%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU266+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 : n011.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 : 23
% Number of leaves : 27
% Syntax : Number of formulae : 162 ( 25 unt; 12 def)
% Number of atoms : 425 ( 59 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 451 ( 188 ~; 195 |; 33 &)
% ( 20 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 241 ( 0 sgn 211 !; 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(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_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(f14,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_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_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_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,X0,X1)
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X4,X3),X2) )
<=> relation_rng_as_subset(X0,X1,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X4,X3),X2) )
<=> relation_rng_as_subset(X0,X1,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(f37,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_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_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f45,plain,
! [X0,X1,X2] :
( element(relation_rng_as_subset(X0,X1,X2),powerset(X1))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
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_rng_as_subset(X0,X1,X2) = relation_rng(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(X4,X3),X2) )
<~> relation_rng_as_subset(X0,X1,X2) = X1 )
& relation_of2_as_subset(X2,X0,X1) ),
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(f59,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK0(X0,X1)),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK2(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(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_rng_as_subset(X0,X1,X2) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X4,X3),X2) ) )
& ( relation_rng_as_subset(X0,X1,X2) = X1
| ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X4,X3),X2) ) )
& relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f51]) ).
fof(f72,plain,
? [X0,X1,X2] :
( ( relation_rng_as_subset(X0,X1,X2) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X4,X3),X2) ) )
& ( relation_rng_as_subset(X0,X1,X2) = X1
| ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X4,X3),X2) ) )
& relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0,X1,X2] :
( ( relation_rng_as_subset(X0,X1,X2) != X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X4,X3),X2) ) )
& ( relation_rng_as_subset(X0,X1,X2) = X1
| ! [X5] :
( ~ in(X5,X1)
| ? [X6] : in(ordered_pair(X6,X5),X2) ) )
& relation_of2_as_subset(X2,X0,X1) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
( ( sK9 != relation_rng_as_subset(sK8,sK9,sK10)
| ( in(sK11,sK9)
& ! [X4] : ~ in(ordered_pair(X4,sK11),sK10) ) )
& ( sK9 = relation_rng_as_subset(sK8,sK9,sK10)
| ! [X5] :
( ~ in(X5,sK9)
| in(ordered_pair(sK12(X5),X5),sK10) ) )
& relation_of2_as_subset(sK10,sK8,sK9) ),
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] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f43]) ).
fof(f80,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK2(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != 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_rng_as_subset(X0,X1,X2),powerset(X1))
| ~ 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_rng_as_subset(X0,X1,X2) = relation_rng(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(f99,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f101,plain,
relation_of2_as_subset(sK10,sK8,sK9),
inference(cnf_transformation,[],[f74]) ).
fof(f102,plain,
! [X5] :
( sK9 = relation_rng_as_subset(sK8,sK9,sK10)
| ~ in(X5,sK9)
| in(ordered_pair(sK12(X5),X5),sK10) ),
inference(cnf_transformation,[],[f74]) ).
fof(f103,plain,
! [X4] :
( sK9 != relation_rng_as_subset(sK8,sK9,sK10)
| ~ in(ordered_pair(X4,sK11),sK10) ),
inference(cnf_transformation,[],[f74]) ).
fof(f104,plain,
( sK9 != relation_rng_as_subset(sK8,sK9,sK10)
| in(sK11,sK9) ),
inference(cnf_transformation,[],[f74]) ).
fof(f105,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f106,plain,
! [X0,X1] :
( in(sK13(X0,X1),X1)
| X0 = X1
| in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f107,plain,
! [X0,X1] :
( ~ in(sK13(X0,X1),X1)
| ~ in(sK13(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f76]) ).
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] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f111,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f59]) ).
fof(f117,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK2(X0,X5),X5),singleton(sK2(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f80,f84]) ).
fof(f120,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f99,f84]) ).
fof(f121,plain,
! [X4] :
( sK9 != relation_rng_as_subset(sK8,sK9,sK10)
| ~ in(unordered_pair(unordered_pair(X4,sK11),singleton(X4)),sK10) ),
inference(definition_unfolding,[],[f103,f84]) ).
fof(f122,plain,
! [X5] :
( sK9 = relation_rng_as_subset(sK8,sK9,sK10)
| ~ in(X5,sK9)
| in(unordered_pair(unordered_pair(sK12(X5),X5),singleton(sK12(X5))),sK10) ),
inference(definition_unfolding,[],[f102,f84]) ).
fof(f124,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK2(X0,X5),X5),singleton(sK2(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f117]) ).
fof(f125,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation(X2) ),
inference(consistent_polarity_flipping,[],[f78]) ).
fof(f129,plain,
! [X0,X5] :
( relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK2(X0,X5),X5),singleton(sK2(X0,X5))),X0) ),
inference(consistent_polarity_flipping,[],[f124]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| ~ element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(consistent_polarity_flipping,[],[f85]) ).
fof(f131,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f132,plain,
! [X0] : ~ element(sK4(X0),X0),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f135,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f138,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| in(X1,relation_rng(X2)) ),
inference(consistent_polarity_flipping,[],[f120]) ).
fof(f139,plain,
~ relation_of2_as_subset(sK10,sK8,sK9),
inference(consistent_polarity_flipping,[],[f101]) ).
fof(f140,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| element(X0,X1) ),
inference(consistent_polarity_flipping,[],[f105]) ).
fof(f142,plain,
! [X2,X0,X1] :
( element(X1,powerset(X2))
| ~ in(X0,X1)
| ~ element(X0,X2) ),
inference(consistent_polarity_flipping,[],[f109]) ).
fof(f143,plain,
! [X2,X0,X1] :
( element(X1,powerset(X2))
| ~ in(X0,X1)
| ~ empty(X2) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f145,definition,
( spl14_1
<=> ! [X5] :
( ~ in(X5,sK9)
| in(unordered_pair(unordered_pair(sK12(X5),X5),singleton(sK12(X5))),sK10) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f146,plain,
( ! [X5] :
( in(unordered_pair(unordered_pair(sK12(X5),X5),singleton(sK12(X5))),sK10)
| ~ in(X5,sK9) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,definition,
( spl14_2
<=> sK9 = relation_rng_as_subset(sK8,sK9,sK10) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f149,plain,
( sK9 != relation_rng_as_subset(sK8,sK9,sK10)
| spl14_2 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f150,plain,
( sK9 = relation_rng_as_subset(sK8,sK9,sK10)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f122,f148,f145]) ).
fof(f153,definition,
( spl14_3
<=> ! [X4] : ~ in(unordered_pair(unordered_pair(X4,sK11),singleton(X4)),sK10) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f154,plain,
( ! [X4] : ~ in(unordered_pair(unordered_pair(X4,sK11),singleton(X4)),sK10)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( spl14_3
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f121,f148,f153]) ).
fof(f157,definition,
( spl14_4
<=> in(sK11,sK9) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f160,plain,
( spl14_4
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f104,f148,f157]) ).
fof(f203,plain,
relation_of2(sK10,sK8,sK9),
inference(resolution,[],[f135,f139]) ).
fof(f209,plain,
! [X0,X1] :
( element(X0,X1)
| in(X0,X1)
| empty_set = X1 ),
inference(resolution,[],[f140,f111]) ).
fof(f229,plain,
! [X0] :
( in(sK4(X0),X0)
| empty_set = X0 ),
inference(resolution,[],[f209,f132]) ).
fof(f240,plain,
~ element(sK10,powerset(cartesian_product2(sK8,sK9))),
inference(resolution,[],[f131,f139]) ).
fof(f243,plain,
~ relation(sK10),
inference(resolution,[],[f240,f125]) ).
fof(f388,plain,
relation_rng_as_subset(sK8,sK9,sK10) = relation_rng(sK10),
inference(resolution,[],[f94,f203]) ).
fof(f391,plain,
( sK9 = relation_rng(sK10)
| ~ spl14_2 ),
inference(superposition,[],[f150,f388]) ).
fof(f435,plain,
~ element(relation_rng_as_subset(sK8,sK9,sK10),powerset(sK9)),
inference(resolution,[],[f130,f203]) ).
fof(f439,plain,
~ element(relation_rng(sK10),powerset(sK9)),
inference(superposition,[],[f435,f388]) ).
fof(f450,plain,
! [X0] :
( ~ element(X0,sK9)
| ~ in(X0,relation_rng(sK10)) ),
inference(resolution,[],[f439,f142]) ).
fof(f451,plain,
! [X0] :
( ~ in(X0,relation_rng(sK10))
| ~ empty(sK9) ),
inference(resolution,[],[f439,f143]) ).
fof(f472,plain,
! [X0] :
( ~ in(X0,relation_rng(sK10))
| in(X0,sK9)
| empty_set = sK9 ),
inference(resolution,[],[f450,f209]) ).
fof(f474,definition,
( spl14_25
<=> empty_set = sK9 ),
introduced(definition,[new_symbols(definition,[spl14_25])],[avatar_definition]) ).
fof(f478,definition,
( spl14_26
<=> ! [X0] :
( ~ in(X0,relation_rng(sK10))
| in(X0,sK9) ) ),
introduced(definition,[new_symbols(definition,[spl14_26])],[avatar_definition]) ).
fof(f479,plain,
( ! [X0] :
( in(X0,sK9)
| ~ in(X0,relation_rng(sK10)) )
| ~ spl14_26 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f480,plain,
( spl14_25
| spl14_26 ),
inference(avatar_split_clause,[],[f472,f478,f474]) ).
fof(f503,definition,
( spl14_27
<=> empty_set = relation_rng(sK10) ),
introduced(definition,[new_symbols(definition,[spl14_27])],[avatar_definition]) ).
fof(f505,plain,
( empty_set = relation_rng(sK10)
| ~ spl14_27 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f584,plain,
( ! [X0] :
( ~ in(sK13(sK9,X0),relation_rng(sK10))
| ~ in(sK13(sK9,X0),X0)
| sK9 = X0 )
| ~ spl14_26 ),
inference(resolution,[],[f107,f479]) ).
fof(f698,plain,
( ~ in(sK13(sK9,relation_rng(sK10)),relation_rng(sK10))
| sK9 = relation_rng(sK10)
| ~ spl14_26 ),
inference(factoring,[],[f584]) ).
fof(f730,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10)
| in(X1,relation_rng(sK10)) ),
inference(resolution,[],[f138,f243]) ).
fof(f840,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK2(sK10,X0),X0),singleton(sK2(sK10,X0))),sK10)
| ~ in(X0,relation_rng(sK10)) ),
inference(resolution,[],[f129,f243]) ).
fof(f853,plain,
( ~ in(sK11,relation_rng(sK10))
| ~ spl14_3 ),
inference(resolution,[],[f840,f154]) ).
fof(f869,definition,
( spl14_57
<=> ! [X0] : ~ in(X0,relation_rng(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_57])],[avatar_definition]) ).
fof(f870,plain,
( ! [X0] : ~ in(X0,relation_rng(sK10))
| ~ spl14_57 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f873,plain,
( ~ in(sK11,sK9)
| ~ spl14_2
| ~ spl14_3 ),
inference(superposition,[],[f853,f391]) ).
fof(f874,plain,
( ~ spl14_4
| ~ spl14_2
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f873,f153,f148,f157]) ).
fof(f876,definition,
( spl14_58
<=> sK9 = relation_rng(sK10) ),
introduced(definition,[new_symbols(definition,[spl14_58])],[avatar_definition]) ).
fof(f877,plain,
( sK9 != relation_rng(sK10)
| spl14_58 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f890,definition,
( spl14_61
<=> in(sK13(sK9,relation_rng(sK10)),relation_rng(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_61])],[avatar_definition]) ).
fof(f892,plain,
( ~ in(sK13(sK9,relation_rng(sK10)),relation_rng(sK10))
| spl14_61 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f893,plain,
( spl14_58
| ~ spl14_61
| ~ spl14_26 ),
inference(avatar_split_clause,[],[f698,f478,f890,f876]) ).
fof(f899,plain,
( sK9 != relation_rng(sK10)
| spl14_2 ),
inference(superposition,[],[f149,f388]) ).
fof(f905,plain,
( sK9 = relation_rng(sK10)
| in(sK13(sK9,relation_rng(sK10)),sK9)
| spl14_61 ),
inference(resolution,[],[f892,f106]) ).
fof(f907,definition,
( spl14_63
<=> in(sK13(sK9,relation_rng(sK10)),sK9) ),
introduced(definition,[new_symbols(definition,[spl14_63])],[avatar_definition]) ).
fof(f910,plain,
( spl14_63
| spl14_58
| spl14_61 ),
inference(avatar_split_clause,[],[f905,f890,f876,f907]) ).
fof(f911,plain,
( ~ spl14_58
| spl14_2 ),
inference(avatar_split_clause,[],[f899,f148,f876]) ).
fof(f930,plain,
( ! [X0] :
( in(X0,relation_rng(sK10))
| ~ in(X0,sK9) )
| ~ spl14_1 ),
inference(resolution,[],[f146,f730]) ).
fof(f942,definition,
( spl14_65
<=> empty(sK9) ),
introduced(definition,[new_symbols(definition,[spl14_65])],[avatar_definition]) ).
fof(f944,plain,
( ~ empty(sK9)
| spl14_65 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f949,plain,
( ~ spl14_65
| spl14_57 ),
inference(avatar_split_clause,[],[f451,f869,f942]) ).
fof(f956,plain,
( ! [X0] :
( element(X0,sK9)
| in(X0,sK9) )
| spl14_65 ),
inference(resolution,[],[f944,f140]) ).
fof(f963,plain,
( ! [X0] :
( in(X0,sK9)
| ~ in(X0,relation_rng(sK10)) )
| spl14_65 ),
inference(resolution,[],[f956,f450]) ).
fof(f985,plain,
( ~ in(sK13(sK9,relation_rng(sK10)),sK9)
| ~ spl14_1
| spl14_61 ),
inference(resolution,[],[f930,f892]) ).
fof(f988,plain,
( ~ spl14_63
| ~ spl14_1
| spl14_61 ),
inference(avatar_split_clause,[],[f985,f890,f145,f907]) ).
fof(f1007,plain,
( spl14_26
| spl14_65 ),
inference(avatar_split_clause,[],[f963,f942,f478]) ).
fof(f1150,plain,
( empty_set = relation_rng(sK10)
| ~ spl14_57 ),
inference(resolution,[],[f870,f229]) ).
fof(f1153,plain,
( spl14_27
| ~ spl14_57 ),
inference(avatar_split_clause,[],[f1150,f869,f503]) ).
fof(f1187,plain,
( empty_set != sK9
| ~ spl14_27
| spl14_58 ),
inference(superposition,[],[f877,f505]) ).
fof(f1190,plain,
( ~ spl14_25
| ~ spl14_27
| spl14_58 ),
inference(avatar_split_clause,[],[f1187,f876,f503,f474]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f151]) ).
cnf(s2,plain,
( ~ spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f155]) ).
cnf(s3,plain,
( ~ spl14_2
| spl14_4 ),
inference(sat_conversion,[],[f160]) ).
cnf(s21,plain,
( spl14_25
| spl14_26 ),
inference(sat_conversion,[],[f480]) ).
cnf(s43,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f874]) ).
cnf(s46,plain,
( ~ spl14_26
| spl14_58
| ~ spl14_61 ),
inference(sat_conversion,[],[f893]) ).
cnf(s48,plain,
( spl14_58
| spl14_61
| spl14_63 ),
inference(sat_conversion,[],[f910]) ).
cnf(s49,plain,
( spl14_2
| ~ spl14_58 ),
inference(sat_conversion,[],[f911]) ).
cnf(s53,plain,
( spl14_57
| ~ spl14_65 ),
inference(sat_conversion,[],[f949]) ).
cnf(s60,plain,
( ~ spl14_1
| spl14_61
| ~ spl14_63 ),
inference(sat_conversion,[],[f988]) ).
cnf(s64,plain,
( spl14_26
| spl14_65 ),
inference(sat_conversion,[],[f1007]) ).
cnf(s70,plain,
( spl14_27
| ~ spl14_57 ),
inference(sat_conversion,[],[f1153]) ).
cnf(s73,plain,
( ~ spl14_25
| ~ spl14_27
| spl14_58 ),
inference(sat_conversion,[],[f1190]) ).
cnf(s74,plain,
~ spl14_2,
inference(rat,[],[s43,s2,s3]) ).
cnf(s75,plain,
~ spl14_58,
inference(rat,[],[s49,s74]) ).
cnf(s76,plain,
spl14_1,
inference(rat,[],[s1,s74]) ).
cnf(s77,plain,
spl14_61,
inference(rat,[],[s48,s60,s75,s76]) ).
cnf(s78,plain,
~ spl14_26,
inference(rat,[],[s46,s75,s77]) ).
cnf(s79,plain,
spl14_65,
inference(rat,[],[s64,s78]) ).
cnf(s80,plain,
spl14_25,
inference(rat,[],[s21,s78]) ).
cnf(s82,plain,
spl14_57,
inference(rat,[],[s53,s79]) ).
cnf(s84,plain,
~ spl14_27,
inference(rat,[],[s73,s75,s80]) ).
cnf(s85,plain,
$false,
inference(rat,[],[s70,s82,s84]) ).
fof(f1191,plain,
$false,
inference(avatar_sat_refutation,[],[s85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU266+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n011.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:24:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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 % (3015486)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (3015491)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2339223985_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % (3015492)% WARNING: option uhcvi not known.
% 0.17/0.50 % TRYING [3]
% 0.17/0.50 % (3015492)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1956382672:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (3015496)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1517761024:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (3015493)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1428409237:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (3015494)dis+10_1_sil=32000:sp=arity:random_seed=1089732819:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (3015495)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3489555200:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % (3015497)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=773545588:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % (3015497) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3015486-3015497"...
% 0.17/0.50 % (3015497)...printing done.
% 0.17/0.50 % (3015497)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 % (3015497)------------------------------
% 0.17/0.50 % (3015497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (3015497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (3015497)CaDiCaL version: 2.1.3
% 0.17/0.50 % (3015497)Termination reason: Refutation
% 0.17/0.50 % (3015497)Time elapsed: 0.027 s
% 0.17/0.50 % (3015497)Peak memory usage: 13 MB
% 0.17/0.50 % (3015497)Instructions burned: 35 (million)
% 0.17/0.50 % (3015486)Success in time 0.069 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------