TSTP Solution File: SET007-1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET007-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 20:38:34 EDT 2024
% Result : Unsatisfiable 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 90 ( 12 unt; 0 def)
% Number of atoms : 226 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 253 ( 117 ~; 128 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [Set1,Set2,Union,Element] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Union)
| member(Element,Set1)
| member(Element,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Set1,Set2,Union,Element] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1)
| member(Element,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Set1,Set2,Union,Element] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set2)
| member(Element,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Set1,Set2,Intersection,Element] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Set1,Set2,Intersection,Element] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
union(b,c,bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
intersection(a,c,aIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
intersection(a,bUc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,plain,
! [Set2,Element] :
( ! [Set1] :
( ! [Union] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Union) )
| member(Element,Set1) )
| member(Element,Set2) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ union(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [Union,Element] :
( ! [Set1] :
( ! [Set2] : ~ union(Set1,Set2,Union)
| ~ member(Element,Set1) )
| member(Element,Union) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( ~ union(X0,X1,X2)
| ~ member(X3,X0)
| member(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f35,plain,
! [Union,Element] :
( ! [Set2] :
( ! [Set1] : ~ union(Set1,Set2,Union)
| ~ member(Element,Set2) )
| member(Element,Union) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ union(X0,X1,X2)
| ~ member(X3,X1)
| member(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,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(f38,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(f39,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(f40,plain,
! [Set1,Element] :
( ! [Intersection] :
( ! [Set2] : ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection) )
| member(Element,Set1) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [Set2,Element] :
( ! [Intersection] :
( ! [Set1] : ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection) )
| member(Element,Set2) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [Intersection,Element] :
( ! [Set1] :
( ! [Set2] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Set2) )
| ~ member(Element,Set1) )
| member(Element,Intersection) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| member(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f49,plain,
union(b,c,bUc),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f50,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f51,plain,
intersection(a,c,aIc),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f52,plain,
intersection(a,bUc,aI_bUc),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f53,plain,
~ union(aIb,aIc,aI_bUc),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f56,plain,
( spl0_0
<=> member(g(aIb,aIc,aI_bUc),aIb) ),
introduced(split_symbol_definition) ).
fof(f58,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIb)
| spl0_0 ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( spl0_1
<=> member(g(aIb,aIc,aI_bUc),aI_bUc) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| spl0_1 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIb)
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f63,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f62,f56,f59]) ).
fof(f67,plain,
( spl0_2
<=> member(g(aIb,aIc,aI_bUc),aIc) ),
introduced(split_symbol_definition) ).
fof(f69,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIc)
| spl0_2 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIc)
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(resolution,[status(thm)],[f39,f53]) ).
fof(f71,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f70,f67,f59]) ).
fof(f72,plain,
! [X0,X1] :
( ~ intersection(X0,X1,aIb)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ member(g(aIb,aIc,aI_bUc),X0)
| spl0_0 ),
inference(resolution,[status(thm)],[f58,f45]) ).
fof(f79,plain,
( spl0_3
<=> union(aIb,aIc,aI_bUc) ),
introduced(split_symbol_definition) ).
fof(f80,plain,
( union(aIb,aIc,aI_bUc)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( union(aIb,aIc,aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIb)
| member(g(aIb,aIc,aI_bUc),aI_bUc)
| spl0_2 ),
inference(resolution,[status(thm)],[f69,f37]) ).
fof(f83,plain,
( spl0_3
| spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f82,f79,f56,f59,f67]) ).
fof(f84,plain,
! [X0,X1] :
( ~ intersection(X0,X1,aIc)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ member(g(aIb,aIc,aI_bUc),X0)
| spl0_2 ),
inference(resolution,[status(thm)],[f69,f45]) ).
fof(f91,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f53]) ).
fof(f92,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f91]) ).
fof(f95,plain,
! [X0,X1] :
( ~ intersection(X0,X1,aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ member(g(aIb,aIc,aI_bUc),X0)
| spl0_1 ),
inference(resolution,[status(thm)],[f61,f45]) ).
fof(f105,plain,
( spl0_4
<=> member(g(aIb,aIc,aI_bUc),bUc) ),
introduced(split_symbol_definition) ).
fof(f107,plain,
( ~ member(g(aIb,aIc,aI_bUc),bUc)
| spl0_4 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( spl0_5
<=> member(g(aIb,aIc,aI_bUc),a) ),
introduced(split_symbol_definition) ).
fof(f110,plain,
( ~ member(g(aIb,aIc,aI_bUc),a)
| spl0_5 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( ~ member(g(aIb,aIc,aI_bUc),bUc)
| ~ member(g(aIb,aIc,aI_bUc),a)
| spl0_1 ),
inference(resolution,[status(thm)],[f95,f52]) ).
fof(f112,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_1 ),
inference(split_clause,[status(thm)],[f111,f105,f108,f59]) ).
fof(f132,plain,
( spl0_6
<=> member(g(aIb,aIc,aI_bUc),b) ),
introduced(split_symbol_definition) ).
fof(f135,plain,
( ~ member(g(aIb,aIc,aI_bUc),b)
| ~ member(g(aIb,aIc,aI_bUc),a)
| spl0_0 ),
inference(resolution,[status(thm)],[f72,f50]) ).
fof(f136,plain,
( ~ spl0_6
| ~ spl0_5
| spl0_0 ),
inference(split_clause,[status(thm)],[f135,f132,f108,f56]) ).
fof(f160,plain,
( spl0_7
<=> member(g(aIb,aIc,aI_bUc),c) ),
introduced(split_symbol_definition) ).
fof(f162,plain,
( ~ member(g(aIb,aIc,aI_bUc),c)
| spl0_7 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( ~ member(g(aIb,aIc,aI_bUc),c)
| ~ member(g(aIb,aIc,aI_bUc),a)
| spl0_2 ),
inference(resolution,[status(thm)],[f84,f51]) ).
fof(f164,plain,
( ~ spl0_7
| ~ spl0_5
| spl0_2 ),
inference(split_clause,[status(thm)],[f163,f160,f108,f67]) ).
fof(f167,plain,
! [X0,X1] :
( ~ intersection(X0,bUc,X1)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| spl0_4 ),
inference(resolution,[status(thm)],[f107,f43]) ).
fof(f170,plain,
! [X0,X1] :
( ~ union(X0,X1,bUc)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| spl0_4 ),
inference(resolution,[status(thm)],[f107,f36]) ).
fof(f172,plain,
! [X0,X1] :
( ~ union(X0,X1,bUc)
| ~ member(g(aIb,aIc,aI_bUc),X0)
| spl0_4 ),
inference(resolution,[status(thm)],[f107,f34]) ).
fof(f203,plain,
( ~ member(g(aIb,aIc,aI_bUc),c)
| spl0_4 ),
inference(resolution,[status(thm)],[f170,f49]) ).
fof(f207,plain,
! [X0,X1] :
( ~ intersection(X0,c,X1)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| spl0_4 ),
inference(resolution,[status(thm)],[f203,f43]) ).
fof(f216,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIc)
| spl0_4 ),
inference(resolution,[status(thm)],[f207,f51]) ).
fof(f217,plain,
( ~ spl0_2
| spl0_4 ),
inference(split_clause,[status(thm)],[f216,f67,f105]) ).
fof(f221,plain,
! [X0,X1] :
( ~ intersection(a,X0,X1)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| spl0_5 ),
inference(resolution,[status(thm)],[f110,f41]) ).
fof(f244,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIb)
| spl0_5 ),
inference(resolution,[status(thm)],[f221,f50]) ).
fof(f245,plain,
( ~ spl0_0
| spl0_5 ),
inference(split_clause,[status(thm)],[f244,f56,f108]) ).
fof(f247,plain,
( ~ member(g(aIb,aIc,aI_bUc),b)
| spl0_4 ),
inference(resolution,[status(thm)],[f172,f49]) ).
fof(f253,plain,
! [X0,X1] :
( ~ union(X0,c,X1)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| member(g(aIb,aIc,aI_bUc),X0)
| spl0_7 ),
inference(resolution,[status(thm)],[f162,f32]) ).
fof(f265,plain,
! [X0,X1] :
( ~ intersection(X0,b,X1)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| spl0_4 ),
inference(resolution,[status(thm)],[f247,f43]) ).
fof(f290,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIb)
| spl0_4 ),
inference(resolution,[status(thm)],[f265,f50]) ).
fof(f291,plain,
( ~ spl0_0
| spl0_4 ),
inference(split_clause,[status(thm)],[f290,f56,f105]) ).
fof(f440,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| spl0_5 ),
inference(resolution,[status(thm)],[f221,f52]) ).
fof(f441,plain,
( ~ spl0_1
| spl0_5 ),
inference(split_clause,[status(thm)],[f440,f59,f108]) ).
fof(f442,plain,
( ~ member(g(aIb,aIc,aI_bUc),aIc)
| spl0_5 ),
inference(resolution,[status(thm)],[f221,f51]) ).
fof(f443,plain,
( ~ spl0_2
| spl0_5 ),
inference(split_clause,[status(thm)],[f442,f67,f108]) ).
fof(f710,plain,
( ~ member(g(aIb,aIc,aI_bUc),bUc)
| member(g(aIb,aIc,aI_bUc),b)
| spl0_7 ),
inference(resolution,[status(thm)],[f253,f49]) ).
fof(f711,plain,
( ~ spl0_4
| spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f710,f105,f132,f160]) ).
fof(f714,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| spl0_4 ),
inference(resolution,[status(thm)],[f167,f52]) ).
fof(f715,plain,
( ~ spl0_1
| spl0_4 ),
inference(split_clause,[status(thm)],[f714,f59,f105]) ).
fof(f718,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f71,f83,f92,f112,f136,f164,f217,f245,f291,f441,f443,f711,f715]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 21:27:41 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.35 % Drodi V3.6.0
% 0.20/0.49 % Refutation found
% 0.20/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.50 % Elapsed time: 0.154114 seconds
% 0.20/0.50 % CPU time: 1.158235 seconds
% 0.20/0.50 % Total memory used: 21.007 MB
% 0.20/0.50 % Net memory used: 20.114 MB
%------------------------------------------------------------------------------