%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU236+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:47:56 PM UTC 2026
% Result : Theorem 6.44s 1.77s
% Output : Refutation 8.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 117 ( 25 unt; 5 def)
% Number of atoms : 371 ( 26 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 413 ( 159 ~; 173 |; 56 &)
% ( 15 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 128 ( 0 sgn 115 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f28,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f32,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f36,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f39,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f105,axiom,
! [X0] :
( ordinal(X0)
=> ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f153,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f158,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f206,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f207,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f206]) ).
fof(f231,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f254,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f313,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f318,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f363,plain,
! [X0] :
( ( ~ empty(succ(X0))
& epsilon_transitive(succ(X0))
& epsilon_connected(succ(X0))
& ordinal(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f105]) ).
fof(f397,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f153]) ).
fof(f398,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f397]) ).
fof(f464,plain,
? [X0] :
( ? [X1] :
( ( in(X0,X1)
<~> ordinal_subset(succ(X0),X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f207]) ).
fof(f482,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f231]) ).
fof(f587,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f313]) ).
fof(f588,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f587]) ).
fof(f589,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK27(X0),X0)
& in(sK27(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f588]) ).
fof(f598,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f599,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f598]) ).
fof(f600,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f599]) ).
fof(f601,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK31(X0,X1,X2),X0)
& ~ in(sK31(X0,X1,X2),X1) )
| ~ in(sK31(X0,X1,X2),X2) )
& ( in(sK31(X0,X1,X2),X0)
| in(sK31(X0,X1,X2),X1)
| in(sK31(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X3,sK31(X0,X1,X2))],[f600]) ).
fof(f611,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f318]) ).
fof(f612,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f611]) ).
fof(f613,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK41(X0,X1),X1)
& in(sK41(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(X2,sK41(X0,X1))],[f612]) ).
fof(f619,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) )
& ( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f620,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) )
& ( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f619]) ).
fof(f675,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f398]) ).
fof(f693,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(succ(X0),X1)
| ~ in(X0,X1) )
& ( ordinal_subset(succ(X0),X1)
| in(X0,X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(nnf_transformation,[],[f464]) ).
fof(f694,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(succ(X0),X1)
| ~ in(X0,X1) )
& ( ordinal_subset(succ(X0),X1)
| in(X0,X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f693]) ).
fof(f695,plain,
( ( ~ ordinal_subset(succ(sK87),sK88)
| ~ in(sK87,sK88) )
& ( ordinal_subset(succ(sK87),sK88)
| in(sK87,sK88) )
& ordinal(sK88)
& ordinal(sK87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88]),skolemize(X0,sK87),skolemize(X1,sK88)],[f694]) ).
fof(f805,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f827,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f589]) ).
fof(f844,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f601]) ).
fof(f846,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f601]) ).
fof(f867,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f613]) ).
fof(f868,plain,
! [X0,X1] :
( in(sK41(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f613]) ).
fof(f869,plain,
! [X0,X1] :
( ~ in(sK41(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f613]) ).
fof(f881,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f620]) ).
fof(f982,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f1070,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1071,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1078,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f158]) ).
fof(f1146,plain,
ordinal(sK87),
inference(cnf_transformation,[],[f695]) ).
fof(f1147,plain,
ordinal(sK88),
inference(cnf_transformation,[],[f695]) ).
fof(f1148,plain,
( ordinal_subset(succ(sK87),sK88)
| in(sK87,sK88) ),
inference(cnf_transformation,[],[f695]) ).
fof(f1149,plain,
( ~ ordinal_subset(succ(sK87),sK88)
| ~ in(sK87,sK88) ),
inference(cnf_transformation,[],[f695]) ).
fof(f1188,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f482]) ).
fof(f1232,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f254]) ).
fof(f1269,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f805,f1232]) ).
fof(f1349,plain,
! [X0] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f982,f1269]) ).
fof(f1367,plain,
! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1078,f1269]) ).
fof(f1384,plain,
( ~ ordinal_subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
| ~ in(sK87,sK88) ),
inference(definition_unfolding,[],[f1149,f1269]) ).
fof(f1385,plain,
( ordinal_subset(set_union2(sK87,unordered_pair(sK87,sK87)),sK88)
| in(sK87,sK88) ),
inference(definition_unfolding,[],[f1148,f1269]) ).
fof(f1393,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(unordered_pair(X0,X0),X1) = X1 ),
inference(definition_unfolding,[],[f1188,f1232]) ).
fof(f1465,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f846]) ).
fof(f1467,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f844]) ).
fof(f1520,definition,
sF100 = unordered_pair(sK87,sK87),
introduced(definition,[new_symbols(definition,[sF100])],[function_definition]) ).
fof(f1521,plain,
unordered_pair(sK87,sK87) = sF100,
inference(reorient_equations,[],[f1520]) ).
fof(f1522,definition,
sF101 = set_union2(sK87,sF100),
introduced(definition,[new_symbols(definition,[sF101])],[function_definition]) ).
fof(f1523,plain,
set_union2(sK87,sF100) = sF101,
inference(reorient_equations,[],[f1522]) ).
fof(f1524,plain,
( ~ ordinal_subset(sF101,sK88)
| ~ in(sK87,sK88) ),
inference(definition_folding,[],[f1384,f1523,f1521]) ).
fof(f1525,plain,
( ordinal_subset(sF101,sK88)
| in(sK87,sK88) ),
inference(definition_folding,[],[f1385,f1523,f1521]) ).
fof(f1529,definition,
( spl102_1
<=> in(sK87,sK88) ),
introduced(definition,[new_symbols(definition,[spl102_1])],[avatar_definition]) ).
fof(f1530,plain,
( ~ in(sK87,sK88)
| spl102_1 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f1531,plain,
( in(sK87,sK88)
| ~ spl102_1 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f1533,definition,
( spl102_2
<=> ordinal_subset(sF101,sK88) ),
introduced(definition,[new_symbols(definition,[spl102_2])],[avatar_definition]) ).
fof(f1534,plain,
( ~ ordinal_subset(sF101,sK88)
| spl102_2 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f1535,plain,
( ordinal_subset(sF101,sK88)
| ~ spl102_2 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f1536,plain,
( spl102_1
| spl102_2 ),
inference(avatar_split_clause,[],[f1525,f1533,f1529]) ).
fof(f1537,plain,
( ~ spl102_1
| ~ spl102_2 ),
inference(avatar_split_clause,[],[f1524,f1533,f1529]) ).
fof(f1565,plain,
! [X0] :
( ~ in(X0,sF101)
| in(X0,sF100)
| in(X0,sK87) ),
inference(superposition,[],[f1467,f1523]) ).
fof(f1595,plain,
in(sK87,set_union2(sK87,sF100)),
inference(superposition,[],[f1367,f1521]) ).
fof(f1596,plain,
in(sK87,sF101),
inference(forward_demodulation,[],[f1595,f1523]) ).
fof(f1628,plain,
( ordinal(set_union2(sK87,sF100))
| ~ ordinal(sK87) ),
inference(superposition,[],[f1349,f1521]) ).
fof(f1686,plain,
epsilon_transitive(sK88),
inference(resolution,[],[f881,f1147]) ).
fof(f1702,plain,
! [X0] :
( in(sK41(sF101,X0),sK87)
| in(sK41(sF101,X0),sF100)
| subset(sF101,X0) ),
inference(resolution,[],[f868,f1565]) ).
fof(f1769,plain,
ordinal(set_union2(sK87,sF100)),
inference(forward_subsumption_resolution,[],[f1628,f1146]) ).
fof(f1783,plain,
ordinal(sF101),
inference(forward_demodulation,[],[f1769,f1523]) ).
fof(f1801,plain,
( subset(sK87,sK88)
| ~ epsilon_transitive(sK88)
| ~ spl102_1 ),
inference(resolution,[],[f1531,f827]) ).
fof(f1802,plain,
( sK88 = set_union2(unordered_pair(sK87,sK87),sK88)
| ~ spl102_1 ),
inference(resolution,[],[f1531,f1393]) ).
fof(f1804,plain,
( sK88 = set_union2(sF100,sK88)
| ~ spl102_1 ),
inference(forward_demodulation,[],[f1802,f1521]) ).
fof(f1805,plain,
( subset(sK87,sK88)
| ~ spl102_1 ),
inference(forward_subsumption_resolution,[],[f1801,f1686]) ).
fof(f1806,plain,
( ! [X0] :
( ~ in(X0,sF100)
| in(X0,sK88) )
| ~ spl102_1 ),
inference(superposition,[],[f1465,f1804]) ).
fof(f1814,plain,
( ! [X0] :
( ~ in(X0,sK87)
| in(X0,sK88) )
| ~ spl102_1 ),
inference(resolution,[],[f1805,f867]) ).
fof(f1830,definition,
( spl102_14
<=> ordinal(sF101) ),
introduced(definition,[new_symbols(definition,[spl102_14])],[avatar_definition]) ).
fof(f1831,plain,
( ordinal(sF101)
| ~ spl102_14 ),
inference(avatar_component_clause,[],[f1830]) ).
fof(f1838,plain,
spl102_14,
inference(avatar_split_clause,[],[f1783,f1830]) ).
fof(f1858,plain,
( ! [X0] :
( in(sK41(sF101,X0),sF100)
| subset(sF101,X0)
| in(sK41(sF101,X0),sK88) )
| ~ spl102_1 ),
inference(resolution,[],[f1702,f1814]) ).
fof(f1866,plain,
( ! [X0] :
( in(sK41(sF101,X0),sK88)
| subset(sF101,X0) )
| ~ spl102_1 ),
inference(forward_subsumption_resolution,[],[f1858,f1806]) ).
fof(f1876,plain,
( subset(sF101,sK88)
| subset(sF101,sK88)
| ~ spl102_1 ),
inference(resolution,[],[f1866,f869]) ).
fof(f1880,plain,
( subset(sF101,sK88)
| ~ spl102_1 ),
inference(duplicate_literal_removal,[],[f1876]) ).
fof(f1884,plain,
( ordinal_subset(sF101,sK88)
| ~ ordinal(sF101)
| ~ ordinal(sK88)
| ~ spl102_1 ),
inference(resolution,[],[f1880,f1071]) ).
fof(f1885,plain,
( ~ ordinal(sF101)
| ~ ordinal(sK88)
| ~ spl102_1
| spl102_2 ),
inference(forward_subsumption_resolution,[],[f1884,f1534]) ).
fof(f1886,plain,
( ~ ordinal(sK88)
| ~ spl102_1
| spl102_2
| ~ spl102_14 ),
inference(forward_subsumption_resolution,[],[f1885,f1831]) ).
fof(f1887,plain,
( $false
| ~ spl102_1
| spl102_2
| ~ spl102_14 ),
inference(forward_subsumption_resolution,[],[f1886,f1147]) ).
fof(f1888,plain,
( ~ spl102_1
| spl102_2
| ~ spl102_14 ),
inference(avatar_contradiction_clause,[],[f1887]) ).
fof(f1889,plain,
( subset(sF101,sK88)
| ~ ordinal(sF101)
| ~ ordinal(sK88)
| ~ spl102_2 ),
inference(resolution,[],[f1535,f1070]) ).
fof(f1890,plain,
( subset(sF101,sK88)
| ~ ordinal(sK88)
| ~ spl102_2
| ~ spl102_14 ),
inference(forward_subsumption_resolution,[],[f1889,f1831]) ).
fof(f1891,plain,
( subset(sF101,sK88)
| ~ spl102_2
| ~ spl102_14 ),
inference(forward_subsumption_resolution,[],[f1890,f1147]) ).
fof(f1896,plain,
( ! [X0] :
( ~ in(X0,sF101)
| in(X0,sK88) )
| ~ spl102_2
| ~ spl102_14 ),
inference(resolution,[],[f1891,f867]) ).
fof(f1901,plain,
( in(sK87,sK88)
| ~ spl102_2
| ~ spl102_14 ),
inference(resolution,[],[f1896,f1596]) ).
fof(f1903,plain,
( $false
| spl102_1
| ~ spl102_2
| ~ spl102_14 ),
inference(forward_subsumption_resolution,[],[f1901,f1530]) ).
fof(f1904,plain,
( spl102_1
| ~ spl102_2
| ~ spl102_14 ),
inference(avatar_contradiction_clause,[],[f1903]) ).
cnf(s1,plain,
( spl102_1
| spl102_2 ),
inference(sat_conversion,[],[f1536]) ).
cnf(s2,plain,
( ~ spl102_1
| ~ spl102_2 ),
inference(sat_conversion,[],[f1537]) ).
cnf(s18,plain,
spl102_14,
inference(sat_conversion,[],[f1838]) ).
cnf(s20,plain,
( ~ spl102_1
| spl102_2
| ~ spl102_14 ),
inference(sat_conversion,[],[f1888]) ).
cnf(s21,plain,
( spl102_1
| ~ spl102_2
| ~ spl102_14 ),
inference(sat_conversion,[],[f1904]) ).
cnf(s24,plain,
spl102_1,
inference(rat,[],[s1,s21,s18]) ).
cnf(s25,plain,
spl102_2,
inference(rat,[],[s20,s18,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s2,s25,s24]) ).
fof(f1907,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU236+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:17:57 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 6.44/1.77 % (3453444)Detected formulas, will run a generic FOF schedule.
% 6.44/1.77 % (3453450)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=489193169:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.44/1.77 % (3453453)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=635481022:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.44/1.77 % (3453449)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=2479368255:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.44/1.77 % (3453452)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4137672577:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.44/1.77 % (3453455)dis-21_1_sil=8000:lcm=predicate:random_seed=1038977283: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)
% 6.44/1.77 % (3453451)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=2996022649:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.44/1.77 % (3453454)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3564324649:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.44/1.77 % (3453455)Instruction limit reached!
% 6.44/1.77 % (3453455)------------------------------
% 6.44/1.77 % (3453455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453455)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453455)Termination reason: Instruction limit
% 6.44/1.77 % (3453455)Termination phase: Saturation
% 6.44/1.77 % (3453455)Time elapsed: 0.062 s
% 6.44/1.77 % (3453455)Peak memory usage: 90 MB
% 6.44/1.77 % (3453455)Instructions burned: 130 (million)
% 6.44/1.77 % (3453452)Instruction limit reached!
% 6.44/1.77 % (3453452)------------------------------
% 6.44/1.77 % (3453452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453452)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453452)Termination reason: Instruction limit
% 6.44/1.77 % (3453452)Termination phase: Saturation
% 6.44/1.77 % (3453452)Time elapsed: 0.068 s
% 6.44/1.77 % (3453452)Peak memory usage: 90 MB
% 6.44/1.77 % (3453452)Instructions burned: 109 (million)
% 6.44/1.77 % (3453453)Instruction limit reached!
% 6.44/1.77 % (3453453)------------------------------
% 6.44/1.77 % (3453453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453453)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453453)Termination reason: Instruction limit
% 6.44/1.77 % (3453453)Termination phase: Saturation
% 6.44/1.77 % (3453453)Time elapsed: 0.074 s
% 6.44/1.77 % (3453453)Peak memory usage: 89 MB
% 6.44/1.77 % (3453453)Instructions burned: 119 (million)
% 6.44/1.77 % (3453454)Instruction limit reached!
% 6.44/1.77 % (3453454)------------------------------
% 6.44/1.77 % (3453454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453454)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453454)Termination reason: Instruction limit
% 6.44/1.77 % (3453454)Termination phase: Saturation
% 6.44/1.77 % (3453454)Time elapsed: 0.098 s
% 6.44/1.77 % (3453454)Peak memory usage: 90 MB
% 6.44/1.77 % (3453454)Instructions burned: 139 (million)
% 6.44/1.77 % (3453464)lrs+10_1_sil=32000:urr=on:br=off:random_seed=466077519:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.44/1.77 % (3453463)lrs+10_1_sil=8000:sp=occurrence:random_seed=28362581:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.44/1.77 % (3453465)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2965716420:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.44/1.77 % (3453466)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=2334282415:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.44/1.77 % (3453464)Instruction limit reached!
% 6.44/1.77 % (3453464)------------------------------
% 6.44/1.77 % (3453464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453464)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453464)Termination reason: Instruction limit
% 6.44/1.77 % (3453464)Termination phase: Saturation
% 6.44/1.77 % (3453464)Time elapsed: 0.086 s
% 6.44/1.77 % (3453464)Peak memory usage: 90 MB
% 6.44/1.77 % (3453464)Instructions burned: 158 (million)
% 6.44/1.77 % (3453466)Instruction limit reached!
% 6.44/1.77 % (3453466)------------------------------
% 6.44/1.77 % (3453466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453466)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453466)Termination reason: Instruction limit
% 6.44/1.77 % (3453466)Termination phase: Saturation
% 6.44/1.77 % (3453466)Time elapsed: 0.092 s
% 6.44/1.77 % (3453466)Peak memory usage: 93 MB
% 6.44/1.77 % (3453466)Instructions burned: 250 (million)
% 6.44/1.77 % (3453463)Instruction limit reached!
% 6.44/1.77 % (3453463)------------------------------
% 6.44/1.77 % (3453463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453463)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453463)Termination reason: Instruction limit
% 6.44/1.77 % (3453463)Termination phase: Saturation
% 6.44/1.77 % (3453463)Time elapsed: 0.188 s
% 6.44/1.77 % (3453463)Peak memory usage: 93 MB
% 6.44/1.77 % (3453463)Instructions burned: 285 (million)
% 6.44/1.77 % (3453472)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2359571629:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.44/1.77 % (3453471)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2384191504:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.44/1.77 % (3453465)Instruction limit reached!
% 6.44/1.77 % (3453465)------------------------------
% 6.44/1.77 % (3453465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453465)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453465)Termination reason: Instruction limit
% 6.44/1.77 % (3453465)Termination phase: Saturation
% 6.44/1.77 % (3453465)Time elapsed: 0.223 s
% 6.44/1.77 % (3453465)Peak memory usage: 93 MB
% 6.44/1.77 % (3453465)Instructions burned: 325 (million)
% 6.44/1.77 % (3453473)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=538322483:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.44/1.77 % (3453476)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=863288816:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.44/1.77 % (3453473)Instruction limit reached!
% 6.44/1.77 % (3453473)------------------------------
% 6.44/1.77 % (3453473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453473)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453473)Termination reason: Instruction limit
% 6.44/1.77 % (3453473)Termination phase: Saturation
% 6.44/1.77 % (3453473)Time elapsed: 0.071 s
% 6.44/1.77 % (3453473)Peak memory usage: 90 MB
% 6.44/1.77 % (3453473)Instructions burned: 114 (million)
% 6.44/1.77 % (3453471)Instruction limit reached!
% 6.44/1.77 % (3453471)------------------------------
% 6.44/1.77 % (3453471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453471)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453471)Termination reason: Instruction limit
% 6.44/1.77 % (3453471)Termination phase: Saturation
% 6.44/1.77 % (3453471)Time elapsed: 0.191 s
% 6.44/1.77 % (3453471)Peak memory usage: 91 MB
% 6.44/1.77 % (3453471)Instructions burned: 296 (million)
% 6.44/1.77 % (3453476)Instruction limit reached!
% 6.44/1.77 % (3453476)------------------------------
% 6.44/1.77 % (3453476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453476)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453476)Termination reason: Instruction limit
% 6.44/1.77 % (3453476)Termination phase: Saturation
% 6.44/1.77 % (3453476)Time elapsed: 0.069 s
% 6.44/1.77 % (3453476)Peak memory usage: 90 MB
% 6.44/1.77 % (3453476)Instructions burned: 128 (million)
% 6.44/1.77 % (3453479)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2986493893:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.44/1.77 % (3453449)First to succeed.
% 6.44/1.77 % (3453449)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3453444"
% 6.44/1.77 % (3453480)lrs+10_1_sil=8000:sp=occurrence:random_seed=39324995:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.44/1.77 % (3453481)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=376102812:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.44/1.77 % (3453479)Instruction limit reached!
% 6.44/1.77 % (3453479)------------------------------
% 6.44/1.77 % (3453479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.77 % (3453479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.77 % (3453479)CaDiCaL version: 2.1.3
% 6.44/1.77 % (3453479)Termination reason: Instruction limit
% 6.44/1.77 % (3453479)Termination phase: Saturation
% 6.44/1.77 % (3453479)Time elapsed: 0.068 s
% 6.44/1.77 % (3453479)Peak memory usage: 89 MB
% 6.44/1.77 % (3453479)Instructions burned: 115 (million)
% 6.44/1.77 % (3453450)Also succeeded, but the first one will report.
% 6.44/1.77 % (3453472)Also succeeded, but the first one will report.
% 6.44/1.77 % (3453485)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2096632845:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.44/1.77 % (3453449)Refutation found. Thanks to Tanya!
% 6.44/1.77 % SZS status Theorem for theBenchmark
% 6.44/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 8.45/1.97 % (3453449)------------------------------
% 8.45/1.97 % (3453449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.45/1.97 % (3453449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.45/1.97 % (3453449)CaDiCaL version: 2.1.3
% 8.45/1.97 % (3453449)Termination reason: Refutation
% 8.45/1.97 % (3453449)Time elapsed: 0.745 s
% 8.45/1.97 % (3453449)Peak memory usage: 133 MB
% 8.45/1.97 % (3453449)Instructions burned: 1149 (million)
% 8.45/1.97 % (3453449)------------------------------
% 8.45/1.97 % (3453449)------------------------------
% 8.45/1.97 % (3453444)Success in time 1.15 s
% 8.45/1.97 % Vampire exiting
%------------------------------------------------------------------------------