%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU291+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 : n017.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 12:52:44 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 20
% Syntax : Number of formulae : 152 ( 29 unt; 8 def)
% Number of atoms : 401 ( 86 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 399 ( 150 ~; 186 |; 32 &)
% ( 15 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 153 ( 0 sgn 144 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f14,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(f18,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f23,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f26,axiom,
! [X0,X1] :
? [X2] :
( relation_of2(X2,X0,X1)
& relation(X2)
& function(X2)
& quasi_total(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
fof(f39,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f40,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(f42,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
fof(f46,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f49,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f52,conjecture,
! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( subset(X1,X2)
=> ( ( X1 = empty_set
& X0 != empty_set )
| ( function(X3)
& quasi_total(X3,X0,X2)
& relation_of2_as_subset(X3,X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
fof(f53,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( subset(X1,X2)
=> ( ( X1 = empty_set
& X0 != empty_set )
| ( function(X3)
& quasi_total(X3,X0,X2)
& relation_of2_as_subset(X3,X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f56,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f18]) ).
fof(f64,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f4]) ).
fof(f67,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,[],[f6]) ).
fof(f68,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,[],[f67]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f73,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f74,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f73]) ).
fof(f77,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f78]) ).
fof(f83,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f46]) ).
fof(f87,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f90,plain,
? [X0,X1,X2,X3] :
( ( empty_set != X1
| empty_set = X0 )
& ( ~ function(X3)
| ~ quasi_total(X3,X0,X2)
| ~ relation_of2_as_subset(X3,X0,X2) )
& subset(X1,X2)
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f91,plain,
? [X0,X1,X2,X3] :
( ( empty_set != X1
| empty_set = X0 )
& ( ~ function(X3)
| ~ quasi_total(X3,X0,X2)
| ~ relation_of2_as_subset(X3,X0,X2) )
& subset(X1,X2)
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(flattening,[],[f90]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set != X0
| relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set = X1
| relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set = X1
| relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f108,plain,
empty(empty_set),
inference(cnf_transformation,[],[f56]) ).
fof(f114,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f119,plain,
! [X0,X1] : quasi_total(sK4(X0,X1),X0,X1),
inference(cnf_transformation,[],[f26]) ).
fof(f121,plain,
! [X0,X1] : relation(sK4(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f122,plain,
! [X0,X1] : relation_of2(sK4(X0,X1),X0,X1),
inference(cnf_transformation,[],[f26]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f149,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f156,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f83]) ).
fof(f159,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f87]) ).
fof(f162,plain,
( empty_set = sK17
| empty_set != sK18 ),
inference(cnf_transformation,[],[f91]) ).
fof(f163,plain,
( ~ relation_of2_as_subset(sK20,sK17,sK19)
| ~ quasi_total(sK20,sK17,sK19)
| ~ function(sK20) ),
inference(cnf_transformation,[],[f91]) ).
fof(f164,plain,
relation_of2_as_subset(sK20,sK17,sK18),
inference(cnf_transformation,[],[f91]) ).
fof(f165,plain,
quasi_total(sK20,sK17,sK18),
inference(cnf_transformation,[],[f91]) ).
fof(f166,plain,
function(sK20),
inference(cnf_transformation,[],[f91]) ).
fof(f167,plain,
subset(sK18,sK19),
inference(cnf_transformation,[],[f91]) ).
fof(f171,plain,
! [X2,X1] :
( ~ relation_of2_as_subset(X2,empty_set,X1)
| empty_set = relation_dom_as_subset(empty_set,X1,X2)
| ~ quasi_total(X2,empty_set,X1) ),
inference(equality_resolution,[],[f97]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ quasi_total(X2,X0,X1)
| empty_set = X1
| relation_dom_as_subset(X0,X1,X2) = X0
| relation_of2_as_subset(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f176,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) != X0
| empty_set = X1
| relation_of2_as_subset(X2,X0,X1)
| quasi_total(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f98]) ).
fof(f177,plain,
! [X2,X1] :
( ~ quasi_total(X2,empty_set,X1)
| empty_set = relation_dom_as_subset(empty_set,X1,X2)
| relation_of2_as_subset(X2,empty_set,X1) ),
inference(consistent_polarity_flipping,[],[f171]) ).
fof(f179,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| relation_of2_as_subset(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f103]) ).
fof(f181,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f149]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f148]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X2,X1)
| subset(X0,X1)
| relation_of2_as_subset(X3,X2,X0) ),
inference(consistent_polarity_flipping,[],[f151]) ).
fof(f187,plain,
! [X0] :
( subset(X0,empty_set)
| empty_set = X0 ),
inference(consistent_polarity_flipping,[],[f156]) ).
fof(f188,plain,
~ subset(sK18,sK19),
inference(consistent_polarity_flipping,[],[f167]) ).
fof(f189,plain,
~ relation_of2_as_subset(sK20,sK17,sK18),
inference(consistent_polarity_flipping,[],[f164]) ).
fof(f190,plain,
( relation_of2_as_subset(sK20,sK17,sK19)
| ~ quasi_total(sK20,sK17,sK19)
| ~ function(sK20) ),
inference(consistent_polarity_flipping,[],[f163]) ).
fof(f192,definition,
( spl21_1
<=> empty_set = sK18 ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f193,plain,
( empty_set = sK18
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f194,plain,
( empty_set != sK18
| spl21_1 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f196,definition,
( spl21_2
<=> empty_set = sK17 ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f198,plain,
( empty_set = sK17
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f199,plain,
( ~ spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f162,f196,f192]) ).
fof(f201,definition,
( spl21_3
<=> function(sK20) ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
fof(f205,definition,
( spl21_4
<=> quasi_total(sK20,sK17,sK19) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
fof(f207,plain,
( ~ quasi_total(sK20,sK17,sK19)
| spl21_4 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f209,definition,
( spl21_5
<=> relation_of2_as_subset(sK20,sK17,sK19) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f211,plain,
( relation_of2_as_subset(sK20,sK17,sK19)
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
( ~ spl21_3
| ~ spl21_4
| spl21_5 ),
inference(avatar_split_clause,[],[f190,f209,f205,f201]) ).
fof(f213,plain,
spl21_3,
inference(avatar_split_clause,[],[f166,f201]) ).
fof(f260,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f179,f95]) ).
fof(f263,plain,
! [X0,X1] : relation_dom_as_subset(X0,X1,sK4(X0,X1)) = relation_dom(sK4(X0,X1)),
inference(resolution,[],[f147,f122]) ).
fof(f265,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(resolution,[],[f147,f181]) ).
fof(f279,plain,
! [X0] :
( empty_set = relation_dom_as_subset(empty_set,X0,sK4(empty_set,X0))
| relation_of2_as_subset(sK4(empty_set,X0),empty_set,X0) ),
inference(resolution,[],[f177,f119]) ).
fof(f283,plain,
( empty_set = sK18
| sK17 = relation_dom_as_subset(sK17,sK18,sK20)
| relation_of2_as_subset(sK20,sK17,sK18) ),
inference(resolution,[],[f175,f165]) ).
fof(f287,plain,
( sK17 = relation_dom_as_subset(sK17,sK18,sK20)
| relation_of2_as_subset(sK20,sK17,sK18)
| spl21_1 ),
inference(forward_subsumption_resolution,[],[f283,f194]) ).
fof(f288,plain,
( sK17 = relation_dom_as_subset(sK17,sK18,sK20)
| spl21_1 ),
inference(forward_subsumption_resolution,[],[f287,f189]) ).
fof(f293,definition,
( spl21_6
<=> relation_of2(sK20,sK17,sK18) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
fof(f294,plain,
( relation_of2(sK20,sK17,sK18)
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f295,plain,
( ~ relation_of2(sK20,sK17,sK18)
| spl21_6 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f301,plain,
( relation_of2_as_subset(sK20,sK17,sK18)
| spl21_6 ),
inference(resolution,[],[f295,f181]) ).
fof(f302,plain,
( $false
| spl21_6 ),
inference(forward_subsumption_resolution,[],[f301,f189]) ).
fof(f303,plain,
spl21_6,
inference(avatar_contradiction_clause,[],[f302]) ).
fof(f321,plain,
( relation_dom_as_subset(sK17,sK18,sK20) = relation_dom(sK20)
| ~ spl21_6 ),
inference(resolution,[],[f294,f147]) ).
fof(f322,plain,
( sK17 = relation_dom(sK20)
| spl21_1
| ~ spl21_6 ),
inference(forward_demodulation,[],[f321,f288]) ).
fof(f323,plain,
relation(sK20),
inference(resolution,[],[f260,f189]) ).
fof(f373,definition,
( spl21_8
<=> empty(sK20) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
fof(f374,plain,
( empty(sK20)
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f401,plain,
relation_dom_as_subset(sK17,sK18,sK20) = relation_dom(sK20),
inference(resolution,[],[f265,f189]) ).
fof(f403,plain,
! [X2,X3,X0,X1] :
( subset(X3,X1)
| relation_of2_as_subset(X2,X0,X3)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(resolution,[],[f265,f184]) ).
fof(f424,plain,
! [X0] :
( relation_of2_as_subset(sK4(empty_set,X0),empty_set,X0)
| empty_set = relation_dom(sK4(empty_set,X0)) ),
inference(forward_demodulation,[],[f279,f263]) ).
fof(f426,plain,
! [X0] :
( empty_set = relation_dom(sK4(empty_set,X0))
| ~ relation_of2(sK4(empty_set,X0),empty_set,X0) ),
inference(resolution,[],[f424,f182]) ).
fof(f427,plain,
! [X0] : empty_set = relation_dom(sK4(empty_set,X0)),
inference(forward_subsumption_resolution,[],[f426,f122]) ).
fof(f445,plain,
! [X0] :
( ~ empty(empty_set)
| empty(sK4(empty_set,X0))
| ~ relation(sK4(empty_set,X0)) ),
inference(superposition,[],[f114,f427]) ).
fof(f448,plain,
! [X0] :
( empty(sK4(empty_set,X0))
| ~ relation(sK4(empty_set,X0)) ),
inference(forward_subsumption_resolution,[],[f445,f108]) ).
fof(f449,plain,
! [X0] : empty(sK4(empty_set,X0)),
inference(forward_subsumption_resolution,[],[f448,f121]) ).
fof(f470,plain,
! [X0] : empty_set = sK4(empty_set,X0),
inference(resolution,[],[f449,f159]) ).
fof(f491,plain,
! [X0] : quasi_total(empty_set,empty_set,X0),
inference(superposition,[],[f119,f470]) ).
fof(f1021,plain,
! [X0] :
( subset(sK18,X0)
| relation_dom(sK20) = relation_dom_as_subset(sK17,X0,sK20) ),
inference(resolution,[],[f403,f189]) ).
fof(f1025,plain,
( ! [X0] :
( subset(sK18,X0)
| sK17 = relation_dom_as_subset(sK17,X0,sK20) )
| spl21_1
| ~ spl21_6 ),
inference(forward_demodulation,[],[f1021,f322]) ).
fof(f1056,plain,
( sK17 = relation_dom_as_subset(sK17,sK19,sK20)
| spl21_1
| ~ spl21_6 ),
inference(resolution,[],[f1025,f188]) ).
fof(f1073,plain,
( sK17 != sK17
| empty_set = sK19
| relation_of2_as_subset(sK20,sK17,sK19)
| quasi_total(sK20,sK17,sK19)
| spl21_1
| ~ spl21_6 ),
inference(superposition,[],[f176,f1056]) ).
fof(f1075,plain,
( empty_set = sK19
| relation_of2_as_subset(sK20,sK17,sK19)
| quasi_total(sK20,sK17,sK19)
| spl21_1
| ~ spl21_6 ),
inference(trivial_inequality_removal,[],[f1073]) ).
fof(f1076,plain,
( empty_set = sK19
| relation_of2_as_subset(sK20,sK17,sK19)
| spl21_1
| spl21_4
| ~ spl21_6 ),
inference(forward_subsumption_resolution,[],[f1075,f207]) ).
fof(f1078,definition,
( spl21_17
<=> empty_set = sK19 ),
introduced(definition,[new_symbols(definition,[spl21_17])],[avatar_definition]) ).
fof(f1080,plain,
( empty_set = sK19
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f1081,plain,
( spl21_5
| spl21_17
| spl21_1
| spl21_4
| ~ spl21_6 ),
inference(avatar_split_clause,[],[f1076,f293,f205,f192,f1078,f209]) ).
fof(f1082,plain,
( ! [X0] :
( relation_of2_as_subset(sK20,sK17,X0)
| subset(X0,sK19) )
| ~ spl21_5 ),
inference(resolution,[],[f211,f184]) ).
fof(f1085,plain,
( subset(sK18,sK19)
| ~ spl21_5 ),
inference(resolution,[],[f1082,f189]) ).
fof(f1088,plain,
( $false
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f1085,f188]) ).
fof(f1089,plain,
~ spl21_5,
inference(avatar_contradiction_clause,[],[f1088]) ).
fof(f1098,plain,
( ~ subset(sK18,empty_set)
| ~ spl21_17 ),
inference(superposition,[],[f188,f1080]) ).
fof(f1100,plain,
( empty_set = sK18
| ~ spl21_17 ),
inference(resolution,[],[f1098,f187]) ).
fof(f1114,plain,
( spl21_1
| ~ spl21_17 ),
inference(avatar_split_clause,[],[f1100,f1078,f192]) ).
fof(f1126,plain,
( quasi_total(sK20,empty_set,sK18)
| ~ spl21_2 ),
inference(superposition,[],[f165,f198]) ).
fof(f1127,plain,
( ~ relation_of2_as_subset(sK20,empty_set,sK18)
| ~ spl21_2 ),
inference(superposition,[],[f189,f198]) ).
fof(f1142,plain,
( ~ relation_of2_as_subset(sK20,empty_set,empty_set)
| ~ spl21_1
| ~ spl21_2 ),
inference(forward_demodulation,[],[f1127,f193]) ).
fof(f1143,plain,
( quasi_total(sK20,empty_set,empty_set)
| ~ spl21_1
| ~ spl21_2 ),
inference(forward_demodulation,[],[f1126,f193]) ).
fof(f1166,plain,
( empty_set = relation_dom_as_subset(empty_set,empty_set,sK20)
| relation_of2_as_subset(sK20,empty_set,empty_set)
| ~ spl21_1
| ~ spl21_2 ),
inference(resolution,[],[f1143,f177]) ).
fof(f1169,plain,
( empty_set = relation_dom_as_subset(empty_set,empty_set,sK20)
| ~ spl21_1
| ~ spl21_2 ),
inference(forward_subsumption_resolution,[],[f1166,f1142]) ).
fof(f1186,plain,
( relation_dom(sK20) = relation_dom_as_subset(sK17,empty_set,sK20)
| ~ spl21_1 ),
inference(forward_demodulation,[],[f401,f193]) ).
fof(f1187,plain,
( relation_dom(sK20) = relation_dom_as_subset(empty_set,empty_set,sK20)
| ~ spl21_1
| ~ spl21_2 ),
inference(forward_demodulation,[],[f1186,f198]) ).
fof(f1188,plain,
( empty_set = relation_dom(sK20)
| ~ spl21_1
| ~ spl21_2 ),
inference(forward_demodulation,[],[f1187,f1169]) ).
fof(f1190,plain,
( ~ empty(empty_set)
| empty(sK20)
| ~ relation(sK20)
| ~ spl21_1
| ~ spl21_2 ),
inference(superposition,[],[f114,f1188]) ).
fof(f1193,plain,
( empty(sK20)
| ~ relation(sK20)
| ~ spl21_1
| ~ spl21_2 ),
inference(forward_subsumption_resolution,[],[f1190,f108]) ).
fof(f1197,plain,
( empty(sK20)
| ~ spl21_1
| ~ spl21_2 ),
inference(forward_subsumption_resolution,[],[f1193,f323]) ).
fof(f1198,plain,
( spl21_8
| ~ spl21_1
| ~ spl21_2 ),
inference(avatar_split_clause,[],[f1197,f196,f192,f373]) ).
fof(f1201,plain,
( empty_set = sK20
| ~ spl21_8 ),
inference(resolution,[],[f374,f159]) ).
fof(f1218,plain,
( ~ quasi_total(empty_set,sK17,sK19)
| spl21_4
| ~ spl21_8 ),
inference(superposition,[],[f207,f1201]) ).
fof(f1234,plain,
( ~ quasi_total(empty_set,empty_set,sK19)
| ~ spl21_2
| spl21_4
| ~ spl21_8 ),
inference(forward_demodulation,[],[f1218,f198]) ).
fof(f1238,plain,
( $false
| ~ spl21_2
| spl21_4
| ~ spl21_8 ),
inference(forward_subsumption_resolution,[],[f1234,f491]) ).
fof(f1239,plain,
( ~ spl21_2
| spl21_4
| ~ spl21_8 ),
inference(avatar_contradiction_clause,[],[f1238]) ).
cnf(s1,plain,
( ~ spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f199]) ).
cnf(s2,plain,
( ~ spl21_3
| ~ spl21_4
| spl21_5 ),
inference(sat_conversion,[],[f212]) ).
cnf(s3,plain,
spl21_3,
inference(sat_conversion,[],[f213]) ).
cnf(s5,plain,
spl21_6,
inference(sat_conversion,[],[f303]) ).
cnf(s27,plain,
( spl21_1
| spl21_4
| spl21_5
| ~ spl21_6
| spl21_17 ),
inference(sat_conversion,[],[f1081]) ).
cnf(s28,plain,
~ spl21_5,
inference(sat_conversion,[],[f1089]) ).
cnf(s31,plain,
( spl21_1
| ~ spl21_17 ),
inference(sat_conversion,[],[f1114]) ).
cnf(s37,plain,
( ~ spl21_1
| ~ spl21_2
| spl21_8 ),
inference(sat_conversion,[],[f1198]) ).
cnf(s39,plain,
( ~ spl21_2
| spl21_4
| ~ spl21_8 ),
inference(sat_conversion,[],[f1239]) ).
cnf(s40,plain,
( spl21_1
| spl21_4
| ~ spl21_6
| spl21_17 ),
inference(rat,[],[s27,s28]) ).
cnf(s43,plain,
~ spl21_4,
inference(rat,[],[s2,s28,s3]) ).
cnf(s44,plain,
spl21_1,
inference(rat,[],[s40,s31,s5,s43]) ).
cnf(s45,plain,
spl21_2,
inference(rat,[],[s1,s44]) ).
cnf(s46,plain,
~ spl21_8,
inference(rat,[],[s39,s43,s45]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s37,s44,s46,s45]) ).
fof(f1242,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU291+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:27:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.16/0.46 % (3200796)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (3200802)% WARNING: option uhcvi not known.
% 0.16/0.46 % (3200802)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1864626232:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (3200801)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1224912967_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (3200803)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3946898984:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (3200806)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3932101751:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (3200804)dis+10_1_sil=32000:sp=arity:random_seed=2396518224:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (3200805)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3175911178:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (3200807)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1814554278:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % (3200802) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3200796-3200802"...
% 0.16/0.46 % (3200802)...printing done.
% 0.16/0.46 % (3200802)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3200802)------------------------------
% 0.16/0.47 % (3200802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3200802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3200802)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3200802)Termination reason: Refutation
% 0.16/0.47 % (3200802)Time elapsed: 0.014 s
% 0.16/0.47 % (3200802)Peak memory usage: 13 MB
% 0.16/0.47 % (3200802)Instructions burned: 32 (million)
% 0.16/0.47 % (3200796)Success in time 0.043 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------