%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM402+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 : Fri Sep 25 02:24:10 PM UTC 2026
% Result : Theorem 87.73s 13.48s
% Output : CNFRefutation 87.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 107 ( 4 unt; 0 def)
% Number of atoms : 372 ( 27 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 434 ( 169 ~; 190 |; 56 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 175 ( 0 sgn 159 !; 16 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f11,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f34,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f35,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f37,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ordinal(X1) )
=> ordinal(union(X0)) ),
file('/export/starexec/sandbox2/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] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f69,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f72,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
? [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ordinal(X1) )
& ~ ordinal(union(X0)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f83,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK0(X0),X0)
& ~ subset(sK0(X0),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(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f86,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ( ~ in(sK2(X0),sK1(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK1(X0),sK2(X0))
& in(sK2(X0),X0)
& in(sK1(X0),X0) )
| 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,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f89,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK3(X0,X1),X0)
& ~ in(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f89]) ).
fof(f91,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f92,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f94,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK6(X0,X5),X0)
& in(X5,sK6(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK4(X0,X1),X1)
| ( in(sK5(X0,X1),X0)
& in(sK4(X0,X1),sK5(X0,X1)) ) )
& ( ~ in(sK4(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK4(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
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,
( ! [X1] :
( ~ in(X1,sK21)
| ordinal(X1) )
& ~ ordinal(union(sK21)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f75]) ).
fof(f123,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,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(f135,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f92]) ).
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] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK6(X0,X5),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f139,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK6(X0,X5)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f140,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f192,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f193,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
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,union(X0))
| in(X5,sK6(X0,X5)) ),
inference(equality_resolution,[],[f139]) ).
fof(f206,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK6(X0,X5),X0) ),
inference(equality_resolution,[],[f138]) ).
tcf(c_58,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_59,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_61,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_62,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_63,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_64,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_65,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_70,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_71,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_72,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( in(X0,sK6(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( in(sK6(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_130,negated_conjecture,
~ ordinal(union(sK21)),
inference(cnf_transformation,[],[f196]) ).
tcf(c_131,negated_conjecture,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK21) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_3320,plain,
( ordinal(union(sK21))
| ~ epsilon_connected(union(sK21))
| ~ epsilon_transitive(union(sK21)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_3352,plain,
( epsilon_transitive(union(sK21))
| ~ subset(sK0(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_3353,plain,
( epsilon_transitive(union(sK21))
| in(sK0(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_3453,plain,
( epsilon_connected(union(sK21))
| ( sK1(union(sK21)) != sK2(union(sK21)) ) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3454,plain,
( epsilon_connected(union(sK21))
| ~ in(sK2(union(sK21)),sK1(union(sK21))) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3455,plain,
( epsilon_connected(union(sK21))
| ~ in(sK1(union(sK21)),sK2(union(sK21))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_3456,plain,
( epsilon_connected(union(sK21))
| in(sK2(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_3457,plain,
( epsilon_connected(union(sK21))
| in(sK1(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_3473,plain,
( in(sK6(sK21,sK0(union(sK21))),sK21)
| ~ in(sK0(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_3888,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK6(X1,X0))
| ~ epsilon_transitive(sK6(X1,X0))
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_77,c_60]) ).
tcf(c_3902,plain,
! [X0: $i] :
( ordinal(sK6(sK21,X0))
| ~ in(X0,union(sK21)) ),
inference(superposition,[status(thm)],[c_78,c_131]) ).
tcf(c_4007,plain,
( subset(sK0(union(sK21)),union(sK21))
| ~ in(sK3(sK0(union(sK21)),union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_4105,plain,
( in(sK2(union(sK21)),sK6(sK21,sK2(union(sK21))))
| ~ in(sK2(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_4111,plain,
( in(sK2(union(sK21)),sK1(union(sK21)))
| in(sK1(union(sK21)),sK2(union(sK21)))
| ( sK1(union(sK21)) = sK2(union(sK21)) )
| ~ ordinal(sK2(union(sK21)))
| ~ ordinal(sK1(union(sK21))) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_4127,plain,
( in(sK1(union(sK21)),sK6(sK21,sK1(union(sK21))))
| ~ in(sK1(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_4648,plain,
( epsilon_transitive(union(sK21))
| ordinal(sK6(sK21,sK0(union(sK21)))) ),
inference(superposition,[status(thm)],[c_59,c_3902]) ).
tcf(c_4650,plain,
( epsilon_connected(union(sK21))
| ordinal(sK6(sK21,sK1(union(sK21)))) ),
inference(superposition,[status(thm)],[c_61,c_3902]) ).
tcf(c_4652,plain,
( epsilon_connected(union(sK21))
| ordinal(sK6(sK21,sK2(union(sK21)))) ),
inference(superposition,[status(thm)],[c_62,c_3902]) ).
tcf(c_4830,plain,
( epsilon_transitive(union(sK21))
| epsilon_transitive(sK6(sK21,sK0(union(sK21)))) ),
inference(superposition,[status(thm)],[c_4648,c_71]) ).
tcf(c_4831,plain,
( epsilon_connected(union(sK21))
| epsilon_connected(sK6(sK21,sK1(union(sK21)))) ),
inference(superposition,[status(thm)],[c_4650,c_72]) ).
tcf(c_5245,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK3(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_69]) ).
tcf(c_5456,plain,
! [X0: $i] :
( in(X0,union(sK21))
| ~ in(sK6(sK21,sK0(union(sK21))),sK21)
| ~ in(X0,sK6(sK21,sK0(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_5613,plain,
( ordinal(sK2(union(sK21)))
| ~ ordinal(sK6(sK21,sK2(union(sK21))))
| ~ in(sK2(union(sK21)),sK6(sK21,sK2(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_5722,plain,
( ordinal(sK1(union(sK21)))
| ~ ordinal(sK6(sK21,sK1(union(sK21))))
| ~ in(sK1(union(sK21)),sK6(sK21,sK1(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_6318,plain,
epsilon_connected(union(sK21)),
inference(global_subsumption_just,[status(thm)],[c_4831,c_3457,c_3456,c_3455,c_3454,c_3453,c_4105,c_4111,c_4127,c_4650,c_4652,c_5613,c_5722]) ).
tcf(c_31424,plain,
( in(sK3(sK0(union(sK21)),union(sK21)),union(sK21))
| ~ in(sK6(sK21,sK0(union(sK21))),sK21)
| ~ in(sK3(sK0(union(sK21)),union(sK21)),sK6(sK21,sK0(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_5456]) ).
tcf(c_37645,plain,
! [X0: $i] :
( subset(sK0(union(sK21)),union(sK21))
| in(sK3(sK0(union(sK21)),union(sK21)),X0)
| ~ subset(sK0(union(sK21)),X0) ),
inference(instantiation,[status(thm)],[c_5245]) ).
tcf(c_37661,plain,
( subset(sK0(union(sK21)),sK6(sK21,sK0(union(sK21))))
| ~ epsilon_transitive(sK6(sK21,sK0(union(sK21))))
| ~ in(sK0(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_3888]) ).
tcf(c_43947,plain,
( subset(sK0(union(sK21)),union(sK21))
| in(sK3(sK0(union(sK21)),union(sK21)),sK6(sK21,sK0(union(sK21))))
| ~ subset(sK0(union(sK21)),sK6(sK21,sK0(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_37645]) ).
tcf(c_43948,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_43947,c_37661,c_31424,c_6318,c_4830,c_4007,c_3473,c_3352,c_3353,c_3320,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM402+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 03:51:24 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 87.73/13.48 % SZS status Started for theBenchmark.p
% 87.73/13.48 % SZS status Theorem for theBenchmark.p
% 87.73/13.48
% 87.73/13.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 87.73/13.48
% 87.73/13.48 % ------ iProver source info
% 87.73/13.48
% 87.73/13.48 % git: date: 2026-07-19 20:42:38 +0200
% 87.73/13.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 87.73/13.48 % git: non_committed_changes: false
% 87.73/13.48
% 87.73/13.48 % ------ Parsing...
% 87.73/13.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 87.73/13.48
% 87.73/13.48 % ------ Preprocessing... sup_sim: 0 sf_s rm: 22 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 87.73/13.48
% 87.73/13.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 87.73/13.48
% 87.73/13.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 87.73/13.48 % ------ Proving...
% 87.73/13.48 % ------ Problem Properties
% 87.73/13.48
% 87.73/13.48 %
% 87.73/13.48 % clauses 61
% 87.73/13.48 % conjectures 2
% 87.73/13.48 % EPR 39
% 87.73/13.48 % Horn 52
% 87.73/13.48 % unary 23
% 87.73/13.48 % binary 24
% 87.73/13.48 % lits 119
% 87.73/13.48 % lits eq 8
% 87.73/13.48 % fd_pure 0
% 87.73/13.48 % fd_pseudo 0
% 87.73/13.48 % fd_cond 1
% 87.73/13.48 % fd_pseudo_cond 6
% 87.73/13.48 % AC symbols 0
% 87.73/13.48
% 87.73/13.48 % ------ Input Options Time Limit: Unbounded
% 87.73/13.48
% 87.73/13.48
% 87.73/13.48 % ------
% 87.73/13.48 % Current options:
% 87.73/13.48 % ------
% 87.73/13.48
% 87.73/13.48
% 87.73/13.48 %
% 87.73/13.48
% 87.73/13.48 % ------ Proving...
% 87.73/13.48 %
% 87.73/13.48
% 87.73/13.48 % SZS status Theorem for theBenchmark.p
% 87.73/13.48
% 87.73/13.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 87.73/13.48
% 87.73/13.48
%------------------------------------------------------------------------------