%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU091+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 : n018.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 9.81s 7.22s
% Output : Refutation 10.20s
% 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(X1,X0)
& ! [X3] :
( in(X3,cartesian_product2(X1,X0))
=> apply(X2,X3) = pair_first(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e3_36__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(X1,X0))
=> ( X0 = empty_set
| finite(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finset_1) ).
fof(f73,negated_conjecture,
~ ! [X0,X1] :
( finite(cartesian_product2(X1,X0))
=> ( 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(X1,X0)
& ! [X3] :
( apply(X2,X3) = pair_first(X3)
| ~ in(X3,cartesian_product2(X1,X0)) ) ),
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(X1,X0)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f148,plain,
? [X0,X1] :
( empty_set != X0
& ~ finite(X1)
& finite(cartesian_product2(X1,X0)) ),
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(X1,X0) = relation_dom(sK29(X0,X1))
& ! [X3] :
( pair_first(X3) = apply(sK29(X0,X1),X3)
| ~ in(X3,cartesian_product2(X1,X0)) ) ),
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(sK31,sK30)) ),
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_first(X3) = apply(sK29(X0,X1),X3)
| ~ in(X3,cartesian_product2(X1,X0)) ),
inference(cnf_transformation,[],[f188]) ).
fof(f340,plain,
! [X0,X1] : cartesian_product2(X1,X0) = 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(f347,plain,
! [X2,X0,X1] :
( in(pair_first(X0),X1)
| ~ 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(sK31,sK30)),
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(f363,plain,
! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
inference(cnf_transformation,[],[f81]) ).
fof(f369,plain,
! [X3,X0,X1] :
( pair_first(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(X3,X2)))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f345,f224,f340]) ).
fof(f373,plain,
! [X2,X0,X1] :
( in(pair_first(X0),X1)
| ~ in(X0,relation_dom(sK29(X2,X1))) ),
inference(definition_unfolding,[],[f347,f340]) ).
fof(f375,plain,
finite(relation_dom(sK29(sK30,sK31))),
inference(definition_unfolding,[],[f351,f340]) ).
fof(f376,plain,
! [X0,X1] : pair_first(unordered_pair(unordered_pair(X0,X1),singleton(X0))) = X0,
inference(definition_unfolding,[],[f363,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(f430,definition,
( spl34_7
<=> ! [X0] :
( finite(relation_image(X0,relation_dom(sK29(sK30,sK31))))
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_7])],[avatar_definition]) ).
fof(f431,plain,
( ! [X0] :
( finite(relation_image(X0,relation_dom(sK29(sK30,sK31))))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl34_7 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f432,plain,
( spl34_7
| ~ spl34_1 ),
inference(avatar_split_clause,[],[f397,f385,f430]) ).
fof(f455,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ relation(sK29(sK30,sK31))
| ~ function(sK29(sK30,sK31))
| ~ relation(sK29(sK30,sK31))
| ~ spl34_7 ),
inference(superposition,[],[f431,f348]) ).
fof(f456,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ relation(sK29(sK30,sK31))
| ~ function(sK29(sK30,sK31))
| ~ spl34_7 ),
inference(duplicate_literal_removal,[],[f455]) ).
fof(f457,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ function(sK29(sK30,sK31))
| ~ spl34_7 ),
inference(forward_subsumption_resolution,[],[f456,f342]) ).
fof(f458,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ spl34_7 ),
inference(forward_subsumption_resolution,[],[f457,f341]) ).
fof(f460,definition,
( spl34_9
<=> finite(relation_rng(sK29(sK30,sK31))) ),
introduced(definition,[new_symbols(definition,[spl34_9])],[avatar_definition]) ).
fof(f462,plain,
( finite(relation_rng(sK29(sK30,sK31)))
| ~ spl34_9 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f463,plain,
( spl34_9
| ~ spl34_7 ),
inference(avatar_split_clause,[],[f458,f430,f460]) ).
fof(f469,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_9 ),
inference(superposition,[],[f462,f221]) ).
fof(f470,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_9 ),
inference(superposition,[],[f462,f222]) ).
fof(f471,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_9 ),
inference(superposition,[],[f462,f223]) ).
fof(f472,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_9 ),
inference(forward_subsumption_resolution,[],[f471,f342]) ).
fof(f473,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_9 ),
inference(forward_subsumption_resolution,[],[f470,f342]) ).
fof(f474,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_9 ),
inference(forward_subsumption_resolution,[],[f469,f342]) ).
fof(f475,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_9 ),
inference(forward_subsumption_resolution,[],[f472,f341]) ).
fof(f476,plain,
( ! [X0] :
( finite(X0)
| in(sK1(sK29(sK30,sK31),X0),relation_dom(sK29(sK30,sK31)))
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_9 ),
inference(forward_subsumption_resolution,[],[f473,f341]) ).
fof(f477,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_9 ),
inference(forward_subsumption_resolution,[],[f474,f341]) ).
fof(f479,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(f480,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,[],[f479]) ).
fof(f481,plain,
( spl34_10
| ~ spl34_9 ),
inference(avatar_split_clause,[],[f476,f460,f479]) ).
fof(f483,plain,
( ! [X0] :
( finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0)
| in(pair_first(sK1(sK29(sK30,sK31),X0)),sK31) )
| ~ spl34_10 ),
inference(resolution,[],[f480,f373]) ).
fof(f516,definition,
( spl34_12
<=> ! [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_12])],[avatar_definition]) ).
fof(f517,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_12 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f518,plain,
( spl34_12
| ~ spl34_9 ),
inference(avatar_split_clause,[],[f475,f460,f516]) ).
fof(f519,plain,
( ! [X0,X1] :
( pair_first(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_12 ),
inference(superposition,[],[f517,f369]) ).
fof(f522,plain,
( ! [X0,X1] :
( pair_first(X0) != sK0(sK29(sK30,sK31),X1)
| ~ in(X0,relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1) )
| ~ spl34_12 ),
inference(duplicate_literal_removal,[],[f519]) ).
fof(f555,definition,
( spl34_15
<=> ! [X0,X1] :
( pair_first(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_15])],[avatar_definition]) ).
fof(f556,plain,
( ! [X0,X1] :
( pair_first(X0) != sK0(sK29(sK30,sK31),X1)
| ~ in(X0,relation_dom(sK29(sK30,sK31)))
| finite(X1)
| ~ in(sK0(sK29(sK30,sK31),X1),X1) )
| ~ spl34_15 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f557,plain,
( spl34_15
| ~ spl34_12 ),
inference(avatar_split_clause,[],[f522,f516,f555]) ).
fof(f558,plain,
( ! [X2,X0,X1] :
( sK0(sK29(sK30,sK31),X2) != X0
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_dom(sK29(sK30,sK31)))
| finite(X2)
| ~ in(sK0(sK29(sK30,sK31),X2),X2) )
| ~ spl34_15 ),
inference(superposition,[],[f556,f376]) ).
fof(f559,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom(sK29(sK30,sK31)))
| sK0(sK29(sK30,sK31),X2) != X0
| finite(X2)
| ~ in(sK0(sK29(sK30,sK31),X2),X2) )
| ~ spl34_15 ),
inference(forward_demodulation,[],[f558,f217]) ).
fof(f561,definition,
( spl34_16
<=> ! [X0] :
( finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0)
| in(pair_first(sK1(sK29(sK30,sK31),X0)),sK31) ) ),
introduced(definition,[new_symbols(definition,[spl34_16])],[avatar_definition]) ).
fof(f562,plain,
( ! [X0] :
( in(pair_first(sK1(sK29(sK30,sK31),X0)),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0) )
| ~ spl34_16 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f563,plain,
( spl34_16
| ~ spl34_10 ),
inference(avatar_split_clause,[],[f483,f479,f561]) ).
fof(f620,definition,
( spl34_19
<=> ! [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_19])],[avatar_definition]) ).
fof(f621,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_19 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f622,plain,
( spl34_19
| ~ spl34_9 ),
inference(avatar_split_clause,[],[f477,f460,f620]) ).
fof(f624,plain,
( ! [X0] :
( sK0(sK29(sK30,sK31),X0) = pair_first(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_19 ),
inference(superposition,[],[f369,f621]) ).
fof(f641,plain,
( ! [X0] :
( sK0(sK29(sK30,sK31),X0) = pair_first(sK1(sK29(sK30,sK31),X0))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_10
| ~ spl34_19 ),
inference(forward_subsumption_resolution,[],[f624,f480]) ).
fof(f653,definition,
( spl34_20
<=> ! [X0] :
( sK0(sK29(sK30,sK31),X0) = pair_first(sK1(sK29(sK30,sK31),X0))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_20])],[avatar_definition]) ).
fof(f654,plain,
( ! [X0] :
( sK0(sK29(sK30,sK31),X0) = pair_first(sK1(sK29(sK30,sK31),X0))
| finite(X0)
| in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_20 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f655,plain,
( spl34_20
| ~ spl34_10
| ~ spl34_19 ),
inference(avatar_split_clause,[],[f641,f620,f479,f653]) ).
fof(f656,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_16
| ~ spl34_20 ),
inference(superposition,[],[f562,f654]) ).
fof(f659,plain,
( ! [X0] :
( in(sK0(sK29(sK30,sK31),X0),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0) )
| ~ spl34_16
| ~ spl34_20 ),
inference(duplicate_literal_removal,[],[f656]) ).
fof(f924,definition,
( spl34_37
<=> ! [X0] :
( in(sK0(sK29(sK30,sK31),X0),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_37])],[avatar_definition]) ).
fof(f925,plain,
( ! [X0] :
( in(sK0(sK29(sK30,sK31),X0),sK31)
| in(sK0(sK29(sK30,sK31),X0),X0)
| finite(X0) )
| ~ spl34_37 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f926,plain,
( spl34_37
| ~ spl34_16
| ~ spl34_20 ),
inference(avatar_split_clause,[],[f659,f653,f561,f924]) ).
fof(f936,plain,
( in(sK0(sK29(sK30,sK31),sK31),sK31)
| finite(sK31)
| ~ spl34_37 ),
inference(factoring,[],[f925]) ).
fof(f937,plain,
( in(sK0(sK29(sK30,sK31),sK31),sK31)
| spl34_2
| ~ spl34_37 ),
inference(forward_subsumption_resolution,[],[f936,f392]) ).
fof(f945,definition,
( spl34_38
<=> in(sK0(sK29(sK30,sK31),sK31),sK31) ),
introduced(definition,[new_symbols(definition,[spl34_38])],[avatar_definition]) ).
fof(f947,plain,
( in(sK0(sK29(sK30,sK31),sK31),sK31)
| ~ spl34_38 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f948,plain,
( spl34_38
| spl34_2
| ~ spl34_37 ),
inference(avatar_split_clause,[],[f937,f924,f390,f945]) ).
fof(f956,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK0(sK29(sK30,sK31),sK31),X0),singleton(sK0(sK29(sK30,sK31),sK31))),relation_dom(sK29(X1,sK31)))
| ~ in(X0,X1) )
| ~ spl34_38 ),
inference(resolution,[],[f947,f370]) ).
fof(f958,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK0(sK29(sK30,sK31),sK31)),unordered_pair(sK0(sK29(sK30,sK31),sK31),X0)),relation_dom(sK29(X1,sK31)))
| ~ in(X0,X1) )
| ~ spl34_38 ),
inference(forward_demodulation,[],[f956,f217]) ).
fof(f967,definition,
( spl34_40
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),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_40])],[avatar_definition]) ).
fof(f968,plain,
( ! [X2,X0,X1] :
( sK0(sK29(sK30,sK31),X2) != X0
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom(sK29(sK30,sK31)))
| finite(X2)
| ~ in(sK0(sK29(sK30,sK31),X2),X2) )
| ~ spl34_40 ),
inference(avatar_component_clause,[],[f967]) ).
fof(f969,plain,
( spl34_40
| ~ spl34_15 ),
inference(avatar_split_clause,[],[f559,f555,f967]) ).
fof(f970,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(sK29(sK30,sK31),X0)),unordered_pair(sK0(sK29(sK30,sK31),X0),X1)),relation_dom(sK29(sK30,sK31)))
| finite(X0)
| ~ in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_40 ),
inference(equality_resolution,[],[f968]) ).
fof(f972,definition,
( spl34_41
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(sK29(sK30,sK31),X0)),unordered_pair(sK0(sK29(sK30,sK31),X0),X1)),relation_dom(sK29(sK30,sK31)))
| finite(X0)
| ~ in(sK0(sK29(sK30,sK31),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl34_41])],[avatar_definition]) ).
fof(f973,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(sK29(sK30,sK31),X0)),unordered_pair(sK0(sK29(sK30,sK31),X0),X1)),relation_dom(sK29(sK30,sK31)))
| finite(X0)
| ~ in(sK0(sK29(sK30,sK31),X0),X0) )
| ~ spl34_41 ),
inference(avatar_component_clause,[],[f972]) ).
fof(f974,plain,
( spl34_41
| ~ spl34_40 ),
inference(avatar_split_clause,[],[f970,f967,f972]) ).
fof(f1341,definition,
( spl34_62
<=> ! [X0,X1] :
( in(unordered_pair(singleton(sK0(sK29(sK30,sK31),sK31)),unordered_pair(sK0(sK29(sK30,sK31),sK31),X0)),relation_dom(sK29(X1,sK31)))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl34_62])],[avatar_definition]) ).
fof(f1342,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK0(sK29(sK30,sK31),sK31)),unordered_pair(sK0(sK29(sK30,sK31),sK31),X0)),relation_dom(sK29(X1,sK31)))
| ~ in(X0,X1) )
| ~ spl34_62 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f1343,plain,
( spl34_62
| ~ spl34_38 ),
inference(avatar_split_clause,[],[f958,f945,f1341]) ).
fof(f1346,plain,
( ! [X0] :
( ~ in(X0,sK30)
| finite(sK31)
| ~ in(sK0(sK29(sK30,sK31),sK31),sK31) )
| ~ spl34_41
| ~ spl34_62 ),
inference(resolution,[],[f1342,f973]) ).
fof(f1368,plain,
( ! [X0] :
( ~ in(X0,sK30)
| ~ in(sK0(sK29(sK30,sK31),sK31),sK31) )
| spl34_2
| ~ spl34_41
| ~ spl34_62 ),
inference(forward_subsumption_resolution,[],[f1346,f392]) ).
fof(f1372,plain,
( ! [X0] : ~ in(X0,sK30)
| spl34_2
| ~ spl34_38
| ~ spl34_41
| ~ spl34_62 ),
inference(forward_subsumption_resolution,[],[f1368,f947]) ).
fof(f1376,definition,
( spl34_63
<=> ! [X0] : ~ in(X0,sK30) ),
introduced(definition,[new_symbols(definition,[spl34_63])],[avatar_definition]) ).
fof(f1377,plain,
( ! [X0] : ~ in(X0,sK30)
| ~ spl34_63 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f1378,plain,
( spl34_63
| spl34_2
| ~ spl34_38
| ~ spl34_41
| ~ spl34_62 ),
inference(avatar_split_clause,[],[f1372,f1341,f972,f945,f390,f1376]) ).
fof(f1379,plain,
( ! [X0] :
( empty(sK30)
| ~ element(X0,sK30) )
| ~ spl34_63 ),
inference(resolution,[],[f1377,f354]) ).
fof(f2523,definition,
( spl34_106
<=> ! [X0] : ~ element(X0,sK30) ),
introduced(definition,[new_symbols(definition,[spl34_106])],[avatar_definition]) ).
fof(f2524,plain,
( ! [X0] : ~ element(X0,sK30)
| ~ spl34_106 ),
inference(avatar_component_clause,[],[f2523]) ).
fof(f2526,definition,
( spl34_107
<=> empty(sK30) ),
introduced(definition,[new_symbols(definition,[spl34_107])],[avatar_definition]) ).
fof(f2528,plain,
( empty(sK30)
| ~ spl34_107 ),
inference(avatar_component_clause,[],[f2526]) ).
fof(f2529,plain,
( spl34_106
| spl34_107
| ~ spl34_63 ),
inference(avatar_split_clause,[],[f1379,f1376,f2526,f2523]) ).
fof(f2549,plain,
( empty_set = sK30
| ~ spl34_107 ),
inference(resolution,[],[f2528,f360]) ).
fof(f2554,plain,
( $false
| spl34_3
| ~ spl34_107 ),
inference(forward_subsumption_resolution,[],[f2549,f404]) ).
fof(f2555,plain,
( spl34_3
| ~ spl34_107 ),
inference(avatar_contradiction_clause,[],[f2554]) ).
fof(f2576,plain,
( $false
| ~ spl34_106 ),
inference(resolution,[],[f2524,f225]) ).
fof(f2577,plain,
~ spl34_106,
inference(avatar_contradiction_clause,[],[f2576]) ).
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(s7,plain,
( ~ spl34_1
| spl34_7 ),
inference(sat_conversion,[],[f432]) ).
cnf(s9,plain,
( ~ spl34_7
| spl34_9 ),
inference(sat_conversion,[],[f463]) ).
cnf(s10,plain,
( ~ spl34_9
| spl34_10 ),
inference(sat_conversion,[],[f481]) ).
cnf(s12,plain,
( ~ spl34_9
| spl34_12 ),
inference(sat_conversion,[],[f518]) ).
cnf(s15,plain,
( ~ spl34_12
| spl34_15 ),
inference(sat_conversion,[],[f557]) ).
cnf(s16,plain,
( ~ spl34_10
| spl34_16 ),
inference(sat_conversion,[],[f563]) ).
cnf(s19,plain,
( ~ spl34_9
| spl34_19 ),
inference(sat_conversion,[],[f622]) ).
cnf(s20,plain,
( ~ spl34_10
| ~ spl34_19
| spl34_20 ),
inference(sat_conversion,[],[f655]) ).
cnf(s37,plain,
( ~ spl34_16
| ~ spl34_20
| spl34_37 ),
inference(sat_conversion,[],[f926]) ).
cnf(s38,plain,
( spl34_2
| ~ spl34_37
| spl34_38 ),
inference(sat_conversion,[],[f948]) ).
cnf(s40,plain,
( ~ spl34_15
| spl34_40 ),
inference(sat_conversion,[],[f969]) ).
cnf(s41,plain,
( ~ spl34_40
| spl34_41 ),
inference(sat_conversion,[],[f974]) ).
cnf(s62,plain,
( ~ spl34_38
| spl34_62 ),
inference(sat_conversion,[],[f1343]) ).
cnf(s63,plain,
( spl34_2
| ~ spl34_38
| ~ spl34_41
| ~ spl34_62
| spl34_63 ),
inference(sat_conversion,[],[f1378]) ).
cnf(s106,plain,
( ~ spl34_63
| spl34_106
| spl34_107 ),
inference(sat_conversion,[],[f2529]) ).
cnf(s107,plain,
( spl34_3
| ~ spl34_107 ),
inference(sat_conversion,[],[f2555]) ).
cnf(s108,plain,
~ spl34_106,
inference(sat_conversion,[],[f2577]) ).
cnf(s109,plain,
( ~ spl34_63
| spl34_107 ),
inference(rat,[],[s106,s108]) ).
cnf(s110,plain,
~ spl34_107,
inference(rat,[],[s107,s3]) ).
cnf(s111,plain,
~ spl34_63,
inference(rat,[],[s109,s110]) ).
cnf(s117,plain,
spl34_7,
inference(rat,[],[s7,s1]) ).
cnf(s122,plain,
spl34_9,
inference(rat,[],[s9,s117]) ).
cnf(s127,plain,
spl34_19,
inference(rat,[],[s19,s122]) ).
cnf(s128,plain,
spl34_12,
inference(rat,[],[s12,s122]) ).
cnf(s129,plain,
spl34_10,
inference(rat,[],[s10,s122]) ).
cnf(s132,plain,
spl34_15,
inference(rat,[],[s15,s128]) ).
cnf(s136,plain,
spl34_20,
inference(rat,[],[s20,s127,s129]) ).
cnf(s137,plain,
spl34_16,
inference(rat,[],[s16,s129]) ).
cnf(s141,plain,
spl34_40,
inference(rat,[],[s40,s132]) ).
cnf(s147,plain,
spl34_37,
inference(rat,[],[s37,s136,s137]) ).
cnf(s149,plain,
spl34_41,
inference(rat,[],[s41,s141]) ).
cnf(s156,plain,
spl34_38,
inference(rat,[],[s38,s2,s147]) ).
cnf(s160,plain,
~ spl34_62,
inference(rat,[],[s63,s111,s149,s2,s156]) ).
cnf(s163,plain,
$false,
inference(rat,[],[s62,s160,s156]) ).
fof(f2578,plain,
$false,
inference(avatar_sat_refutation,[],[s163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU091+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n018.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 03:35:16 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 9.81/7.22 % (2970146)Detected formulas, will run a generic FOF schedule.
% 9.81/7.22 % (2970151)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=1648208671:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.81/7.22 % (2970157)dis-21_1_sil=8000:lcm=predicate:random_seed=2815671702: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)
% 9.81/7.22 % (2970154)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2882330627:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.81/7.22 % (2970156)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1904676414:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.81/7.22 % (2970152)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=92615088:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.81/7.22 % (2970153)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=1279980609:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.81/7.22 % (2970155)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2301098866:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.81/7.22 % (2970154)Refutation not found, incomplete strategy
% 9.81/7.22 % (2970154)------------------------------
% 9.81/7.22 % (2970154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970154)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970154)Termination reason: Refutation not found, incomplete strategy
% 9.81/7.22 % (2970154)Time elapsed: 0.002 s
% 9.81/7.22 % (2970154)Peak memory usage: 88 MB
% 9.81/7.22 % (2970154)Instructions burned: 1 (million)
% 9.81/7.22 % (2970157)Instruction limit reached!
% 9.81/7.22 % (2970157)------------------------------
% 9.81/7.22 % (2970157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970157)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970157)Termination reason: Instruction limit
% 9.81/7.22 % (2970157)Termination phase: Saturation
% 9.81/7.22 % (2970157)Time elapsed: 0.069 s
% 9.81/7.22 % (2970157)Peak memory usage: 88 MB
% 9.81/7.22 % (2970157)Instructions burned: 131 (million)
% 9.81/7.22 % (2970155)Instruction limit reached!
% 9.81/7.22 % (2970155)------------------------------
% 9.81/7.22 % (2970155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970155)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970155)Termination reason: Instruction limit
% 9.81/7.22 % (2970155)Termination phase: Saturation
% 9.81/7.22 % (2970155)Time elapsed: 0.069 s
% 9.81/7.22 % (2970155)Peak memory usage: 88 MB
% 9.81/7.22 % (2970155)Instructions burned: 121 (million)
% 9.81/7.22 % (2970156)Instruction limit reached!
% 9.81/7.22 % (2970156)------------------------------
% 9.81/7.22 % (2970156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970156)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970156)Termination reason: Instruction limit
% 9.81/7.22 % (2970156)Termination phase: Saturation
% 9.81/7.22 % (2970156)Time elapsed: 0.087 s
% 9.81/7.22 % (2970156)Peak memory usage: 89 MB
% 9.81/7.22 % (2970156)Instructions burned: 140 (million)
% 9.81/7.22 % (2970166)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3366823525:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.81/7.22 % (2970165)lrs+10_1_sil=8000:sp=occurrence:random_seed=1214935588:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.81/7.22 % (2970154)------------------------------
% 9.81/7.22 % (2970154)------------------------------
% 9.81/7.22 % (2970167)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1865027922:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.81/7.22 % (2970166)Instruction limit reached!
% 9.81/7.22 % (2970166)------------------------------
% 9.81/7.22 % (2970166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970166)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970166)Termination reason: Instruction limit
% 9.81/7.22 % (2970166)Termination phase: Saturation
% 9.81/7.22 % (2970166)Time elapsed: 0.076 s
% 9.81/7.22 % (2970166)Peak memory usage: 91 MB
% 9.81/7.22 % (2970166)Instructions burned: 159 (million)
% 9.81/7.22 % (2970165)Instruction limit reached!
% 9.81/7.22 % (2970165)------------------------------
% 9.81/7.22 % (2970165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970165)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970165)Termination reason: Instruction limit
% 9.81/7.22 % (2970165)Termination phase: Saturation
% 9.81/7.22 % (2970165)Time elapsed: 0.164 s
% 9.81/7.22 % (2970165)Peak memory usage: 91 MB
% 9.81/7.22 % (2970165)Instructions burned: 286 (million)
% 9.81/7.22 % (2970171)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=2475611240:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.81/7.22 % (2970167)Instruction limit reached!
% 9.81/7.22 % (2970167)------------------------------
% 9.81/7.22 % (2970167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970167)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970167)Termination reason: Instruction limit
% 9.81/7.22 % (2970167)Termination phase: Saturation
% 9.81/7.22 % (2970167)Time elapsed: 0.192 s
% 9.81/7.22 % (2970167)Peak memory usage: 91 MB
% 9.81/7.22 % (2970167)Instructions burned: 325 (million)
% 9.81/7.22 % (2970172)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2240987808:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.81/7.22 % (2970172)Refutation not found, incomplete strategy
% 9.81/7.22 % (2970172)------------------------------
% 9.81/7.22 % (2970172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970172)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970172)Termination reason: Refutation not found, incomplete strategy
% 9.81/7.22 % (2970172)Time elapsed: 0.004 s
% 9.81/7.22 % (2970172)Peak memory usage: 88 MB
% 9.81/7.22 % (2970172)Instructions burned: 4 (million)
% 9.81/7.22 % (2970173)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2076400936:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.81/7.22 % (2970171)Instruction limit reached!
% 9.81/7.22 % (2970171)------------------------------
% 9.81/7.22 % (2970171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970171)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970171)Termination reason: Instruction limit
% 9.81/7.22 % (2970171)Termination phase: Saturation
% 9.81/7.22 % (2970171)Time elapsed: 0.142 s
% 9.81/7.22 % (2970171)Peak memory usage: 95 MB
% 9.81/7.22 % (2970171)Instructions burned: 248 (million)
% 9.81/7.22 % (2970176)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1383504099:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 9.81/7.22 % (2970172)------------------------------
% 9.81/7.22 % (2970172)------------------------------
% 9.81/7.22 % (2970176)Instruction limit reached!
% 9.81/7.22 % (2970176)------------------------------
% 9.81/7.22 % (2970176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970176)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970176)Termination reason: Instruction limit
% 9.81/7.22 % (2970176)Termination phase: Saturation
% 9.81/7.22 % (2970176)Time elapsed: 0.075 s
% 9.81/7.22 % (2970176)Peak memory usage: 90 MB
% 9.81/7.22 % (2970176)Instructions burned: 114 (million)
% 9.81/7.22 % (2970178)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1349994091:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 9.81/7.22 % (2970178)Instruction limit reached!
% 9.81/7.22 % (2970178)------------------------------
% 9.81/7.22 % (2970178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970178)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970178)Termination reason: Instruction limit
% 9.81/7.22 % (2970178)Termination phase: Saturation
% 9.81/7.22 % (2970178)Time elapsed: 0.064 s
% 9.81/7.22 % (2970178)Peak memory usage: 89 MB
% 9.81/7.22 % (2970178)Instructions burned: 128 (million)
% 9.81/7.22 % (2970180)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4178586487:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 9.81/7.22 % (2970181)lrs+10_1_sil=8000:sp=occurrence:random_seed=1537961408:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.81/7.22 % (2970180)Instruction limit reached!
% 9.81/7.22 % (2970180)------------------------------
% 9.81/7.22 % (2970180)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970180)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970180)Termination reason: Instruction limit
% 9.81/7.22 % (2970180)Termination phase: Saturation
% 9.81/7.22 % (2970180)Time elapsed: 0.058 s
% 9.81/7.22 % (2970180)Peak memory usage: 89 MB
% 9.81/7.22 % (2970180)Instructions burned: 115 (million)
% 9.81/7.22 % (2970153)First to succeed.
% 9.81/7.22 % (2970153)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2970146"
% 9.81/7.22 % (2970183)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=577307166:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.81/7.22 % (2970183)Refutation not found, incomplete strategy
% 9.81/7.22 % (2970183)------------------------------
% 9.81/7.22 % (2970183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.81/7.22 % (2970183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.81/7.22 % (2970183)CaDiCaL version: 2.1.3
% 9.81/7.22 % (2970183)Termination reason: Refutation not found, incomplete strategy
% 9.81/7.22 % (2970183)Time elapsed: 0.004 s
% 9.81/7.22 % (2970183)Peak memory usage: 88 MB
% 9.81/7.22 % (2970183)Instructions burned: 5 (million)
% 9.81/7.22 % (2970186)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1304429607:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 9.81/7.22 % (2970183)------------------------------
% 9.81/7.22 % (2970183)------------------------------
% 9.81/7.22 % (2970153)Refutation found. Thanks to Tanya!
% 9.81/7.22 % SZS status Theorem for theBenchmark
% 9.81/7.22 % SZS output start Proof for theBenchmark
% See solution above
% 10.20/7.41 % (2970153)------------------------------
% 10.20/7.41 % (2970153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.20/7.41 % (2970153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.20/7.41 % (2970153)CaDiCaL version: 2.1.3
% 10.20/7.41 % (2970153)Termination reason: Refutation
% 10.20/7.41 % (2970153)Time elapsed: 0.924 s
% 10.20/7.41 % (2970153)Peak memory usage: 132 MB
% 10.20/7.41 % (2970153)Instructions burned: 1361 (million)
% 10.20/7.41 % (2970153)------------------------------
% 10.20/7.41 % (2970153)------------------------------
% 10.20/7.41 % (2970146)Success in time 1.355 s
% 10.20/7.41 % Vampire exiting
%------------------------------------------------------------------------------