%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU039+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:51:50 PM UTC 2026
% Result : Theorem 0.59s 0.56s
% Output : Refutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 124 ( 25 unt; 11 def)
% Number of atoms : 474 ( 86 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 566 ( 216 ~; 238 |; 78 &)
% ( 22 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 166 ( 0 sgn 145 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f8,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f15,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0) )
=> ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f39,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f42,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( in(X1,relation_dom(X2))
& in(X1,X0) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_1) ).
fof(f43,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( in(X1,relation_dom(X2))
& in(X1,X0) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f64,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f63]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f79]) ).
fof(f82,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f41]) ).
fof(f83,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,relation_dom(X2))
& in(X1,X0)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f85,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,relation_dom(X2))
& in(X1,X0)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f84]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X0)
& in(sK0(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f90]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK1(X0,X1) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK2(X0,X1),relation_dom(X0))
& sK1(X0,X1) = apply(X0,sK2(X0,X1)) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK3(X0,X5),relation_dom(X0))
& apply(X0,sK3(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f93]) ).
fof(f106,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f80]) ).
fof(f107,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ( apply(X1,sK15(X1,X2)) != apply(X2,sK15(X1,X2))
& in(sK15(X1,X2),relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X3,sK15(X1,X2))],[f108]) ).
fof(f110,plain,
( ~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16)))
& in(sK17,relation_dom(sK18))
& in(sK17,sK16)
& relation(sK18)
& function(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f85]) ).
fof(f119,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f125,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f129,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f139,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f177,plain,
! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f181,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f182,plain,
function(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f183,plain,
relation(sK18),
inference(cnf_transformation,[],[f110]) ).
fof(f184,plain,
in(sK17,sK16),
inference(cnf_transformation,[],[f110]) ).
fof(f185,plain,
in(sK17,relation_dom(sK18)),
inference(cnf_transformation,[],[f110]) ).
fof(f186,plain,
~ in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16))),
inference(cnf_transformation,[],[f110]) ).
fof(f189,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f119]) ).
fof(f192,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f193,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f192]) ).
fof(f196,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f177]) ).
fof(f205,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| relation(X0)
| function(X0) ),
inference(consistent_polarity_flipping,[],[f193]) ).
fof(f208,plain,
! [X0,X1] :
( ~ relation(relation_dom_restriction(X0,X1))
| relation(X0) ),
inference(consistent_polarity_flipping,[],[f129]) ).
fof(f215,plain,
! [X0,X1] :
( relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| function(X0) ),
inference(consistent_polarity_flipping,[],[f139]) ).
fof(f240,plain,
! [X2,X0] :
( relation(relation_dom_restriction(X2,X0))
| relation(X2)
| function(X2)
| set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| function(relation_dom_restriction(X2,X0)) ),
inference(consistent_polarity_flipping,[],[f196]) ).
fof(f242,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| function(X2) ),
inference(consistent_polarity_flipping,[],[f181]) ).
fof(f243,plain,
~ relation(sK18),
inference(consistent_polarity_flipping,[],[f183]) ).
fof(f244,plain,
~ function(sK18),
inference(consistent_polarity_flipping,[],[f182]) ).
fof(f2317,plain,
! [X0] :
( ~ function(relation_dom_restriction(sK18,X0))
| function(sK18) ),
inference(resolution,[],[f215,f243]) ).
fof(f2319,definition,
( spl19_23
<=> function(sK18) ),
introduced(definition,[new_symbols(definition,[spl19_23])],[avatar_definition]) ).
fof(f2321,plain,
( function(sK18)
| ~ spl19_23 ),
inference(avatar_component_clause,[],[f2319]) ).
fof(f2323,definition,
( spl19_24
<=> ! [X0] : ~ function(relation_dom_restriction(sK18,X0)) ),
introduced(definition,[new_symbols(definition,[spl19_24])],[avatar_definition]) ).
fof(f2324,plain,
( ! [X0] : ~ function(relation_dom_restriction(sK18,X0))
| ~ spl19_24 ),
inference(avatar_component_clause,[],[f2323]) ).
fof(f2325,plain,
( spl19_23
| spl19_24 ),
inference(avatar_split_clause,[],[f2317,f2323,f2319]) ).
fof(f2454,plain,
( $false
| ~ spl19_23 ),
inference(resolution,[],[f2321,f244]) ).
fof(f2456,plain,
~ spl19_23,
inference(avatar_contradiction_clause,[],[f2454]) ).
fof(f6309,definition,
( spl19_219
<=> relation(sK18) ),
introduced(definition,[new_symbols(definition,[spl19_219])],[avatar_definition]) ).
fof(f6311,plain,
( relation(sK18)
| ~ spl19_219 ),
inference(avatar_component_clause,[],[f6309]) ).
fof(f6316,plain,
( $false
| ~ spl19_219 ),
inference(resolution,[],[f6311,f243]) ).
fof(f6318,plain,
~ spl19_219,
inference(avatar_contradiction_clause,[],[f6316]) ).
fof(f6339,definition,
( spl19_224
<=> in(sK17,relation_dom(sK18)) ),
introduced(definition,[new_symbols(definition,[spl19_224])],[avatar_definition]) ).
fof(f6341,plain,
( ~ in(sK17,relation_dom(sK18))
| spl19_224 ),
inference(avatar_component_clause,[],[f6339]) ).
fof(f6343,plain,
( $false
| spl19_224 ),
inference(resolution,[],[f6341,f185]) ).
fof(f6344,plain,
spl19_224,
inference(avatar_contradiction_clause,[],[f6343]) ).
fof(f6409,plain,
! [X0,X1] :
( ~ in(X0,X1)
| apply(sK18,X0) = apply(relation_dom_restriction(sK18,X1),X0)
| function(sK18) ),
inference(resolution,[],[f242,f243]) ).
fof(f6411,definition,
( spl19_228
<=> ! [X0,X1] :
( ~ in(X0,X1)
| apply(sK18,X0) = apply(relation_dom_restriction(sK18,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_228])],[avatar_definition]) ).
fof(f6412,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| apply(sK18,X0) = apply(relation_dom_restriction(sK18,X1),X0) )
| ~ spl19_228 ),
inference(avatar_component_clause,[],[f6411]) ).
fof(f6413,plain,
( spl19_23
| spl19_228 ),
inference(avatar_split_clause,[],[f6409,f6411,f2319]) ).
fof(f6521,plain,
( apply(sK18,sK17) = apply(relation_dom_restriction(sK18,sK16),sK17)
| ~ spl19_228 ),
inference(resolution,[],[f6412,f184]) ).
fof(f6523,plain,
( in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16)))
| ~ in(sK17,relation_dom(relation_dom_restriction(sK18,sK16)))
| relation(relation_dom_restriction(sK18,sK16))
| function(relation_dom_restriction(sK18,sK16))
| ~ spl19_228 ),
inference(superposition,[],[f205,f6521]) ).
fof(f6525,definition,
( spl19_251
<=> function(relation_dom_restriction(sK18,sK16)) ),
introduced(definition,[new_symbols(definition,[spl19_251])],[avatar_definition]) ).
fof(f6527,plain,
( function(relation_dom_restriction(sK18,sK16))
| ~ spl19_251 ),
inference(avatar_component_clause,[],[f6525]) ).
fof(f6529,definition,
( spl19_252
<=> relation(relation_dom_restriction(sK18,sK16)) ),
introduced(definition,[new_symbols(definition,[spl19_252])],[avatar_definition]) ).
fof(f6530,plain,
( ~ relation(relation_dom_restriction(sK18,sK16))
| spl19_252 ),
inference(avatar_component_clause,[],[f6529]) ).
fof(f6531,plain,
( relation(relation_dom_restriction(sK18,sK16))
| ~ spl19_252 ),
inference(avatar_component_clause,[],[f6529]) ).
fof(f6533,definition,
( spl19_253
<=> in(sK17,relation_dom(relation_dom_restriction(sK18,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_253])],[avatar_definition]) ).
fof(f6535,plain,
( ~ in(sK17,relation_dom(relation_dom_restriction(sK18,sK16)))
| spl19_253 ),
inference(avatar_component_clause,[],[f6533]) ).
fof(f6537,definition,
( spl19_254
<=> in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_254])],[avatar_definition]) ).
fof(f6539,plain,
( in(apply(sK18,sK17),relation_rng(relation_dom_restriction(sK18,sK16)))
| ~ spl19_254 ),
inference(avatar_component_clause,[],[f6537]) ).
fof(f6540,plain,
( spl19_251
| spl19_252
| ~ spl19_253
| spl19_254
| ~ spl19_228 ),
inference(avatar_split_clause,[],[f6523,f6411,f6537,f6533,f6529,f6525]) ).
fof(f6572,plain,
( $false
| ~ spl19_24
| ~ spl19_251 ),
inference(resolution,[],[f6527,f2324]) ).
fof(f6574,plain,
( ~ spl19_24
| ~ spl19_251 ),
inference(avatar_contradiction_clause,[],[f6572]) ).
fof(f6576,plain,
( relation(sK18)
| ~ spl19_252 ),
inference(resolution,[],[f6531,f208]) ).
fof(f6578,plain,
( spl19_219
| ~ spl19_252 ),
inference(avatar_split_clause,[],[f6576,f6529,f6309]) ).
fof(f7153,plain,
( relation(sK18)
| function(sK18)
| relation_dom(relation_dom_restriction(sK18,sK16)) = set_intersection2(relation_dom(sK18),sK16)
| function(relation_dom_restriction(sK18,sK16))
| spl19_252 ),
inference(resolution,[],[f240,f6530]) ).
fof(f7158,definition,
( spl19_346
<=> relation_dom(relation_dom_restriction(sK18,sK16)) = set_intersection2(relation_dom(sK18),sK16) ),
introduced(definition,[new_symbols(definition,[spl19_346])],[avatar_definition]) ).
fof(f7160,plain,
( relation_dom(relation_dom_restriction(sK18,sK16)) = set_intersection2(relation_dom(sK18),sK16)
| ~ spl19_346 ),
inference(avatar_component_clause,[],[f7158]) ).
fof(f7161,plain,
( spl19_251
| spl19_346
| spl19_23
| spl19_219
| spl19_252 ),
inference(avatar_split_clause,[],[f7153,f6529,f6309,f2319,f7158,f6525]) ).
fof(f7189,plain,
( ~ in(sK17,set_intersection2(relation_dom(sK18),sK16))
| spl19_253
| ~ spl19_346 ),
inference(superposition,[],[f6535,f7160]) ).
fof(f7207,plain,
( ~ in(sK17,relation_dom(sK18))
| ~ in(sK17,sK16)
| spl19_253
| ~ spl19_346 ),
inference(resolution,[],[f7189,f189]) ).
fof(f7211,definition,
( spl19_352
<=> in(sK17,sK16) ),
introduced(definition,[new_symbols(definition,[spl19_352])],[avatar_definition]) ).
fof(f7213,plain,
( ~ in(sK17,sK16)
| spl19_352 ),
inference(avatar_component_clause,[],[f7211]) ).
fof(f7214,plain,
( ~ spl19_352
| ~ spl19_224
| spl19_253
| ~ spl19_346 ),
inference(avatar_split_clause,[],[f7207,f7158,f6533,f6339,f7211]) ).
fof(f7215,plain,
( $false
| spl19_352 ),
inference(resolution,[],[f7213,f184]) ).
fof(f7216,plain,
spl19_352,
inference(avatar_contradiction_clause,[],[f7215]) ).
fof(f7230,plain,
( $false
| ~ spl19_254 ),
inference(resolution,[],[f6539,f186]) ).
fof(f7233,plain,
~ spl19_254,
inference(avatar_contradiction_clause,[],[f7230]) ).
cnf(s24,plain,
( spl19_23
| spl19_24 ),
inference(sat_conversion,[],[f2325]) ).
cnf(s41,plain,
~ spl19_23,
inference(sat_conversion,[],[f2456]) ).
cnf(s325,plain,
~ spl19_219,
inference(sat_conversion,[],[f6318]) ).
cnf(s329,plain,
spl19_224,
inference(sat_conversion,[],[f6344]) ).
cnf(s334,plain,
( spl19_23
| spl19_228 ),
inference(sat_conversion,[],[f6413]) ).
cnf(s358,plain,
( ~ spl19_228
| spl19_251
| spl19_252
| ~ spl19_253
| spl19_254 ),
inference(sat_conversion,[],[f6540]) ).
cnf(s364,plain,
( ~ spl19_24
| ~ spl19_251 ),
inference(sat_conversion,[],[f6574]) ).
cnf(s365,plain,
( spl19_219
| ~ spl19_252 ),
inference(sat_conversion,[],[f6578]) ).
cnf(s447,plain,
( spl19_23
| spl19_219
| spl19_251
| spl19_252
| spl19_346 ),
inference(sat_conversion,[],[f7161]) ).
cnf(s453,plain,
( ~ spl19_224
| spl19_253
| ~ spl19_346
| ~ spl19_352 ),
inference(sat_conversion,[],[f7214]) ).
cnf(s454,plain,
spl19_352,
inference(sat_conversion,[],[f7216]) ).
cnf(s455,plain,
~ spl19_254,
inference(sat_conversion,[],[f7233]) ).
cnf(s456,plain,
( ~ spl19_224
| spl19_253
| ~ spl19_346 ),
inference(rat,[],[s453,s454]) ).
cnf(s457,plain,
( ~ spl19_228
| spl19_251
| spl19_252
| ~ spl19_253 ),
inference(rat,[],[s358,s455]) ).
cnf(s464,plain,
~ spl19_252,
inference(rat,[],[s365,s325]) ).
cnf(s661,plain,
spl19_228,
inference(rat,[],[s334,s41]) ).
cnf(s684,plain,
spl19_24,
inference(rat,[],[s24,s41]) ).
cnf(s689,plain,
~ spl19_251,
inference(rat,[],[s364,s684]) ).
cnf(s708,plain,
~ spl19_253,
inference(rat,[],[s457,s661,s464,s689]) ).
cnf(s709,plain,
spl19_346,
inference(rat,[],[s447,s41,s464,s325,s689]) ).
cnf(s710,plain,
$false,
inference(rat,[],[s456,s329,s709,s708]) ).
fof(f7234,plain,
$false,
inference(avatar_sat_refutation,[],[s710]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU039+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n026.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 03:27:25 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.56 % (3435624)Will run a generic schedule for satisfiability detection.
% 0.59/0.56 % (3435633)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1624808113:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.59/0.56 % (3435630)% WARNING: option uhcvi not known.
% 0.59/0.56 % (3435629)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3135482082_2999 on theBenchmark for (2999ds/0Mi)
% 0.59/0.56 % (3435630)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2386177425:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.59/0.56 % (3435632)dis+10_1_sil=32000:sp=arity:random_seed=3308662336:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.59/0.56 % (3435631)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2397375542:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.59/0.56 % (3435634)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=500008022:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.59/0.56 % (3435635)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=263582919:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.59/0.56 % TRYING [1]
% 0.59/0.56 % TRYING [2]
% 0.59/0.56 % TRYING [3]
% 0.59/0.56 % TRYING [4]
% 0.59/0.56 % TRYING [5]
% 0.59/0.56 % (3435633)Instruction limit reached!
% 0.59/0.56 % (3435633)------------------------------
% 0.59/0.56 % (3435633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.56 % (3435633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.56 % (3435633)CaDiCaL version: 2.1.3
% 0.59/0.56 % (3435633)Termination reason: Instruction limit
% 0.59/0.56 % (3435633)Termination phase: Saturation
% 0.59/0.56 % (3435633)Time elapsed: 0.038 s
% 0.59/0.56 % (3435633)Peak memory usage: 13 MB
% 0.59/0.56 % (3435633)Instructions burned: 119 (million)
% 0.59/0.56 % (3435643)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2450676398:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.59/0.56 % TRYING [1]
% 0.59/0.56 % TRYING [2]
% 0.59/0.56 % TRYING [3]
% 0.59/0.56 % TRYING [4]
% 0.59/0.56 % TRYING [5]
% 0.59/0.56 % TRYING [6]
% 0.59/0.56 % (3435632)Instruction limit reached!
% 0.59/0.56 % (3435632)------------------------------
% 0.59/0.56 % (3435632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.56 % (3435632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.56 % (3435632)CaDiCaL version: 2.1.3
% 0.59/0.56 % (3435632)Termination reason: Instruction limit
% 0.59/0.56 % (3435632)Termination phase: Saturation
% 0.59/0.56 % (3435632)Time elapsed: 0.063 s
% 0.59/0.56 % (3435632)Peak memory usage: 12 MB
% 0.59/0.56 % (3435632)Instructions burned: 104 (million)
% 0.59/0.56 % TRYING [6]
% 0.59/0.56 % (3435634)Instruction limit reached!
% 0.59/0.56 % (3435634)------------------------------
% 0.59/0.56 % (3435634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.56 % (3435634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.56 % (3435634)CaDiCaL version: 2.1.3
% 0.59/0.56 % (3435634)Termination reason: Instruction limit
% 0.59/0.56 % (3435634)Termination phase: Saturation
% 0.59/0.56 % (3435634)Time elapsed: 0.073 s
% 0.59/0.56 % (3435634)Peak memory usage: 13 MB
% 0.59/0.56 % (3435634)Instructions burned: 132 (million)
% 0.59/0.56 % (3435635) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3435624-3435635"...
% 0.59/0.56 % (3435635)...printing done.
% 0.59/0.56 % (3435635)Refutation found. Thanks to Tanya!
% 0.59/0.56 % SZS status Theorem for theBenchmark
% 0.59/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.59/0.57 % (3435635)------------------------------
% 0.59/0.57 % (3435635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.57 % (3435635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.57 % (3435635)CaDiCaL version: 2.1.3
% 0.59/0.57 % (3435635)Termination reason: Refutation
% 0.59/0.57 % (3435635)Time elapsed: 0.076 s
% 0.59/0.57 % (3435635)Peak memory usage: 14 MB
% 0.59/0.57 % (3435635)Instructions burned: 127 (million)
% 0.59/0.57 % (3435624)Success in time 0.12 s
% 0.59/0.57 % Vampire exiting
%------------------------------------------------------------------------------