%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU092+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:47:13 PM UTC 2026
% Result : Theorem 11.57s 7.52s
% Output : Refutation 12.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 32
% Syntax : Number of formulae : 190 ( 41 unt; 19 def)
% Number of atoms : 588 ( 83 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 673 ( 275 ~; 319 |; 44 &)
% ( 26 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 20 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-2 aty)
% Number of variables : 219 ( 0 sgn 203 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f15,axiom,
! [X0] :
( ( 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(f16,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f17,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f19,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& finite(X1) )
=> finite(relation_image(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(f66,axiom,
! [X0,X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = cartesian_product2(X0,X1)
& ! [X3] :
( in(X3,cartesian_product2(X0,X1))
=> apply(X2,X3) = pair_second(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e3_37__finset_1) ).
fof(f67,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f68,axiom,
! [X0,X1,X2] :
( in(X0,cartesian_product2(X1,X2))
=> ( in(pair_first(X0),X1)
& in(pair_second(X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_mcart_1) ).
fof(f69,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f72,conjecture,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
=> ( X0 = empty_set
| finite(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finset_1) ).
fof(f73,negated_conjecture,
~ ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
=> ( X0 = empty_set
| finite(X1) ) ),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f74,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f79,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f81,axiom,
! [X0,X1] :
( pair_first(ordered_pair(X0,X1)) = X0
& pair_second(ordered_pair(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(f119,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,[],[f15]) ).
fof(f120,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,[],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f122,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(flattening,[],[f121]) ).
fof(f141,plain,
! [X0,X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = cartesian_product2(X0,X1)
& ! [X3] :
( apply(X2,X3) = pair_second(X3)
| ~ in(X3,cartesian_product2(X0,X1)) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ( in(pair_first(X0),X1)
& in(pair_second(X0),X2) )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f68]) ).
fof(f143,plain,
! [X0] :
( relation_image(X0,relation_dom(X0)) = relation_rng(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f147,plain,
? [X0,X1] :
( empty_set != X0
& ~ finite(X1)
& finite(cartesian_product2(X0,X1)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f148,plain,
? [X0,X1] :
( empty_set != X0
& ~ finite(X1)
& finite(cartesian_product2(X0,X1)) ),
inference(flattening,[],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f74]) ).
fof(f150,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f149]) ).
fof(f156,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f159,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,[],[f120]) ).
fof(f160,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,[],[f159]) ).
fof(f161,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK0(X0,X1) )
| ~ in(sK0(X0,X1),X1) )
& ( ( in(sK1(X0,X1),relation_dom(X0))
& sK0(X0,X1) = apply(X0,sK1(X0,X1)) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK2(X0,X5),relation_dom(X0))
& apply(X0,sK2(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f160]) ).
fof(f162,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f17]) ).
fof(f188,plain,
! [X0,X1] :
( relation(sK29(X0,X1))
& function(sK29(X0,X1))
& cartesian_product2(X0,X1) = relation_dom(sK29(X0,X1))
& ! [X3] :
( pair_second(X3) = apply(sK29(X0,X1),X3)
| ~ in(X3,cartesian_product2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X2,sK29(X0,X1))],[f141]) ).
fof(f189,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,[],[f67]) ).
fof(f190,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,[],[f189]) ).
fof(f191,plain,
( empty_set != sK30
& ~ finite(sK31)
& finite(cartesian_product2(sK30,sK31)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30,sK31]),skolemize(X0,sK30),skolemize(X1,sK31)],[f148]) ).
fof(f217,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f221,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| sK0(X0,X1) = apply(X0,sK1(X0,X1))
| in(sK0(X0,X1),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f222,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(sK1(X0,X1),relation_dom(X0))
| in(sK0(X0,X1),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f223,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK0(X0,X1)
| ~ in(sK0(X0,X1),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f224,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f225,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f162]) ).
fof(f228,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f339,plain,
! [X3,X0,X1] :
( pair_second(X3) = apply(sK29(X0,X1),X3)
| ~ in(X3,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f188]) ).
fof(f340,plain,
! [X0,X1] : cartesian_product2(X0,X1) = relation_dom(sK29(X0,X1)),
inference(cnf_transformation,[],[f188]) ).
fof(f341,plain,
! [X0,X1] : function(sK29(X0,X1)),
inference(cnf_transformation,[],[f188]) ).
fof(f342,plain,
! [X0,X1] : relation(sK29(X0,X1)),
inference(cnf_transformation,[],[f188]) ).
fof(f345,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f190]) ).
fof(f346,plain,
! [X2,X0,X1] :
( in(pair_second(X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f348,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f351,plain,
finite(cartesian_product2(sK30,sK31)),
inference(cnf_transformation,[],[f191]) ).
fof(f352,plain,
~ finite(sK31),
inference(cnf_transformation,[],[f191]) ).
fof(f353,plain,
empty_set != sK30,
inference(cnf_transformation,[],[f191]) ).
fof(f354,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f360,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f362,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(cnf_transformation,[],[f81]) ).
fof(f369,plain,
! [X3,X0,X1] :
( pair_second(X3) = apply(sK29(X0,X1),X3)
| ~ in(X3,relation_dom(sK29(X0,X1))) ),
inference(definition_unfolding,[],[f339,f340]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom(sK29(X2,X3)))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f345,f224,f340]) ).
fof(f374,plain,
! [X2,X0,X1] :
( in(pair_second(X0),X2)
| ~ in(X0,relation_dom(sK29(X1,X2))) ),
inference(definition_unfolding,[],[f346,f340]) ).
fof(f375,plain,
finite(relation_dom(sK29(sK30,sK31))),
inference(definition_unfolding,[],[f351,f340]) ).
fof(f377,plain,
! [X0,X1] : pair_second(unordered_pair(unordered_pair(X0,X1),singleton(X0))) = X1,
inference(definition_unfolding,[],[f362,f224]) ).
fof(f385,definition,
( spl34_1
<=> finite(relation_dom(sK29(sK30,sK31))) ),
introduced(definition,[new_symbols(definition,[spl34_1])],[avatar_definition]) ).
fof(f387,plain,
( finite(relation_dom(sK29(sK30,sK31)))
| ~ spl34_1 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f388,plain,
spl34_1,
inference(avatar_split_clause,[],[f375,f385]) ).
fof(f390,definition,
( spl34_2
<=> finite(sK31) ),
introduced(definition,[new_symbols(definition,[spl34_2])],[avatar_definition]) ).
fof(f392,plain,
( ~ finite(sK31)
| spl34_2 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f393,plain,
~ spl34_2,
inference(avatar_split_clause,[],[f352,f390]) ).
fof(f397,plain,
( ! [X0] :
( finite(relation_image(X0,relation_dom(sK29(sK30,sK31))))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl34_1 ),
inference(resolution,[],[f387,f228]) ).
fof(f402,definition,
( spl34_3
<=> empty_set = sK30 ),
introduced(definition,[new_symbols(definition,[spl34_3])],[avatar_definition]) ).
fof(f404,plain,
( empty_set != sK30
| spl34_3 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f405,plain,
~ spl34_3,
inference(avatar_split_clause,[],[f353,f402]) ).
fof(f431,definition,
( spl34_6
<=> ! [X0] :
( finite(relation_image(X0,relation_dom(sK29(sK30,sK31))))
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_6])],[avatar_definition]) ).
fof(f432,plain,
( ! [X0] :
( finite(relation_image(X0,relation_dom(sK29(sK30,sK31))))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl34_6 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f433,plain,
( spl34_6
| ~ spl34_1 ),
inference(avatar_split_clause,[],[f397,f385,f431]) ).
fof(f443,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ relation(sK29(sK30,sK31))
| ~ function(sK29(sK30,sK31))
| ~ relation(sK29(sK30,sK31))
| ~ spl34_6 ),
inference(superposition,[],[f432,f348]) ).
fof(f444,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ relation(sK29(sK30,sK31))
| ~ function(sK29(sK30,sK31))
| ~ spl34_6 ),
inference(duplicate_literal_removal,[],[f443]) ).
fof(f445,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ function(sK29(sK30,sK31))
| ~ spl34_6 ),
inference(forward_subsumption_resolution,[],[f444,f342]) ).
fof(f446,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ spl34_6 ),
inference(forward_subsumption_resolution,[],[f445,f341]) ).
fof(f448,definition,
( spl34_8
<=> finite(relation_rng(sK29(sK30,sK31))) ),
introduced(definition,[new_symbols(definition,[spl34_8])],[avatar_definition]) ).
fof(f450,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ spl34_8 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f451,plain,
( spl34_8
| ~ spl34_6 ),
inference(avatar_split_clause,[],[f446,f431,f448]) ).
fof(f457,plain,
( ! [X0] :
( finite(X0)
| sK0(sK29(sK30,sK31),X0) = apply(sK29(sK30,sK31),sK1(sK29(sK30,sK31),X0))
| in(sK0(sK29(sK30,sK31),X0),X0)
| ~ relation(sK29(sK30,sK31))
| ~ function(sK29(sK30,sK31)) )
| ~ spl34_8 ),
inference(superposition,[],[f450,f221]) ).
fof(f458,plain,
( ! [X0] :
( finite(X0)
| in(sK1(sK29(sK30,sK31),X0),relation_dom(sK29(sK30,sK31)))
| in(sK0(sK29(sK30,sK31),X0),X0)
| ~ relation(sK29(sK30,sK31))
| ~ function(sK29(sK30,sK31)) )
| ~ spl34_8 ),
inference(superposition,[],[f450,f222]) ).
fof(f459,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK29(sK30,sK31)))
| sK0(sK29(sK30,sK31),X0) != apply(sK29(sK30,sK31),X1)
| ~ in(sK0(sK29(sK30,sK31),X0),X0)
| ~ relation(sK29(sK30,sK31))
| ~ function(sK29(sK30,sK31)) )
| ~ spl34_8 ),
inference(superposition,[],[f450,f223]) ).
fof(f460,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK29(sK30,sK31)))
| sK0(sK29(sK30,sK31),X0) != apply(sK29(sK30,sK31),X1)
| ~ in(sK0(sK29(sK30,sK31),X0),X0)
| ~ function(sK29(sK30,sK31)) )
| ~ spl34_8 ),
inference(forward_subsumption_resolution,[],[f459,f342]) ).
fof(f461,plain,
( ! [X0] :
( finite(X0)
| in(sK1(sK29(sK30,sK31),X0),relation_dom(sK29(sK30,sK31)))
| in(sK0(sK29(sK30,sK31),X0),X0)
| ~ function(sK29(sK30,sK31)) )
| ~ spl34_8 ),
inference(forward_subsumption_resolution,[],[f458,f342]) ).
fof(f462,plain,
( ! [X0] :
( finite(X0)
| sK0(sK29(sK30,sK31),X0) = apply(sK29(sK30,sK31),sK1(sK29(sK30,sK31),X0))
| in(sK0(sK29(sK30,sK31),X0),X0)
| ~ function(sK29(sK30,sK31)) )
| ~ spl34_8 ),
inference(forward_subsumption_resolution,[],[f457,f342]) ).
fof(f463,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK29(sK30,sK31)))
| sK0(sK29(sK30,sK31),X0) != apply(sK29(sK30,sK31),X1)
| ~ in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_8 ),
inference(forward_subsumption_resolution,[],[f460,f341]) ).
fof(f464,plain,
( ! [X0] :
( finite(X0)
| in(sK1(sK29(sK30,sK31),X0),relation_dom(sK29(sK30,sK31)))
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_8 ),
inference(forward_subsumption_resolution,[],[f461,f341]) ).
fof(f465,plain,
( ! [X0] :
( finite(X0)
| sK0(sK29(sK30,sK31),X0) = apply(sK29(sK30,sK31),sK1(sK29(sK30,sK31),X0))
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_8 ),
inference(forward_subsumption_resolution,[],[f462,f341]) ).
fof(f484,definition,
( spl34_10
<=> ! [X0] :
( finite(X0)
| in(sK1(sK29(sK30,sK31),X0),relation_dom(sK29(sK30,sK31)))
| in(sK0(sK29(sK30,sK31),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_10])],[avatar_definition]) ).
fof(f485,plain,
( ! [X0] :
( in(sK1(sK29(sK30,sK31),X0),relation_dom(sK29(sK30,sK31)))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_10 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f486,plain,
( spl34_10
| ~ spl34_8 ),
inference(avatar_split_clause,[],[f464,f448,f484]) ).
fof(f487,plain,
( ! [X0] :
( finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0)
| in(pair_second(sK1(sK29(sK30,sK31),X0)),sK31) )
| ~ spl34_10 ),
inference(resolution,[],[f485,f374]) ).
fof(f521,definition,
( spl34_12
<=> ! [X0] :
( finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0)
| in(pair_second(sK1(sK29(sK30,sK31),X0)),sK31) ) ),
introduced(definition,[new_symbols(definition,[spl34_12])],[avatar_definition]) ).
fof(f522,plain,
( ! [X0] :
( in(pair_second(sK1(sK29(sK30,sK31),X0)),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0) )
| ~ spl34_12 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f523,plain,
( spl34_12
| ~ spl34_10 ),
inference(avatar_split_clause,[],[f487,f484,f521]) ).
fof(f535,definition,
( spl34_13
<=> ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK29(sK30,sK31)))
| sK0(sK29(sK30,sK31),X0) != apply(sK29(sK30,sK31),X1)
| ~ in(sK0(sK29(sK30,sK31),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_13])],[avatar_definition]) ).
fof(f536,plain,
( ! [X0,X1] :
( sK0(sK29(sK30,sK31),X0) != apply(sK29(sK30,sK31),X1)
| ~ in(X1,relation_dom(sK29(sK30,sK31)))
| finite(X0)
| ~ in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_13 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f537,plain,
( spl34_13
| ~ spl34_8 ),
inference(avatar_split_clause,[],[f463,f448,f535]) ).
fof(f538,plain,
( ! [X0,X1] :
( pair_second(X0) != sK0(sK29(sK30,sK31),X1)
| ~ in(X0,relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1)
| ~ in(X0,relation_dom(sK29(sK30,sK31))) )
| ~ spl34_13 ),
inference(superposition,[],[f536,f369]) ).
fof(f541,plain,
( ! [X0,X1] :
( pair_second(X0) != sK0(sK29(sK30,sK31),X1)
| ~ in(X0,relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1) )
| ~ spl34_13 ),
inference(duplicate_literal_removal,[],[f538]) ).
fof(f574,definition,
( spl34_16
<=> ! [X0,X1] :
( pair_second(X0) != sK0(sK29(sK30,sK31),X1)
| ~ in(X0,relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl34_16])],[avatar_definition]) ).
fof(f575,plain,
( ! [X0,X1] :
( pair_second(X0) != sK0(sK29(sK30,sK31),X1)
| ~ in(X0,relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1) )
| ~ spl34_16 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f576,plain,
( spl34_16
| ~ spl34_13 ),
inference(avatar_split_clause,[],[f541,f535,f574]) ).
fof(f577,plain,
( ! [X2,X0,X1] :
( sK0(sK29(sK30,sK31),X2) != X0
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),relation_dom(sK29(sK30,sK31)))
| finite(X2)
| ~ in(sK0(sK29(sK30,sK31),X2),X2) )
| ~ spl34_16 ),
inference(superposition,[],[f575,f377]) ).
fof(f578,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),relation_dom(sK29(sK30,sK31)))
| sK0(sK29(sK30,sK31),X2) != X0
| finite(X2)
| ~ in(sK0(sK29(sK30,sK31),X2),X2) )
| ~ spl34_16 ),
inference(forward_demodulation,[],[f577,f217]) ).
fof(f580,definition,
( spl34_17
<=> ! [X0] :
( finite(X0)
| sK0(sK29(sK30,sK31),X0) = apply(sK29(sK30,sK31),sK1(sK29(sK30,sK31),X0))
| in(sK0(sK29(sK30,sK31),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_17])],[avatar_definition]) ).
fof(f581,plain,
( ! [X0] :
( sK0(sK29(sK30,sK31),X0) = apply(sK29(sK30,sK31),sK1(sK29(sK30,sK31),X0))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_17 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f582,plain,
( spl34_17
| ~ spl34_8 ),
inference(avatar_split_clause,[],[f465,f448,f580]) ).
fof(f584,plain,
( ! [X0] :
( sK0(sK29(sK30,sK31),X0) = pair_second(sK1(sK29(sK30,sK31),X0))
| ~ in(sK1(sK29(sK30,sK31),X0),relation_dom(sK29(sK30,sK31)))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_17 ),
inference(superposition,[],[f369,f581]) ).
fof(f601,plain,
( ! [X0] :
( sK0(sK29(sK30,sK31),X0) = pair_second(sK1(sK29(sK30,sK31),X0))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_10
| ~ spl34_17 ),
inference(forward_subsumption_resolution,[],[f584,f485]) ).
fof(f613,definition,
( spl34_18
<=> ! [X0] :
( sK0(sK29(sK30,sK31),X0) = pair_second(sK1(sK29(sK30,sK31),X0))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_18])],[avatar_definition]) ).
fof(f614,plain,
( ! [X0] :
( sK0(sK29(sK30,sK31),X0) = pair_second(sK1(sK29(sK30,sK31),X0))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_18 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f615,plain,
( spl34_18
| ~ spl34_10
| ~ spl34_17 ),
inference(avatar_split_clause,[],[f601,f580,f484,f613]) ).
fof(f616,plain,
( ! [X0] :
( in(sK0(sK29(sK30,sK31),X0),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0)
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_12
| ~ spl34_18 ),
inference(superposition,[],[f522,f614]) ).
fof(f619,plain,
( ! [X0] :
( in(sK0(sK29(sK30,sK31),X0),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0) )
| ~ spl34_12
| ~ spl34_18 ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f1319,definition,
( spl34_53
<=> ! [X0] :
( in(sK0(sK29(sK30,sK31),X0),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_53])],[avatar_definition]) ).
fof(f1320,plain,
( ! [X0] :
( in(sK0(sK29(sK30,sK31),X0),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0) )
| ~ spl34_53 ),
inference(avatar_component_clause,[],[f1319]) ).
fof(f1321,plain,
( spl34_53
| ~ spl34_12
| ~ spl34_18 ),
inference(avatar_split_clause,[],[f619,f613,f521,f1319]) ).
fof(f1331,plain,
( in(sK0(sK29(sK30,sK31),sK31),sK31)
| finite(sK31)
| ~ spl34_53 ),
inference(factoring,[],[f1320]) ).
fof(f1332,plain,
( in(sK0(sK29(sK30,sK31),sK31),sK31)
| spl34_2
| ~ spl34_53 ),
inference(forward_subsumption_resolution,[],[f1331,f392]) ).
fof(f1340,definition,
( spl34_54
<=> in(sK0(sK29(sK30,sK31),sK31),sK31) ),
introduced(definition,[new_symbols(definition,[spl34_54])],[avatar_definition]) ).
fof(f1342,plain,
( in(sK0(sK29(sK30,sK31),sK31),sK31)
| ~ spl34_54 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1343,plain,
( spl34_54
| spl34_2
| ~ spl34_53 ),
inference(avatar_split_clause,[],[f1332,f1319,f390,f1340]) ).
fof(f1350,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK0(sK29(sK30,sK31),sK31)),singleton(X0)),relation_dom(sK29(X1,sK31)))
| ~ in(X0,X1) )
| ~ spl34_54 ),
inference(resolution,[],[f1342,f370]) ).
fof(f1354,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK0(sK29(sK30,sK31),sK31))),relation_dom(sK29(X1,sK31)))
| ~ in(X0,X1) )
| ~ spl34_54 ),
inference(forward_demodulation,[],[f1350,f217]) ).
fof(f1613,definition,
( spl34_69
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),relation_dom(sK29(sK30,sK31)))
| sK0(sK29(sK30,sK31),X2) != X0
| finite(X2)
| ~ in(sK0(sK29(sK30,sK31),X2),X2) ) ),
introduced(definition,[new_symbols(definition,[spl34_69])],[avatar_definition]) ).
fof(f1614,plain,
( ! [X2,X0,X1] :
( sK0(sK29(sK30,sK31),X2) != X0
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),relation_dom(sK29(sK30,sK31)))
| finite(X2)
| ~ in(sK0(sK29(sK30,sK31),X2),X2) )
| ~ spl34_69 ),
inference(avatar_component_clause,[],[f1613]) ).
fof(f1615,plain,
( spl34_69
| ~ spl34_16 ),
inference(avatar_split_clause,[],[f578,f574,f1613]) ).
fof(f1616,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK0(sK29(sK30,sK31),X1))),relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1) )
| ~ spl34_69 ),
inference(equality_resolution,[],[f1614]) ).
fof(f1618,definition,
( spl34_70
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK0(sK29(sK30,sK31),X1))),relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl34_70])],[avatar_definition]) ).
fof(f1619,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK0(sK29(sK30,sK31),X1))),relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1) )
| ~ spl34_70 ),
inference(avatar_component_clause,[],[f1618]) ).
fof(f1620,plain,
( spl34_70
| ~ spl34_69 ),
inference(avatar_split_clause,[],[f1616,f1613,f1618]) ).
fof(f3170,definition,
( spl34_141
<=> ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK0(sK29(sK30,sK31),sK31))),relation_dom(sK29(X1,sK31)))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl34_141])],[avatar_definition]) ).
fof(f3171,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK0(sK29(sK30,sK31),sK31))),relation_dom(sK29(X1,sK31)))
| ~ in(X0,X1) )
| ~ spl34_141 ),
inference(avatar_component_clause,[],[f3170]) ).
fof(f3172,plain,
( spl34_141
| ~ spl34_54 ),
inference(avatar_split_clause,[],[f1354,f1340,f3170]) ).
fof(f3177,plain,
( ! [X0] :
( ~ in(X0,sK30)
| finite(sK31)
| ~ in(sK0(sK29(sK30,sK31),sK31),sK31) )
| ~ spl34_70
| ~ spl34_141 ),
inference(resolution,[],[f3171,f1619]) ).
fof(f3197,plain,
( ! [X0] :
( ~ in(X0,sK30)
| ~ in(sK0(sK29(sK30,sK31),sK31),sK31) )
| spl34_2
| ~ spl34_70
| ~ spl34_141 ),
inference(forward_subsumption_resolution,[],[f3177,f392]) ).
fof(f3200,plain,
( ! [X0] : ~ in(X0,sK30)
| spl34_2
| ~ spl34_54
| ~ spl34_70
| ~ spl34_141 ),
inference(forward_subsumption_resolution,[],[f3197,f1342]) ).
fof(f3223,definition,
( spl34_142
<=> ! [X0] : ~ in(X0,sK30) ),
introduced(definition,[new_symbols(definition,[spl34_142])],[avatar_definition]) ).
fof(f3224,plain,
( ! [X0] : ~ in(X0,sK30)
| ~ spl34_142 ),
inference(avatar_component_clause,[],[f3223]) ).
fof(f3225,plain,
( spl34_142
| spl34_2
| ~ spl34_54
| ~ spl34_70
| ~ spl34_141 ),
inference(avatar_split_clause,[],[f3200,f3170,f1618,f1340,f390,f3223]) ).
fof(f3226,plain,
( ! [X0] :
( empty(sK30)
| ~ element(X0,sK30) )
| ~ spl34_142 ),
inference(resolution,[],[f3224,f354]) ).
fof(f4566,definition,
( spl34_189
<=> ! [X0] : ~ element(X0,sK30) ),
introduced(definition,[new_symbols(definition,[spl34_189])],[avatar_definition]) ).
fof(f4567,plain,
( ! [X0] : ~ element(X0,sK30)
| ~ spl34_189 ),
inference(avatar_component_clause,[],[f4566]) ).
fof(f4569,definition,
( spl34_190
<=> empty(sK30) ),
introduced(definition,[new_symbols(definition,[spl34_190])],[avatar_definition]) ).
fof(f4571,plain,
( empty(sK30)
| ~ spl34_190 ),
inference(avatar_component_clause,[],[f4569]) ).
fof(f4572,plain,
( spl34_189
| spl34_190
| ~ spl34_142 ),
inference(avatar_split_clause,[],[f3226,f3223,f4569,f4566]) ).
fof(f4594,plain,
( empty_set = sK30
| ~ spl34_190 ),
inference(resolution,[],[f4571,f360]) ).
fof(f4599,plain,
( $false
| spl34_3
| ~ spl34_190 ),
inference(forward_subsumption_resolution,[],[f4594,f404]) ).
fof(f4600,plain,
( spl34_3
| ~ spl34_190 ),
inference(avatar_contradiction_clause,[],[f4599]) ).
fof(f4635,plain,
( $false
| ~ spl34_189 ),
inference(resolution,[],[f4567,f225]) ).
fof(f4636,plain,
~ spl34_189,
inference(avatar_contradiction_clause,[],[f4635]) ).
cnf(s1,plain,
spl34_1,
inference(sat_conversion,[],[f388]) ).
cnf(s2,plain,
~ spl34_2,
inference(sat_conversion,[],[f393]) ).
cnf(s3,plain,
~ spl34_3,
inference(sat_conversion,[],[f405]) ).
cnf(s6,plain,
( ~ spl34_1
| spl34_6 ),
inference(sat_conversion,[],[f433]) ).
cnf(s8,plain,
( ~ spl34_6
| spl34_8 ),
inference(sat_conversion,[],[f451]) ).
cnf(s10,plain,
( ~ spl34_8
| spl34_10 ),
inference(sat_conversion,[],[f486]) ).
cnf(s12,plain,
( ~ spl34_10
| spl34_12 ),
inference(sat_conversion,[],[f523]) ).
cnf(s13,plain,
( ~ spl34_8
| spl34_13 ),
inference(sat_conversion,[],[f537]) ).
cnf(s16,plain,
( ~ spl34_13
| spl34_16 ),
inference(sat_conversion,[],[f576]) ).
cnf(s17,plain,
( ~ spl34_8
| spl34_17 ),
inference(sat_conversion,[],[f582]) ).
cnf(s18,plain,
( ~ spl34_10
| ~ spl34_17
| spl34_18 ),
inference(sat_conversion,[],[f615]) ).
cnf(s53,plain,
( ~ spl34_12
| ~ spl34_18
| spl34_53 ),
inference(sat_conversion,[],[f1321]) ).
cnf(s54,plain,
( spl34_2
| ~ spl34_53
| spl34_54 ),
inference(sat_conversion,[],[f1343]) ).
cnf(s69,plain,
( ~ spl34_16
| spl34_69 ),
inference(sat_conversion,[],[f1615]) ).
cnf(s70,plain,
( ~ spl34_69
| spl34_70 ),
inference(sat_conversion,[],[f1620]) ).
cnf(s141,plain,
( ~ spl34_54
| spl34_141 ),
inference(sat_conversion,[],[f3172]) ).
cnf(s142,plain,
( spl34_2
| ~ spl34_54
| ~ spl34_70
| ~ spl34_141
| spl34_142 ),
inference(sat_conversion,[],[f3225]) ).
cnf(s189,plain,
( ~ spl34_142
| spl34_189
| spl34_190 ),
inference(sat_conversion,[],[f4572]) ).
cnf(s190,plain,
( spl34_3
| ~ spl34_190 ),
inference(sat_conversion,[],[f4600]) ).
cnf(s191,plain,
~ spl34_189,
inference(sat_conversion,[],[f4636]) ).
cnf(s192,plain,
( ~ spl34_142
| spl34_190 ),
inference(rat,[],[s189,s191]) ).
cnf(s193,plain,
~ spl34_190,
inference(rat,[],[s190,s3]) ).
cnf(s194,plain,
~ spl34_142,
inference(rat,[],[s192,s193]) ).
cnf(s201,plain,
spl34_6,
inference(rat,[],[s6,s1]) ).
cnf(s206,plain,
spl34_8,
inference(rat,[],[s8,s201]) ).
cnf(s211,plain,
spl34_17,
inference(rat,[],[s17,s206]) ).
cnf(s212,plain,
spl34_13,
inference(rat,[],[s13,s206]) ).
cnf(s213,plain,
spl34_10,
inference(rat,[],[s10,s206]) ).
cnf(s222,plain,
spl34_16,
inference(rat,[],[s16,s212]) ).
cnf(s229,plain,
spl34_18,
inference(rat,[],[s18,s211,s213]) ).
cnf(s230,plain,
spl34_12,
inference(rat,[],[s12,s213]) ).
cnf(s242,plain,
spl34_69,
inference(rat,[],[s69,s222]) ).
cnf(s249,plain,
spl34_53,
inference(rat,[],[s53,s229,s230]) ).
cnf(s253,plain,
spl34_70,
inference(rat,[],[s70,s242]) ).
cnf(s268,plain,
spl34_54,
inference(rat,[],[s54,s2,s249]) ).
cnf(s282,plain,
~ spl34_141,
inference(rat,[],[s142,s194,s253,s2,s268]) ).
cnf(s286,plain,
$false,
inference(rat,[],[s141,s282,s268]) ).
fof(f4637,plain,
$false,
inference(avatar_sat_refutation,[],[s286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU092+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n009.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Mon Sep 28 03:33:08 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 11.57/7.52 % (2637654)Detected formulas, will run a generic FOF schedule.
% 11.57/7.52 % (2637659)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=659041959:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.57/7.52 % (2637664)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2706827794:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.57/7.52 % (2637661)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=4211805615:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.57/7.52 % (2637660)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=168612888:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.57/7.52 % (2637662)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3310756449:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.57/7.52 % (2637665)dis-21_1_sil=8000:lcm=predicate:random_seed=2330381067: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)
% 11.57/7.52 % (2637663)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=504914115:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.57/7.52 % (2637662)Refutation not found, incomplete strategy
% 11.57/7.52 % (2637662)------------------------------
% 11.57/7.52 % (2637662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637662)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637662)Termination reason: Refutation not found, incomplete strategy
% 11.57/7.52 % (2637662)Time elapsed: 0.002 s
% 11.57/7.52 % (2637662)Peak memory usage: 88 MB
% 11.57/7.52 % (2637662)Instructions burned: 1 (million)
% 11.57/7.52 % (2637665)Instruction limit reached!
% 11.57/7.52 % (2637665)------------------------------
% 11.57/7.52 % (2637665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637665)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637665)Termination reason: Instruction limit
% 11.57/7.52 % (2637665)Termination phase: Saturation
% 11.57/7.52 % (2637665)Time elapsed: 0.069 s
% 11.57/7.52 % (2637665)Peak memory usage: 88 MB
% 11.57/7.52 % (2637665)Instructions burned: 130 (million)
% 11.57/7.52 % (2637663)Instruction limit reached!
% 11.57/7.52 % (2637663)------------------------------
% 11.57/7.52 % (2637663)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637663)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637663)Termination reason: Instruction limit
% 11.57/7.52 % (2637663)Termination phase: Saturation
% 11.57/7.52 % (2637663)Time elapsed: 0.069 s
% 11.57/7.52 % (2637663)Peak memory usage: 88 MB
% 11.57/7.52 % (2637663)Instructions burned: 121 (million)
% 11.57/7.52 % (2637664)Instruction limit reached!
% 11.57/7.52 % (2637664)------------------------------
% 11.57/7.52 % (2637664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637664)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637664)Termination reason: Instruction limit
% 11.57/7.52 % (2637664)Termination phase: Saturation
% 11.57/7.52 % (2637664)Time elapsed: 0.087 s
% 11.57/7.52 % (2637664)Peak memory usage: 89 MB
% 11.57/7.52 % (2637664)Instructions burned: 140 (million)
% 11.57/7.52 % (2637673)lrs+10_1_sil=8000:sp=occurrence:random_seed=2614782485:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.57/7.52 % (2637675)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1935655438:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.57/7.52 % (2637674)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3475182553:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.57/7.52 % (2637662)------------------------------
% 11.57/7.52 % (2637662)------------------------------
% 11.57/7.52 % (2637674)Instruction limit reached!
% 11.57/7.52 % (2637674)------------------------------
% 11.57/7.52 % (2637674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637674)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637674)Termination reason: Instruction limit
% 11.57/7.52 % (2637674)Termination phase: Saturation
% 11.57/7.52 % (2637674)Time elapsed: 0.075 s
% 11.57/7.52 % (2637674)Peak memory usage: 91 MB
% 11.57/7.52 % (2637674)Instructions burned: 158 (million)
% 11.57/7.52 % (2637673)Instruction limit reached!
% 11.57/7.52 % (2637673)------------------------------
% 11.57/7.52 % (2637673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637673)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637673)Termination reason: Instruction limit
% 11.57/7.52 % (2637673)Termination phase: Saturation
% 11.57/7.52 % (2637673)Time elapsed: 0.163 s
% 11.57/7.52 % (2637673)Peak memory usage: 91 MB
% 11.57/7.52 % (2637673)Instructions burned: 286 (million)
% 11.57/7.52 % (2637675)Instruction limit reached!
% 11.57/7.52 % (2637675)------------------------------
% 11.57/7.52 % (2637675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637675)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637675)Termination reason: Instruction limit
% 11.57/7.52 % (2637675)Termination phase: Saturation
% 11.57/7.52 % (2637675)Time elapsed: 0.187 s
% 11.57/7.52 % (2637675)Peak memory usage: 91 MB
% 11.57/7.52 % (2637675)Instructions burned: 325 (million)
% 11.57/7.52 % (2637679)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=549432736:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 11.57/7.52 % (2637680)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1082242631:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 11.57/7.52 % (2637680)Refutation not found, incomplete strategy
% 11.57/7.52 % (2637680)------------------------------
% 11.57/7.52 % (2637680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637680)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637680)Termination reason: Refutation not found, incomplete strategy
% 11.57/7.52 % (2637680)Time elapsed: 0.004 s
% 11.57/7.52 % (2637680)Peak memory usage: 88 MB
% 11.57/7.52 % (2637680)Instructions burned: 4 (million)
% 11.57/7.52 % (2637681)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1561893806:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 11.57/7.52 % (2637679)Instruction limit reached!
% 11.57/7.52 % (2637679)------------------------------
% 11.57/7.52 % (2637679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637679)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637679)Termination reason: Instruction limit
% 11.57/7.52 % (2637679)Termination phase: Saturation
% 11.57/7.52 % (2637679)Time elapsed: 0.143 s
% 11.57/7.52 % (2637679)Peak memory usage: 95 MB
% 11.57/7.52 % (2637679)Instructions burned: 250 (million)
% 11.57/7.52 % (2637682)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=783811093:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 11.57/7.52 % (2637682)Instruction limit reached!
% 11.57/7.52 % (2637682)------------------------------
% 11.57/7.52 % (2637682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637682)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637682)Termination reason: Instruction limit
% 11.57/7.52 % (2637682)Termination phase: Saturation
% 11.57/7.52 % (2637682)Time elapsed: 0.074 s
% 11.57/7.52 % (2637682)Peak memory usage: 90 MB
% 11.57/7.52 % (2637682)Instructions burned: 114 (million)
% 11.57/7.52 % (2637680)------------------------------
% 11.57/7.52 % (2637680)------------------------------
% 11.57/7.52 % (2637686)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1732261561:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 11.57/7.52 % (2637688)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=795306157:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.57/7.52 % (2637686)Instruction limit reached!
% 11.57/7.52 % (2637686)------------------------------
% 11.57/7.52 % (2637686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637686)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637686)Termination reason: Instruction limit
% 11.57/7.52 % (2637686)Termination phase: Saturation
% 11.57/7.52 % (2637686)Time elapsed: 0.065 s
% 11.57/7.52 % (2637686)Peak memory usage: 89 MB
% 11.57/7.52 % (2637686)Instructions burned: 128 (million)
% 11.57/7.52 % (2637688)Instruction limit reached!
% 11.57/7.52 % (2637688)------------------------------
% 11.57/7.52 % (2637688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637688)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637688)Termination reason: Instruction limit
% 11.57/7.52 % (2637688)Termination phase: Saturation
% 11.57/7.52 % (2637688)Time elapsed: 0.059 s
% 11.57/7.52 % (2637688)Peak memory usage: 89 MB
% 11.57/7.52 % (2637688)Instructions burned: 115 (million)
% 11.57/7.52 % (2637689)lrs+10_1_sil=8000:sp=occurrence:random_seed=3573625282:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 11.57/7.52 % (2637692)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=706849312:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 11.57/7.52 % (2637692)Refutation not found, incomplete strategy
% 11.57/7.52 % (2637692)------------------------------
% 11.57/7.52 % (2637692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637692)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637692)Termination reason: Refutation not found, incomplete strategy
% 11.57/7.52 % (2637692)Time elapsed: 0.004 s
% 11.57/7.52 % (2637692)Peak memory usage: 88 MB
% 11.57/7.52 % (2637692)Instructions burned: 5 (million)
% 11.57/7.52 % (2637693)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=438230583:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 11.57/7.52 % (2637692)------------------------------
% 11.57/7.52 % (2637692)------------------------------
% 11.57/7.52 % (2637661)First to succeed.
% 11.57/7.52 % (2637661)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2637654"
% 11.57/7.52 % (2637697)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1642524513:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 11.57/7.52 % (2637689)Instruction limit reached!
% 11.57/7.52 % (2637689)------------------------------
% 11.57/7.52 % (2637689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637689)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637689)Termination reason: Instruction limit
% 11.57/7.52 % (2637689)Termination phase: Saturation
% 11.57/7.52 % (2637689)Time elapsed: 0.504 s
% 11.57/7.52 % (2637689)Peak memory usage: 97 MB
% 11.57/7.52 % (2637689)Instructions burned: 908 (million)
% 11.57/7.52 % (2637697)Instruction limit reached!
% 11.57/7.52 % (2637697)------------------------------
% 11.57/7.52 % (2637697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.57/7.52 % (2637697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.57/7.52 % (2637697)CaDiCaL version: 2.1.3
% 11.57/7.52 % (2637697)Termination reason: Instruction limit
% 11.57/7.52 % (2637697)Termination phase: Saturation
% 11.57/7.52 % (2637697)Time elapsed: 0.077 s
% 11.57/7.52 % (2637697)Peak memory usage: 92 MB
% 11.57/7.52 % (2637697)Instructions burned: 135 (million)
% 11.57/7.52 % (2637661)Refutation found. Thanks to Tanya!
% 11.57/7.52 % SZS status Theorem for theBenchmark
% 11.57/7.52 % SZS output start Proof for theBenchmark
% See solution above
% 12.25/7.72 % (2637661)------------------------------
% 12.25/7.72 % (2637661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/7.72 % (2637661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/7.72 % (2637661)CaDiCaL version: 2.1.3
% 12.25/7.72 % (2637661)Termination reason: Refutation
% 12.25/7.72 % (2637661)Time elapsed: 1.213 s
% 12.25/7.72 % (2637661)Peak memory usage: 135 MB
% 12.25/7.72 % (2637661)Instructions burned: 1772 (million)
% 12.25/7.72 % (2637661)------------------------------
% 12.25/7.72 % (2637661)------------------------------
% 12.25/7.72 % (2637654)Success in time 1.649 s
% 12.25/7.72 % Vampire exiting
%------------------------------------------------------------------------------