%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n020.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 12:52:39 PM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 23
% Syntax : Number of formulae : 155 ( 18 unt; 6 def)
% Number of atoms : 454 ( 67 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 510 ( 211 ~; 236 |; 34 &)
% ( 14 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 259 ( 0 sgn 229 !; 30 ?)
% 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(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
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(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_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(f28,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
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(f33,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
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(f38,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
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(f48,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
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(f54,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
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(f60,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f38]) ).
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(f66,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f19]) ).
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(f75,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK13(X0,X1),X1)
| ~ in(sK13(X0,X1),X0) )
& ( in(sK13(X0,X1),X1)
| in(sK13(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f75]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f79,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
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_dom(X0) = X1
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f83,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f84,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
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(f88,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f66]) ).
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_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f98,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f100,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(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(f106,plain,
! [X0,X1] :
( in(sK13(X0,X1),X1)
| in(sK13(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f107,plain,
! [X0,X1] :
( ~ in(sK13(X0,X1),X1)
| X0 = X1
| ~ in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| ~ empty(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f112,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f114,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),X3),singleton(sK0(X0,X1))),X0)
| ~ in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f83,f84]) ).
fof(f115,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f82,f84]) ).
fof(f117,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f80,f84]) ).
fof(f119,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f100,f84]) ).
fof(f121,plain,
! [X4] :
( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| ~ in(unordered_pair(unordered_pair(sK11,X4),singleton(sK11)),sK10) ),
inference(definition_unfolding,[],[f103,f84]) ).
fof(f122,plain,
! [X5] :
( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| ~ in(X5,sK9)
| in(unordered_pair(unordered_pair(X5,sK12(X5)),singleton(X5)),sK10) ),
inference(definition_unfolding,[],[f102,f84]) ).
fof(f124,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f117]) ).
fof(f126,definition,
( spl14_1
<=> ! [X5] :
( ~ in(X5,sK9)
| in(unordered_pair(unordered_pair(X5,sK12(X5)),singleton(X5)),sK10) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f127,plain,
( ! [X5] :
( ~ in(X5,sK9)
| in(unordered_pair(unordered_pair(X5,sK12(X5)),singleton(X5)),sK10) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,definition,
( spl14_2
<=> sK9 = relation_dom_as_subset(sK9,sK8,sK10) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f130,plain,
( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| spl14_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f122,f129,f126]) ).
fof(f134,definition,
( spl14_3
<=> ! [X4] : ~ in(unordered_pair(unordered_pair(sK11,X4),singleton(sK11)),sK10) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f135,plain,
( ! [X4] : ~ in(unordered_pair(unordered_pair(sK11,X4),singleton(sK11)),sK10)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f136,plain,
( spl14_3
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f121,f129,f134]) ).
fof(f138,definition,
( spl14_4
<=> in(sK11,sK9) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f140,plain,
( in(sK11,sK9)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,plain,
( spl14_4
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f104,f129,f138]) ).
fof(f149,plain,
( ! [X0] : ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),sK10)
| ~ spl14_3 ),
inference(superposition,[],[f135,f79]) ).
fof(f166,plain,
relation_of2(sK10,sK9,sK8),
inference(resolution,[],[f95,f101]) ).
fof(f170,plain,
! [X0] :
( in(sK4(X0),X0)
| empty(X0) ),
inference(resolution,[],[f105,f88]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f86,f78]) ).
fof(f186,plain,
relation(sK10),
inference(resolution,[],[f177,f101]) ).
fof(f191,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,relation_dom_as_subset(X1,X2,X0))
| ~ relation_of2(X0,X1,X2)
| ~ empty(X1) ),
inference(resolution,[],[f85,f110]) ).
fof(f196,plain,
relation_dom_as_subset(sK9,sK8,sK10) = relation_dom(sK10),
inference(resolution,[],[f94,f166]) ).
fof(f198,plain,
( sK9 = relation_dom(sK10)
| ~ spl14_2 ),
inference(forward_demodulation,[],[f196,f131]) ).
fof(f211,plain,
( ! [X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,sK12(X5))),sK10)
| ~ in(X5,sK9) )
| ~ spl14_1 ),
inference(forward_demodulation,[],[f127,f79]) ).
fof(f213,plain,
( element(relation_dom(sK10),powerset(sK9))
| ~ relation_of2(sK10,sK9,sK8) ),
inference(superposition,[],[f85,f196]) ).
fof(f214,plain,
element(relation_dom(sK10),powerset(sK9)),
inference(forward_subsumption_resolution,[],[f213,f166]) ).
fof(f240,plain,
! [X0,X1] :
( in(sK13(X0,X1),X0)
| X0 = X1
| ~ empty(X1) ),
inference(resolution,[],[f106,f112]) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| in(X0,relation_dom(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f119,f79]) ).
fof(f264,plain,
! [X0,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,sK2(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f124,f79]) ).
fof(f266,plain,
( ~ in(sK11,relation_dom(sK10))
| ~ relation(sK10)
| ~ spl14_3 ),
inference(resolution,[],[f264,f149]) ).
fof(f274,plain,
( ~ in(sK11,relation_dom(sK10))
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f266,f186]) ).
fof(f275,plain,
( ~ in(sK11,sK9)
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_demodulation,[],[f274,f198]) ).
fof(f276,plain,
( $false
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f275,f140]) ).
fof(f277,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(avatar_contradiction_clause,[],[f276]) ).
fof(f281,plain,
( sK9 != relation_dom(sK10)
| spl14_2 ),
inference(forward_demodulation,[],[f130,f196]) ).
fof(f283,definition,
( spl14_9
<=> empty(sK9) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
fof(f285,plain,
( ~ empty(sK9)
| spl14_9 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f293,plain,
( ! [X0] :
( ~ in(X0,sK9)
| in(X0,relation_dom(sK10))
| ~ relation(sK10) )
| ~ spl14_1 ),
inference(resolution,[],[f211,f247]) ).
fof(f297,plain,
( ! [X0] :
( in(X0,relation_dom(sK10))
| ~ in(X0,sK9) )
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f293,f186]) ).
fof(f299,plain,
! [X3,X0,X1] :
( ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),X3)),X0)
| relation_dom(X0) = X1
| ~ in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f114,f79]) ).
fof(f302,plain,
( ! [X0] :
( relation_dom(sK10) = X0
| ~ in(sK0(sK10,X0),X0)
| ~ relation(sK10)
| ~ in(sK0(sK10,X0),sK9) )
| ~ spl14_1 ),
inference(resolution,[],[f299,f211]) ).
fof(f306,plain,
( ! [X0] :
( ~ in(sK0(sK10,X0),sK9)
| ~ in(sK0(sK10,X0),X0)
| relation_dom(sK10) = X0 )
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f302,f186]) ).
fof(f314,plain,
( ! [X0] :
( ~ in(sK13(X0,relation_dom(sK10)),sK9)
| relation_dom(sK10) = X0
| ~ in(sK13(X0,relation_dom(sK10)),X0) )
| ~ spl14_1 ),
inference(resolution,[],[f297,f107]) ).
fof(f332,definition,
( spl14_15
<=> empty(relation_dom(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
fof(f334,plain,
( ~ empty(relation_dom(sK10))
| spl14_15 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f336,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f115,f79]) ).
fof(f338,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(sK0(X0,X1),X1)
| ~ relation(X0)
| in(sK0(X0,X1),relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[],[f336,f247]) ).
fof(f344,plain,
! [X0,X1] :
( in(sK0(X0,X1),relation_dom(X0))
| in(sK0(X0,X1),X1)
| ~ relation(X0)
| relation_dom(X0) = X1 ),
inference(duplicate_literal_removal,[],[f338]) ).
fof(f423,plain,
! [X0] :
( ~ in(X0,relation_dom(sK10))
| element(X0,sK9) ),
inference(resolution,[],[f214,f109]) ).
fof(f477,plain,
! [X2,X0,X1] :
( empty(relation_dom_as_subset(X1,X2,X0))
| ~ empty(X1)
| ~ relation_of2(X0,X1,X2) ),
inference(resolution,[],[f191,f170]) ).
fof(f678,plain,
! [X0] :
( in(sK0(sK10,X0),X0)
| ~ relation(sK10)
| relation_dom(sK10) = X0
| element(sK0(sK10,X0),sK9) ),
inference(resolution,[],[f344,f423]) ).
fof(f694,plain,
! [X0] :
( element(sK0(sK10,X0),sK9)
| in(sK0(sK10,X0),X0)
| relation_dom(sK10) = X0 ),
inference(forward_subsumption_resolution,[],[f678,f186]) ).
fof(f740,plain,
( sK9 = relation_dom(sK10)
| ~ in(sK13(sK9,relation_dom(sK10)),sK9)
| sK9 = relation_dom(sK10)
| ~ empty(relation_dom(sK10))
| ~ spl14_1 ),
inference(resolution,[],[f314,f240]) ).
fof(f741,plain,
( sK9 = relation_dom(sK10)
| ~ in(sK13(sK9,relation_dom(sK10)),sK9)
| ~ empty(relation_dom(sK10))
| ~ spl14_1 ),
inference(duplicate_literal_removal,[],[f740]) ).
fof(f742,plain,
( sK9 = relation_dom(sK10)
| ~ empty(relation_dom(sK10))
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f741,f240]) ).
fof(f1080,plain,
( empty(relation_dom(sK10))
| ~ empty(sK9)
| ~ relation_of2(sK10,sK9,sK8) ),
inference(superposition,[],[f477,f196]) ).
fof(f1139,plain,
! [X0] :
( element(sK0(sK10,X0),sK9)
| element(sK0(sK10,X0),X0)
| relation_dom(sK10) = X0 ),
inference(resolution,[],[f694,f98]) ).
fof(f1198,plain,
( element(sK0(sK10,sK9),sK9)
| sK9 = relation_dom(sK10) ),
inference(factoring,[],[f1139]) ).
fof(f1199,plain,
( element(sK0(sK10,sK9),sK9)
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f1198,f281]) ).
fof(f1219,plain,
( in(sK0(sK10,sK9),sK9)
| empty(sK9)
| spl14_2 ),
inference(resolution,[],[f1199,f105]) ).
fof(f1220,plain,
( in(sK0(sK10,sK9),sK9)
| spl14_2
| spl14_9 ),
inference(forward_subsumption_resolution,[],[f1219,f285]) ).
fof(f1239,plain,
( ~ in(sK0(sK10,sK9),sK9)
| sK9 = relation_dom(sK10)
| ~ spl14_1
| spl14_2
| spl14_9 ),
inference(resolution,[],[f1220,f306]) ).
fof(f1243,plain,
( sK9 = relation_dom(sK10)
| ~ spl14_1
| spl14_2
| spl14_9 ),
inference(forward_subsumption_resolution,[],[f1239,f1220]) ).
fof(f1244,plain,
( $false
| ~ spl14_1
| spl14_2
| spl14_9 ),
inference(forward_subsumption_resolution,[],[f1243,f281]) ).
fof(f1245,plain,
( ~ spl14_1
| spl14_2
| spl14_9 ),
inference(avatar_contradiction_clause,[],[f1244]) ).
fof(f1264,plain,
( ~ empty(sK9)
| ~ relation_of2(sK10,sK9,sK8)
| spl14_15 ),
inference(forward_subsumption_resolution,[],[f1080,f334]) ).
fof(f1283,plain,
( ~ empty(sK9)
| spl14_15 ),
inference(forward_subsumption_resolution,[],[f1264,f166]) ).
fof(f1284,plain,
( ~ spl14_9
| spl14_15 ),
inference(avatar_split_clause,[],[f1283,f332,f283]) ).
fof(f1291,plain,
( ~ empty(relation_dom(sK10))
| ~ spl14_1
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f742,f281]) ).
fof(f1293,plain,
( ~ spl14_15
| ~ spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f1291,f129,f126,f332]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f132]) ).
cnf(s2,plain,
( ~ spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f136]) ).
cnf(s3,plain,
( ~ spl14_2
| spl14_4 ),
inference(sat_conversion,[],[f141]) ).
cnf(s7,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f277]) ).
cnf(s63,plain,
( ~ spl14_1
| spl14_2
| spl14_9 ),
inference(sat_conversion,[],[f1245]) ).
cnf(s73,plain,
( ~ spl14_9
| spl14_15 ),
inference(sat_conversion,[],[f1284]) ).
cnf(s76,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_15 ),
inference(sat_conversion,[],[f1293]) ).
cnf(s83,plain,
~ spl14_2,
inference(rat,[],[s7,s2,s3]) ).
cnf(s84,plain,
spl14_1,
inference(rat,[],[s1,s83]) ).
cnf(s85,plain,
~ spl14_15,
inference(rat,[],[s76,s83,s84]) ).
cnf(s87,plain,
spl14_9,
inference(rat,[],[s63,s83,s84]) ).
cnf(s89,plain,
$false,
inference(rat,[],[s73,s85,s87]) ).
fof(f1295,plain,
$false,
inference(avatar_sat_refutation,[],[s89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 SAT
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:23:50 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.50 % (4020719)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (4020729)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2311654018:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (4020725)% WARNING: option uhcvi not known.
% 0.17/0.50 % (4020724)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2525357126_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % (4020725)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=411625604:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (4020726)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2025210537:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (4020727)dis+10_1_sil=32000:sp=arity:random_seed=1483838306:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (4020728)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3832964668:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % (4020730)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=339985203:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % TRYING [3]
% 0.17/0.50 % (4020727) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4020719-4020727"...
% 0.17/0.50 % (4020727)...printing done.
% 0.17/0.50 % (4020729)Instruction limit reached!
% 0.17/0.50 % (4020729)------------------------------
% 0.17/0.50 % (4020729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (4020729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (4020729)CaDiCaL version: 2.1.3
% 0.17/0.50 % (4020729)Termination reason: Instruction limit
% 0.17/0.50 % (4020729)Termination phase: Saturation
% 0.17/0.50 % (4020729)Time elapsed: 0.046 s
% 0.17/0.50 % (4020729)Peak memory usage: 13 MB
% 0.17/0.50 % (4020729)Instructions burned: 132 (million)
% 0.17/0.50 % (4020727)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Theorem for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (4020727)------------------------------
% 0.17/0.50 % (4020727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (4020727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (4020727)CaDiCaL version: 2.1.3
% 0.17/0.50 % (4020727)Termination reason: Refutation
% 0.17/0.50 % (4020727)Time elapsed: 0.037 s
% 0.17/0.50 % (4020727)Peak memory usage: 13 MB
% 0.17/0.50 % (4020727)Instructions burned: 52 (million)
% 0.17/0.50 % (4020719)Success in time 0.077 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------