%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU296+3 : 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 : n013.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 12:48:13 PM UTC 2026
% Result : Theorem 4.33s 1.62s
% Output : Refutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 136 ( 27 unt; 14 def)
% Number of atoms : 434 ( 32 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 541 ( 243 ~; 237 |; 33 &)
% ( 15 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 15 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 105 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( finite(X0)
<=> ? [X1] :
( relation(X1)
& function(X1)
& relation_rng(X1) = X0
& in(relation_dom(X1),omega) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_finset_1) ).
fof(f16,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f18,axiom,
! [X0,X1] :
( finite(X1)
=> finite(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
fof(f22,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f65,axiom,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f67,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
fof(f68,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(X0)
=> finite(relation_image(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
fof(f69,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(X0)
=> finite(relation_image(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
fof(f70,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f75,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f119,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f125,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f126,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f125]) ).
fof(f143,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f146,plain,
? [X0,X1] :
( ~ finite(relation_image(X1,X0))
& finite(X0)
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f69]) ).
fof(f147,plain,
? [X0,X1] :
( ~ finite(relation_image(X1,X0))
& finite(X0)
& relation(X1)
& function(X1) ),
inference(flattening,[],[f146]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f151]) ).
fof(f159,plain,
! [X0] :
( ( finite(X0)
| ! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_rng(X1) != X0
| ~ in(relation_dom(X1),omega) ) )
& ( ? [X1] :
( relation(X1)
& function(X1)
& relation_rng(X1) = X0
& in(relation_dom(X1),omega) )
| ~ finite(X0) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f160,plain,
! [X0] :
( ( finite(X0)
| ! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_rng(X1) != X0
| ~ in(relation_dom(X1),omega) ) )
& ( ? [X2] :
( relation(X2)
& function(X2)
& relation_rng(X2) = X0
& in(relation_dom(X2),omega) )
| ~ finite(X0) ) ),
inference(rectify,[],[f159]) ).
fof(f161,plain,
! [X0] :
( ( finite(X0)
| ! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_rng(X1) != X0
| ~ in(relation_dom(X1),omega) ) )
& ( ( relation(sK0(X0))
& function(sK0(X0))
& relation_rng(sK0(X0)) = X0
& in(relation_dom(sK0(X0)),omega) )
| ~ finite(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f160]) ).
fof(f188,plain,
( ~ finite(relation_image(sK28,sK27))
& finite(sK27)
& relation(sK28)
& function(sK28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27,sK28]),skolemize(X0,sK27),skolemize(X1,sK28)],[f147]) ).
fof(f216,plain,
! [X0] :
( in(relation_dom(sK0(X0)),omega)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f217,plain,
! [X0] :
( relation_rng(sK0(X0)) = X0
| ~ finite(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f218,plain,
! [X0] :
( function(sK0(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f219,plain,
! [X0] :
( relation(sK0(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f220,plain,
! [X0,X1] :
( finite(X0)
| ~ relation(X1)
| ~ function(X1)
| relation_rng(X1) != X0
| ~ in(relation_dom(X1),omega) ),
inference(cnf_transformation,[],[f161]) ).
fof(f221,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f223,plain,
! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f229,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f337,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f339,plain,
! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f340,plain,
function(sK28),
inference(cnf_transformation,[],[f188]) ).
fof(f341,plain,
relation(sK28),
inference(cnf_transformation,[],[f188]) ).
fof(f342,plain,
finite(sK27),
inference(cnf_transformation,[],[f188]) ).
fof(f343,plain,
~ finite(relation_image(sK28,sK27)),
inference(cnf_transformation,[],[f188]) ).
fof(f344,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f70]) ).
fof(f350,plain,
! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f356,plain,
! [X1] :
( finite(relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(relation_dom(X1),omega) ),
inference(equality_resolution,[],[f220]) ).
fof(f360,definition,
( spl30_1
<=> finite(relation_image(sK28,sK27)) ),
introduced(definition,[new_symbols(definition,[spl30_1])],[avatar_definition]) ).
fof(f362,plain,
( ~ finite(relation_image(sK28,sK27))
| spl30_1 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f363,plain,
~ spl30_1,
inference(avatar_split_clause,[],[f343,f360]) ).
fof(f367,definition,
( spl30_2
<=> finite(sK27) ),
introduced(definition,[new_symbols(definition,[spl30_2])],[avatar_definition]) ).
fof(f369,plain,
( finite(sK27)
| ~ spl30_2 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f370,plain,
spl30_2,
inference(avatar_split_clause,[],[f342,f367]) ).
fof(f372,definition,
( spl30_3
<=> function(sK28) ),
introduced(definition,[new_symbols(definition,[spl30_3])],[avatar_definition]) ).
fof(f374,plain,
( function(sK28)
| ~ spl30_3 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f375,plain,
spl30_3,
inference(avatar_split_clause,[],[f340,f372]) ).
fof(f401,definition,
( spl30_4
<=> relation(sK28) ),
introduced(definition,[new_symbols(definition,[spl30_4])],[avatar_definition]) ).
fof(f403,plain,
( relation(sK28)
| ~ spl30_4 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f404,plain,
spl30_4,
inference(avatar_split_clause,[],[f341,f401]) ).
fof(f406,plain,
( ! [X0] :
( relation(relation_composition(X0,sK28))
| ~ relation(X0) )
| ~ spl30_4 ),
inference(resolution,[],[f403,f221]) ).
fof(f428,plain,
( ! [X0] : relation_image(sK28,X0) = relation_image(sK28,set_intersection2(relation_dom(sK28),X0))
| ~ spl30_4 ),
inference(resolution,[],[f403,f337]) ).
fof(f430,plain,
( ! [X0] :
( relation_rng(relation_composition(X0,sK28)) = relation_image(sK28,relation_rng(X0))
| ~ relation(X0) )
| ~ spl30_4 ),
inference(resolution,[],[f403,f339]) ).
fof(f432,plain,
( ! [X0] :
( relation_dom(X0) = relation_dom(relation_composition(X0,sK28))
| ~ subset(relation_rng(X0),relation_dom(sK28))
| ~ relation(X0) )
| ~ spl30_4 ),
inference(resolution,[],[f403,f350]) ).
fof(f443,plain,
( ! [X0] : finite(set_intersection2(X0,sK27))
| ~ spl30_2 ),
inference(resolution,[],[f369,f223]) ).
fof(f486,definition,
( spl30_10
<=> ! [X0] : relation_image(sK28,X0) = relation_image(sK28,set_intersection2(relation_dom(sK28),X0)) ),
introduced(definition,[new_symbols(definition,[spl30_10])],[avatar_definition]) ).
fof(f487,plain,
( ! [X0] : relation_image(sK28,X0) = relation_image(sK28,set_intersection2(relation_dom(sK28),X0))
| ~ spl30_10 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f488,plain,
( spl30_10
| ~ spl30_4 ),
inference(avatar_split_clause,[],[f428,f401,f486]) ).
fof(f582,definition,
( spl30_14
<=> ! [X0] :
( relation_rng(relation_composition(X0,sK28)) = relation_image(sK28,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl30_14])],[avatar_definition]) ).
fof(f583,plain,
( ! [X0] :
( relation_rng(relation_composition(X0,sK28)) = relation_image(sK28,relation_rng(X0))
| ~ relation(X0) )
| ~ spl30_14 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f584,plain,
( spl30_14
| ~ spl30_4 ),
inference(avatar_split_clause,[],[f430,f401,f582]) ).
fof(f631,definition,
( spl30_19
<=> ! [X0] :
( relation_dom(X0) = relation_dom(relation_composition(X0,sK28))
| ~ subset(relation_rng(X0),relation_dom(sK28))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl30_19])],[avatar_definition]) ).
fof(f632,plain,
( ! [X0] :
( relation_dom(X0) = relation_dom(relation_composition(X0,sK28))
| ~ subset(relation_rng(X0),relation_dom(sK28))
| ~ relation(X0) )
| ~ spl30_19 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f633,plain,
( spl30_19
| ~ spl30_4 ),
inference(avatar_split_clause,[],[f432,f401,f631]) ).
fof(f635,definition,
( spl30_20
<=> ! [X0] : finite(set_intersection2(X0,sK27)) ),
introduced(definition,[new_symbols(definition,[spl30_20])],[avatar_definition]) ).
fof(f636,plain,
( ! [X0] : finite(set_intersection2(X0,sK27))
| ~ spl30_20 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f637,plain,
( spl30_20
| ~ spl30_2 ),
inference(avatar_split_clause,[],[f443,f367,f635]) ).
fof(f658,plain,
( ! [X0] :
( ~ in(relation_dom(X0),omega)
| finite(relation_rng(relation_composition(X0,sK28)))
| ~ relation(relation_composition(X0,sK28))
| ~ function(relation_composition(X0,sK28))
| ~ subset(relation_rng(X0),relation_dom(sK28))
| ~ relation(X0) )
| ~ spl30_19 ),
inference(superposition,[],[f356,f632]) ).
fof(f659,plain,
( ! [X0] :
( ~ in(relation_dom(X0),omega)
| finite(relation_rng(relation_composition(X0,sK28)))
| ~ function(relation_composition(X0,sK28))
| ~ subset(relation_rng(X0),relation_dom(sK28))
| ~ relation(X0) )
| ~ spl30_4
| ~ spl30_19 ),
inference(forward_subsumption_resolution,[],[f658,f406]) ).
fof(f693,plain,
( ! [X0] :
( relation_image(sK28,X0) = relation_rng(relation_composition(sK0(X0),sK28))
| ~ relation(sK0(X0))
| ~ finite(X0) )
| ~ spl30_14 ),
inference(superposition,[],[f583,f217]) ).
fof(f698,plain,
( ! [X0] :
( relation_image(sK28,X0) = relation_rng(relation_composition(sK0(X0),sK28))
| ~ finite(X0) )
| ~ spl30_14 ),
inference(forward_subsumption_resolution,[],[f693,f219]) ).
fof(f772,definition,
( spl30_27
<=> ! [X0] :
( relation_image(sK28,X0) = relation_rng(relation_composition(sK0(X0),sK28))
| ~ finite(X0) ) ),
introduced(definition,[new_symbols(definition,[spl30_27])],[avatar_definition]) ).
fof(f773,plain,
( ! [X0] :
( relation_image(sK28,X0) = relation_rng(relation_composition(sK0(X0),sK28))
| ~ finite(X0) )
| ~ spl30_27 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f774,plain,
( spl30_27
| ~ spl30_14 ),
inference(avatar_split_clause,[],[f698,f582,f772]) ).
fof(f865,definition,
( spl30_33
<=> ! [X0] :
( ~ in(relation_dom(X0),omega)
| finite(relation_rng(relation_composition(X0,sK28)))
| ~ function(relation_composition(X0,sK28))
| ~ subset(relation_rng(X0),relation_dom(sK28))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl30_33])],[avatar_definition]) ).
fof(f866,plain,
( ! [X0] :
( ~ subset(relation_rng(X0),relation_dom(sK28))
| finite(relation_rng(relation_composition(X0,sK28)))
| ~ function(relation_composition(X0,sK28))
| ~ in(relation_dom(X0),omega)
| ~ relation(X0) )
| ~ spl30_33 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f867,plain,
( spl30_33
| ~ spl30_4
| ~ spl30_19 ),
inference(avatar_split_clause,[],[f659,f631,f401,f865]) ).
fof(f869,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_rng(relation_composition(sK0(X0),sK28)))
| ~ function(relation_composition(sK0(X0),sK28))
| ~ in(relation_dom(sK0(X0)),omega)
| ~ relation(sK0(X0))
| ~ finite(X0) )
| ~ spl30_33 ),
inference(superposition,[],[f866,f217]) ).
fof(f875,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_rng(relation_composition(sK0(X0),sK28)))
| ~ function(relation_composition(sK0(X0),sK28))
| ~ relation(sK0(X0))
| ~ finite(X0) )
| ~ spl30_33 ),
inference(forward_subsumption_resolution,[],[f869,f216]) ).
fof(f876,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_rng(relation_composition(sK0(X0),sK28)))
| ~ function(relation_composition(sK0(X0),sK28))
| ~ finite(X0) )
| ~ spl30_33 ),
inference(forward_subsumption_resolution,[],[f875,f219]) ).
fof(f878,definition,
( spl30_34
<=> ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_rng(relation_composition(sK0(X0),sK28)))
| ~ function(relation_composition(sK0(X0),sK28))
| ~ finite(X0) ) ),
introduced(definition,[new_symbols(definition,[spl30_34])],[avatar_definition]) ).
fof(f879,plain,
( ! [X0] :
( finite(relation_rng(relation_composition(sK0(X0),sK28)))
| ~ subset(X0,relation_dom(sK28))
| ~ function(relation_composition(sK0(X0),sK28))
| ~ finite(X0) )
| ~ spl30_34 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f880,plain,
( spl30_34
| ~ spl30_33 ),
inference(avatar_split_clause,[],[f876,f865,f878]) ).
fof(f891,plain,
( ! [X0] :
( finite(relation_image(sK28,X0))
| ~ subset(X0,relation_dom(sK28))
| ~ function(relation_composition(sK0(X0),sK28))
| ~ finite(X0)
| ~ finite(X0) )
| ~ spl30_27
| ~ spl30_34 ),
inference(superposition,[],[f879,f773]) ).
fof(f892,plain,
( ! [X0] :
( finite(relation_image(sK28,X0))
| ~ subset(X0,relation_dom(sK28))
| ~ function(relation_composition(sK0(X0),sK28))
| ~ finite(X0) )
| ~ spl30_27
| ~ spl30_34 ),
inference(duplicate_literal_removal,[],[f891]) ).
fof(f948,definition,
( spl30_39
<=> ! [X0] :
( finite(relation_image(sK28,X0))
| ~ subset(X0,relation_dom(sK28))
| ~ function(relation_composition(sK0(X0),sK28))
| ~ finite(X0) ) ),
introduced(definition,[new_symbols(definition,[spl30_39])],[avatar_definition]) ).
fof(f949,plain,
( ! [X0] :
( ~ function(relation_composition(sK0(X0),sK28))
| ~ subset(X0,relation_dom(sK28))
| finite(relation_image(sK28,X0))
| ~ finite(X0) )
| ~ spl30_39 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f950,plain,
( spl30_39
| ~ spl30_27
| ~ spl30_34 ),
inference(avatar_split_clause,[],[f892,f878,f772,f948]) ).
fof(f953,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_image(sK28,X0))
| ~ finite(X0)
| ~ relation(sK0(X0))
| ~ function(sK0(X0))
| ~ relation(sK28)
| ~ function(sK28) )
| ~ spl30_39 ),
inference(resolution,[],[f949,f229]) ).
fof(f955,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_image(sK28,X0))
| ~ finite(X0)
| ~ relation(sK0(X0))
| ~ function(sK0(X0))
| ~ function(sK28) )
| ~ spl30_4
| ~ spl30_39 ),
inference(forward_subsumption_resolution,[],[f953,f403]) ).
fof(f957,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_image(sK28,X0))
| ~ finite(X0)
| ~ relation(sK0(X0))
| ~ function(sK0(X0)) )
| ~ spl30_3
| ~ spl30_4
| ~ spl30_39 ),
inference(forward_subsumption_resolution,[],[f955,f374]) ).
fof(f959,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_image(sK28,X0))
| ~ finite(X0)
| ~ function(sK0(X0)) )
| ~ spl30_3
| ~ spl30_4
| ~ spl30_39 ),
inference(forward_subsumption_resolution,[],[f957,f219]) ).
fof(f961,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_image(sK28,X0))
| ~ finite(X0) )
| ~ spl30_3
| ~ spl30_4
| ~ spl30_39 ),
inference(forward_subsumption_resolution,[],[f959,f218]) ).
fof(f1404,definition,
( spl30_67
<=> ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_image(sK28,X0))
| ~ finite(X0) ) ),
introduced(definition,[new_symbols(definition,[spl30_67])],[avatar_definition]) ).
fof(f1405,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK28))
| finite(relation_image(sK28,X0))
| ~ finite(X0) )
| ~ spl30_67 ),
inference(avatar_component_clause,[],[f1404]) ).
fof(f1406,plain,
( spl30_67
| ~ spl30_3
| ~ spl30_4
| ~ spl30_39 ),
inference(avatar_split_clause,[],[f961,f948,f401,f372,f1404]) ).
fof(f1408,plain,
( ! [X0] :
( finite(relation_image(sK28,set_intersection2(relation_dom(sK28),X0)))
| ~ finite(set_intersection2(relation_dom(sK28),X0)) )
| ~ spl30_67 ),
inference(resolution,[],[f1405,f344]) ).
fof(f1410,plain,
( ! [X0] :
( finite(relation_image(sK28,X0))
| ~ finite(set_intersection2(relation_dom(sK28),X0)) )
| ~ spl30_10
| ~ spl30_67 ),
inference(forward_demodulation,[],[f1408,f487]) ).
fof(f1412,definition,
( spl30_68
<=> ! [X0] :
( finite(relation_image(sK28,X0))
| ~ finite(set_intersection2(relation_dom(sK28),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl30_68])],[avatar_definition]) ).
fof(f1413,plain,
( ! [X0] :
( ~ finite(set_intersection2(relation_dom(sK28),X0))
| finite(relation_image(sK28,X0)) )
| ~ spl30_68 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f1414,plain,
( spl30_68
| ~ spl30_10
| ~ spl30_67 ),
inference(avatar_split_clause,[],[f1410,f1404,f486,f1412]) ).
fof(f1418,plain,
( finite(relation_image(sK28,sK27))
| ~ spl30_20
| ~ spl30_68 ),
inference(resolution,[],[f1413,f636]) ).
fof(f1426,plain,
( $false
| spl30_1
| ~ spl30_20
| ~ spl30_68 ),
inference(forward_subsumption_resolution,[],[f1418,f362]) ).
fof(f1427,plain,
( spl30_1
| ~ spl30_20
| ~ spl30_68 ),
inference(avatar_contradiction_clause,[],[f1426]) ).
cnf(s1,plain,
~ spl30_1,
inference(sat_conversion,[],[f363]) ).
cnf(s2,plain,
spl30_2,
inference(sat_conversion,[],[f370]) ).
cnf(s3,plain,
spl30_3,
inference(sat_conversion,[],[f375]) ).
cnf(s4,plain,
spl30_4,
inference(sat_conversion,[],[f404]) ).
cnf(s9,plain,
( ~ spl30_4
| spl30_10 ),
inference(sat_conversion,[],[f488]) ).
cnf(s13,plain,
( ~ spl30_4
| spl30_14 ),
inference(sat_conversion,[],[f584]) ).
cnf(s18,plain,
( ~ spl30_4
| spl30_19 ),
inference(sat_conversion,[],[f633]) ).
cnf(s19,plain,
( ~ spl30_2
| spl30_20 ),
inference(sat_conversion,[],[f637]) ).
cnf(s26,plain,
( ~ spl30_14
| spl30_27 ),
inference(sat_conversion,[],[f774]) ).
cnf(s32,plain,
( ~ spl30_4
| ~ spl30_19
| spl30_33 ),
inference(sat_conversion,[],[f867]) ).
cnf(s33,plain,
( ~ spl30_33
| spl30_34 ),
inference(sat_conversion,[],[f880]) ).
cnf(s37,plain,
( ~ spl30_27
| ~ spl30_34
| spl30_39 ),
inference(sat_conversion,[],[f950]) ).
cnf(s65,plain,
( ~ spl30_3
| ~ spl30_4
| ~ spl30_39
| spl30_67 ),
inference(sat_conversion,[],[f1406]) ).
cnf(s66,plain,
( ~ spl30_10
| ~ spl30_67
| spl30_68 ),
inference(sat_conversion,[],[f1414]) ).
cnf(s67,plain,
( spl30_1
| ~ spl30_20
| ~ spl30_68 ),
inference(sat_conversion,[],[f1427]) ).
cnf(s72,plain,
spl30_19,
inference(rat,[],[s18,s4]) ).
cnf(s73,plain,
spl30_14,
inference(rat,[],[s13,s4]) ).
cnf(s74,plain,
spl30_10,
inference(rat,[],[s9,s4]) ).
cnf(s78,plain,
spl30_33,
inference(rat,[],[s32,s4,s72]) ).
cnf(s79,plain,
spl30_27,
inference(rat,[],[s26,s73]) ).
cnf(s80,plain,
spl30_34,
inference(rat,[],[s33,s78]) ).
cnf(s82,plain,
spl30_39,
inference(rat,[],[s37,s79,s80]) ).
cnf(s84,plain,
spl30_67,
inference(rat,[],[s65,s82,s4,s3]) ).
cnf(s86,plain,
spl30_68,
inference(rat,[],[s66,s74,s84]) ).
cnf(s88,plain,
spl30_20,
inference(rat,[],[s19,s2]) ).
cnf(s95,plain,
spl30_1,
inference(rat,[],[s67,s86,s88]) ).
cnf(s120,plain,
$false,
inference(rat,[],[s1,s95]) ).
fof(f1428,plain,
$false,
inference(avatar_sat_refutation,[],[s120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU296+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:32:37 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 4.33/1.62 % (801298)Detected formulas, will run a generic FOF schedule.
% 4.33/1.62 % (801305)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=838049191:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.33/1.62 % (801307)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2783994969:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.33/1.62 % (801303)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=1828120315:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.33/1.62 % (801306)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=243722767:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.33/1.62 % (801304)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=1030533695:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.33/1.62 % (801308)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2027458295:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.33/1.62 % (801309)dis-21_1_sil=8000:lcm=predicate:random_seed=2341497820: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)
% 4.33/1.62 % (801306)Refutation not found, incomplete strategy
% 4.33/1.62 % (801306)------------------------------
% 4.33/1.62 % (801306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801306)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801306)Termination reason: Refutation not found, incomplete strategy
% 4.33/1.62 % (801306)Time elapsed: 0.001 s
% 4.33/1.62 % (801306)Peak memory usage: 88 MB
% 4.33/1.62 % (801307)Instruction limit reached!
% 4.33/1.62 % (801307)------------------------------
% 4.33/1.62 % (801307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801307)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801307)Termination reason: Instruction limit
% 4.33/1.62 % (801307)Termination phase: Saturation
% 4.33/1.62 % (801307)Time elapsed: 0.059 s
% 4.33/1.62 % (801307)Peak memory usage: 88 MB
% 4.33/1.62 % (801307)Instructions burned: 120 (million)
% 4.33/1.62 % (801309)Instruction limit reached!
% 4.33/1.62 % (801309)------------------------------
% 4.33/1.62 % (801309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801309)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801309)Termination reason: Instruction limit
% 4.33/1.62 % (801309)Termination phase: Saturation
% 4.33/1.62 % (801309)Time elapsed: 0.072 s
% 4.33/1.62 % (801309)Peak memory usage: 91 MB
% 4.33/1.62 % (801309)Instructions burned: 131 (million)
% 4.33/1.62 % (801308)Instruction limit reached!
% 4.33/1.62 % (801308)------------------------------
% 4.33/1.62 % (801308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801308)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801308)Termination reason: Instruction limit
% 4.33/1.62 % (801308)Termination phase: Saturation
% 4.33/1.62 % (801308)Time elapsed: 0.096 s
% 4.33/1.62 % (801308)Peak memory usage: 90 MB
% 4.33/1.62 % (801308)Instructions burned: 140 (million)
% 4.33/1.62 % (801317)lrs+10_1_sil=8000:sp=occurrence:random_seed=412996774:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.33/1.62 % (801318)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1930676364:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.33/1.62 % (801318)Refutation not found, incomplete strategy
% 4.33/1.62 % (801318)------------------------------
% 4.33/1.62 % (801318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801318)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801318)Termination reason: Refutation not found, incomplete strategy
% 4.33/1.62 % (801318)Time elapsed: 0.003 s
% 4.33/1.62 % (801318)Peak memory usage: 89 MB
% 4.33/1.62 % (801318)Instructions burned: 4 (million)
% 4.33/1.62 % (801319)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1474057846:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.33/1.62 % (801306)------------------------------
% 4.33/1.62 % (801306)------------------------------
% 4.33/1.62 % (801317)Instruction limit reached!
% 4.33/1.62 % (801317)------------------------------
% 4.33/1.62 % (801317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801317)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801317)Termination reason: Instruction limit
% 4.33/1.62 % (801317)Termination phase: Saturation
% 4.33/1.62 % (801317)Time elapsed: 0.159 s
% 4.33/1.62 % (801317)Peak memory usage: 93 MB
% 4.33/1.62 % (801317)Instructions burned: 287 (million)
% 4.33/1.62 % (801323)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=134841965:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.33/1.62 % (801319)Instruction limit reached!
% 4.33/1.62 % (801319)------------------------------
% 4.33/1.62 % (801319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801319)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801319)Termination reason: Instruction limit
% 4.33/1.62 % (801319)Termination phase: Saturation
% 4.33/1.62 % (801319)Time elapsed: 0.167 s
% 4.33/1.62 % (801319)Peak memory usage: 91 MB
% 4.33/1.62 % (801319)Instructions burned: 326 (million)
% 4.33/1.62 % (801318)------------------------------
% 4.33/1.62 % (801318)------------------------------
% 4.33/1.62 % (801305)First to succeed.
% 4.33/1.62 % (801305)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-801298"
% 4.33/1.62 % (801324)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1151420797:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.33/1.62 % (801324)Refutation not found, incomplete strategy
% 4.33/1.62 % (801324)------------------------------
% 4.33/1.62 % (801324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801324)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801324)Termination reason: Refutation not found, incomplete strategy
% 4.33/1.62 % (801324)Time elapsed: 0.003 s
% 4.33/1.62 % (801324)Peak memory usage: 88 MB
% 4.33/1.62 % (801324)Instructions burned: 4 (million)
% 4.33/1.62 % (801323)Instruction limit reached!
% 4.33/1.62 % (801323)------------------------------
% 4.33/1.62 % (801323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.62 % (801323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.62 % (801323)CaDiCaL version: 2.1.3
% 4.33/1.62 % (801323)Termination reason: Instruction limit
% 4.33/1.62 % (801323)Termination phase: Saturation
% 4.33/1.62 % (801323)Time elapsed: 0.137 s
% 4.33/1.62 % (801323)Peak memory usage: 94 MB
% 4.33/1.62 % (801323)Instructions burned: 248 (million)
% 4.33/1.62 % (801326)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2453213050:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.33/1.62 % (801327)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3383990882:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.33/1.62 % (801305)Refutation found. Thanks to Tanya!
% 4.33/1.62 % SZS status Theorem for theBenchmark
% 4.33/1.62 % SZS output start Proof for theBenchmark
% See solution above
% 6.05/1.82 % (801305)------------------------------
% 6.05/1.82 % (801305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.82 % (801305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.82 % (801305)CaDiCaL version: 2.1.3
% 6.05/1.82 % (801305)Termination reason: Refutation
% 6.05/1.82 % (801305)Time elapsed: 0.486 s
% 6.05/1.82 % (801305)Peak memory usage: 132 MB
% 6.05/1.82 % (801305)Instructions burned: 1115 (million)
% 6.05/1.82 % (801305)------------------------------
% 6.05/1.82 % (801305)------------------------------
% 6.05/1.82 % (801298)Success in time 0.771 s
% 6.05/1.82 % Vampire exiting
%------------------------------------------------------------------------------