%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU293+1 : 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 : n003.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 12:48:12 PM UTC 2026
% Result : Theorem 2.58s 1.27s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 94 ( 13 unt; 5 def)
% Number of atoms : 379 ( 62 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 460 ( 175 ~; 183 |; 68 &)
% ( 20 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 151 ( 0 sgn 128 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( ( X1 = empty_set
=> X0 = empty_set )
=> ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) )
& ( X1 = empty_set
=> ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f17,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(f42,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f43,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(f48,conjecture,
! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( X1 != empty_set
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(X4,X0)
& in(apply(X3,X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).
fof(f49,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( X1 != empty_set
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(X4,X0)
& in(apply(X3,X4),X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f66,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f4]) ).
fof(f69,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f70,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f74,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f81,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f86,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(X4,X0)
& in(apply(X3,X4),X2) ) )
& X1 != empty_set
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f87,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(X4,X0)
& in(apply(X3,X4),X2) ) )
& X1 != empty_set
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f94,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f70]) ).
fof(f95,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK0(X0,X1,X2)),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( ( ( ( quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) != X0 )
& ( X0 = relation_dom_as_subset(X0,X1,X2)
| ~ quasi_total(X2,X0,X1) ) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( ( quasi_total(X2,X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| ~ quasi_total(X2,X0,X1) ) )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f72]) ).
fof(f116,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,[],[f43]) ).
fof(f117,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(X4,X0)
| ~ in(apply(X3,X4),X2)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(X4,X0)
& in(apply(X3,X4),X2) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& X1 != empty_set
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(nnf_transformation,[],[f87]) ).
fof(f118,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(X4,X0)
| ~ in(apply(X3,X4),X2)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(X4,X0)
& in(apply(X3,X4),X2) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& X1 != empty_set
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ( ~ in(sK22,sK18)
| ~ in(apply(sK21,sK22),sK20)
| ~ in(sK22,relation_inverse_image(sK21,sK20)) )
& ( ( in(sK22,sK18)
& in(apply(sK21,sK22),sK20) )
| in(sK22,relation_inverse_image(sK21,sK20)) )
& empty_set != sK19
& function(sK21)
& quasi_total(sK21,sK18,sK19)
& relation_of2_as_subset(sK21,sK18,sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X2,sK20),skolemize(X3,sK21),skolemize(X4,sK22)],[f118]) ).
fof(f123,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f127,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f134,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1)
| empty_set = X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f139,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f183,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f184,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f190,plain,
relation_of2_as_subset(sK21,sK18,sK19),
inference(cnf_transformation,[],[f119]) ).
fof(f191,plain,
quasi_total(sK21,sK18,sK19),
inference(cnf_transformation,[],[f119]) ).
fof(f192,plain,
function(sK21),
inference(cnf_transformation,[],[f119]) ).
fof(f193,plain,
empty_set != sK19,
inference(cnf_transformation,[],[f119]) ).
fof(f194,plain,
( in(apply(sK21,sK22),sK20)
| in(sK22,relation_inverse_image(sK21,sK20)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f195,plain,
( in(sK22,sK18)
| in(sK22,relation_inverse_image(sK21,sK20)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f196,plain,
( ~ in(sK22,sK18)
| ~ in(apply(sK21,sK22),sK20)
| ~ in(sK22,relation_inverse_image(sK21,sK20)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f202,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1))
| ~ in(apply(X0,X4),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f203,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f127]) ).
fof(f204,plain,
! [X0,X1,X4] :
( ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f126]) ).
fof(f211,definition,
( spl23_1
<=> in(sK22,relation_inverse_image(sK21,sK20)) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
fof(f213,plain,
( in(sK22,relation_inverse_image(sK21,sK20))
| ~ spl23_1 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f215,definition,
( spl23_2
<=> in(apply(sK21,sK22),sK20) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
fof(f217,plain,
( in(apply(sK21,sK22),sK20)
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f194,f215,f211]) ).
fof(f220,definition,
( spl23_3
<=> in(sK22,sK18) ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
fof(f223,plain,
( spl23_1
| spl23_3 ),
inference(avatar_split_clause,[],[f195,f220,f211]) ).
fof(f224,plain,
( ~ spl23_1
| ~ spl23_2
| ~ spl23_3 ),
inference(avatar_split_clause,[],[f196,f220,f215,f211]) ).
fof(f283,plain,
! [X2,X0,X1] :
( relation_dom(X2) = X0
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| empty_set = X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(superposition,[],[f183,f134]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| empty_set = X1
| relation_dom(X2) = X0 ),
inference(forward_subsumption_resolution,[],[f283,f184]) ).
fof(f394,plain,
( ~ quasi_total(sK21,sK18,sK19)
| empty_set = sK19
| sK18 = relation_dom(sK21) ),
inference(resolution,[],[f284,f190]) ).
fof(f397,plain,
( empty_set = sK19
| sK18 = relation_dom(sK21) ),
inference(forward_subsumption_resolution,[],[f394,f191]) ).
fof(f398,plain,
sK18 = relation_dom(sK21),
inference(forward_subsumption_resolution,[],[f397,f193]) ).
fof(f403,plain,
! [X0,X1] :
( ~ in(X0,sK18)
| in(X0,relation_inverse_image(sK21,X1))
| ~ in(apply(sK21,X0),X1)
| ~ relation(sK21)
| ~ function(sK21) ),
inference(superposition,[],[f202,f398]) ).
fof(f416,plain,
! [X0,X1] :
( ~ in(X0,sK18)
| in(X0,relation_inverse_image(sK21,X1))
| ~ in(apply(sK21,X0),X1)
| ~ relation(sK21) ),
inference(forward_subsumption_resolution,[],[f403,f192]) ).
fof(f426,definition,
( spl23_11
<=> relation(sK21) ),
introduced(definition,[new_symbols(definition,[spl23_11])],[avatar_definition]) ).
fof(f427,plain,
( relation(sK21)
| ~ spl23_11 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f428,plain,
( ~ relation(sK21)
| spl23_11 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f430,definition,
( spl23_12
<=> ! [X0,X1] :
( ~ in(X0,sK18)
| ~ in(apply(sK21,X0),X1)
| in(X0,relation_inverse_image(sK21,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl23_12])],[avatar_definition]) ).
fof(f431,plain,
( ! [X0,X1] :
( ~ in(apply(sK21,X0),X1)
| ~ in(X0,sK18)
| in(X0,relation_inverse_image(sK21,X1)) )
| ~ spl23_12 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f432,plain,
( ~ spl23_11
| spl23_12 ),
inference(avatar_split_clause,[],[f416,f430,f426]) ).
fof(f450,plain,
( ! [X0,X1] : ~ element(sK21,powerset(cartesian_product2(X0,X1)))
| spl23_11 ),
inference(resolution,[],[f428,f123]) ).
fof(f470,plain,
( ! [X0,X1] : ~ relation_of2_as_subset(sK21,X0,X1)
| spl23_11 ),
inference(resolution,[],[f450,f139]) ).
fof(f477,plain,
( $false
| spl23_11 ),
inference(resolution,[],[f470,f190]) ).
fof(f479,plain,
spl23_11,
inference(avatar_contradiction_clause,[],[f477]) ).
fof(f486,plain,
( ~ in(sK22,sK18)
| in(sK22,relation_inverse_image(sK21,sK20))
| ~ spl23_2
| ~ spl23_12 ),
inference(resolution,[],[f431,f217]) ).
fof(f493,plain,
( spl23_1
| ~ spl23_3
| ~ spl23_2
| ~ spl23_12 ),
inference(avatar_split_clause,[],[f486,f430,f215,f220,f211]) ).
fof(f505,plain,
( in(apply(sK21,sK22),sK20)
| ~ relation(sK21)
| ~ function(sK21)
| ~ spl23_1 ),
inference(resolution,[],[f213,f204]) ).
fof(f506,plain,
( in(sK22,relation_dom(sK21))
| ~ relation(sK21)
| ~ function(sK21)
| ~ spl23_1 ),
inference(resolution,[],[f213,f203]) ).
fof(f509,plain,
( in(sK22,relation_dom(sK21))
| ~ function(sK21)
| ~ spl23_1
| ~ spl23_11 ),
inference(forward_subsumption_resolution,[],[f506,f427]) ).
fof(f510,plain,
( in(sK22,relation_dom(sK21))
| ~ spl23_1
| ~ spl23_11 ),
inference(forward_subsumption_resolution,[],[f509,f192]) ).
fof(f511,plain,
( in(sK22,sK18)
| ~ spl23_1
| ~ spl23_11 ),
inference(forward_demodulation,[],[f510,f398]) ).
fof(f515,plain,
( spl23_3
| ~ spl23_1
| ~ spl23_11 ),
inference(avatar_split_clause,[],[f511,f426,f211,f220]) ).
fof(f516,plain,
( in(apply(sK21,sK22),sK20)
| ~ function(sK21)
| ~ spl23_1
| ~ spl23_11 ),
inference(forward_subsumption_resolution,[],[f505,f427]) ).
fof(f517,plain,
( in(apply(sK21,sK22),sK20)
| ~ spl23_1
| ~ spl23_11 ),
inference(forward_subsumption_resolution,[],[f516,f192]) ).
fof(f518,plain,
( spl23_2
| ~ spl23_1
| ~ spl23_11 ),
inference(avatar_split_clause,[],[f517,f426,f211,f215]) ).
cnf(s1,plain,
( spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f218]) ).
cnf(s2,plain,
( spl23_1
| spl23_3 ),
inference(sat_conversion,[],[f223]) ).
cnf(s3,plain,
( ~ spl23_1
| ~ spl23_2
| ~ spl23_3 ),
inference(sat_conversion,[],[f224]) ).
cnf(s16,plain,
( ~ spl23_11
| spl23_12 ),
inference(sat_conversion,[],[f432]) ).
cnf(s18,plain,
spl23_11,
inference(sat_conversion,[],[f479]) ).
cnf(s21,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| ~ spl23_12 ),
inference(sat_conversion,[],[f493]) ).
cnf(s26,plain,
( ~ spl23_1
| spl23_3
| ~ spl23_11 ),
inference(sat_conversion,[],[f515]) ).
cnf(s27,plain,
( ~ spl23_1
| spl23_2
| ~ spl23_11 ),
inference(sat_conversion,[],[f518]) ).
cnf(s30,plain,
spl23_12,
inference(rat,[],[s16,s18]) ).
cnf(s32,plain,
spl23_1,
inference(rat,[],[s21,s1,s2,s30]) ).
cnf(s33,plain,
spl23_2,
inference(rat,[],[s27,s18,s32]) ).
cnf(s34,plain,
spl23_3,
inference(rat,[],[s26,s18,s32]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s3,s33,s34,s32]) ).
fof(f519,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU293+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:33:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.58/1.27 % (1187800)Detected formulas, will run a generic FOF schedule.
% 2.58/1.27 % (1187808)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2482250469:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.27 % (1187808)Refutation not found, incomplete strategy
% 2.58/1.27 % (1187808)------------------------------
% 2.58/1.27 % (1187808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.27 % (1187808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.27 % (1187808)CaDiCaL version: 2.1.3
% 2.58/1.27 % (1187808)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.27 % (1187808)Time elapsed: 0.002 s
% 2.58/1.27 % (1187808)Peak memory usage: 88 MB
% 2.58/1.27 % (1187808)Instructions burned: 4 (million)
% 2.58/1.27 % (1187809)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4132670165:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.27 % (1187810)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2042292269:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.27 % (1187807)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=450276325:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.27 % (1187805)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=2487821937:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.27 % (1187806)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=931622064:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.27 % (1187811)dis-21_1_sil=8000:lcm=predicate:random_seed=2463214818: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)
% 2.58/1.27 % (1187810)First to succeed.
% 2.58/1.27 % (1187810)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1187800"
% 2.58/1.27 % (1187811)Instruction limit reached!
% 2.58/1.27 % (1187811)------------------------------
% 2.58/1.27 % (1187811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.27 % (1187811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.27 % (1187811)CaDiCaL version: 2.1.3
% 2.58/1.27 % (1187811)Termination reason: Instruction limit
% 2.58/1.27 % (1187811)Termination phase: Saturation
% 2.58/1.27 % (1187811)Time elapsed: 0.071 s
% 2.58/1.27 % (1187811)Peak memory usage: 90 MB
% 2.58/1.27 % (1187811)Instructions burned: 129 (million)
% 2.58/1.27 % (1187809)Instruction limit reached!
% 2.58/1.27 % (1187809)------------------------------
% 2.58/1.27 % (1187809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.27 % (1187809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.27 % (1187809)CaDiCaL version: 2.1.3
% 2.58/1.27 % (1187809)Termination reason: Instruction limit
% 2.58/1.27 % (1187809)Termination phase: Saturation
% 2.58/1.27 % (1187809)Time elapsed: 0.077 s
% 2.58/1.27 % (1187809)Peak memory usage: 88 MB
% 2.58/1.27 % (1187809)Instructions burned: 121 (million)
% 2.58/1.27 % (1187808)------------------------------
% 2.58/1.27 % (1187808)------------------------------
% 2.58/1.27 % (1187820)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2410918272:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.58/1.27 % (1187819)lrs+10_1_sil=8000:sp=occurrence:random_seed=3081509081:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.58/1.27 % (1187820)Refutation not found, incomplete strategy
% 2.58/1.27 % (1187820)------------------------------
% 2.58/1.27 % (1187820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.27 % (1187820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.27 % (1187820)CaDiCaL version: 2.1.3
% 2.58/1.27 % (1187820)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.27 % (1187820)Time elapsed: 0.010 s
% 2.58/1.27 % (1187820)Peak memory usage: 89 MB
% 2.58/1.27 % (1187820)Instructions burned: 14 (million)
% 2.58/1.27 % (1187819)Also succeeded, but the first one will report.
% 2.58/1.27 % (1187821)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3000554159:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.58/1.27 % (1187810)Refutation found. Thanks to Tanya!
% 2.58/1.27 % SZS status Theorem for theBenchmark
% 2.58/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.47 % (1187810)------------------------------
% 3.56/1.47 % (1187810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (1187810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (1187810)CaDiCaL version: 2.1.3
% 3.56/1.47 % (1187810)Termination reason: Refutation
% 3.56/1.47 % (1187810)Time elapsed: 0.014 s
% 3.56/1.47 % (1187810)Peak memory usage: 90 MB
% 3.56/1.47 % (1187810)Instructions burned: 17 (million)
% 3.56/1.47 % (1187810)------------------------------
% 3.56/1.47 % (1187810)------------------------------
% 3.56/1.47 % (1187800)Success in time 0.422 s
% 3.56/1.47 % Vampire exiting
%------------------------------------------------------------------------------