%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET972+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 3.81s 1.46s
% Output : Refutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 205 ( 19 unt; 23 def)
% Number of atoms : 573 ( 34 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 643 ( 275 ~; 306 |; 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(f3,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f4,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(f6,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(f9,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,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(f12,conjecture,
! [X0,X1,X2] :
( cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( cartesian_product2(set_difference(X0,X1),X2) = set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& cartesian_product2(X2,set_difference(X0,X1)) = set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f15,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f9]) ).
fof(f18,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,[],[f11]) ).
fof(f19,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,[],[f18]) ).
fof(f20,plain,
? [X0,X1,X2] :
( cartesian_product2(set_difference(X0,X1),X2) != set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| cartesian_product2(X2,set_difference(X0,X1)) != set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f23]) ).
fof(f25,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,[],[f6]) ).
fof(f26,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,[],[f25]) ).
fof(f29,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,[],[f19]) ).
fof(f30,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))],[f29]) ).
fof(f31,plain,
( cartesian_product2(set_difference(sK5,sK6),sK7) != set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))
| cartesian_product2(sK7,set_difference(sK5,sK6)) != set_difference(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)],[f20]) ).
fof(f34,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f49,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,[],[f30]) ).
fof(f50,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,[],[f30]) ).
fof(f51,plain,
( cartesian_product2(set_difference(sK5,sK6),sK7) != set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))
| cartesian_product2(sK7,set_difference(sK5,sK6)) != set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f52,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f14]) ).
fof(f54,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,[],[f44,f40]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f43,f40]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f42,f40]) ).
fof(f58,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,[],[f50,f40,f40]) ).
fof(f59,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,[],[f49,f40,f40]) ).
fof(f60,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f36]) ).
fof(f61,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f35]) ).
fof(f62,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f34]) ).
fof(f63,definition,
! [X0,X1] :
( sQ8_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ8_eqProxy])],[equality_proxy_definition]) ).
fof(f68,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,[],[f58,f63]) ).
fof(f69,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,[],[f59,f63]) ).
fof(f70,plain,
( ~ sQ8_eqProxy(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| ~ sQ8_eqProxy(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))) ),
inference(equality_proxy_replacement,[],[f51,f63,f63]) ).
fof(f74,definition,
( spl9_1
<=> sQ8_eqProxy(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f75,plain,
( ~ sQ8_eqProxy(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| spl9_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,definition,
( spl9_2
<=> sQ8_eqProxy(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f78,plain,
( ~ sQ8_eqProxy(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| spl9_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f70,f77,f74]) ).
fof(f148,definition,
( spl9_10
<=> ! [X2,X3] : ~ subset(cartesian_product2(set_difference(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_difference(sK5,sK6),sK7),cartesian_product2(X2,X3))
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,definition,
( spl9_11
<=> ! [X0,X1] : ~ subset(set_difference(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_difference(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_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_difference(sK5,sK6),sK7)) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
fof(f156,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_difference(sK5,sK6),sK7))
| spl9_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,definition,
( spl9_13
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_difference(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_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| spl9_13 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f163,definition,
( spl9_14
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(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_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(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_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(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_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(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_difference(sK5,sK6),sK7),set_difference(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_difference(sK5,sK6),sK7),set_difference(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_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5) ),
introduced(definition,[new_symbols(definition,[spl9_17])],[avatar_definition]) ).
fof(f176,plain,
( ~ in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| spl9_17 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f199,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(set_difference(sK5,sK6),sK7),cartesian_product2(X0,X1))
| ~ subset(set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)),cartesian_product2(X2,X3))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_difference(sK5,sK6),sK7)) )
| spl9_2 ),
inference(resolution,[],[f69,f78]) ).
fof(f204,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_difference(sK5,sK6),sK7))
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f205,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f206,plain,
( spl9_12
| spl9_13
| spl9_11
| spl9_10
| spl9_2 ),
inference(avatar_split_clause,[],[f199,f77,f148,f151,f158,f155]) ).
fof(f207,plain,
( $false
| ~ spl9_10 ),
inference(resolution,[],[f149,f47]) ).
fof(f208,plain,
~ spl9_10,
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f209,plain,
( $false
| ~ spl9_11 ),
inference(resolution,[],[f152,f52]) ).
fof(f210,plain,
~ spl9_11,
inference(avatar_contradiction_clause,[],[f209]) ).
fof(f211,plain,
( in(sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| ~ spl9_12 ),
inference(resolution,[],[f204,f56]) ).
fof(f212,plain,
( in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),set_difference(sK5,sK6))
| ~ spl9_12 ),
inference(resolution,[],[f204,f55]) ).
fof(f215,plain,
( $false
| ~ spl9_12
| spl9_16 ),
inference(resolution,[],[f211,f173]) ).
fof(f218,plain,
( ~ spl9_12
| spl9_16 ),
inference(avatar_contradiction_clause,[],[f215]) ).
fof(f225,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK6,sK7))
| ~ spl9_13 ),
inference(resolution,[],[f205,f62]) ).
fof(f226,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK5,sK7))
| ~ spl9_13 ),
inference(resolution,[],[f205,f61]) ).
fof(f232,plain,
( in(sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| ~ spl9_13 ),
inference(resolution,[],[f226,f56]) ).
fof(f233,plain,
( in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| ~ spl9_13 ),
inference(resolution,[],[f226,f55]) ).
fof(f237,plain,
( $false
| ~ spl9_13
| spl9_16 ),
inference(resolution,[],[f232,f173]) ).
fof(f240,plain,
( ~ spl9_13
| spl9_16 ),
inference(avatar_contradiction_clause,[],[f237]) ).
fof(f247,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK5,sK7))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(sK6,sK7))
| spl9_13 ),
inference(resolution,[],[f159,f60]) ).
fof(f248,plain,
( spl9_14
| ~ spl9_15
| spl9_13 ),
inference(avatar_split_clause,[],[f247,f158,f166,f163]) ).
fof(f249,plain,
( ~ in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| ~ spl9_12 ),
inference(resolution,[],[f212,f62]) ).
fof(f250,plain,
( in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| ~ spl9_12 ),
inference(resolution,[],[f212,f61]) ).
fof(f254,plain,
( in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| ~ spl9_14 ),
inference(resolution,[],[f164,f55]) ).
fof(f261,plain,
( $false
| ~ spl9_12
| ~ spl9_14 ),
inference(resolution,[],[f254,f249]) ).
fof(f264,plain,
( ~ spl9_12
| ~ spl9_14 ),
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f268,plain,
( ~ in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| ~ in(sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| spl9_15 ),
inference(resolution,[],[f167,f54]) ).
fof(f269,plain,
( ~ spl9_16
| ~ spl9_17
| spl9_15 ),
inference(avatar_split_clause,[],[f268,f166,f175,f172]) ).
fof(f270,plain,
( $false
| ~ spl9_12
| spl9_17 ),
inference(resolution,[],[f176,f250]) ).
fof(f271,plain,
( ~ spl9_12
| spl9_17 ),
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f273,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(sK7,set_difference(sK5,sK6)),cartesian_product2(X0,X1))
| ~ subset(set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)),cartesian_product2(X2,X3))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_difference(sK5,sK6))) )
| spl9_1 ),
inference(resolution,[],[f75,f68]) ).
fof(f276,definition,
( spl9_22
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_difference(sK5,sK6))) ),
introduced(definition,[new_symbols(definition,[spl9_22])],[avatar_definition]) ).
fof(f277,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_difference(sK5,sK6)))
| spl9_22 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f279,definition,
( spl9_23
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))) ),
introduced(definition,[new_symbols(definition,[spl9_23])],[avatar_definition]) ).
fof(f280,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| spl9_23 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f282,definition,
( spl9_24
<=> ! [X2,X3] : ~ subset(set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)),cartesian_product2(X2,X3)) ),
introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition]) ).
fof(f283,plain,
( ! [X2,X3] : ~ subset(set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)),cartesian_product2(X2,X3))
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,definition,
( spl9_25
<=> ! [X0,X1] : ~ subset(cartesian_product2(sK7,set_difference(sK5,sK6)),cartesian_product2(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl9_25])],[avatar_definition]) ).
fof(f286,plain,
( ! [X0,X1] : ~ subset(cartesian_product2(sK7,set_difference(sK5,sK6)),cartesian_product2(X0,X1))
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f287,plain,
( ~ spl9_22
| ~ spl9_23
| spl9_24
| spl9_25
| spl9_1 ),
inference(avatar_split_clause,[],[f273,f74,f285,f282,f279,f276]) ).
fof(f288,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_difference(sK5,sK6)))
| ~ spl9_22 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f289,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f291,plain,
( $false
| ~ spl9_24 ),
inference(resolution,[],[f283,f52]) ).
fof(f292,plain,
~ spl9_24,
inference(avatar_contradiction_clause,[],[f291]) ).
fof(f321,definition,
( spl9_29
<=> in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),set_difference(sK5,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_29])],[avatar_definition]) ).
fof(f322,plain,
( ~ in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),set_difference(sK5,sK6))
| spl9_29 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f324,definition,
( spl9_30
<=> in(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7) ),
introduced(definition,[new_symbols(definition,[spl9_30])],[avatar_definition]) ).
fof(f325,plain,
( ~ in(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| spl9_30 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f332,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK6))
| ~ spl9_23 ),
inference(resolution,[],[f289,f62]) ).
fof(f333,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK5))
| ~ spl9_23 ),
inference(resolution,[],[f289,f61]) ).
fof(f338,plain,
( ~ in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| spl9_29 ),
inference(resolution,[],[f322,f60]) ).
fof(f340,definition,
( spl9_31
<=> in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6) ),
introduced(definition,[new_symbols(definition,[spl9_31])],[avatar_definition]) ).
fof(f343,definition,
( spl9_32
<=> in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5) ),
introduced(definition,[new_symbols(definition,[spl9_32])],[avatar_definition]) ).
fof(f344,plain,
( ~ in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| spl9_32 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f345,plain,
( spl9_31
| ~ spl9_32
| spl9_29 ),
inference(avatar_split_clause,[],[f338,f321,f343,f340]) ).
fof(f347,plain,
( ~ in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| ~ in(sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| ~ spl9_13 ),
inference(resolution,[],[f225,f54]) ).
fof(f353,plain,
( ~ in(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| ~ spl9_23 ),
inference(resolution,[],[f332,f54]) ).
fof(f355,plain,
( ~ spl9_31
| ~ spl9_30
| ~ spl9_23 ),
inference(avatar_split_clause,[],[f353,f279,f324,f340]) ).
fof(f356,plain,
( in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| ~ spl9_23 ),
inference(resolution,[],[f333,f56]) ).
fof(f357,plain,
( in(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ spl9_23 ),
inference(resolution,[],[f333,f55]) ).
fof(f360,plain,
( $false
| ~ spl9_23
| spl9_32 ),
inference(resolution,[],[f356,f344]) ).
fof(f363,plain,
( ~ spl9_23
| spl9_32 ),
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f364,plain,
( $false
| ~ spl9_23
| spl9_30 ),
inference(resolution,[],[f357,f325]) ).
fof(f367,plain,
( ~ spl9_23
| spl9_30 ),
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f368,plain,
( in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),set_difference(sK5,sK6))
| ~ spl9_22 ),
inference(resolution,[],[f288,f56]) ).
fof(f369,plain,
( in(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ spl9_22 ),
inference(resolution,[],[f288,f55]) ).
fof(f374,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK5))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK6))
| spl9_23 ),
inference(resolution,[],[f280,f60]) ).
fof(f376,definition,
( spl9_33
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_33])],[avatar_definition]) ).
fof(f377,plain,
( in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK6))
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f379,definition,
( spl9_34
<=> in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK5)) ),
introduced(definition,[new_symbols(definition,[spl9_34])],[avatar_definition]) ).
fof(f380,plain,
( ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,sK5))
| spl9_34 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f381,plain,
( spl9_33
| ~ spl9_34
| spl9_23 ),
inference(avatar_split_clause,[],[f374,f279,f379,f376]) ).
fof(f382,plain,
( ~ in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| ~ spl9_22 ),
inference(resolution,[],[f368,f62]) ).
fof(f383,plain,
( in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| ~ spl9_22 ),
inference(resolution,[],[f368,f61]) ).
fof(f386,plain,
( ~ spl9_31
| ~ spl9_22 ),
inference(avatar_split_clause,[],[f382,f276,f340]) ).
fof(f388,plain,
( ~ in(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK5)
| spl9_34 ),
inference(resolution,[],[f380,f54]) ).
fof(f398,plain,
( $false
| ~ spl9_22
| spl9_32 ),
inference(resolution,[],[f383,f344]) ).
fof(f401,plain,
( ~ spl9_22
| spl9_32 ),
inference(avatar_contradiction_clause,[],[f398]) ).
fof(f403,definition,
( spl9_37
<=> in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),set_difference(sK5,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_37])],[avatar_definition]) ).
fof(f404,plain,
( ~ in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),set_difference(sK5,sK6))
| spl9_37 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f408,definition,
( spl9_38
<=> in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6) ),
introduced(definition,[new_symbols(definition,[spl9_38])],[avatar_definition]) ).
fof(f411,plain,
( ~ spl9_16
| ~ spl9_38
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f347,f158,f408,f172]) ).
fof(f423,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(set_difference(sK5,sK6),sK7),cartesian_product2(X0,X1))
| ~ subset(set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)),cartesian_product2(X2,X3))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))
| ~ in(unordered_pair(unordered_pair(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7)))),singleton(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))))),cartesian_product2(set_difference(sK5,sK6),sK7)) )
| spl9_2 ),
inference(resolution,[],[f78,f68]) ).
fof(f425,plain,
( ~ spl9_12
| ~ spl9_13
| spl9_11
| spl9_10
| spl9_2 ),
inference(avatar_split_clause,[],[f423,f77,f148,f151,f158,f155]) ).
fof(f436,plain,
( ~ in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),set_difference(sK5,sK6))
| ~ in(sK4(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK7)
| spl9_12 ),
inference(resolution,[],[f156,f54]) ).
fof(f437,plain,
( ~ spl9_16
| ~ spl9_37
| spl9_12 ),
inference(avatar_split_clause,[],[f436,f155,f403,f172]) ).
fof(f441,plain,
( ~ in(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK7)
| ~ in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),set_difference(sK5,sK6))
| spl9_22 ),
inference(resolution,[],[f277,f54]) ).
fof(f442,plain,
( ~ spl9_29
| ~ spl9_30
| spl9_22 ),
inference(avatar_split_clause,[],[f441,f276,f324,f321]) ).
fof(f444,plain,
( ~ in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK5)
| in(sK3(cartesian_product2(set_difference(sK5,sK6),sK7),set_difference(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK7))),sK6)
| spl9_37 ),
inference(resolution,[],[f404,f60]) ).
fof(f446,plain,
( spl9_38
| ~ spl9_17
| spl9_37 ),
inference(avatar_split_clause,[],[f444,f403,f175,f408]) ).
fof(f447,plain,
( $false
| ~ spl9_13
| spl9_17 ),
inference(resolution,[],[f176,f233]) ).
fof(f448,plain,
( ~ spl9_13
| spl9_17 ),
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f451,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(sK7,set_difference(sK5,sK6)),cartesian_product2(X0,X1))
| ~ subset(set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)),cartesian_product2(X2,X3))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))
| in(unordered_pair(unordered_pair(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6)))),singleton(sK3(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))))),cartesian_product2(sK7,set_difference(sK5,sK6))) )
| spl9_1 ),
inference(resolution,[],[f75,f69]) ).
fof(f454,plain,
( spl9_22
| spl9_23
| spl9_24
| spl9_25
| spl9_1 ),
inference(avatar_split_clause,[],[f451,f74,f285,f282,f279,f276]) ).
fof(f488,plain,
( in(sK4(cartesian_product2(sK7,set_difference(sK5,sK6)),set_difference(cartesian_product2(sK7,sK5),cartesian_product2(sK7,sK6))),sK6)
| ~ spl9_33 ),
inference(resolution,[],[f377,f56]) ).
fof(f492,plain,
( spl9_31
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f488,f376,f340]) ).
fof(f493,plain,
( ~ spl9_32
| ~ spl9_30
| spl9_34 ),
inference(avatar_split_clause,[],[f388,f379,f324,f343]) ).
fof(f494,plain,
( $false
| ~ spl9_22
| spl9_30 ),
inference(resolution,[],[f325,f369]) ).
fof(f495,plain,
( ~ spl9_22
| spl9_30 ),
inference(avatar_contradiction_clause,[],[f494]) ).
fof(f496,plain,
( $false
| ~ spl9_25 ),
inference(resolution,[],[f286,f47]) ).
fof(f497,plain,
~ spl9_25,
inference(avatar_contradiction_clause,[],[f496]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f79]) ).
cnf(s12,plain,
( spl9_2
| spl9_10
| spl9_11
| spl9_12
| spl9_13 ),
inference(sat_conversion,[],[f206]) ).
cnf(s13,plain,
~ spl9_10,
inference(sat_conversion,[],[f208]) ).
cnf(s14,plain,
~ spl9_11,
inference(sat_conversion,[],[f210]) ).
cnf(s15,plain,
( ~ spl9_12
| spl9_16 ),
inference(sat_conversion,[],[f218]) ).
cnf(s17,plain,
( ~ spl9_13
| spl9_16 ),
inference(sat_conversion,[],[f240]) ).
cnf(s18,plain,
( spl9_13
| spl9_14
| ~ spl9_15 ),
inference(sat_conversion,[],[f248]) ).
cnf(s19,plain,
( ~ spl9_12
| ~ spl9_14 ),
inference(sat_conversion,[],[f264]) ).
cnf(s22,plain,
( spl9_15
| ~ spl9_16
| ~ spl9_17 ),
inference(sat_conversion,[],[f269]) ).
cnf(s23,plain,
( ~ spl9_12
| spl9_17 ),
inference(sat_conversion,[],[f271]) ).
cnf(s24,plain,
( spl9_1
| ~ spl9_22
| ~ spl9_23
| spl9_24
| spl9_25 ),
inference(sat_conversion,[],[f287]) ).
cnf(s26,plain,
~ spl9_24,
inference(sat_conversion,[],[f292]) ).
cnf(s33,plain,
( spl9_29
| spl9_31
| ~ spl9_32 ),
inference(sat_conversion,[],[f345]) ).
cnf(s34,plain,
( ~ spl9_23
| ~ spl9_30
| ~ spl9_31 ),
inference(sat_conversion,[],[f355]) ).
cnf(s35,plain,
( ~ spl9_23
| spl9_32 ),
inference(sat_conversion,[],[f363]) ).
cnf(s36,plain,
( ~ spl9_23
| spl9_30 ),
inference(sat_conversion,[],[f367]) ).
cnf(s37,plain,
( spl9_23
| spl9_33
| ~ spl9_34 ),
inference(sat_conversion,[],[f381]) ).
cnf(s38,plain,
( ~ spl9_22
| ~ spl9_31 ),
inference(sat_conversion,[],[f386]) ).
cnf(s40,plain,
( ~ spl9_22
| spl9_32 ),
inference(sat_conversion,[],[f401]) ).
cnf(s44,plain,
( ~ spl9_13
| ~ spl9_16
| ~ spl9_38 ),
inference(sat_conversion,[],[f411]) ).
cnf(s45,plain,
( spl9_2
| spl9_10
| spl9_11
| ~ spl9_12
| ~ spl9_13 ),
inference(sat_conversion,[],[f425]) ).
cnf(s47,plain,
( spl9_12
| ~ spl9_16
| ~ spl9_37 ),
inference(sat_conversion,[],[f437]) ).
cnf(s48,plain,
( spl9_22
| ~ spl9_29
| ~ spl9_30 ),
inference(sat_conversion,[],[f442]) ).
cnf(s49,plain,
( ~ spl9_17
| spl9_37
| spl9_38 ),
inference(sat_conversion,[],[f446]) ).
cnf(s50,plain,
( ~ spl9_13
| spl9_17 ),
inference(sat_conversion,[],[f448]) ).
cnf(s53,plain,
( spl9_1
| spl9_22
| spl9_23
| spl9_24
| spl9_25 ),
inference(sat_conversion,[],[f454]) ).
cnf(s56,plain,
( spl9_31
| ~ spl9_33 ),
inference(sat_conversion,[],[f492]) ).
cnf(s57,plain,
( ~ spl9_30
| ~ spl9_32
| spl9_34 ),
inference(sat_conversion,[],[f493]) ).
cnf(s58,plain,
( ~ spl9_22
| spl9_30 ),
inference(sat_conversion,[],[f495]) ).
cnf(s59,plain,
~ spl9_25,
inference(sat_conversion,[],[f497]) ).
cnf(s61,plain,
( spl9_1
| spl9_22
| spl9_23
| spl9_24 ),
inference(rat,[],[s53,s59]) ).
cnf(s65,plain,
( spl9_1
| ~ spl9_22
| ~ spl9_23 ),
inference(rat,[],[s24,s59,s26]) ).
cnf(s66,plain,
( spl9_2
| spl9_12
| spl9_13 ),
inference(rat,[],[s12,s14,s13]) ).
cnf(s70,plain,
( spl9_12
| spl9_2 ),
inference(rat,[],[s49,s44,s47,s17,s50,s66]) ).
cnf(s71,plain,
spl9_2,
inference(rat,[],[s22,s18,s45,s15,s19,s23,s70,s14,s13]) ).
cnf(s73,plain,
( spl9_22
| spl9_1 ),
inference(rat,[],[s33,s48,s34,s35,s36,s61,s26]) ).
cnf(s74,plain,
spl9_1,
inference(rat,[],[s37,s56,s57,s65,s38,s40,s58,s73]) ).
cnf(s75,plain,
$false,
inference(rat,[],[s1,s71,s74]) ).
fof(f498,plain,
$false,
inference(avatar_sat_refutation,[],[s75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET972+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n005.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 03:16:31 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.81/1.46 % (399218)Detected formulas, will run a generic FOF schedule.
% 3.81/1.46 % (399329)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=89970570:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.81/1.46 % (399326)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=2092093565:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.81/1.46 % (399324)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=1305255695:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.81/1.46 % (399330)dis-21_1_sil=8000:lcm=predicate:random_seed=3556783772: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)
% 3.81/1.46 % (399328)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=749149281:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.81/1.46 % (399325)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=3852528697:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.81/1.46 % (399330)First to succeed.
% 3.81/1.46 % (399329)Instruction limit reached!
% 3.81/1.46 % (399329)------------------------------
% 3.81/1.46 % (399329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.46 % (399329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.46 % (399329)CaDiCaL version: 2.1.3
% 3.81/1.46 % (399329)Termination reason: Instruction limit
% 3.81/1.46 % (399329)Termination phase: Saturation
% 3.81/1.46 % (399329)Time elapsed: 0.048 s
% 3.81/1.46 % (399329)Peak memory usage: 90 MB
% 3.81/1.46 % (399329)Instructions burned: 139 (million)
% 3.81/1.46 % (399330)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-399218"
% 3.81/1.46 % (399327)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2197644996:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.81/1.46 % (399327)Refutation not found, incomplete strategy
% 3.81/1.46 % (399327)------------------------------
% 3.81/1.46 % (399327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.46 % (399327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.46 % (399327)CaDiCaL version: 2.1.3
% 3.81/1.46 % (399327)Termination reason: Refutation not found, incomplete strategy
% 3.81/1.46 % (399327)Time elapsed: 0.002 s
% 3.81/1.46 % (399327)Peak memory usage: 88 MB
% 3.81/1.46 % (399327)Instructions burned: 1 (million)
% 3.81/1.46 % (399328)Instruction limit reached!
% 3.81/1.46 % (399328)------------------------------
% 3.81/1.46 % (399328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.46 % (399328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.46 % (399328)CaDiCaL version: 2.1.3
% 3.81/1.46 % (399328)Termination reason: Instruction limit
% 3.81/1.46 % (399328)Termination phase: Saturation
% 3.81/1.46 % (399328)Time elapsed: 0.087 s
% 3.81/1.46 % (399328)Peak memory usage: 88 MB
% 3.81/1.46 % (399328)Instructions burned: 119 (million)
% 3.81/1.46 % (399338)lrs+10_1_sil=8000:sp=occurrence:random_seed=794182264:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.81/1.46 % (399338)Instruction limit reached!
% 3.81/1.46 % (399338)------------------------------
% 3.81/1.46 % (399338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.46 % (399338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.46 % (399338)CaDiCaL version: 2.1.3
% 3.81/1.46 % (399338)Termination reason: Instruction limit
% 3.81/1.46 % (399338)Termination phase: Saturation
% 3.81/1.46 % (399338)Time elapsed: 0.135 s
% 3.81/1.46 % (399338)Peak memory usage: 89 MB
% 3.81/1.46 % (399338)Instructions burned: 286 (million)
% 3.81/1.46 % (399359)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1423661300:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.81/1.46 % (399327)------------------------------
% 3.81/1.46 % (399327)------------------------------
% 3.81/1.46 % (399359)Refutation not found, incomplete strategy
% 3.81/1.46 % (399359)------------------------------
% 3.81/1.46 % (399359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.46 % (399359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.46 % (399359)CaDiCaL version: 2.1.3
% 3.81/1.46 % (399359)Termination reason: Refutation not found, incomplete strategy
% 3.81/1.46 % (399359)Time elapsed: 0.007 s
% 3.81/1.46 % (399359)Peak memory usage: 89 MB
% 3.81/1.46 % (399359)Instructions burned: 4 (million)
% 3.81/1.46 % (399330)Refutation found. Thanks to Tanya!
% 3.81/1.46 % SZS status Theorem for theBenchmark
% 3.81/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 4.64/1.66 % (399330)------------------------------
% 4.64/1.66 % (399330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.66 % (399330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.66 % (399330)CaDiCaL version: 2.1.3
% 4.64/1.66 % (399330)Termination reason: Refutation
% 4.64/1.66 % (399330)Time elapsed: 0.013 s
% 4.64/1.66 % (399330)Peak memory usage: 89 MB
% 4.64/1.66 % (399330)Instructions burned: 19 (million)
% 4.64/1.66 % (399330)------------------------------
% 4.64/1.66 % (399330)------------------------------
% 4.64/1.66 % (399218)Success in time 0.571 s
% 4.64/1.66 % Vampire exiting
%------------------------------------------------------------------------------