%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET969+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Tue Sep 29 12:42:26 PM UTC 2026
% Result : Theorem 0.81s 1.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 212 ( 19 unt; 23 def)
% Number of atoms : 589 ( 34 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 657 ( 280 ~; 315 |; 32 &)
% ( 27 <=>; 1 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 27 ( 25 usr; 23 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 209 ( 1 sgn 197 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f11,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f13,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( subset(X0,cartesian_product2(X1,X2))
& subset(X3,cartesian_product2(X4,X5))
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) ) )
=> X0 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
fof(f14,conjecture,
! [X0,X1,X2] :
( cartesian_product2(set_intersection2(X0,X1),X2) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& cartesian_product2(X2,set_intersection2(X0,X1)) = set_intersection2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_zfmisc_1) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( cartesian_product2(set_intersection2(X0,X1),X2) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& cartesian_product2(X2,set_intersection2(X0,X1)) = set_intersection2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f18,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f11]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X3
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| ? [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<~> in(ordered_pair(X6,X7),X3) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X3
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| ? [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<~> in(ordered_pair(X6,X7),X3) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
? [X0,X1,X2] :
( cartesian_product2(set_intersection2(X0,X1),X2) != set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| cartesian_product2(X2,set_intersection2(X0,X1)) != set_intersection2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X0)
& in(sK0(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f28]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X3
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| ? [X6,X7] :
( ( ~ in(ordered_pair(X6,X7),X3)
| ~ in(ordered_pair(X6,X7),X0) )
& ( in(ordered_pair(X6,X7),X3)
| in(ordered_pair(X6,X7),X0) ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X3
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| ( ( ~ in(ordered_pair(sK3(X0,X3),sK4(X0,X3)),X3)
| ~ in(ordered_pair(sK3(X0,X3),sK4(X0,X3)),X0) )
& ( in(ordered_pair(sK3(X0,X3),sK4(X0,X3)),X3)
| in(ordered_pair(sK3(X0,X3),sK4(X0,X3)),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X6,sK3(X0,X3)),skolemize(X7,sK4(X0,X3))],[f32]) ).
fof(f34,plain,
( cartesian_product2(set_intersection2(sK5,sK6),sK7) != set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))
| cartesian_product2(sK7,set_intersection2(sK5,sK6)) != set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f23]) ).
fof(f38,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f44,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f18]) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| in(ordered_pair(sK3(X0,X3),sK4(X0,X3)),X3)
| in(ordered_pair(sK3(X0,X3),sK4(X0,X3)),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ in(ordered_pair(sK3(X0,X3),sK4(X0,X3)),X3)
| ~ in(ordered_pair(sK3(X0,X3),sK4(X0,X3)),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
( cartesian_product2(set_intersection2(sK5,sK6),sK7) != set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))
| cartesian_product2(sK7,set_intersection2(sK5,sK6)) != set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f16]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f49,f44]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f48,f44]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f47,f44]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ in(unordered_pair(unordered_pair(sK3(X0,X3),sK4(X0,X3)),singleton(sK3(X0,X3))),X3)
| ~ in(unordered_pair(unordered_pair(sK3(X0,X3),sK4(X0,X3)),singleton(sK3(X0,X3))),X0) ),
inference(definition_unfolding,[],[f55,f44,f44]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| in(unordered_pair(unordered_pair(sK3(X0,X3),sK4(X0,X3)),singleton(sK3(X0,X3))),X3)
| in(unordered_pair(unordered_pair(sK3(X0,X3),sK4(X0,X3)),singleton(sK3(X0,X3))),X0) ),
inference(definition_unfolding,[],[f54,f44,f44]) ).
fof(f65,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f40]) ).
fof(f66,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f39]) ).
fof(f67,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f38]) ).
fof(f68,definition,
! [X0,X1] :
( sQ8_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ8_eqProxy])],[equality_proxy_definition]) ).
fof(f75,plain,
! [X2,X3,X0,X1,X4,X5] :
( sQ8_eqProxy(X0,X3)
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| ~ in(unordered_pair(unordered_pair(sK3(X0,X3),sK4(X0,X3)),singleton(sK3(X0,X3))),X3)
| ~ in(unordered_pair(unordered_pair(sK3(X0,X3),sK4(X0,X3)),singleton(sK3(X0,X3))),X0) ),
inference(equality_proxy_replacement,[],[f63,f68]) ).
fof(f76,plain,
! [X2,X3,X0,X1,X4,X5] :
( sQ8_eqProxy(X0,X3)
| ~ subset(X0,cartesian_product2(X1,X2))
| ~ subset(X3,cartesian_product2(X4,X5))
| in(unordered_pair(unordered_pair(sK3(X0,X3),sK4(X0,X3)),singleton(sK3(X0,X3))),X3)
| in(unordered_pair(unordered_pair(sK3(X0,X3),sK4(X0,X3)),singleton(sK3(X0,X3))),X0) ),
inference(equality_proxy_replacement,[],[f64,f68]) ).
fof(f77,plain,
( ~ sQ8_eqProxy(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| ~ sQ8_eqProxy(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))) ),
inference(equality_proxy_replacement,[],[f56,f68,f68]) ).
fof(f81,definition,
( spl9_1
<=> sQ8_eqProxy(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f82,plain,
( ~ sQ8_eqProxy(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| spl9_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl9_2
<=> sQ8_eqProxy(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f85,plain,
( ~ sQ8_eqProxy(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| spl9_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f77,f84,f81]) ).
fof(f139,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(set_intersection2(sK5,sK6),sK7),cartesian_product2(X0,X1))
| ~ subset(set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)),cartesian_product2(X2,X3))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_intersection2(sK5,sK6),sK7)) )
| spl9_2 ),
inference(resolution,[],[f75,f85]) ).
fof(f148,definition,
( spl9_10
<=> ! [X2,X3] : ~ subset(cartesian_product2(set_intersection2(sK5,sK6),sK7),cartesian_product2(X2,X3)) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
fof(f149,plain,
( ! [X2,X3] : ~ subset(cartesian_product2(set_intersection2(sK5,sK6),sK7),cartesian_product2(X2,X3))
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,definition,
( spl9_11
<=> ! [X0,X1] : ~ subset(set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)),cartesian_product2(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f152,plain,
( ! [X0,X1] : ~ subset(set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)),cartesian_product2(X0,X1))
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f155,definition,
( spl9_12
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_intersection2(sK5,sK6),sK7)) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
fof(f156,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_intersection2(sK5,sK6),sK7))
| spl9_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,definition,
( spl9_13
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
fof(f159,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| spl9_13 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f160,plain,
( ~ spl9_12
| ~ spl9_13
| spl9_11
| spl9_10
| spl9_2 ),
inference(avatar_split_clause,[],[f139,f84,f148,f151,f158,f155]) ).
fof(f163,definition,
( spl9_14
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK6,sK7)) ),
introduced(definition,[new_symbols(definition,[spl9_14])],[avatar_definition]) ).
fof(f164,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK6,sK7))
| spl9_14 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,definition,
( spl9_15
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK5,sK7)) ),
introduced(definition,[new_symbols(definition,[spl9_15])],[avatar_definition]) ).
fof(f167,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK5,sK7))
| spl9_15 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f172,definition,
( spl9_16
<=> in(sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7) ),
introduced(definition,[new_symbols(definition,[spl9_16])],[avatar_definition]) ).
fof(f173,plain,
( ~ in(sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| spl9_16 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,definition,
( spl9_17
<=> in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6) ),
introduced(definition,[new_symbols(definition,[spl9_17])],[avatar_definition]) ).
fof(f176,plain,
( ~ in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| spl9_17 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f205,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_intersection2(sK5,sK6),sK7))
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f206,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f208,plain,
( $false
| ~ spl9_10 ),
inference(resolution,[],[f149,f52]) ).
fof(f209,plain,
~ spl9_10,
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f210,plain,
( $false
| ~ spl9_11 ),
inference(resolution,[],[f152,f57]) ).
fof(f211,plain,
~ spl9_11,
inference(avatar_contradiction_clause,[],[f210]) ).
fof(f212,plain,
( in(sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| ~ spl9_12 ),
inference(resolution,[],[f205,f61]) ).
fof(f213,plain,
( in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),set_intersection2(sK5,sK6))
| ~ spl9_12 ),
inference(resolution,[],[f205,f60]) ).
fof(f219,plain,
( $false
| ~ spl9_12
| spl9_16 ),
inference(resolution,[],[f212,f173]) ).
fof(f222,plain,
( ~ spl9_12
| spl9_16 ),
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f225,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK6,sK7))
| ~ spl9_13 ),
inference(resolution,[],[f206,f67]) ).
fof(f226,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK5,sK7))
| ~ spl9_13 ),
inference(resolution,[],[f206,f66]) ).
fof(f231,plain,
( in(sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| ~ spl9_13 ),
inference(resolution,[],[f225,f61]) ).
fof(f232,plain,
( in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| ~ spl9_13 ),
inference(resolution,[],[f225,f60]) ).
fof(f238,plain,
( in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| ~ spl9_13 ),
inference(resolution,[],[f226,f60]) ).
fof(f241,plain,
( $false
| ~ spl9_13
| spl9_16 ),
inference(resolution,[],[f231,f173]) ).
fof(f244,plain,
( ~ spl9_13
| spl9_16 ),
inference(avatar_contradiction_clause,[],[f241]) ).
fof(f252,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK5,sK7))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK6,sK7))
| spl9_13 ),
inference(resolution,[],[f159,f65]) ).
fof(f253,plain,
( ~ spl9_14
| ~ spl9_15
| spl9_13 ),
inference(avatar_split_clause,[],[f252,f158,f166,f163]) ).
fof(f254,plain,
( in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| ~ spl9_12 ),
inference(resolution,[],[f213,f67]) ).
fof(f255,plain,
( in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| ~ spl9_12 ),
inference(resolution,[],[f213,f66]) ).
fof(f259,plain,
( ~ in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| ~ in(sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| spl9_15 ),
inference(resolution,[],[f167,f59]) ).
fof(f261,definition,
( spl9_22
<=> in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5) ),
introduced(definition,[new_symbols(definition,[spl9_22])],[avatar_definition]) ).
fof(f262,plain,
( ~ in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| spl9_22 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f270,plain,
( $false
| ~ spl9_12
| spl9_22 ),
inference(resolution,[],[f262,f255]) ).
fof(f271,plain,
( ~ spl9_12
| spl9_22 ),
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f275,plain,
( ~ in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| ~ in(sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| spl9_14 ),
inference(resolution,[],[f164,f59]) ).
fof(f276,plain,
( ~ spl9_16
| ~ spl9_17
| spl9_14 ),
inference(avatar_split_clause,[],[f275,f163,f175,f172]) ).
fof(f277,plain,
( $false
| ~ spl9_12
| spl9_17 ),
inference(resolution,[],[f176,f254]) ).
fof(f278,plain,
( ~ spl9_12
| spl9_17 ),
inference(avatar_contradiction_clause,[],[f277]) ).
fof(f280,definition,
( spl9_23
<=> in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),set_intersection2(sK5,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_23])],[avatar_definition]) ).
fof(f281,plain,
( ~ in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),set_intersection2(sK5,sK6))
| spl9_23 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f283,plain,
( ~ spl9_16
| ~ spl9_22
| spl9_15 ),
inference(avatar_split_clause,[],[f259,f166,f261,f172]) ).
fof(f284,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(sK7,set_intersection2(sK5,sK6)),cartesian_product2(X0,X1))
| ~ subset(set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)),cartesian_product2(X2,X3))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_intersection2(sK5,sK6))) )
| spl9_1 ),
inference(resolution,[],[f82,f76]) ).
fof(f285,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(sK7,set_intersection2(sK5,sK6)),cartesian_product2(X0,X1))
| ~ subset(set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)),cartesian_product2(X2,X3))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_intersection2(sK5,sK6))) )
| spl9_1 ),
inference(resolution,[],[f82,f75]) ).
fof(f288,definition,
( spl9_24
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_intersection2(sK5,sK6))) ),
introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition]) ).
fof(f289,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_intersection2(sK5,sK6)))
| spl9_24 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f291,definition,
( spl9_25
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))) ),
introduced(definition,[new_symbols(definition,[spl9_25])],[avatar_definition]) ).
fof(f292,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| spl9_25 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f294,definition,
( spl9_26
<=> ! [X2,X3] : ~ subset(set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)),cartesian_product2(X2,X3)) ),
introduced(definition,[new_symbols(definition,[spl9_26])],[avatar_definition]) ).
fof(f295,plain,
( ! [X2,X3] : ~ subset(set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)),cartesian_product2(X2,X3))
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f297,definition,
( spl9_27
<=> ! [X0,X1] : ~ subset(cartesian_product2(sK7,set_intersection2(sK5,sK6)),cartesian_product2(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl9_27])],[avatar_definition]) ).
fof(f298,plain,
( ! [X0,X1] : ~ subset(cartesian_product2(sK7,set_intersection2(sK5,sK6)),cartesian_product2(X0,X1))
| ~ spl9_27 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( ~ spl9_24
| ~ spl9_25
| spl9_26
| spl9_27
| spl9_1 ),
inference(avatar_split_clause,[],[f285,f81,f297,f294,f291,f288]) ).
fof(f300,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_intersection2(sK5,sK6)))
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f301,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f302,plain,
( spl9_24
| spl9_25
| spl9_26
| spl9_27
| spl9_1 ),
inference(avatar_split_clause,[],[f284,f81,f297,f294,f291,f288]) ).
fof(f329,plain,
( ~ in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),set_intersection2(sK5,sK6))
| ~ in(sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| spl9_12 ),
inference(resolution,[],[f156,f59]) ).
fof(f330,plain,
( ~ spl9_16
| ~ spl9_23
| spl9_12 ),
inference(avatar_split_clause,[],[f329,f155,f280,f172]) ).
fof(f348,definition,
( spl9_31
<=> in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),set_intersection2(sK5,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_31])],[avatar_definition]) ).
fof(f349,plain,
( ~ in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),set_intersection2(sK5,sK6))
| spl9_31 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f351,definition,
( spl9_32
<=> in(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7) ),
introduced(definition,[new_symbols(definition,[spl9_32])],[avatar_definition]) ).
fof(f352,plain,
( ~ in(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| spl9_32 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f354,plain,
( ~ in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| ~ in(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| spl9_23 ),
inference(resolution,[],[f281,f65]) ).
fof(f355,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK6))
| ~ spl9_25 ),
inference(resolution,[],[f301,f67]) ).
fof(f356,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK5))
| ~ spl9_25 ),
inference(resolution,[],[f301,f66]) ).
fof(f361,definition,
( spl9_33
<=> in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6) ),
introduced(definition,[new_symbols(definition,[spl9_33])],[avatar_definition]) ).
fof(f362,plain,
( ~ in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| spl9_33 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f364,definition,
( spl9_34
<=> in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5) ),
introduced(definition,[new_symbols(definition,[spl9_34])],[avatar_definition]) ).
fof(f365,plain,
( ~ in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| spl9_34 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f372,plain,
( in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| ~ spl9_25 ),
inference(resolution,[],[f355,f61]) ).
fof(f373,plain,
( in(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ spl9_25 ),
inference(resolution,[],[f355,f60]) ).
fof(f376,plain,
( $false
| ~ spl9_25
| spl9_33 ),
inference(resolution,[],[f372,f362]) ).
fof(f379,plain,
( ~ spl9_25
| spl9_33 ),
inference(avatar_contradiction_clause,[],[f376]) ).
fof(f380,plain,
( $false
| ~ spl9_27 ),
inference(resolution,[],[f298,f52]) ).
fof(f381,plain,
~ spl9_27,
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f383,plain,
( in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),set_intersection2(sK5,sK6))
| ~ spl9_24 ),
inference(resolution,[],[f300,f61]) ).
fof(f384,plain,
( in(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ spl9_24 ),
inference(resolution,[],[f300,f60]) ).
fof(f391,definition,
( spl9_35
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_35])],[avatar_definition]) ).
fof(f392,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK6))
| spl9_35 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f394,definition,
( spl9_36
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK5)) ),
introduced(definition,[new_symbols(definition,[spl9_36])],[avatar_definition]) ).
fof(f395,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK5))
| spl9_36 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f406,plain,
( in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| ~ spl9_24 ),
inference(resolution,[],[f383,f67]) ).
fof(f407,plain,
( in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| ~ spl9_24 ),
inference(resolution,[],[f383,f66]) ).
fof(f412,plain,
( ~ in(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| spl9_35 ),
inference(resolution,[],[f392,f59]) ).
fof(f413,plain,
( $false
| ~ spl9_24
| spl9_33 ),
inference(resolution,[],[f406,f362]) ).
fof(f416,plain,
( ~ spl9_24
| spl9_33 ),
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f418,plain,
( $false
| ~ spl9_26 ),
inference(resolution,[],[f295,f57]) ).
fof(f419,plain,
~ spl9_26,
inference(avatar_contradiction_clause,[],[f418]) ).
fof(f426,plain,
( $false
| ~ spl9_24
| spl9_32 ),
inference(resolution,[],[f384,f352]) ).
fof(f429,plain,
( ~ spl9_24
| spl9_32 ),
inference(avatar_contradiction_clause,[],[f426]) ).
fof(f438,plain,
( $false
| ~ spl9_25
| spl9_32 ),
inference(resolution,[],[f373,f352]) ).
fof(f441,plain,
( ~ spl9_25
| spl9_32 ),
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f455,plain,
( in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| ~ spl9_25 ),
inference(resolution,[],[f356,f61]) ).
fof(f459,plain,
( $false
| ~ spl9_25
| spl9_34 ),
inference(resolution,[],[f455,f365]) ).
fof(f462,plain,
( ~ spl9_25
| spl9_34 ),
inference(avatar_contradiction_clause,[],[f459]) ).
fof(f470,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK5))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK6))
| spl9_25 ),
inference(resolution,[],[f292,f65]) ).
fof(f471,plain,
( ~ spl9_35
| ~ spl9_36
| spl9_25 ),
inference(avatar_split_clause,[],[f470,f291,f394,f391]) ).
fof(f481,plain,
( ~ in(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| spl9_36 ),
inference(resolution,[],[f395,f59]) ).
fof(f482,plain,
( ~ spl9_34
| ~ spl9_32
| spl9_36 ),
inference(avatar_split_clause,[],[f481,f394,f351,f364]) ).
fof(f483,plain,
( $false
| ~ spl9_24
| spl9_34 ),
inference(resolution,[],[f365,f407]) ).
fof(f484,plain,
( ~ spl9_24
| spl9_34 ),
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f487,plain,
( ~ spl9_33
| ~ spl9_32
| spl9_35 ),
inference(avatar_split_clause,[],[f412,f391,f351,f361]) ).
fof(f488,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(set_intersection2(sK5,sK6),sK7),cartesian_product2(X0,X1))
| ~ subset(set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)),cartesian_product2(X2,X3))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_intersection2(sK5,sK6),sK7),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_intersection2(sK5,sK6),sK7)) )
| spl9_2 ),
inference(resolution,[],[f85,f76]) ).
fof(f491,plain,
( spl9_12
| spl9_13
| spl9_11
| spl9_10
| spl9_2 ),
inference(avatar_split_clause,[],[f488,f84,f148,f151,f158,f155]) ).
fof(f502,plain,
( ~ in(sK3(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),set_intersection2(sK5,sK6))
| spl9_24 ),
inference(resolution,[],[f289,f59]) ).
fof(f503,plain,
( ~ spl9_31
| ~ spl9_32
| spl9_24 ),
inference(avatar_split_clause,[],[f502,f288,f351,f348]) ).
fof(f510,plain,
( ~ in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| ~ in(sK4(cartesian_product2(sK7,set_intersection2(sK5,sK6)),set_intersection2(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| spl9_31 ),
inference(resolution,[],[f349,f65]) ).
fof(f511,plain,
( ~ spl9_33
| ~ spl9_34
| spl9_31 ),
inference(avatar_split_clause,[],[f510,f348,f364,f361]) ).
fof(f512,plain,
( $false
| ~ spl9_13
| spl9_22 ),
inference(resolution,[],[f238,f262]) ).
fof(f515,plain,
( ~ spl9_13
| spl9_22 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f516,plain,
( ~ spl9_17
| ~ spl9_22
| spl9_23 ),
inference(avatar_split_clause,[],[f354,f280,f261,f175]) ).
fof(f522,plain,
( $false
| ~ spl9_13
| spl9_17 ),
inference(resolution,[],[f176,f232]) ).
fof(f523,plain,
( ~ spl9_13
| spl9_17 ),
inference(avatar_contradiction_clause,[],[f522]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f86]) ).
cnf(s6,plain,
( spl9_2
| spl9_10
| spl9_11
| ~ spl9_12
| ~ spl9_13 ),
inference(sat_conversion,[],[f160]) ).
cnf(s13,plain,
~ spl9_10,
inference(sat_conversion,[],[f209]) ).
cnf(s14,plain,
~ spl9_11,
inference(sat_conversion,[],[f211]) ).
cnf(s15,plain,
( ~ spl9_12
| spl9_16 ),
inference(sat_conversion,[],[f222]) ).
cnf(s17,plain,
( ~ spl9_13
| spl9_16 ),
inference(sat_conversion,[],[f244]) ).
cnf(s18,plain,
( spl9_13
| ~ spl9_14
| ~ spl9_15 ),
inference(sat_conversion,[],[f253]) ).
cnf(s20,plain,
( ~ spl9_12
| spl9_22 ),
inference(sat_conversion,[],[f271]) ).
cnf(s23,plain,
( spl9_14
| ~ spl9_16
| ~ spl9_17 ),
inference(sat_conversion,[],[f276]) ).
cnf(s24,plain,
( ~ spl9_12
| spl9_17 ),
inference(sat_conversion,[],[f278]) ).
cnf(s26,plain,
( spl9_15
| ~ spl9_16
| ~ spl9_22 ),
inference(sat_conversion,[],[f283]) ).
cnf(s27,plain,
( spl9_1
| ~ spl9_24
| ~ spl9_25
| spl9_26
| spl9_27 ),
inference(sat_conversion,[],[f299]) ).
cnf(s28,plain,
( spl9_1
| spl9_24
| spl9_25
| spl9_26
| spl9_27 ),
inference(sat_conversion,[],[f302]) ).
cnf(s34,plain,
( spl9_12
| ~ spl9_16
| ~ spl9_23 ),
inference(sat_conversion,[],[f330]) ).
cnf(s37,plain,
( ~ spl9_25
| spl9_33 ),
inference(sat_conversion,[],[f379]) ).
cnf(s38,plain,
~ spl9_27,
inference(sat_conversion,[],[f381]) ).
cnf(s41,plain,
( ~ spl9_24
| spl9_33 ),
inference(sat_conversion,[],[f416]) ).
cnf(s43,plain,
~ spl9_26,
inference(sat_conversion,[],[f419]) ).
cnf(s45,plain,
( ~ spl9_24
| spl9_32 ),
inference(sat_conversion,[],[f429]) ).
cnf(s46,plain,
( ~ spl9_25
| spl9_32 ),
inference(sat_conversion,[],[f441]) ).
cnf(s50,plain,
( ~ spl9_25
| spl9_34 ),
inference(sat_conversion,[],[f462]) ).
cnf(s51,plain,
( spl9_25
| ~ spl9_35
| ~ spl9_36 ),
inference(sat_conversion,[],[f471]) ).
cnf(s52,plain,
( ~ spl9_32
| ~ spl9_34
| spl9_36 ),
inference(sat_conversion,[],[f482]) ).
cnf(s53,plain,
( ~ spl9_24
| spl9_34 ),
inference(sat_conversion,[],[f484]) ).
cnf(s56,plain,
( ~ spl9_32
| ~ spl9_33
| spl9_35 ),
inference(sat_conversion,[],[f487]) ).
cnf(s57,plain,
( spl9_2
| spl9_10
| spl9_11
| spl9_12
| spl9_13 ),
inference(sat_conversion,[],[f491]) ).
cnf(s59,plain,
( spl9_24
| ~ spl9_31
| ~ spl9_32 ),
inference(sat_conversion,[],[f503]) ).
cnf(s60,plain,
( spl9_31
| ~ spl9_33
| ~ spl9_34 ),
inference(sat_conversion,[],[f511]) ).
cnf(s61,plain,
( ~ spl9_13
| spl9_22 ),
inference(sat_conversion,[],[f515]) ).
cnf(s62,plain,
( ~ spl9_17
| ~ spl9_22
| spl9_23 ),
inference(sat_conversion,[],[f516]) ).
cnf(s63,plain,
( ~ spl9_13
| spl9_17 ),
inference(sat_conversion,[],[f523]) ).
cnf(s66,plain,
( spl9_1
| spl9_24
| spl9_25 ),
inference(rat,[],[s28,s38,s43]) ).
cnf(s67,plain,
( spl9_1
| ~ spl9_24
| ~ spl9_25 ),
inference(rat,[],[s27,s38,s43]) ).
cnf(s70,plain,
( spl9_2
| ~ spl9_12
| ~ spl9_13 ),
inference(rat,[],[s6,s14,s13]) ).
cnf(s72,plain,
( spl9_12
| spl9_2 ),
inference(rat,[],[s34,s62,s17,s61,s63,s57,s13,s14]) ).
cnf(s73,plain,
spl9_2,
inference(rat,[],[s18,s23,s26,s70,s15,s20,s24,s72]) ).
cnf(s75,plain,
( spl9_24
| spl9_1 ),
inference(rat,[],[s60,s59,s37,s46,s50,s66]) ).
cnf(s76,plain,
spl9_1,
inference(rat,[],[s51,s56,s52,s67,s41,s45,s53,s75]) ).
cnf(s77,plain,
$false,
inference(rat,[],[s1,s73,s76]) ).
fof(f524,plain,
$false,
inference(avatar_sat_refutation,[],[s77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET969+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n005.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 03:16:46 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.81/1.48 % (399805)Detected formulas, will run a generic FOF schedule.
% 0.81/1.48 % (399816)dis-21_1_sil=8000:lcm=predicate:random_seed=3775318878:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.81/1.48 % (399810)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=379112802:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.81/1.48 % (399816)First to succeed.
% 0.81/1.48 % (399816)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-399805"
% 0.81/1.48 % (399813)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1716699899:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.81/1.48 % (399812)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2331361515:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.81/1.48 % (399814)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1294756575:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.81/1.48 % (399811)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=788562295:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.81/1.48 % (399815)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2121634967:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.81/1.48 % (399813)Refutation not found, incomplete strategy
% 0.81/1.48 % (399813)------------------------------
% 0.81/1.48 % (399813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.81/1.48 % (399813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/1.48 % (399813)CaDiCaL version: 2.1.3
% 0.81/1.48 % (399813)Termination reason: Refutation not found, incomplete strategy
% 0.81/1.48 % (399813)Time elapsed: 0.003 s
% 0.81/1.48 % (399813)Peak memory usage: 88 MB
% 0.81/1.48 % (399813)Instructions burned: 1 (million)
% 0.81/1.48 % (399814)Instruction limit reached!
% 0.81/1.48 % (399814)------------------------------
% 0.81/1.48 % (399814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.81/1.48 % (399814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/1.48 % (399814)CaDiCaL version: 2.1.3
% 0.81/1.48 % (399814)Termination reason: Instruction limit
% 0.81/1.48 % (399814)Termination phase: Saturation
% 0.81/1.48 % (399814)Time elapsed: 0.106 s
% 0.81/1.48 % (399814)Peak memory usage: 88 MB
% 0.81/1.48 % (399814)Instructions burned: 120 (million)
% 0.81/1.48 % (399815)Instruction limit reached!
% 0.81/1.48 % (399815)------------------------------
% 0.81/1.48 % (399815)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.81/1.48 % (399815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/1.48 % (399815)CaDiCaL version: 2.1.3
% 0.81/1.48 % (399815)Termination reason: Instruction limit
% 0.81/1.48 % (399815)Termination phase: Saturation
% 0.81/1.48 % (399815)Time elapsed: 0.139 s
% 0.81/1.48 % (399815)Peak memory usage: 89 MB
% 0.81/1.48 % (399815)Instructions burned: 139 (million)
% 0.81/1.48 % (399816)Refutation found. Thanks to Tanya!
% 0.81/1.48 % SZS status Theorem for theBenchmark
% 0.81/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.71 % (399816)------------------------------
% 0.21/1.71 % (399816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.71 % (399816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.71 % (399816)CaDiCaL version: 2.1.3
% 0.21/1.71 % (399816)Termination reason: Refutation
% 0.21/1.71 % (399816)Time elapsed: 0.013 s
% 0.21/1.71 % (399816)Peak memory usage: 89 MB
% 0.21/1.71 % (399816)Instructions burned: 20 (million)
% 0.21/1.71 % (399816)------------------------------
% 0.21/1.71 % (399816)------------------------------
% 0.21/1.71 % (399805)Success in time 0.431 s
% 0.21/1.71 % Vampire exiting
%------------------------------------------------------------------------------