%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU339+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:48:25 PM UTC 2026
% Result : Theorem 4.27s 1.59s
% Output : Refutation 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 25
% Syntax : Number of formulae : 138 ( 29 unt; 13 def)
% Number of atoms : 426 ( 20 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 500 ( 212 ~; 198 |; 50 &)
% ( 21 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 13 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn 161 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ( antisymmetric_relstr(X0)
<=> is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_orders_2) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f18,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f37,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f39,conjecture,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( related(X0,X1,X2)
& related(X0,X2,X1) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_orders_2) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( related(X0,X1,X2)
& related(X0,X2,X1) )
=> X1 = X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f44,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f53,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ( antisymmetric_relstr(X0)
<=> is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f59,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& related(X0,X1,X2)
& related(X0,X2,X1)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f65,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& related(X0,X1,X2)
& related(X0,X2,X1)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& antisymmetric_relstr(X0)
& rel_str(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f67,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f69,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f44]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f55]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X4),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ( sK0(X0,X1) != sK1(X0,X1)
& in(sK0(X0,X1),X1)
& in(sK1(X0,X1),X1)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X4),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f76]) ).
fof(f78,plain,
! [X0] :
( ( ( antisymmetric_relstr(X0)
| ~ is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) )
& ( is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0))
| ~ antisymmetric_relstr(X0) ) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f56]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0)) )
& ( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
( sK11 != sK12
& related(sK10,sK11,sK12)
& related(sK10,sK12,sK11)
& element(sK12,the_carrier(sK10))
& element(sK11,the_carrier(sK10))
& antisymmetric_relstr(sK10)
& rel_str(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f65]) ).
fof(f93,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f53]) ).
fof(f95,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X4),X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f101,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f102,plain,
! [X0] :
( ~ antisymmetric_relstr(X0)
| is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f104,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f58]) ).
fof(f107,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f130,plain,
rel_str(sK10),
inference(cnf_transformation,[],[f91]) ).
fof(f131,plain,
antisymmetric_relstr(sK10),
inference(cnf_transformation,[],[f91]) ).
fof(f132,plain,
element(sK11,the_carrier(sK10)),
inference(cnf_transformation,[],[f91]) ).
fof(f133,plain,
element(sK12,the_carrier(sK10)),
inference(cnf_transformation,[],[f91]) ).
fof(f134,plain,
related(sK10,sK12,sK11),
inference(cnf_transformation,[],[f91]) ).
fof(f135,plain,
related(sK10,sK11,sK12),
inference(cnf_transformation,[],[f91]) ).
fof(f136,plain,
sK11 != sK12,
inference(cnf_transformation,[],[f91]) ).
fof(f137,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f139,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| ~ empty(X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f146,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f95,f101,f101]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ related(X0,X1,X2)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f104,f101]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f126,f101]) ).
fof(f152,definition,
! [X0,X1] :
( sQ13_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ13_eqProxy])],[equality_proxy_definition]) ).
fof(f155,plain,
! [X0,X1,X4,X5] :
( sQ13_eqProxy(X4,X5)
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f146,f152]) ).
fof(f156,plain,
~ sQ13_eqProxy(sK11,sK12),
inference(equality_proxy_replacement,[],[f136,f152]) ).
fof(f191,definition,
( spl14_4
<=> in(sK12,the_carrier(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f195,definition,
( spl14_5
<=> in(sK11,the_carrier(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f199,plain,
( is_antisymmetric_in(the_InternalRel(sK10),the_carrier(sK10))
| ~ rel_str(sK10) ),
inference(resolution,[],[f102,f131]) ).
fof(f201,definition,
( spl14_6
<=> rel_str(sK10) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
fof(f202,plain,
( ~ rel_str(sK10)
| spl14_6 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,definition,
( spl14_7
<=> is_antisymmetric_in(the_InternalRel(sK10),the_carrier(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
fof(f205,plain,
( is_antisymmetric_in(the_InternalRel(sK10),the_carrier(sK10))
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f206,plain,
( ~ spl14_6
| spl14_7 ),
inference(avatar_split_clause,[],[f199,f204,f201]) ).
fof(f207,plain,
( $false
| spl14_6 ),
inference(resolution,[],[f202,f130]) ).
fof(f208,plain,
spl14_6,
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f236,plain,
! [X0] :
( ~ rel_str(X0)
| element(the_InternalRel(X0),powerset(cartesian_product2(the_carrier(X0),the_carrier(X0)))) ),
inference(resolution,[],[f106,f107]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| in(X0,X2)
| empty(X2) ),
inference(resolution,[],[f139,f137]) ).
fof(f255,plain,
( in(unordered_pair(unordered_pair(sK12,sK11),singleton(sK12)),the_InternalRel(sK10))
| ~ element(sK11,the_carrier(sK10))
| ~ element(sK12,the_carrier(sK10))
| ~ rel_str(sK10) ),
inference(resolution,[],[f148,f134]) ).
fof(f256,plain,
( in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),the_InternalRel(sK10))
| ~ element(sK12,the_carrier(sK10))
| ~ element(sK11,the_carrier(sK10))
| ~ rel_str(sK10) ),
inference(resolution,[],[f148,f135]) ).
fof(f260,definition,
( spl14_8
<=> element(sK11,the_carrier(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
fof(f261,plain,
( ~ element(sK11,the_carrier(sK10))
| spl14_8 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f263,definition,
( spl14_9
<=> element(sK12,the_carrier(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
fof(f264,plain,
( ~ element(sK12,the_carrier(sK10))
| spl14_9 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,definition,
( spl14_10
<=> in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),the_InternalRel(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition]) ).
fof(f267,plain,
( in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),the_InternalRel(sK10))
| ~ spl14_10 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( ~ spl14_6
| ~ spl14_8
| ~ spl14_9
| spl14_10 ),
inference(avatar_split_clause,[],[f256,f266,f263,f260,f201]) ).
fof(f270,definition,
( spl14_11
<=> in(unordered_pair(unordered_pair(sK12,sK11),singleton(sK12)),the_InternalRel(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
fof(f271,plain,
( in(unordered_pair(unordered_pair(sK12,sK11),singleton(sK12)),the_InternalRel(sK10))
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f272,plain,
( ~ spl14_6
| ~ spl14_9
| ~ spl14_8
| spl14_11 ),
inference(avatar_split_clause,[],[f255,f270,f260,f263,f201]) ).
fof(f273,plain,
( $false
| spl14_8 ),
inference(resolution,[],[f261,f132]) ).
fof(f276,plain,
spl14_8,
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f277,plain,
( $false
| spl14_9 ),
inference(resolution,[],[f264,f133]) ).
fof(f280,plain,
spl14_9,
inference(avatar_contradiction_clause,[],[f277]) ).
fof(f285,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(sK12,X0)
| ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),X1)
| ~ in(unordered_pair(unordered_pair(sK12,sK11),singleton(sK12)),X1)
| ~ is_antisymmetric_in(X1,X0)
| ~ in(sK11,X0) ),
inference(resolution,[],[f155,f156]) ).
fof(f288,plain,
! [X2,X3,X0,X1] :
( ~ is_antisymmetric_in(X1,X0)
| ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),X1)
| ~ in(unordered_pair(unordered_pair(sK12,sK11),singleton(sK12)),X1)
| ~ in(sK12,X0)
| ~ in(sK11,X0)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(resolution,[],[f285,f93]) ).
fof(f294,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK11,sK12),singleton(sK11)),the_InternalRel(sK10))
| ~ in(unordered_pair(unordered_pair(sK12,sK11),singleton(sK12)),the_InternalRel(sK10))
| ~ in(sK12,the_carrier(sK10))
| ~ in(sK11,the_carrier(sK10))
| ~ element(the_InternalRel(sK10),powerset(cartesian_product2(X0,X1))) )
| ~ spl14_7 ),
inference(resolution,[],[f288,f205]) ).
fof(f456,plain,
element(the_InternalRel(sK10),powerset(cartesian_product2(the_carrier(sK10),the_carrier(sK10)))),
inference(resolution,[],[f236,f130]) ).
fof(f556,plain,
! [X0] :
( ~ in(X0,the_InternalRel(sK10))
| ~ empty(cartesian_product2(the_carrier(sK10),the_carrier(sK10))) ),
inference(resolution,[],[f456,f140]) ).
fof(f566,definition,
( spl14_14
<=> empty(cartesian_product2(the_carrier(sK10),the_carrier(sK10))) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
fof(f569,definition,
( spl14_15
<=> ! [X0] : ~ in(X0,the_InternalRel(sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
fof(f570,plain,
( ! [X0] : ~ in(X0,the_InternalRel(sK10))
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f571,plain,
( ~ spl14_14
| spl14_15 ),
inference(avatar_split_clause,[],[f556,f569,f566]) ).
fof(f646,plain,
! [X0] :
( ~ in(X0,the_InternalRel(sK10))
| in(X0,cartesian_product2(the_carrier(sK10),the_carrier(sK10)))
| empty(cartesian_product2(the_carrier(sK10),the_carrier(sK10))) ),
inference(resolution,[],[f237,f456]) ).
fof(f653,definition,
( spl14_16
<=> ! [X0] :
( ~ in(X0,the_InternalRel(sK10))
| in(X0,cartesian_product2(the_carrier(sK10),the_carrier(sK10))) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
fof(f654,plain,
( ! [X0] :
( in(X0,cartesian_product2(the_carrier(sK10),the_carrier(sK10)))
| ~ in(X0,the_InternalRel(sK10)) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f655,plain,
( spl14_14
| spl14_16 ),
inference(avatar_split_clause,[],[f646,f653,f566]) ).
fof(f657,plain,
( $false
| ~ spl14_11
| ~ spl14_15 ),
inference(resolution,[],[f570,f271]) ).
fof(f659,plain,
( ~ spl14_11
| ~ spl14_15 ),
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f707,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),the_InternalRel(sK10))
| in(X1,the_carrier(sK10)) )
| ~ spl14_16 ),
inference(resolution,[],[f654,f151]) ).
fof(f878,definition,
( spl14_59
<=> ! [X0,X1] : ~ element(the_InternalRel(sK10),powerset(cartesian_product2(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl14_59])],[avatar_definition]) ).
fof(f879,plain,
( ! [X0,X1] : ~ element(the_InternalRel(sK10),powerset(cartesian_product2(X0,X1)))
| ~ spl14_59 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f884,plain,
( spl14_59
| ~ spl14_5
| ~ spl14_4
| ~ spl14_11
| ~ spl14_10
| ~ spl14_7 ),
inference(avatar_split_clause,[],[f294,f204,f266,f270,f191,f195,f878]) ).
fof(f1036,plain,
( in(sK12,the_carrier(sK10))
| ~ spl14_10
| ~ spl14_16 ),
inference(resolution,[],[f707,f267]) ).
fof(f1037,plain,
( in(sK11,the_carrier(sK10))
| ~ spl14_11
| ~ spl14_16 ),
inference(resolution,[],[f707,f271]) ).
fof(f1038,plain,
( spl14_5
| ~ spl14_11
| ~ spl14_16 ),
inference(avatar_split_clause,[],[f1037,f653,f270,f195]) ).
fof(f1039,plain,
( spl14_4
| ~ spl14_10
| ~ spl14_16 ),
inference(avatar_split_clause,[],[f1036,f653,f266,f191]) ).
fof(f1040,plain,
( $false
| ~ spl14_59 ),
inference(resolution,[],[f879,f456]) ).
fof(f1043,plain,
~ spl14_59,
inference(avatar_contradiction_clause,[],[f1040]) ).
cnf(s5,plain,
( ~ spl14_6
| spl14_7 ),
inference(sat_conversion,[],[f206]) ).
cnf(s6,plain,
spl14_6,
inference(sat_conversion,[],[f208]) ).
cnf(s7,plain,
( ~ spl14_6
| ~ spl14_8
| ~ spl14_9
| spl14_10 ),
inference(sat_conversion,[],[f268]) ).
cnf(s8,plain,
( ~ spl14_6
| ~ spl14_8
| ~ spl14_9
| spl14_11 ),
inference(sat_conversion,[],[f272]) ).
cnf(s9,plain,
spl14_8,
inference(sat_conversion,[],[f276]) ).
cnf(s10,plain,
spl14_9,
inference(sat_conversion,[],[f280]) ).
cnf(s12,plain,
( ~ spl14_14
| spl14_15 ),
inference(sat_conversion,[],[f571]) ).
cnf(s14,plain,
( spl14_14
| spl14_16 ),
inference(sat_conversion,[],[f655]) ).
cnf(s15,plain,
( ~ spl14_11
| ~ spl14_15 ),
inference(sat_conversion,[],[f659]) ).
cnf(s59,plain,
( ~ spl14_4
| ~ spl14_5
| ~ spl14_7
| ~ spl14_10
| ~ spl14_11
| spl14_59 ),
inference(sat_conversion,[],[f884]) ).
cnf(s74,plain,
( spl14_5
| ~ spl14_11
| ~ spl14_16 ),
inference(sat_conversion,[],[f1038]) ).
cnf(s75,plain,
( spl14_4
| ~ spl14_10
| ~ spl14_16 ),
inference(sat_conversion,[],[f1039]) ).
cnf(s76,plain,
~ spl14_59,
inference(sat_conversion,[],[f1043]) ).
cnf(s77,plain,
( ~ spl14_4
| ~ spl14_5
| ~ spl14_7
| ~ spl14_10
| ~ spl14_11 ),
inference(rat,[],[s59,s76]) ).
cnf(s79,plain,
( ~ spl14_6
| spl14_11 ),
inference(rat,[],[s8,s10,s9]) ).
cnf(s80,plain,
( ~ spl14_6
| spl14_10 ),
inference(rat,[],[s7,s10,s9]) ).
cnf(s81,plain,
spl14_11,
inference(rat,[],[s79,s6]) ).
cnf(s82,plain,
spl14_10,
inference(rat,[],[s80,s6]) ).
cnf(s83,plain,
~ spl14_15,
inference(rat,[],[s15,s81]) ).
cnf(s84,plain,
~ spl14_14,
inference(rat,[],[s12,s83]) ).
cnf(s85,plain,
spl14_16,
inference(rat,[],[s14,s84]) ).
cnf(s87,plain,
spl14_5,
inference(rat,[],[s74,s81,s85]) ).
cnf(s88,plain,
spl14_4,
inference(rat,[],[s75,s82,s85]) ).
cnf(s90,plain,
~ spl14_7,
inference(rat,[],[s77,s81,s82,s87,s88]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s5,s90,s6]) ).
fof(f1044,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU339+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n009.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 28 04:48:30 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/1.59 % (2666502)Detected formulas, will run a generic FOF schedule.
% 4.27/1.59 % (2666511)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=4068369288:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.27/1.59 % (2666515)dis-21_1_sil=8000:lcm=predicate:random_seed=2293926826: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)
% 4.27/1.59 % (2666515)First to succeed.
% 4.27/1.59 % (2666515)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2666502"
% 4.27/1.59 % (2666510)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=2905260629:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.27/1.59 % (2666509)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=2824250727:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.27/1.59 % (2666512)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2110230384:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.27/1.59 % (2666512)Refutation not found, incomplete strategy
% 4.27/1.59 % (2666512)------------------------------
% 4.27/1.59 % (2666512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.59 % (2666512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.59 % (2666512)CaDiCaL version: 2.1.3
% 4.27/1.59 % (2666512)Termination reason: Refutation not found, incomplete strategy
% 4.27/1.59 % (2666512)Time elapsed: 0.002 s
% 4.27/1.59 % (2666512)Peak memory usage: 88 MB
% 4.27/1.59 % (2666514)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3555723837:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.27/1.59 % (2666513)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=875004785:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.27/1.59 % (2666514)Also succeeded, but the first one will report.
% 4.27/1.59 % (2666513)Instruction limit reached!
% 4.27/1.59 % (2666513)------------------------------
% 4.27/1.59 % (2666513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.59 % (2666513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.59 % (2666513)CaDiCaL version: 2.1.3
% 4.27/1.59 % (2666513)Termination reason: Instruction limit
% 4.27/1.59 % (2666513)Termination phase: Saturation
% 4.27/1.59 % (2666513)Time elapsed: 0.117 s
% 4.27/1.59 % (2666513)Peak memory usage: 88 MB
% 4.27/1.59 % (2666513)Instructions burned: 120 (million)
% 4.27/1.59 % (2666515)Refutation found. Thanks to Tanya!
% 4.27/1.59 % SZS status Theorem for theBenchmark
% 4.27/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 5.20/1.88 % (2666515)------------------------------
% 5.20/1.88 % (2666515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.88 % (2666515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.88 % (2666515)CaDiCaL version: 2.1.3
% 5.20/1.88 % (2666515)Termination reason: Refutation
% 5.20/1.88 % (2666515)Time elapsed: 0.033 s
% 5.20/1.88 % (2666515)Peak memory usage: 90 MB
% 5.20/1.88 % (2666515)Instructions burned: 31 (million)
% 5.20/1.88 % (2666515)------------------------------
% 5.20/1.88 % (2666515)------------------------------
% 5.20/1.88 % (2666502)Success in time 0.63 s
% 5.20/1.88 % Vampire exiting
%------------------------------------------------------------------------------