%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU266+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:48:05 PM UTC 2026
% Result : Theorem 5.18s 1.81s
% Output : Refutation 7.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 105 ( 15 unt; 4 def)
% Number of atoms : 309 ( 50 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 344 ( 140 ~; 138 |; 41 &)
% ( 14 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 201 ( 0 sgn 172 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f10,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f15,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f44,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f56,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f58,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f111,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f184,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(f188,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f203,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_dom(X2),X0)
& subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f231,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/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f242,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/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
fof(f243,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)],[f242]) ).
fof(f314,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f353,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f384,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f394,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f428,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f111]) ).
fof(f484,plain,
! [X0,X1,X2] :
( relation_rng_as_subset(X0,X1,X2) = relation_rng(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f184]) ).
fof(f503,plain,
! [X0,X1,X2] :
( ( subset(relation_dom(X2),X0)
& subset(relation_rng(X2),X1) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f203]) ).
fof(f539,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,[],[f231]) ).
fof(f540,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f539]) ).
fof(f557,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,[],[f243]) ).
fof(f674,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f675,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f674]) ).
fof(f754,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f384]) ).
fof(f755,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f754]) ).
fof(f756,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK44(X0,X1),X1)
& in(sK44(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(X2,sK44(X0,X1))],[f755]) ).
fof(f785,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,[],[f394]) ).
fof(f786,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,[],[f785]) ).
fof(f787,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK60(X0,X1)),X0)
| ~ in(sK60(X0,X1),X1) )
& ( in(ordered_pair(sK61(X0,X1),sK60(X0,X1)),X0)
| in(sK60(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK62(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60,sK61,sK62]),skolemize(X2,sK60(X0,X1)),skolemize(X4,sK61(X0,X1)),skolemize(X7,sK62(X0,X5))],[f786]) ).
fof(f856,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,[],[f188]) ).
fof(f876,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,[],[f557]) ).
fof(f877,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,[],[f876]) ).
fof(f878,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,[],[f877]) ).
fof(f879,plain,
( ( sK111 != relation_rng_as_subset(sK110,sK111,sK112)
| ( in(sK113,sK111)
& ! [X4] : ~ in(ordered_pair(X4,sK113),sK112) ) )
& ( sK111 = relation_rng_as_subset(sK110,sK111,sK112)
| ! [X5] :
( ~ in(X5,sK111)
| in(ordered_pair(sK114(X5),X5),sK112) ) )
& relation_of2_as_subset(sK112,sK110,sK111) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110,sK111,sK112,sK113,sK114]),skolemize(X0,sK110),skolemize(X1,sK111),skolemize(X2,sK112),skolemize(X3,sK113),skolemize(X6,sK114(X5))],[f878]) ).
fof(f931,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f353]) ).
fof(f939,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f951,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f675]) ).
fof(f1083,plain,
! [X0,X1] :
( in(sK44(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f756]) ).
fof(f1084,plain,
! [X0,X1] :
( ~ in(sK44(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f756]) ).
fof(f1138,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK62(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f787]) ).
fof(f1143,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f58]) ).
fof(f1222,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f428]) ).
fof(f1366,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_rng(X2) = relation_rng_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f484]) ).
fof(f1370,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f856]) ).
fof(f1392,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_rng(X2),X1) ),
inference(cnf_transformation,[],[f503]) ).
fof(f1433,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f540]) ).
fof(f1450,plain,
relation_of2_as_subset(sK112,sK110,sK111),
inference(cnf_transformation,[],[f879]) ).
fof(f1451,plain,
! [X5] :
( sK111 = relation_rng_as_subset(sK110,sK111,sK112)
| ~ in(X5,sK111)
| in(ordered_pair(sK114(X5),X5),sK112) ),
inference(cnf_transformation,[],[f879]) ).
fof(f1452,plain,
! [X4] :
( sK111 != relation_rng_as_subset(sK110,sK111,sK112)
| ~ in(ordered_pair(X4,sK113),sK112) ),
inference(cnf_transformation,[],[f879]) ).
fof(f1453,plain,
( sK111 != relation_rng_as_subset(sK110,sK111,sK112)
| in(sK113,sK111) ),
inference(cnf_transformation,[],[f879]) ).
fof(f1579,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f314]) ).
fof(f1619,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1143,f1579]) ).
fof(f1688,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK62(X0,X5),X5),unordered_pair(sK62(X0,X5),sK62(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1138,f1619]) ).
fof(f1765,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_rng(X2)) ),
inference(definition_unfolding,[],[f1433,f1619]) ).
fof(f1768,plain,
! [X4] :
( sK111 != relation_rng_as_subset(sK110,sK111,sK112)
| ~ in(unordered_pair(unordered_pair(X4,sK113),unordered_pair(X4,X4)),sK112) ),
inference(definition_unfolding,[],[f1452,f1619]) ).
fof(f1769,plain,
! [X5] :
( sK111 = relation_rng_as_subset(sK110,sK111,sK112)
| ~ in(X5,sK111)
| in(unordered_pair(unordered_pair(sK114(X5),X5),unordered_pair(sK114(X5),sK114(X5))),sK112) ),
inference(definition_unfolding,[],[f1451,f1619]) ).
fof(f1891,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK62(X0,X5),X5),unordered_pair(sK62(X0,X5),sK62(X0,X5))),X0) ),
inference(equality_resolution,[],[f1688]) ).
fof(f1923,definition,
( spl131_1
<=> ! [X5] :
( ~ in(X5,sK111)
| in(unordered_pair(unordered_pair(sK114(X5),X5),unordered_pair(sK114(X5),sK114(X5))),sK112) ) ),
introduced(definition,[new_symbols(definition,[spl131_1])],[avatar_definition]) ).
fof(f1924,plain,
( ! [X5] :
( ~ in(X5,sK111)
| in(unordered_pair(unordered_pair(sK114(X5),X5),unordered_pair(sK114(X5),sK114(X5))),sK112) )
| ~ spl131_1 ),
inference(avatar_component_clause,[],[f1923]) ).
fof(f1926,definition,
( spl131_2
<=> sK111 = relation_rng_as_subset(sK110,sK111,sK112) ),
introduced(definition,[new_symbols(definition,[spl131_2])],[avatar_definition]) ).
fof(f1927,plain,
( sK111 = relation_rng_as_subset(sK110,sK111,sK112)
| ~ spl131_2 ),
inference(avatar_component_clause,[],[f1926]) ).
fof(f1928,plain,
( spl131_1
| spl131_2 ),
inference(avatar_split_clause,[],[f1769,f1926,f1923]) ).
fof(f1930,definition,
( spl131_3
<=> ! [X4] : ~ in(unordered_pair(unordered_pair(X4,sK113),unordered_pair(X4,X4)),sK112) ),
introduced(definition,[new_symbols(definition,[spl131_3])],[avatar_definition]) ).
fof(f1931,plain,
( ! [X4] : ~ in(unordered_pair(unordered_pair(X4,sK113),unordered_pair(X4,X4)),sK112)
| ~ spl131_3 ),
inference(avatar_component_clause,[],[f1930]) ).
fof(f1932,plain,
( sK111 != relation_rng_as_subset(sK110,sK111,sK112)
| spl131_2 ),
inference(avatar_component_clause,[],[f1926]) ).
fof(f1933,plain,
( spl131_3
| ~ spl131_2 ),
inference(avatar_split_clause,[],[f1768,f1926,f1930]) ).
fof(f1935,definition,
( spl131_4
<=> in(sK113,sK111) ),
introduced(definition,[new_symbols(definition,[spl131_4])],[avatar_definition]) ).
fof(f1936,plain,
( in(sK113,sK111)
| ~ spl131_4 ),
inference(avatar_component_clause,[],[f1935]) ).
fof(f1937,plain,
( spl131_4
| ~ spl131_2 ),
inference(avatar_split_clause,[],[f1453,f1926,f1935]) ).
fof(f1974,plain,
( ! [X0] : ~ in(unordered_pair(unordered_pair(sK113,X0),unordered_pair(X0,X0)),sK112)
| ~ spl131_3 ),
inference(superposition,[],[f1931,f939]) ).
fof(f1980,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_rng(X0) = relation_rng_as_subset(X1,X2,X0) ),
inference(resolution,[],[f1366,f1370]) ).
fof(f1981,plain,
relation_rng_as_subset(sK110,sK111,sK112) = relation_rng(sK112),
inference(resolution,[],[f1980,f1450]) ).
fof(f1982,plain,
( sK111 = relation_rng(sK112)
| ~ spl131_2 ),
inference(forward_demodulation,[],[f1981,f1927]) ).
fof(f2009,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f931,f1222]) ).
fof(f2011,plain,
relation(sK112),
inference(resolution,[],[f2009,f1450]) ).
fof(f2038,plain,
subset(relation_rng(sK112),sK111),
inference(resolution,[],[f1392,f1450]) ).
fof(f2114,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK112)
| in(X1,relation_rng(sK112)) ),
inference(resolution,[],[f1765,f2011]) ).
fof(f2841,plain,
( sK111 != relation_rng(sK112)
| spl131_2 ),
inference(superposition,[],[f1932,f1981]) ).
fof(f2862,plain,
( ~ subset(sK111,relation_rng(sK112))
| sK111 = relation_rng(sK112) ),
inference(resolution,[],[f2038,f951]) ).
fof(f2880,plain,
( ! [X5] :
( ~ in(X5,sK111)
| in(unordered_pair(unordered_pair(X5,sK114(X5)),unordered_pair(sK114(X5),sK114(X5))),sK112) )
| ~ spl131_1 ),
inference(forward_demodulation,[],[f1924,f939]) ).
fof(f2881,plain,
( ~ subset(sK111,relation_rng(sK112))
| spl131_2 ),
inference(forward_subsumption_resolution,[],[f2862,f2841]) ).
fof(f2951,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),sK112)
| in(X0,relation_rng(sK112)) ),
inference(superposition,[],[f2114,f939]) ).
fof(f4602,plain,
! [X0] :
( ~ in(X0,relation_rng(sK112))
| in(unordered_pair(unordered_pair(sK62(sK112,X0),X0),unordered_pair(sK62(sK112,X0),sK62(sK112,X0))),sK112) ),
inference(resolution,[],[f1891,f2011]) ).
fof(f4603,plain,
( ! [X0] :
( ~ in(X0,sK111)
| in(unordered_pair(unordered_pair(sK62(sK112,X0),X0),unordered_pair(sK62(sK112,X0),sK62(sK112,X0))),sK112) )
| ~ spl131_2 ),
inference(forward_demodulation,[],[f4602,f1982]) ).
fof(f4604,plain,
( ! [X0] :
( ~ in(X0,sK111)
| in(unordered_pair(unordered_pair(X0,sK62(sK112,X0)),unordered_pair(sK62(sK112,X0),sK62(sK112,X0))),sK112) )
| ~ spl131_2 ),
inference(forward_demodulation,[],[f4603,f939]) ).
fof(f4612,plain,
( in(unordered_pair(unordered_pair(sK113,sK62(sK112,sK113)),unordered_pair(sK62(sK112,sK113),sK62(sK112,sK113))),sK112)
| ~ spl131_2
| ~ spl131_4 ),
inference(resolution,[],[f4604,f1936]) ).
fof(f4615,plain,
( $false
| ~ spl131_2
| ~ spl131_3
| ~ spl131_4 ),
inference(forward_subsumption_resolution,[],[f4612,f1974]) ).
fof(f4616,plain,
( ~ spl131_2
| ~ spl131_3
| ~ spl131_4 ),
inference(avatar_contradiction_clause,[],[f4615]) ).
fof(f4716,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK44(sK111,X0),sK114(sK44(sK111,X0))),unordered_pair(sK114(sK44(sK111,X0)),sK114(sK44(sK111,X0)))),sK112)
| subset(sK111,X0) )
| ~ spl131_1 ),
inference(resolution,[],[f2880,f1083]) ).
fof(f4794,plain,
( ! [X0] :
( in(sK44(sK111,X0),relation_rng(sK112))
| subset(sK111,X0) )
| ~ spl131_1 ),
inference(resolution,[],[f4716,f2951]) ).
fof(f4950,plain,
( subset(sK111,relation_rng(sK112))
| subset(sK111,relation_rng(sK112))
| ~ spl131_1 ),
inference(resolution,[],[f4794,f1084]) ).
fof(f4957,plain,
( subset(sK111,relation_rng(sK112))
| ~ spl131_1 ),
inference(duplicate_literal_removal,[],[f4950]) ).
fof(f4959,plain,
( $false
| ~ spl131_1
| spl131_2 ),
inference(forward_subsumption_resolution,[],[f4957,f2881]) ).
fof(f4960,plain,
( ~ spl131_1
| spl131_2 ),
inference(avatar_contradiction_clause,[],[f4959]) ).
cnf(s1,plain,
( spl131_1
| spl131_2 ),
inference(sat_conversion,[],[f1928]) ).
cnf(s2,plain,
( ~ spl131_2
| spl131_3 ),
inference(sat_conversion,[],[f1933]) ).
cnf(s3,plain,
( ~ spl131_2
| spl131_4 ),
inference(sat_conversion,[],[f1937]) ).
cnf(s197,plain,
( ~ spl131_2
| ~ spl131_3
| ~ spl131_4 ),
inference(sat_conversion,[],[f4616]) ).
cnf(s223,plain,
( ~ spl131_1
| spl131_2 ),
inference(sat_conversion,[],[f4960]) ).
cnf(s228,plain,
~ spl131_2,
inference(rat,[],[s197,s2,s3]) ).
cnf(s229,plain,
~ spl131_1,
inference(rat,[],[s223,s228]) ).
cnf(s231,plain,
$false,
inference(rat,[],[s1,s228,s229]) ).
fof(f4961,plain,
$false,
inference(avatar_sat_refutation,[],[s231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU266+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 04:24:25 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.42 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
% 5.18/1.81 % (1869259)Detected formulas, will run a generic FOF schedule.
% 5.18/1.81 % (1869265)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=446052265:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.18/1.81 % (1869267)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4028844128:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.18/1.81 % (1869266)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=2921225242:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.18/1.81 % (1869264)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=3103750764:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.18/1.81 % (1869268)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=85021057:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.18/1.81 % (1869270)dis-21_1_sil=8000:lcm=predicate:random_seed=159113663: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)
% 5.18/1.81 % (1869269)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1416510405:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.18/1.81 % (1869267)Instruction limit reached!
% 5.18/1.81 % (1869267)------------------------------
% 5.18/1.81 % (1869267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869267)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869267)Termination reason: Instruction limit
% 5.18/1.81 % (1869267)Termination phase: Saturation
% 5.18/1.81 % (1869267)Time elapsed: 0.069 s
% 5.18/1.81 % (1869267)Peak memory usage: 91 MB
% 5.18/1.81 % (1869267)Instructions burned: 110 (million)
% 5.18/1.81 % (1869268)Instruction limit reached!
% 5.18/1.81 % (1869268)------------------------------
% 5.18/1.81 % (1869268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869268)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869268)Termination reason: Instruction limit
% 5.18/1.81 % (1869268)Termination phase: Saturation
% 5.18/1.81 % (1869268)Time elapsed: 0.073 s
% 5.18/1.81 % (1869268)Peak memory usage: 89 MB
% 5.18/1.81 % (1869268)Instructions burned: 119 (million)
% 5.18/1.81 % (1869270)Instruction limit reached!
% 5.18/1.81 % (1869270)------------------------------
% 5.18/1.81 % (1869270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869270)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869270)Termination reason: Instruction limit
% 5.18/1.81 % (1869270)Termination phase: Saturation
% 5.18/1.81 % (1869270)Time elapsed: 0.075 s
% 5.18/1.81 % (1869270)Peak memory usage: 90 MB
% 5.18/1.81 % (1869270)Instructions burned: 129 (million)
% 5.18/1.81 % (1869269)Instruction limit reached!
% 5.18/1.81 % (1869269)------------------------------
% 5.18/1.81 % (1869269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869269)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869269)Termination reason: Instruction limit
% 5.18/1.81 % (1869269)Termination phase: Saturation
% 5.18/1.81 % (1869269)Time elapsed: 0.095 s
% 5.18/1.81 % (1869269)Peak memory usage: 90 MB
% 5.18/1.81 % (1869269)Instructions burned: 140 (million)
% 5.18/1.81 % (1869278)lrs+10_1_sil=8000:sp=occurrence:random_seed=3129451408:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.18/1.81 % (1869279)lrs+10_1_sil=32000:urr=on:br=off:random_seed=860900758:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.18/1.81 % (1869280)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1301669383:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.18/1.81 % (1869281)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=4264794835:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.18/1.81 % (1869279)Instruction limit reached!
% 5.18/1.81 % (1869279)------------------------------
% 5.18/1.81 % (1869279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869279)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869279)Termination reason: Instruction limit
% 5.18/1.81 % (1869279)Termination phase: Saturation
% 5.18/1.81 % (1869279)Time elapsed: 0.090 s
% 5.18/1.81 % (1869279)Peak memory usage: 91 MB
% 5.18/1.81 % (1869279)Instructions burned: 159 (million)
% 5.18/1.81 % (1869278)Instruction limit reached!
% 5.18/1.81 % (1869278)------------------------------
% 5.18/1.81 % (1869278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869278)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869278)Termination reason: Instruction limit
% 5.18/1.81 % (1869278)Termination phase: Saturation
% 5.18/1.81 % (1869278)Time elapsed: 0.190 s
% 5.18/1.81 % (1869278)Peak memory usage: 93 MB
% 5.18/1.81 % (1869278)Instructions burned: 286 (million)
% 5.18/1.81 % (1869281)Instruction limit reached!
% 5.18/1.81 % (1869281)------------------------------
% 5.18/1.81 % (1869281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869281)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869281)Termination reason: Instruction limit
% 5.18/1.81 % (1869281)Termination phase: Saturation
% 5.18/1.81 % (1869281)Time elapsed: 0.150 s
% 5.18/1.81 % (1869281)Peak memory usage: 93 MB
% 5.18/1.81 % (1869281)Instructions burned: 249 (million)
% 5.18/1.81 % (1869286)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=367860063:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.18/1.81 % (1869280)Instruction limit reached!
% 5.18/1.81 % (1869280)------------------------------
% 5.18/1.81 % (1869280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869280)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869280)Termination reason: Instruction limit
% 5.18/1.81 % (1869280)Termination phase: Saturation
% 5.18/1.81 % (1869280)Time elapsed: 0.223 s
% 5.18/1.81 % (1869280)Peak memory usage: 93 MB
% 5.18/1.81 % (1869280)Instructions burned: 325 (million)
% 5.18/1.81 % (1869287)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3558346074:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.18/1.81 % (1869288)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=245955565:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.18/1.81 % (1869290)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2163472126:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.18/1.81 % (1869288)Instruction limit reached!
% 5.18/1.81 % (1869288)------------------------------
% 5.18/1.81 % (1869288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869288)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869288)Termination reason: Instruction limit
% 5.18/1.81 % (1869288)Termination phase: Saturation
% 5.18/1.81 % (1869288)Time elapsed: 0.070 s
% 5.18/1.81 % (1869288)Peak memory usage: 90 MB
% 5.18/1.81 % (1869288)Instructions burned: 114 (million)
% 5.18/1.81 % (1869286)Instruction limit reached!
% 5.18/1.81 % (1869286)------------------------------
% 5.18/1.81 % (1869286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869286)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869286)Termination reason: Instruction limit
% 5.18/1.81 % (1869286)Termination phase: Saturation
% 5.18/1.81 % (1869286)Time elapsed: 0.190 s
% 5.18/1.81 % (1869286)Peak memory usage: 91 MB
% 5.18/1.81 % (1869286)Instructions burned: 295 (million)
% 5.18/1.81 % (1869265)First to succeed.
% 5.18/1.81 % (1869265)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1869259"
% 5.18/1.81 % (1869290)Instruction limit reached!
% 5.18/1.81 % (1869290)------------------------------
% 5.18/1.81 % (1869290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.81 % (1869290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.81 % (1869290)CaDiCaL version: 2.1.3
% 5.18/1.81 % (1869290)Termination reason: Instruction limit
% 5.18/1.81 % (1869290)Termination phase: Saturation
% 5.18/1.81 % (1869290)Time elapsed: 0.068 s
% 5.18/1.81 % (1869290)Peak memory usage: 90 MB
% 5.18/1.81 % (1869290)Instructions burned: 128 (million)
% 5.18/1.81 % (1869294)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1344018330:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.18/1.81 % (1869295)lrs+10_1_sil=8000:sp=occurrence:random_seed=2256508991:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 5.18/1.81 % (1869296)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3337333596:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.18/1.81 % (1869265)Refutation found. Thanks to Tanya!
% 5.18/1.81 % SZS status Theorem for theBenchmark
% 5.18/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 7.20/2.00 % (1869265)------------------------------
% 7.20/2.00 % (1869265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.20/2.00 % (1869265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.20/2.00 % (1869265)CaDiCaL version: 2.1.3
% 7.20/2.00 % (1869265)Termination reason: Refutation
% 7.20/2.00 % (1869265)Time elapsed: 0.674 s
% 7.20/2.00 % (1869265)Peak memory usage: 139 MB
% 7.20/2.00 % (1869265)Instructions burned: 1833 (million)
% 7.20/2.00 % (1869265)------------------------------
% 7.20/2.00 % (1869265)------------------------------
% 7.20/2.00 % (1869259)Success in time 0.952 s
% 7.20/2.00 % Vampire exiting
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