(cDa,cDb,cD_aIb) ),
introduced(split_symbol_definition) ).
fof(f165,plain,
( union(cDa,cDb,cD_aIb)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f394,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f68]) ).
fof(f395,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f396,plain,
( union(cDa,cDb,cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cD_aIb)
| spl0_0 ),
inference(resolution,[status(thm)],[f71,f43]) ).
fof(f397,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_0 ),
inference(split_clause,[status(thm)],[f396,f164,f161,f72,f69]) ).
fof(f416,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDb)
| union(cDa,cDb,cD_aIb)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f73,f45]) ).
fof(f417,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f416,f161,f164,f72]) ).
fof(f432,plain,
! [X0] :
( ~ member(X0,cD_aIb)
| member(X0,c) ),
inference(resolution,[status(thm)],[f56,f67]) ).
fof(f433,plain,
! [X0] :
( ~ member(X0,cDb)
| member(X0,c) ),
inference(resolution,[status(thm)],[f56,f66]) ).
fof(f434,plain,
! [X0] :
( ~ member(X0,cDa)
| member(X0,c) ),
inference(resolution,[status(thm)],[f56,f65]) ).
fof(f435,plain,
! [X0] :
( ~ member(X0,aIb)
| ~ member(X0,cD_aIb) ),
inference(resolution,[status(thm)],[f58,f67]) ).
fof(f436,plain,
! [X0] :
( ~ member(X0,b)
| ~ member(X0,cDb) ),
inference(resolution,[status(thm)],[f58,f66]) ).
fof(f437,plain,
! [X0] :
( ~ member(X0,a)
| ~ member(X0,cDa) ),
inference(resolution,[status(thm)],[f58,f65]) ).
fof(f468,plain,
! [X0] :
( ~ member(X0,c)
| member(X0,cD_aIb)
| member(X0,aIb) ),
inference(resolution,[status(thm)],[f60,f67]) ).
fof(f469,plain,
! [X0] :
( ~ member(X0,c)
| member(X0,cDb)
| member(X0,b) ),
inference(resolution,[status(thm)],[f60,f66]) ).
fof(f470,plain,
! [X0] :
( ~ member(X0,c)
| member(X0,cDa)
| member(X0,a) ),
inference(resolution,[status(thm)],[f60,f65]) ).
fof(f499,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f434,f70]) ).
fof(f524,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,a) ),
inference(resolution,[status(thm)],[f47,f64]) ).
fof(f535,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,b) ),
inference(resolution,[status(thm)],[f49,f64]) ).
fof(f546,plain,
( spl0_17
<=> member(g(cDa,cDb,cD_aIb),aIb) ),
introduced(split_symbol_definition) ).
fof(f547,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),aIb)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f468,f499]) ).
fof(f550,plain,
( spl0_1
| spl0_17
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f549,f72,f546,f69]) ).
fof(f557,plain,
( member(g(cDa,cDb,cD_aIb),a)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f547,f524]) ).
fof(f560,plain,
( ~ member(g(cDa,cDb,cD_aIb),cDa)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f557,f437]) ).
fof(f561,plain,
( ~ spl0_0
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f560,f69,f546]) ).
fof(f573,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f162,f433]) ).
fof(f574,plain,
( ~ member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f162,f436]) ).
fof(f587,plain,
( member(g(cDa,cDb,cD_aIb),c)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f73,f432]) ).
fof(f588,plain,
( ~ member(g(cDa,cDb,cD_aIb),aIb)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f73,f435]) ).
fof(f590,plain,
! [X0] :
( ~ member(X0,b)
| ~ member(X0,a)
| member(X0,aIb) ),
inference(resolution,[status(thm)],[f51,f64]) ).
fof(f626,plain,
( spl0_19
<=> member(g(cDa,cDb,cD_aIb),a) ),
introduced(split_symbol_definition) ).
fof(f629,plain,
( member(g(cDa,cDb,cD_aIb),cDa)
| member(g(cDa,cDb,cD_aIb),a)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f587,f470]) ).
fof(f630,plain,
( spl0_0
| spl0_19
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f629,f69,f626,f72]) ).
fof(f631,plain,
( spl0_20
<=> member(g(cDa,cDb,cD_aIb),b) ),
introduced(split_symbol_definition) ).
fof(f632,plain,
( member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f631]) ).
fof(f634,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f587,f469]) ).
fof(f635,plain,
( spl0_2
| spl0_20
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f634,f161,f631,f72]) ).
fof(f651,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),aIb)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f573,f468]) ).
fof(f652,plain,
( spl0_1
| spl0_17
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f651,f72,f546,f161]) ).
fof(f666,plain,
( ~ member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),aIb)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f632,f590]) ).
fof(f667,plain,
( ~ spl0_19
| spl0_17
| ~ spl0_20 ),
inference(split_clause,[status(thm)],[f666,f626,f546,f631]) ).
fof(f682,plain,
( $false
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f588]) ).
fof(f683,plain,
( ~ spl0_1
| ~ spl0_17 ),
inference(contradiction_clause,[status(thm)],[f682]) ).
fof(f704,plain,
( member(g(cDa,cDb,cD_aIb),b)
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f547,f535]) ).
fof(f705,plain,
( $false
| ~ spl0_2
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f704,f574]) ).
fof(f706,plain,
( ~ spl0_2
| ~ spl0_17 ),
inference(contradiction_clause,[status(thm)],[f705]) ).
fof(f707,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f395,f397,f417,f550,f561,f630,f635,f652,f667,f683,f706]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n012.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 : Tue May 30 10:12:25 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 0.20/0.48 % Refutation found
% 0.20/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.50 % Elapsed time: 0.146677 seconds
% 0.20/0.50 % CPU time: 1.091215 seconds
% 0.20/0.50 % Memory used: 16.261 MB
%------------------------------------------------------------------------------