%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU265+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:48:04 PM UTC 2026
% Result : Theorem 3.52s 1.34s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 136 ( 12 unt; 10 def)
% Number of atoms : 434 ( 44 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 514 ( 216 ~; 238 |; 31 &)
% ( 17 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 250 ( 0 sgn 223 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f17,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f25,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f29,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f30,conjecture,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f36,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f43,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f45,plain,
! [X0,X1,X2] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f46,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f47,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) )
<~> relation_dom_as_subset(X1,X0,X2) = X1 )
& relation_of2_as_subset(X2,X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f52,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f53,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f63]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f71,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f72,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X5] :
( ~ in(X5,X1)
| ? [X6] : in(ordered_pair(X5,X6),X2) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
( ( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| ( in(sK11,sK9)
& ! [X4] : ~ in(ordered_pair(sK11,X4),sK10) ) )
& ( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| ! [X5] :
( ~ in(X5,sK9)
| in(ordered_pair(X5,sK12(X5)),sK10) ) )
& relation_of2_as_subset(sK10,sK9,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X6,sK12(X5))],[f73]) ).
fof(f78,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f43]) ).
fof(f80,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f82,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f64]) ).
fof(f83,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f64]) ).
fof(f85,plain,
! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f86,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f95,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f101,plain,
relation_of2_as_subset(sK10,sK9,sK8),
inference(cnf_transformation,[],[f74]) ).
fof(f102,plain,
! [X5] :
( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| ~ in(X5,sK9)
| in(ordered_pair(X5,sK12(X5)),sK10) ),
inference(cnf_transformation,[],[f74]) ).
fof(f103,plain,
! [X4] :
( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| ~ in(ordered_pair(sK11,X4),sK10) ),
inference(cnf_transformation,[],[f74]) ).
fof(f104,plain,
( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| in(sK11,sK9) ),
inference(cnf_transformation,[],[f74]) ).
fof(f105,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f109,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f115,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(ordered_pair(X5,sK2(X0,X5)),X0) ),
inference(equality_resolution,[],[f80]) ).
fof(f117,definition,
( spl14_1
<=> ! [X5] :
( ~ in(X5,sK9)
| in(ordered_pair(X5,sK12(X5)),sK10) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f118,plain,
( ! [X5] :
( ~ in(X5,sK9)
| in(ordered_pair(X5,sK12(X5)),sK10) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,definition,
( spl14_2
<=> sK9 = relation_dom_as_subset(sK9,sK8,sK10) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f121,plain,
( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| spl14_2 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f102,f120,f117]) ).
fof(f125,definition,
( spl14_3
<=> ! [X4] : ~ in(ordered_pair(sK11,X4),sK10) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f126,plain,
( ! [X4] : ~ in(ordered_pair(sK11,X4),sK10)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( spl14_3
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f103,f120,f125]) ).
fof(f129,definition,
( spl14_4
<=> in(sK11,sK9) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f131,plain,
( in(sK11,sK9)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl14_4
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f104,f120,f129]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| in(X0,X2)
| empty(X2) ),
inference(resolution,[],[f109,f105]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| in(X0,X2) ),
inference(forward_subsumption_resolution,[],[f157,f110]) ).
fof(f166,definition,
( spl14_5
<=> relation_of2(sK10,sK9,sK8) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f167,plain,
( relation_of2(sK10,sK9,sK8)
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f168,plain,
( ~ relation_of2(sK10,sK9,sK8)
| spl14_5 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f174,plain,
( ~ relation_of2_as_subset(sK10,sK9,sK8)
| spl14_5 ),
inference(resolution,[],[f168,f95]) ).
fof(f175,plain,
( $false
| spl14_5 ),
inference(forward_subsumption_resolution,[],[f174,f101]) ).
fof(f176,plain,
spl14_5,
inference(avatar_contradiction_clause,[],[f175]) ).
fof(f179,plain,
( relation_dom_as_subset(sK9,sK8,sK10) = relation_dom(sK10)
| ~ spl14_5 ),
inference(resolution,[],[f167,f94]) ).
fof(f180,plain,
( sK9 = relation_dom(sK10)
| ~ spl14_2
| ~ spl14_5 ),
inference(forward_demodulation,[],[f179,f122]) ).
fof(f208,plain,
! [X2,X3,X0,X1] :
( in(sK0(X0,X3),X3)
| in(ordered_pair(sK0(X0,X3),sK1(X0,X3)),X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation_dom(X0) = X3 ),
inference(resolution,[],[f78,f82]) ).
fof(f209,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK0(X0,X3),X3)
| ~ in(ordered_pair(sK0(X0,X3),X4),X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation_dom(X0) = X3 ),
inference(resolution,[],[f78,f83]) ).
fof(f210,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,relation_dom(X0))
| ~ element(X0,powerset(cartesian_product2(X1,X2)))
| in(ordered_pair(X3,sK2(X0,X3)),X0) ),
inference(resolution,[],[f78,f115]) ).
fof(f211,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2)))
| in(X3,relation_dom(X0)) ),
inference(resolution,[],[f78,f100]) ).
fof(f446,definition,
( spl14_19
<=> ! [X2,X1] : ~ element(sK10,powerset(cartesian_product2(X1,X2))) ),
introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition]) ).
fof(f447,plain,
( ! [X2,X1] : ~ element(sK10,powerset(cartesian_product2(X1,X2)))
| ~ spl14_19 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f449,definition,
( spl14_20
<=> ! [X0] :
( ~ in(X0,sK9)
| in(ordered_pair(X0,sK2(sK10,X0)),sK10) ) ),
introduced(definition,[new_symbols(definition,[spl14_20])],[avatar_definition]) ).
fof(f450,plain,
( ! [X0] :
( ~ in(X0,sK9)
| in(ordered_pair(X0,sK2(sK10,X0)),sK10) )
| ~ spl14_20 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f468,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK9)
| ~ element(sK10,powerset(cartesian_product2(X1,X2)))
| in(ordered_pair(X0,sK2(sK10,X0)),sK10) )
| ~ spl14_2
| ~ spl14_5 ),
inference(superposition,[],[f210,f180]) ).
fof(f469,plain,
( spl14_19
| spl14_20
| ~ spl14_2
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f468,f166,f120,f449,f446]) ).
fof(f471,plain,
( ! [X0,X1] : ~ relation_of2_as_subset(sK10,X0,X1)
| ~ spl14_19 ),
inference(resolution,[],[f447,f86]) ).
fof(f514,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ element(X0,powerset(cartesian_product2(X2,X3)))
| relation_dom(X0) = X1
| ~ in(ordered_pair(sK0(X0,X1),X4),X0)
| ~ element(X0,powerset(cartesian_product2(X5,X6)))
| relation_dom(X0) = X1 ),
inference(resolution,[],[f208,f209]) ).
fof(f520,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ in(ordered_pair(sK0(X0,X1),X4),X0)
| ~ element(X0,powerset(cartesian_product2(X2,X3)))
| relation_dom(X0) = X1
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ element(X0,powerset(cartesian_product2(X5,X6))) ),
inference(duplicate_literal_removal,[],[f514]) ).
fof(f525,plain,
( in(ordered_pair(sK11,sK2(sK10,sK11)),sK10)
| ~ spl14_4
| ~ spl14_20 ),
inference(resolution,[],[f450,f131]) ).
fof(f534,plain,
( $false
| ~ spl14_3
| ~ spl14_4
| ~ spl14_20 ),
inference(forward_subsumption_resolution,[],[f525,f126]) ).
fof(f535,plain,
( ~ spl14_3
| ~ spl14_4
| ~ spl14_20 ),
inference(avatar_contradiction_clause,[],[f534]) ).
fof(f558,plain,
( ! [X2,X0,X1] :
( in(ordered_pair(sK0(X0,sK9),sK12(sK0(X0,sK9))),sK10)
| in(ordered_pair(sK0(X0,sK9),sK1(X0,sK9)),X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation_dom(X0) = sK9 )
| ~ spl14_1 ),
inference(resolution,[],[f118,f208]) ).
fof(f600,plain,
( sK9 != relation_dom(sK10)
| spl14_2
| ~ spl14_5 ),
inference(superposition,[],[f121,f179]) ).
fof(f601,plain,
( element(relation_dom(sK10),powerset(sK9))
| ~ relation_of2(sK10,sK9,sK8)
| ~ spl14_5 ),
inference(superposition,[],[f85,f179]) ).
fof(f602,plain,
( element(relation_dom(sK10),powerset(sK9))
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f601,f167]) ).
fof(f1665,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ element(sK10,powerset(cartesian_product2(X0,X1)))
| sK9 = relation_dom(sK10)
| in(ordered_pair(sK0(sK10,sK9),sK1(sK10,sK9)),sK10)
| ~ element(sK10,powerset(cartesian_product2(X2,X3)))
| in(ordered_pair(sK0(sK10,sK9),sK1(sK10,sK9)),sK10)
| ~ element(sK10,powerset(cartesian_product2(X4,X5)))
| sK9 = relation_dom(sK10) )
| ~ spl14_1 ),
inference(resolution,[],[f520,f558]) ).
fof(f1666,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ element(sK10,powerset(cartesian_product2(X0,X1)))
| sK9 = relation_dom(sK10)
| in(ordered_pair(sK0(sK10,sK9),sK1(sK10,sK9)),sK10)
| ~ element(sK10,powerset(cartesian_product2(X2,X3)))
| ~ element(sK10,powerset(cartesian_product2(X4,X5))) )
| ~ spl14_1 ),
inference(duplicate_literal_removal,[],[f1665]) ).
fof(f1667,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ element(sK10,powerset(cartesian_product2(X0,X1)))
| in(ordered_pair(sK0(sK10,sK9),sK1(sK10,sK9)),sK10)
| ~ element(sK10,powerset(cartesian_product2(X2,X3)))
| ~ element(sK10,powerset(cartesian_product2(X4,X5))) )
| ~ spl14_1
| spl14_2
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f1666,f600]) ).
fof(f1669,definition,
( spl14_52
<=> in(ordered_pair(sK0(sK10,sK9),sK1(sK10,sK9)),sK10) ),
introduced(definition,[new_symbols(definition,[spl14_52])],[avatar_definition]) ).
fof(f1671,plain,
( in(ordered_pair(sK0(sK10,sK9),sK1(sK10,sK9)),sK10)
| ~ spl14_52 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f1672,plain,
( spl14_19
| spl14_19
| spl14_52
| spl14_19
| ~ spl14_1
| spl14_2
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f1667,f166,f120,f117,f446,f1669,f446,f446]) ).
fof(f1674,plain,
( ! [X0,X1] :
( ~ element(sK10,powerset(cartesian_product2(X0,X1)))
| in(sK0(sK10,sK9),relation_dom(sK10)) )
| ~ spl14_52 ),
inference(resolution,[],[f1671,f211]) ).
fof(f1681,definition,
( spl14_53
<=> in(sK0(sK10,sK9),relation_dom(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_53])],[avatar_definition]) ).
fof(f1683,plain,
( in(sK0(sK10,sK9),relation_dom(sK10))
| ~ spl14_53 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f1684,plain,
( spl14_53
| spl14_19
| ~ spl14_52 ),
inference(avatar_split_clause,[],[f1674,f1669,f446,f1681]) ).
fof(f1699,plain,
( ! [X0] :
( ~ element(relation_dom(sK10),powerset(X0))
| in(sK0(sK10,sK9),X0) )
| ~ spl14_53 ),
inference(resolution,[],[f1683,f159]) ).
fof(f2243,plain,
( in(sK0(sK10,sK9),sK9)
| ~ spl14_5
| ~ spl14_53 ),
inference(resolution,[],[f1699,f602]) ).
fof(f2249,plain,
( ! [X2,X0,X1] :
( ~ in(ordered_pair(sK0(sK10,sK9),X0),sK10)
| ~ element(sK10,powerset(cartesian_product2(X1,X2)))
| sK9 = relation_dom(sK10) )
| ~ spl14_5
| ~ spl14_53 ),
inference(resolution,[],[f2243,f209]) ).
fof(f2257,plain,
( ! [X2,X0,X1] :
( ~ in(ordered_pair(sK0(sK10,sK9),X0),sK10)
| ~ element(sK10,powerset(cartesian_product2(X1,X2))) )
| spl14_2
| ~ spl14_5
| ~ spl14_53 ),
inference(forward_subsumption_resolution,[],[f2249,f600]) ).
fof(f2259,definition,
( spl14_60
<=> ! [X0] : ~ in(ordered_pair(sK0(sK10,sK9),X0),sK10) ),
introduced(definition,[new_symbols(definition,[spl14_60])],[avatar_definition]) ).
fof(f2260,plain,
( ! [X0] : ~ in(ordered_pair(sK0(sK10,sK9),X0),sK10)
| ~ spl14_60 ),
inference(avatar_component_clause,[],[f2259]) ).
fof(f2261,plain,
( spl14_19
| spl14_60
| spl14_2
| ~ spl14_5
| ~ spl14_53 ),
inference(avatar_split_clause,[],[f2257,f1681,f166,f120,f2259,f446]) ).
fof(f2277,plain,
( $false
| ~ spl14_52
| ~ spl14_60 ),
inference(resolution,[],[f2260,f1671]) ).
fof(f2278,plain,
( ~ spl14_52
| ~ spl14_60 ),
inference(avatar_contradiction_clause,[],[f2277]) ).
fof(f2283,plain,
( $false
| ~ spl14_19 ),
inference(resolution,[],[f471,f101]) ).
fof(f2285,plain,
~ spl14_19,
inference(avatar_contradiction_clause,[],[f2283]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s2,plain,
( ~ spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f127]) ).
cnf(s3,plain,
( ~ spl14_2
| spl14_4 ),
inference(sat_conversion,[],[f132]) ).
cnf(s5,plain,
spl14_5,
inference(sat_conversion,[],[f176]) ).
cnf(s18,plain,
( ~ spl14_2
| ~ spl14_5
| spl14_19
| spl14_20 ),
inference(sat_conversion,[],[f469]) ).
cnf(s21,plain,
( ~ spl14_3
| ~ spl14_4
| ~ spl14_20 ),
inference(sat_conversion,[],[f535]) ).
cnf(s60,plain,
( spl14_19
| spl14_19
| ~ spl14_5
| ~ spl14_1
| spl14_2
| spl14_19
| spl14_52 ),
inference(sat_conversion,[],[f1672]) ).
cnf(s61,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_5
| spl14_19
| spl14_52 ),
inference(rat,[],[s60]) ).
cnf(s62,plain,
( spl14_19
| ~ spl14_52
| spl14_53 ),
inference(sat_conversion,[],[f1684]) ).
cnf(s73,plain,
( spl14_2
| ~ spl14_5
| spl14_19
| ~ spl14_53
| spl14_60 ),
inference(sat_conversion,[],[f2261]) ).
cnf(s75,plain,
( ~ spl14_52
| ~ spl14_60 ),
inference(sat_conversion,[],[f2278]) ).
cnf(s76,plain,
~ spl14_19,
inference(sat_conversion,[],[f2285]) ).
cnf(s78,plain,
( spl14_2
| ~ spl14_5
| ~ spl14_53
| spl14_60 ),
inference(rat,[],[s73,s76]) ).
cnf(s86,plain,
( ~ spl14_52
| spl14_53 ),
inference(rat,[],[s62,s76]) ).
cnf(s87,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_5
| spl14_52 ),
inference(rat,[],[s61,s76]) ).
cnf(s103,plain,
( ~ spl14_2
| ~ spl14_5
| spl14_20 ),
inference(rat,[],[s18,s76]) ).
cnf(s106,plain,
~ spl14_2,
inference(rat,[],[s21,s2,s3,s103,s5]) ).
cnf(s107,plain,
spl14_1,
inference(rat,[],[s1,s106]) ).
cnf(s115,plain,
spl14_52,
inference(rat,[],[s87,s106,s5,s107]) ).
cnf(s118,plain,
~ spl14_60,
inference(rat,[],[s75,s115]) ).
cnf(s120,plain,
spl14_53,
inference(rat,[],[s86,s115]) ).
cnf(s122,plain,
$false,
inference(rat,[],[s78,s106,s5,s118,s120]) ).
fof(f2286,plain,
$false,
inference(avatar_sat_refutation,[],[s122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU265+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 04:25:37 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.52/1.34 % (4142540)Detected formulas, will run a generic FOF schedule.
% 3.52/1.34 % (4142549)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=75551205:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.52/1.34 % (4142549)Instruction limit reached!
% 3.52/1.34 % (4142549)------------------------------
% 3.52/1.34 % (4142549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.34 % (4142549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.34 % (4142549)CaDiCaL version: 2.1.3
% 3.52/1.34 % (4142549)Termination reason: Instruction limit
% 3.52/1.34 % (4142549)Termination phase: Saturation
% 3.52/1.34 % (4142549)Time elapsed: 0.039 s
% 3.52/1.34 % (4142549)Peak memory usage: 88 MB
% 3.52/1.34 % (4142549)Instructions burned: 120 (million)
% 3.52/1.34 % (4142550)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4011790410:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.52/1.34 % (4142545)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=1556674425:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.52/1.34 % (4142546)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=2535007608:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.52/1.34 % (4142547)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=715779469:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.52/1.34 % (4142548)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4202628198:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.52/1.34 % (4142551)dis-21_1_sil=8000:lcm=predicate:random_seed=2134649405: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)
% 3.52/1.34 % (4142548)Refutation not found, incomplete strategy
% 3.52/1.34 % (4142548)------------------------------
% 3.52/1.34 % (4142548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.34 % (4142548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.34 % (4142548)CaDiCaL version: 2.1.3
% 3.52/1.34 % (4142548)Termination reason: Refutation not found, incomplete strategy
% 3.52/1.34 % (4142548)Time elapsed: 0.002 s
% 3.52/1.34 % (4142548)Peak memory usage: 88 MB
% 3.52/1.34 % (4142548)Instructions burned: 1 (million)
% 3.52/1.34 % (4142550)First to succeed.
% 3.52/1.34 % (4142551)Instruction limit reached!
% 3.52/1.34 % (4142551)------------------------------
% 3.52/1.34 % (4142551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.34 % (4142551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.34 % (4142551)CaDiCaL version: 2.1.3
% 3.52/1.34 % (4142551)Termination reason: Instruction limit
% 3.52/1.34 % (4142551)Termination phase: Saturation
% 3.52/1.34 % (4142551)Time elapsed: 0.085 s
% 3.52/1.34 % (4142551)Peak memory usage: 90 MB
% 3.52/1.34 % (4142551)Instructions burned: 129 (million)
% 3.52/1.34 % (4142550)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4142540"
% 3.52/1.34 % (4142559)lrs+10_1_sil=8000:sp=occurrence:random_seed=1085910695:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.52/1.34 % (4142559)Also succeeded, but the first one will report.
% 3.52/1.34 % (4142548)------------------------------
% 3.52/1.34 % (4142548)------------------------------
% 3.52/1.34 % (4142560)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4214646487:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.52/1.34 % (4142560)Refutation not found, incomplete strategy
% 3.52/1.34 % (4142560)------------------------------
% 3.52/1.34 % (4142560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.34 % (4142560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.34 % (4142560)CaDiCaL version: 2.1.3
% 3.52/1.34 % (4142560)Termination reason: Refutation not found, incomplete strategy
% 3.52/1.34 % (4142560)Time elapsed: 0.003 s
% 3.52/1.34 % (4142560)Peak memory usage: 89 MB
% 3.52/1.34 % (4142560)Instructions burned: 2 (million)
% 3.52/1.34 % (4142550)Refutation found. Thanks to Tanya!
% 3.52/1.34 % SZS status Theorem for theBenchmark
% 3.52/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 4.11/1.43 % (4142550)------------------------------
% 4.11/1.43 % (4142550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.43 % (4142550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.43 % (4142550)CaDiCaL version: 2.1.3
% 4.11/1.43 % (4142550)Termination reason: Refutation
% 4.11/1.43 % (4142550)Time elapsed: 0.087 s
% 4.11/1.43 % (4142550)Peak memory usage: 91 MB
% 4.11/1.43 % (4142550)Instructions burned: 138 (million)
% 4.11/1.43 % (4142550)------------------------------
% 4.11/1.43 % (4142550)------------------------------
% 4.11/1.43 % (4142540)Success in time 0.512 s
% 4.11/1.43 % Vampire exiting
%------------------------------------------------------------------------------