%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 02:56:19 PM UTC 2026
% Result : Theorem 2.28s 1.29s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 86 ( 6 unt; 0 def)
% Number of atoms : 343 ( 61 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 427 ( 170 ~; 207 |; 39 &)
% ( 6 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn 122 !; 13 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> ! [X1] :
~ ( ! [X2] :
~ ( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
& X1 != empty_set
& subset(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
~ ( ! [X3] :
~ ( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
& X2 != empty_set
& subset(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
fof(f34,conjecture,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f41,plain,
? [X0] :
( relation(X0)
& ( well_founded_relation(X0)
<~> is_well_founded_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f42,plain,
! [X0] :
( ~ relation(X0)
| ( well_founded_relation(X0)
<=> ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f57,plain,
? [X0] :
( relation(X0)
& ( well_founded_relation(X0)
| is_well_founded_in(X0,relation_field(X0)) )
& ( ~ well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0)) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f58,plain,
? [X0] :
( relation(X0)
& ( well_founded_relation(X0)
| is_well_founded_in(X0,relation_field(X0)) )
& ( ~ well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0)) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
( relation(sK0)
& ( well_founded_relation(sK0)
| is_well_founded_in(sK0,relation_field(sK0)) )
& ( ~ well_founded_relation(sK0)
| ~ is_well_founded_in(sK0,relation_field(sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f58]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) )
& ( ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X3] :
( ? [X4] :
( disjoint(fiber(X0,X4),X3)
& in(X4,X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ) )
& ( ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X3] :
( ( disjoint(fiber(X0,sK2(X0,X3)),X3)
& in(sK2(X0,X3),X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ) )
& ( ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK1(X0))
| ~ in(X2,sK1(X0)) )
& empty_set != sK1(X0)
& subset(sK1(X0),relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X4,sK2(X0,X3))],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_well_founded_in(X0,X1)
| ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) ) )
& ( ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) )
| is_well_founded_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_well_founded_in(X0,X1)
| ! [X4] :
( ? [X5] :
( disjoint(fiber(X0,X5),X4)
& in(X5,X4) )
| empty_set = X4
| ~ subset(X4,X1) ) )
& ( ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) )
| is_well_founded_in(X0,X1) ) ) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_well_founded_in(X0,X1)
| ! [X4] :
( ( disjoint(fiber(X0,sK4(X0,X4)),X4)
& in(sK4(X0,X4),X4) )
| empty_set = X4
| ~ subset(X4,X1) ) )
& ( ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK3(X0,X1))
| ~ in(X3,sK3(X0,X1)) )
& empty_set != sK3(X0,X1)
& subset(sK3(X0,X1),X1) )
| is_well_founded_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3(X0,X1)),skolemize(X5,sK4(X0,X4))],[f64]) ).
fof(f70,plain,
relation(sK0),
inference(cnf_transformation,[],[f59]) ).
fof(f71,plain,
( well_founded_relation(sK0)
| is_well_founded_in(sK0,relation_field(sK0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f72,plain,
( ~ well_founded_relation(sK0)
| ~ is_well_founded_in(sK0,relation_field(sK0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f73,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| disjoint(fiber(X0,sK2(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f74,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| in(sK2(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f75,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ disjoint(fiber(X0,X2),sK1(X0))
| ~ in(X2,sK1(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f76,plain,
! [X0] :
( ~ relation(X0)
| empty_set != sK1(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f77,plain,
! [X0] :
( ~ relation(X0)
| subset(sK1(X0),relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f78,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| disjoint(fiber(X0,sK4(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f79,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| in(sK4(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f80,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ disjoint(fiber(X0,X3),sK3(X0,X1))
| ~ in(X3,sK3(X0,X1))
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f81,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set != sK3(X0,X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f82,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(sK3(X0,X1),X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_49,negated_conjecture,
( ~ well_founded_relation(sK0)
| ~ is_well_founded_in(sK0,relation_field(sK0)) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_50,negated_conjecture,
( well_founded_relation(sK0)
| is_well_founded_in(sK0,relation_field(sK0)) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_51,negated_conjecture,
relation(sK0),
inference(cnf_transformation,[],[f70]) ).
tcf(c_52,plain,
! [X0: $i] :
( well_founded_relation(X0)
| subset(sK1(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_53,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ( sK1(X0) != empty_set ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ in(X1,sK1(X0))
| ~ disjoint(fiber(X0,X1),sK1(X0)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0),X0)
| ( X0 = empty_set )
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X1,sK2(X1,X0)),X0)
| ( X0 = empty_set )
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| subset(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| ~ relation(X0)
| ( sK3(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_well_founded_in(X0,X2)
| ~ relation(X0)
| ~ in(X1,sK3(X0,X2))
| ~ disjoint(fiber(X0,X1),sK3(X0,X2)) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2),X2)
| ( X2 = empty_set )
| ~ relation(X0)
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK4(X0,X2)),X2)
| ( X2 = empty_set )
| ~ relation(X0)
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK4(X0,X2)),X2)
| ( X2 = empty_set )
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_61]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(sK0,sK4(sK0,X0)),X0)
| ( X0 = empty_set )
| ~ is_well_founded_in(sK0,X1)
| ~ subset(X0,X1) ),
inference(unflattening,[status(thm)],[c_613]) ).
tcf(c_628,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X0,X2),X2)
| ( X2 = empty_set )
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_60]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK0,X0),X0)
| ( X0 = empty_set )
| ~ is_well_founded_in(sK0,X1)
| ~ subset(X0,X1) ),
inference(unflattening,[status(thm)],[c_628]) ).
tcf(c_643,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_well_founded_in(X0,X2)
| ~ in(X1,sK3(X0,X2))
| ~ disjoint(fiber(X0,X1),sK3(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_59]) ).
tcf(c_644,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(sK0,X1)
| ~ in(X0,sK3(sK0,X1))
| ~ disjoint(fiber(sK0,X0),sK3(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_643]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| ( X0 != sK0 )
| ( sK3(X0,X1) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_58]) ).
tcf(c_656,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| ( sK3(sK0,X0) != empty_set ) ),
inference(unflattening,[status(thm)],[c_655]) ).
tcf(c_664,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| subset(sK3(X0,X1),X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_57]) ).
tcf(c_665,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| subset(sK3(sK0,X0),X0) ),
inference(unflattening,[status(thm)],[c_664]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(X0)
| ~ in(X1,sK1(X0))
| ~ disjoint(fiber(X0,X1),sK1(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).
tcf(c_674,plain,
! [X0: $i] :
( well_founded_relation(sK0)
| ~ in(X0,sK1(sK0))
| ~ disjoint(fiber(sK0,X0),sK1(sK0)) ),
inference(unflattening,[status(thm)],[c_673]) ).
tcf(c_685,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ( X0 != sK0 )
| ( sK1(X0) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_53]) ).
tcf(c_686,plain,
( well_founded_relation(sK0)
| ( sK1(sK0) != empty_set ) ),
inference(unflattening,[status(thm)],[c_685]) ).
tcf(c_693,plain,
! [X0: $i] :
( well_founded_relation(X0)
| subset(sK1(X0),relation_field(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_52]) ).
tcf(c_694,plain,
( well_founded_relation(sK0)
| subset(sK1(sK0),relation_field(sK0)) ),
inference(unflattening,[status(thm)],[c_693]) ).
tcf(c_701,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK2(X0,X1)),X1)
| ( X1 = empty_set )
| ~ well_founded_relation(X0)
| ~ subset(X1,relation_field(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).
tcf(c_702,plain,
! [X0: $i] :
( disjoint(fiber(sK0,sK2(sK0,X0)),X0)
| ( X0 = empty_set )
| ~ well_founded_relation(sK0)
| ~ subset(X0,relation_field(sK0)) ),
inference(unflattening,[status(thm)],[c_701]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1),X1)
| ( X1 = empty_set )
| ~ well_founded_relation(X0)
| ~ subset(X1,relation_field(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_55]) ).
tcf(c_717,plain,
! [X0: $i] :
( in(sK2(sK0,X0),X0)
| ( X0 = empty_set )
| ~ well_founded_relation(sK0)
| ~ subset(X0,relation_field(sK0)) ),
inference(unflattening,[status(thm)],[c_716]) ).
tcf(c_1267,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK0)
| in(sK4(sK0,X0),X0)
| ( X0 = empty_set )
| ~ is_well_founded_in(sK0,X1)
| ( sK1(sK0) != X0 )
| ( relation_field(sK0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_629,c_694]) ).
tcf(c_1268,plain,
( well_founded_relation(sK0)
| in(sK4(sK0,sK1(sK0)),sK1(sK0))
| ( sK1(sK0) = empty_set )
| ~ is_well_founded_in(sK0,relation_field(sK0)) ),
inference(unflattening,[status(thm)],[c_1267]) ).
tcf(c_1269,plain,
( well_founded_relation(sK0)
| in(sK4(sK0,sK1(sK0)),sK1(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1268,c_50,c_686,c_1268]) ).
tcf(c_1277,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK0)
| disjoint(fiber(sK0,sK4(sK0,X0)),X0)
| ( X0 = empty_set )
| ~ is_well_founded_in(sK0,X1)
| ( sK1(sK0) != X0 )
| ( relation_field(sK0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_614,c_694]) ).
tcf(c_1278,plain,
( well_founded_relation(sK0)
| disjoint(fiber(sK0,sK4(sK0,sK1(sK0))),sK1(sK0))
| ( sK1(sK0) = empty_set )
| ~ is_well_founded_in(sK0,relation_field(sK0)) ),
inference(unflattening,[status(thm)],[c_1277]) ).
tcf(c_1279,plain,
( well_founded_relation(sK0)
| disjoint(fiber(sK0,sK4(sK0,sK1(sK0))),sK1(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1278,c_50,c_686,c_1278]) ).
tcf(c_1464,plain,
( subset(sK1(sK0),relation_field(sK0))
| well_founded_relation(sK0) ),
inference(prop_impl_just,[status(thm)],[c_694]) ).
tcf(c_1465,plain,
( well_founded_relation(sK0)
| subset(sK1(sK0),relation_field(sK0)) ),
inference(renaming,[status(thm)],[c_1464]) ).
tcf(c_1498,plain,
! [X0: $i] :
( subset(sK3(sK0,X0),X0)
| is_well_founded_in(sK0,X0) ),
inference(prop_impl_just,[status(thm)],[c_665]) ).
tcf(c_1499,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| subset(sK3(sK0,X0),X0) ),
inference(renaming,[status(thm)],[c_1498]) ).
tcf(c_3445,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| ( sK3(sK0,X0) = empty_set )
| ~ well_founded_relation(sK0)
| ~ subset(sK3(sK0,X0),relation_field(sK0))
| ~ in(sK2(sK0,sK3(sK0,X0)),sK3(sK0,X0)) ),
inference(superposition,[status(thm)],[c_702,c_644]) ).
tcf(c_3537,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| ~ in(sK2(sK0,sK3(sK0,X0)),sK3(sK0,X0))
| ~ subset(sK3(sK0,X0),relation_field(sK0))
| ~ well_founded_relation(sK0) ),
inference(global_subsumption_just,[status(thm)],[c_3445,c_656,c_3445]) ).
tcf(c_3538,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| ~ well_founded_relation(sK0)
| ~ subset(sK3(sK0,X0),relation_field(sK0))
| ~ in(sK2(sK0,sK3(sK0,X0)),sK3(sK0,X0)) ),
inference(renaming,[status(thm)],[c_3537]) ).
tcf(c_3548,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| ( sK3(sK0,X0) = empty_set )
| ~ well_founded_relation(sK0)
| ~ subset(sK3(sK0,X0),relation_field(sK0)) ),
inference(superposition,[status(thm)],[c_717,c_3538]) ).
tcf(c_3554,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| ~ subset(sK3(sK0,X0),relation_field(sK0))
| ~ well_founded_relation(sK0) ),
inference(global_subsumption_just,[status(thm)],[c_3548,c_656,c_3548]) ).
tcf(c_3555,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| ~ well_founded_relation(sK0)
| ~ subset(sK3(sK0,X0),relation_field(sK0)) ),
inference(renaming,[status(thm)],[c_3554]) ).
tcf(c_3613,plain,
( well_founded_relation(sK0)
| disjoint(fiber(sK0,sK4(sK0,sK1(sK0))),sK1(sK0))
| ( sK1(sK0) = empty_set )
| ~ is_well_founded_in(sK0,relation_field(sK0)) ),
inference(superposition,[status(thm)],[c_1465,c_614]) ).
tcf(c_3668,plain,
( well_founded_relation(sK0)
| disjoint(fiber(sK0,sK4(sK0,sK1(sK0))),sK1(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_3613,c_1279]) ).
tcf(c_3675,plain,
( well_founded_relation(sK0)
| ~ in(sK4(sK0,sK1(sK0)),sK1(sK0)) ),
inference(superposition,[status(thm)],[c_3668,c_674]) ).
tcf(c_3680,plain,
well_founded_relation(sK0),
inference(global_subsumption_just,[status(thm)],[c_3675,c_1269,c_3675]) ).
tcf(c_3684,plain,
! [X0: $i] :
( is_well_founded_in(sK0,X0)
| ~ subset(sK3(sK0,X0),relation_field(sK0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3555,c_3680]) ).
tcf(c_3688,plain,
~ is_well_founded_in(sK0,relation_field(sK0)),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_3680]) ).
tcf(c_3859,plain,
is_well_founded_in(sK0,relation_field(sK0)),
inference(superposition,[status(thm)],[c_1499,c_3684]) ).
tcf(c_3860,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3859,c_3688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 13:28:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 2.28/1.29 % SZS status Started for theBenchmark.p
% 2.28/1.29 % SZS status Theorem for theBenchmark.p
% 2.28/1.29
% 2.28/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.28/1.29
% 2.28/1.29 % ------ iProver source info
% 2.28/1.29
% 2.28/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.28/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.28/1.29 % git: non_committed_changes: false
% 2.28/1.29
% 2.28/1.29 % ------ Parsing...
% 2.28/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.28/1.29
% 2.28/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.28/1.29
% 2.28/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.28/1.29
% 2.28/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.28/1.29 % ------ Proving...
% 2.28/1.29 % ------ Problem Properties
% 2.28/1.29
% 2.28/1.29 %
% 2.28/1.29 % clauses 33
% 2.28/1.29 % conjectures 2
% 2.28/1.29 % EPR 13
% 2.28/1.29 % Horn 25
% 2.28/1.29 % unary 8
% 2.28/1.29 % binary 15
% 2.28/1.29 % lits 72
% 2.28/1.29 % lits eq 11
% 2.28/1.29 % fd_pure 0
% 2.28/1.29 % fd_pseudo 0
% 2.28/1.29 % fd_cond 5
% 2.28/1.29 % fd_pseudo_cond 1
% 2.28/1.29 % AC symbols 0
% 2.28/1.29
% 2.28/1.29 % ------ Schedule dynamic 5 is on
% 2.28/1.29
% 2.28/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.28/1.29
% 2.28/1.29
% 2.28/1.29 % ------
% 2.28/1.29 % Current options:
% 2.28/1.29 % ------
% 2.28/1.29
% 2.28/1.29
% 2.28/1.29 %
% 2.28/1.29
% 2.28/1.29 % ------ Proving...
% 2.28/1.29 %
% 2.28/1.29
% 2.28/1.29 % SZS status Theorem for theBenchmark.p
% 2.28/1.29
% 2.28/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.28/1.29
% 2.28/1.29
%------------------------------------------------------------------------------