%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM402+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:15:04 PM UTC 2026
% Result : Theorem 5.48s 2.15s
% Output : Refutation 9.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 109 ( 11 unt; 4 def)
% Number of atoms : 381 ( 27 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 455 ( 183 ~; 194 |; 56 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 172 ( 0 sgn 156 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f11,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f34,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f35,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X0,X1)
& X0 != X1
& ~ in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f37,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ordinal(X1) )
=> ordinal(union(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_ordinal1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( in(X1,X0)
=> ordinal(X1) )
=> ordinal(union(X0)) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f64,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( ~ in(X1,X0)
| ~ in(X2,X0)
| in(X1,X2)
| X1 = X2
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f69,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
? [X0] :
( ~ ordinal(union(X0))
& ! [X1] :
( ordinal(X1)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,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,[],[f64]) ).
fof(f83,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f83]) ).
fof(f85,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) )
& ( ! [X1,X2] :
( ~ in(X1,X0)
| ~ in(X2,X0)
| in(X1,X2)
| X1 = X2
| in(X2,X1) )
| ~ epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f86,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) )
& ( ! [X3,X4] :
( ~ in(X3,X0)
| ~ in(X4,X0)
| in(X3,X4)
| X3 = X4
| in(X4,X3) )
| ~ epsilon_connected(X0) ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( in(sK1(X0),X0)
& in(sK2(X0),X0)
& ~ in(sK1(X0),sK2(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK2(X0),sK1(X0)) ) )
& ( ! [X3,X4] :
( ~ in(X3,X0)
| ~ in(X4,X0)
| in(X3,X4)
| X3 = X4
| in(X4,X3) )
| ~ epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f86]) ).
fof(f88,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,[],[f66]) ).
fof(f89,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,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f89]) ).
fof(f91,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) )
& ( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f92,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) )
& ( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f94,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X2,X4)
& in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ? [X7] :
( in(X5,X7)
& in(X7,X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK4(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK4(X0,X1),X1) )
& ( ( in(sK4(X0,X1),sK5(X0,X1))
& in(sK5(X0,X1),X0) )
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK6(X0,X5))
& in(sK6(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f94]) ).
fof(f110,plain,
( ~ ordinal(union(sK21))
& ! [X1] :
( ordinal(X1)
| ~ in(X1,sK21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f75]) ).
fof(f123,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f124,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f125,plain,
! [X0] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f127,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f128,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f129,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f130,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f131,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f132,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f133,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f134,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f136,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f137,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f138,plain,
! [X0,X1,X5] :
( in(sK6(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f95]) ).
fof(f139,plain,
! [X0,X1,X5] :
( in(X5,sK6(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f95]) ).
fof(f140,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X5,X6)
| ~ in(X6,X0)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f95]) ).
fof(f192,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f193,plain,
! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f195,plain,
! [X1] :
( ~ in(X1,sK21)
| ordinal(X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f196,plain,
~ ordinal(union(sK21)),
inference(cnf_transformation,[],[f110]) ).
fof(f204,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f140]) ).
fof(f205,plain,
! [X0,X5] :
( in(X5,sK6(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f139]) ).
fof(f206,plain,
! [X0,X5] :
( in(sK6(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f138]) ).
fof(f207,definition,
sF22 = union(sK21),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f208,plain,
union(sK21) = sF22,
inference(reorient_equations,[],[f207]) ).
fof(f209,plain,
~ ordinal(sF22),
inference(definition_folding,[],[f196,f208]) ).
fof(f210,plain,
! [X0,X1] :
( ~ ordinal(sK6(X1,X0))
| ordinal(X0)
| ~ in(X0,union(X1)) ),
inference(resolution,[],[f192,f205]) ).
fof(f211,plain,
! [X0] :
( ~ in(X0,union(sK21))
| ordinal(sK6(sK21,X0)) ),
inference(resolution,[],[f206,f195]) ).
fof(f213,plain,
! [X0] :
( ordinal(sK6(sK21,X0))
| ~ in(X0,sF22) ),
inference(forward_demodulation,[],[f211,f208]) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ in(X0,sK6(X1,X2))
| in(X0,union(X1))
| ~ in(X2,union(X1)) ),
inference(resolution,[],[f204,f206]) ).
fof(f225,plain,
! [X0] :
( in(sK1(X0),sK2(X0))
| sK1(X0) = sK2(X0)
| ~ ordinal(sK1(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f193,f127]) ).
fof(f230,plain,
! [X0] :
( sK1(X0) = sK2(X0)
| ~ ordinal(sK1(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[],[f225,f129]) ).
fof(f232,plain,
! [X0] :
( ~ ordinal(sK2(X0))
| ~ ordinal(sK1(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[],[f230,f128]) ).
fof(f256,plain,
! [X0] :
( ordinal(X0)
| ~ in(X0,union(sK21))
| ~ in(X0,sF22) ),
inference(resolution,[],[f210,f213]) ).
fof(f257,plain,
! [X0] :
( ~ in(X0,sF22)
| ordinal(X0)
| ~ in(X0,sF22) ),
inference(forward_demodulation,[],[f256,f208]) ).
fof(f258,plain,
! [X0] :
( ~ in(X0,sF22)
| ordinal(X0) ),
inference(duplicate_literal_removal,[],[f257]) ).
fof(f261,plain,
( ordinal(sK1(sF22))
| epsilon_connected(sF22) ),
inference(resolution,[],[f258,f131]) ).
fof(f262,plain,
( ordinal(sK2(sF22))
| epsilon_connected(sF22) ),
inference(resolution,[],[f258,f130]) ).
fof(f266,definition,
( spl23_3
<=> epsilon_connected(sF22) ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
fof(f267,plain,
( ~ epsilon_connected(sF22)
| spl23_3 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( epsilon_connected(sF22)
| ~ spl23_3 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f270,definition,
( spl23_4
<=> ordinal(sK2(sF22)) ),
introduced(definition,[new_symbols(definition,[spl23_4])],[avatar_definition]) ).
fof(f272,plain,
( ordinal(sK2(sF22))
| ~ spl23_4 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,plain,
( spl23_3
| spl23_4 ),
inference(avatar_split_clause,[],[f262,f270,f266]) ).
fof(f275,definition,
( spl23_5
<=> ordinal(sK1(sF22)) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
fof(f277,plain,
( ordinal(sK1(sF22))
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f278,plain,
( spl23_3
| spl23_5 ),
inference(avatar_split_clause,[],[f261,f275,f266]) ).
fof(f308,plain,
! [X0,X1] :
( subset(X0,sK6(X1,X0))
| ~ epsilon_transitive(sK6(X1,X0))
| ~ in(X0,union(X1)) ),
inference(resolution,[],[f123,f205]) ).
fof(f327,plain,
( ~ epsilon_transitive(sF22)
| ordinal(sF22)
| ~ spl23_3 ),
inference(resolution,[],[f268,f137]) ).
fof(f328,plain,
( ~ epsilon_transitive(sF22)
| ~ spl23_3 ),
inference(forward_subsumption_resolution,[],[f327,f209]) ).
fof(f400,plain,
! [X2,X0,X1] :
( in(X2,sK6(X0,X1))
| ~ in(X1,union(X0))
| ~ in(X2,X1)
| ~ epsilon_transitive(sK6(X0,X1)) ),
inference(resolution,[],[f308,f132]) ).
fof(f422,plain,
! [X0] :
( epsilon_transitive(sK6(sK21,X0))
| ~ in(X0,sF22) ),
inference(resolution,[],[f136,f213]) ).
fof(f533,plain,
! [X2,X0,X1] :
( ~ in(X0,union(X1))
| ~ in(X2,X0)
| ~ epsilon_transitive(sK6(X1,X0))
| in(X2,union(X1))
| ~ in(X0,union(X1)) ),
inference(resolution,[],[f400,f217]) ).
fof(f542,plain,
! [X2,X0,X1] :
( ~ epsilon_transitive(sK6(X1,X0))
| ~ in(X2,X0)
| ~ in(X0,union(X1))
| in(X2,union(X1)) ),
inference(duplicate_literal_removal,[],[f533]) ).
fof(f1564,plain,
! [X0,X1] :
( ~ in(X0,sF22)
| ~ in(X1,X0)
| ~ in(X0,union(sK21))
| in(X1,union(sK21)) ),
inference(resolution,[],[f422,f542]) ).
fof(f1565,plain,
! [X0,X1] :
( ~ in(X0,sF22)
| ~ in(X0,sF22)
| ~ in(X1,X0)
| in(X1,union(sK21)) ),
inference(forward_demodulation,[],[f1564,f208]) ).
fof(f1566,plain,
! [X0,X1] :
( ~ in(X0,sF22)
| ~ in(X1,X0)
| in(X1,union(sK21)) ),
inference(duplicate_literal_removal,[],[f1565]) ).
fof(f1567,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,sF22)
| in(X1,sF22) ),
inference(forward_demodulation,[],[f1566,f208]) ).
fof(f1595,plain,
! [X0,X1] :
( in(sK3(X0,X1),sF22)
| ~ in(X0,sF22)
| subset(X0,X1) ),
inference(resolution,[],[f1567,f133]) ).
fof(f1630,plain,
! [X0] :
( ~ in(X0,sF22)
| subset(X0,sF22)
| subset(X0,sF22) ),
inference(resolution,[],[f1595,f134]) ).
fof(f1642,plain,
! [X0] :
( ~ in(X0,sF22)
| subset(X0,sF22) ),
inference(duplicate_literal_removal,[],[f1630]) ).
fof(f1648,plain,
( subset(sK0(sF22),sF22)
| epsilon_transitive(sF22) ),
inference(resolution,[],[f1642,f124]) ).
fof(f1667,plain,
epsilon_transitive(sF22),
inference(forward_subsumption_resolution,[],[f1648,f125]) ).
fof(f1668,plain,
( $false
| ~ spl23_3 ),
inference(forward_subsumption_resolution,[],[f1667,f328]) ).
fof(f1669,plain,
~ spl23_3,
inference(avatar_contradiction_clause,[],[f1668]) ).
fof(f1697,plain,
( ~ ordinal(sK1(sF22))
| epsilon_connected(sF22)
| ~ spl23_4 ),
inference(resolution,[],[f272,f232]) ).
fof(f1700,plain,
( epsilon_connected(sF22)
| ~ spl23_4
| ~ spl23_5 ),
inference(forward_subsumption_resolution,[],[f1697,f277]) ).
fof(f1701,plain,
( $false
| spl23_3
| ~ spl23_4
| ~ spl23_5 ),
inference(forward_subsumption_resolution,[],[f1700,f267]) ).
fof(f1702,plain,
( spl23_3
| ~ spl23_4
| ~ spl23_5 ),
inference(avatar_contradiction_clause,[],[f1701]) ).
cnf(s2,plain,
( spl23_3
| spl23_4 ),
inference(sat_conversion,[],[f273]) ).
cnf(s3,plain,
( spl23_3
| spl23_5 ),
inference(sat_conversion,[],[f278]) ).
cnf(s27,plain,
~ spl23_3,
inference(sat_conversion,[],[f1669]) ).
cnf(s33,plain,
( spl23_3
| ~ spl23_4
| ~ spl23_5 ),
inference(sat_conversion,[],[f1702]) ).
cnf(s36,plain,
spl23_5,
inference(rat,[],[s3,s27]) ).
cnf(s37,plain,
~ spl23_4,
inference(rat,[],[s33,s27,s36]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s2,s37,s27]) ).
fof(f1703,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM402+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 19:47:34 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 5.48/2.15 % (3703520)Detected formulas, will run a generic FOF schedule.
% 5.48/2.15 % (3703528)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=845887573:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.48/2.15 % (3703528)Refutation not found, incomplete strategy
% 5.48/2.15 % (3703528)------------------------------
% 5.48/2.15 % (3703528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703528)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703528)Termination reason: Refutation not found, incomplete strategy
% 5.48/2.15 % (3703528)Time elapsed: 0.001 s
% 5.48/2.15 % (3703528)Peak memory usage: 88 MB
% 5.48/2.15 % (3703528)Instructions burned: 1 (million)
% 5.48/2.15 % (3703531)dis-21_1_sil=8000:lcm=predicate:random_seed=3263600554: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)
% 5.48/2.15 % (3703527)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=1102662024:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.48/2.15 % (3703526)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=1474584113:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.48/2.15 % (3703529)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1607536734:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.48/2.15 % (3703525)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=1530022112:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.48/2.15 % (3703530)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=782684624:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.48/2.15 % (3703529)Instruction limit reached!
% 5.48/2.15 % (3703529)------------------------------
% 5.48/2.15 % (3703529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703529)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703529)Termination reason: Instruction limit
% 5.48/2.15 % (3703529)Termination phase: Saturation
% 5.48/2.15 % (3703529)Time elapsed: 0.071 s
% 5.48/2.15 % (3703529)Peak memory usage: 88 MB
% 5.48/2.15 % (3703529)Instructions burned: 119 (million)
% 5.48/2.15 % (3703531)Instruction limit reached!
% 5.48/2.15 % (3703531)------------------------------
% 5.48/2.15 % (3703531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703531)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703531)Termination reason: Instruction limit
% 5.48/2.15 % (3703531)Termination phase: Saturation
% 5.48/2.15 % (3703531)Time elapsed: 0.074 s
% 5.48/2.15 % (3703531)Peak memory usage: 89 MB
% 5.48/2.15 % (3703531)Instructions burned: 129 (million)
% 5.48/2.15 % (3703530)Instruction limit reached!
% 5.48/2.15 % (3703530)------------------------------
% 5.48/2.15 % (3703530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703530)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703530)Termination reason: Instruction limit
% 5.48/2.15 % (3703530)Termination phase: Saturation
% 5.48/2.15 % (3703530)Time elapsed: 0.093 s
% 5.48/2.15 % (3703530)Peak memory usage: 90 MB
% 5.48/2.15 % (3703530)Instructions burned: 140 (million)
% 5.48/2.15 % (3703528)------------------------------
% 5.48/2.15 % (3703528)------------------------------
% 5.48/2.15 % (3703539)lrs+10_1_sil=8000:sp=occurrence:random_seed=228309467:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.48/2.15 % (3703540)lrs+10_1_sil=32000:urr=on:br=off:random_seed=869260479:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.48/2.15 % (3703540)Refutation not found, incomplete strategy
% 5.48/2.15 % (3703540)------------------------------
% 5.48/2.15 % (3703540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703540)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703540)Termination reason: Refutation not found, incomplete strategy
% 5.48/2.15 % (3703540)Time elapsed: 0.002 s
% 5.48/2.15 % (3703540)Peak memory usage: 88 MB
% 5.48/2.15 % (3703540)Instructions burned: 1 (million)
% 5.48/2.15 % (3703542)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=3984965343:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.48/2.15 % (3703541)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1221529583:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.48/2.15 % (3703542)Instruction limit reached!
% 5.48/2.15 % (3703542)------------------------------
% 5.48/2.15 % (3703542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703542)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703542)Termination reason: Instruction limit
% 5.48/2.15 % (3703542)Termination phase: Saturation
% 5.48/2.15 % (3703542)Time elapsed: 0.068 s
% 5.48/2.15 % (3703542)Peak memory usage: 89 MB
% 5.48/2.15 % (3703542)Instructions burned: 250 (million)
% 5.48/2.15 % (3703539)Instruction limit reached!
% 5.48/2.15 % (3703539)------------------------------
% 5.48/2.15 % (3703539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703539)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703539)Termination reason: Instruction limit
% 5.48/2.15 % (3703539)Termination phase: Saturation
% 5.48/2.15 % (3703539)Time elapsed: 0.169 s
% 5.48/2.15 % (3703539)Peak memory usage: 90 MB
% 5.48/2.15 % (3703539)Instructions burned: 286 (million)
% 5.48/2.15 % (3703547)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3321486281:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.48/2.15 % (3703547)Refutation not found, incomplete strategy
% 5.48/2.15 % (3703547)------------------------------
% 5.48/2.15 % (3703547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703547)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703547)Termination reason: Refutation not found, incomplete strategy
% 5.48/2.15 % (3703547)Time elapsed: 0.002 s
% 5.48/2.15 % (3703547)Peak memory usage: 88 MB
% 5.48/2.15 % (3703547)Instructions burned: 4 (million)
% 5.48/2.15 % (3703541)Instruction limit reached!
% 5.48/2.15 % (3703541)------------------------------
% 5.48/2.15 % (3703541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703541)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703541)Termination reason: Instruction limit
% 5.48/2.15 % (3703541)Termination phase: Saturation
% 5.48/2.15 % (3703541)Time elapsed: 0.209 s
% 5.48/2.15 % (3703541)Peak memory usage: 91 MB
% 5.48/2.15 % (3703541)Instructions burned: 326 (million)
% 5.48/2.15 % (3703540)------------------------------
% 5.48/2.15 % (3703540)------------------------------
% 5.48/2.15 % (3703548)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2278478214:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.48/2.15 % (3703547)------------------------------
% 5.48/2.15 % (3703547)------------------------------
% 5.48/2.15 % (3703550)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2681546428:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.48/2.15 % (3703551)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3513396326:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.48/2.15 % (3703550)Instruction limit reached!
% 5.48/2.15 % (3703550)------------------------------
% 5.48/2.15 % (3703550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703550)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703550)Termination reason: Instruction limit
% 5.48/2.15 % (3703550)Termination phase: Saturation
% 5.48/2.15 % (3703550)Time elapsed: 0.077 s
% 5.48/2.15 % (3703550)Peak memory usage: 90 MB
% 5.48/2.15 % (3703550)Instructions burned: 113 (million)
% 5.48/2.15 % (3703551)Instruction limit reached!
% 5.48/2.15 % (3703551)------------------------------
% 5.48/2.15 % (3703551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703551)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703551)Termination reason: Instruction limit
% 5.48/2.15 % (3703551)Termination phase: Saturation
% 5.48/2.15 % (3703551)Time elapsed: 0.068 s
% 5.48/2.15 % (3703551)Peak memory usage: 89 MB
% 5.48/2.15 % (3703551)Instructions burned: 129 (million)
% 5.48/2.15 % (3703553)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2240511904:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.48/2.15 % (3703553)Instruction limit reached!
% 5.48/2.15 % (3703553)------------------------------
% 5.48/2.15 % (3703553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703553)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703553)Termination reason: Instruction limit
% 5.48/2.15 % (3703553)Termination phase: Saturation
% 5.48/2.15 % (3703553)Time elapsed: 0.032 s
% 5.48/2.15 % (3703553)Peak memory usage: 88 MB
% 5.48/2.15 % (3703553)Instructions burned: 115 (million)
% 5.48/2.15 % (3703525)First to succeed.
% 5.48/2.15 % (3703525)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3703520"
% 5.48/2.15 % (3703556)lrs+10_1_sil=8000:sp=occurrence:random_seed=3852039570:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 5.48/2.15 % (3703557)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3825906377:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 5.48/2.15 % (3703559)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3866056427:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 5.48/2.15 % (3703557)Instruction limit reached!
% 5.48/2.15 % (3703557)------------------------------
% 5.48/2.15 % (3703557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/2.15 % (3703557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/2.15 % (3703557)CaDiCaL version: 2.1.3
% 5.48/2.15 % (3703557)Termination reason: Instruction limit
% 5.48/2.15 % (3703557)Termination phase: Saturation
% 5.48/2.15 % (3703557)Time elapsed: 0.221 s
% 5.48/2.15 % (3703557)Peak memory usage: 89 MB
% 5.48/2.15 % (3703557)Instructions burned: 437 (million)
% 5.48/2.15 % (3703525)Refutation found. Thanks to Tanya!
% 5.48/2.15 % SZS status Theorem for theBenchmark
% 5.48/2.15 % SZS output start Proof for theBenchmark
% See solution above
% 9.73/2.34 % (3703525)------------------------------
% 9.73/2.34 % (3703525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.73/2.34 % (3703525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.73/2.34 % (3703525)CaDiCaL version: 2.1.3
% 9.73/2.34 % (3703525)Termination reason: Refutation
% 9.73/2.34 % (3703525)Time elapsed: 0.857 s
% 9.73/2.34 % (3703525)Peak memory usage: 131 MB
% 9.73/2.34 % (3703525)Instructions burned: 1303 (million)
% 9.73/2.34 % (3703525)------------------------------
% 9.73/2.34 % (3703525)------------------------------
% 9.73/2.34 % (3703520)Success in time 1.29 s
% 9.73/2.34 % Vampire exiting
%------------------------------------------------------------------------------