%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU376+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 : n011.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 02:57:16 PM UTC 2026
% Result : Theorem 8.52s 1.99s
% Output : CNFRefutation 8.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 86 ( 16 unt; 0 def)
% Number of atoms : 507 ( 10 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 681 ( 260 ~; 303 |; 88 &)
% ( 9 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 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 : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 218 ( 0 sgn 189 !; 29 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( element(X4,the_carrier(X1))
=> ( related(X1,X3,X4)
=> in(apply_netmap(X0,X1,X4),X2) ) )
& element(X3,the_carrier(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_waybel_0) ).
fof(f9,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ? [X4] :
( in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_waybel_0) ).
fof(f10,axiom,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ( directed_relstr(X0)
<=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ? [X3] :
( related(X0,X2,X3)
& related(X0,X1,X3)
& element(X3,the_carrier(X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_yellow_6) ).
fof(f20,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(f54,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
=> is_often_in(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_yellow_6) ).
fof(f55,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
=> is_often_in(X0,X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f65,plain,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
=> is_often_in(X0,X1,X2) ) ) ),
inference(pure_predicate_removal,[],[f55]) ).
fof(f80,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ related(X1,X3,X4)
| in(apply_netmap(X0,X1,X4),X2) )
& element(X3,the_carrier(X1)) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f81,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ related(X1,X3,X4)
| in(apply_netmap(X0,X1,X4),X2) )
& element(X3,the_carrier(X1)) ) ) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,the_carrier(X1))
| ? [X4] :
( in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f83,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,the_carrier(X1))
| ? [X4] :
( in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) ) ) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ( directed_relstr(X0)
<=> ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ? [X3] :
( related(X0,X2,X3)
& related(X0,X1,X3)
& element(X3,the_carrier(X0)) ) ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f85,plain,
! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ( directed_relstr(X0)
<=> ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ? [X3] :
( related(X0,X2,X3)
& related(X0,X1,X3)
& element(X3,the_carrier(X0)) ) ) ) ) ),
inference(flattening,[],[f84]) ).
fof(f93,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| rel_str(X1) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f110,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& ~ empty_carrier(X1)
& ? [X2] :
( is_eventually_in(X0,X1,X2)
& ~ is_often_in(X0,X1,X2) ) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f111,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( net_str(X1,X0)
& directed_relstr(X1)
& ~ empty_carrier(X1)
& ? [X2] :
( is_eventually_in(X0,X1,X2)
& ~ is_often_in(X0,X1,X2) ) ) ),
inference(flattening,[],[f110]) ).
fof(f121,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ( ~ is_eventually_in(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ related(X1,X3,X4)
| in(apply_netmap(X0,X1,X4),X2) )
& element(X3,the_carrier(X1)) ) )
& ( ! [X3] :
( ? [X4] :
( element(X4,the_carrier(X1))
& related(X1,X3,X4)
& ~ in(apply_netmap(X0,X1,X4),X2) )
| ~ element(X3,the_carrier(X1)) )
| is_eventually_in(X0,X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f122,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ( ~ is_eventually_in(X0,X1,X2)
| ? [X5] :
( ! [X6] :
( ~ element(X6,the_carrier(X1))
| ~ related(X1,X5,X6)
| in(apply_netmap(X0,X1,X6),X2) )
& element(X5,the_carrier(X1)) ) )
& ( ! [X3] :
( ? [X4] :
( element(X4,the_carrier(X1))
& related(X1,X3,X4)
& ~ in(apply_netmap(X0,X1,X4),X2) )
| ~ element(X3,the_carrier(X1)) )
| is_eventually_in(X0,X1,X2) ) ) ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ( ~ is_eventually_in(X0,X1,X2)
| ( ! [X6] :
( ~ element(X6,the_carrier(X1))
| ~ related(X1,sK1(X0,X1,X2),X6)
| in(apply_netmap(X0,X1,X6),X2) )
& element(sK1(X0,X1,X2),the_carrier(X1)) ) )
& ( ! [X3] :
( ( element(sK0(X0,X1,X2,X3),the_carrier(X1))
& related(X1,X3,sK0(X0,X1,X2,X3))
& ~ in(apply_netmap(X0,X1,sK0(X0,X1,X2,X3)),X2) )
| ~ element(X3,the_carrier(X1)) )
| is_eventually_in(X0,X1,X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0(X0,X1,X2,X3)),skolemize(X5,sK1(X0,X1,X2))],[f122]) ).
fof(f124,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ( ~ is_often_in(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ? [X4] :
( in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) )
& ( ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ) )
| is_often_in(X0,X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f125,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ( ~ is_often_in(X0,X1,X2)
| ! [X5] :
( ~ element(X5,the_carrier(X1))
| ? [X6] :
( in(apply_netmap(X0,X1,X6),X2)
& related(X1,X5,X6)
& element(X6,the_carrier(X1)) ) ) )
& ( ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ) )
| is_often_in(X0,X1,X2) ) ) ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ( ~ is_often_in(X0,X1,X2)
| ! [X5] :
( ~ element(X5,the_carrier(X1))
| ( in(apply_netmap(X0,X1,sK3(X0,X1,X2,X5)),X2)
& related(X1,X5,sK3(X0,X1,X2,X5))
& element(sK3(X0,X1,X2,X5),the_carrier(X1)) ) ) )
& ( ( element(sK2(X0,X1,X2),the_carrier(X1))
& ! [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,sK2(X0,X1,X2),X4)
| ~ element(X4,the_carrier(X1)) ) )
| is_often_in(X0,X1,X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X6,sK3(X0,X1,X2,X5))],[f125]) ).
fof(f127,plain,
! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ( ( ~ directed_relstr(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ? [X3] :
( related(X0,X2,X3)
& related(X0,X1,X3)
& element(X3,the_carrier(X0)) ) ) ) )
& ( ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& ! [X3] :
( ~ related(X0,X2,X3)
| ~ related(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
| directed_relstr(X0) ) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f128,plain,
! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ( ( ~ directed_relstr(X0)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ! [X5] :
( ~ element(X5,the_carrier(X0))
| ? [X6] :
( related(X0,X5,X6)
& related(X0,X4,X6)
& element(X6,the_carrier(X0)) ) ) ) )
& ( ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& ! [X3] :
( ~ related(X0,X2,X3)
| ~ related(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) ) ) )
| directed_relstr(X0) ) ) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ( ( ~ directed_relstr(X0)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ! [X5] :
( ~ element(X5,the_carrier(X0))
| ( related(X0,X5,sK6(X0,X4,X5))
& related(X0,X4,sK6(X0,X4,X5))
& element(sK6(X0,X4,X5),the_carrier(X0)) ) ) ) )
& ( ( element(sK4(X0),the_carrier(X0))
& element(sK5(X0),the_carrier(X0))
& ! [X3] :
( ~ related(X0,sK5(X0),X3)
| ~ related(X0,sK4(X0),X3)
| ~ element(X3,the_carrier(X0)) ) )
| directed_relstr(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0)),skolemize(X6,sK6(X0,X4,X5))],[f128]) ).
fof(f149,plain,
( one_sorted_str(sK25)
& ~ empty_carrier(sK25)
& net_str(sK26,sK25)
& directed_relstr(sK26)
& ~ empty_carrier(sK26)
& is_eventually_in(sK25,sK26,sK27)
& ~ is_often_in(sK25,sK26,sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X0,sK25),skolemize(X1,sK26),skolemize(X2,sK27)],[f111]) ).
fof(f156,plain,
! [X2,X0,X1,X6] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ is_eventually_in(X0,X1,X2)
| ~ element(X6,the_carrier(X1))
| ~ related(X1,sK1(X0,X1,X2),X6)
| in(apply_netmap(X0,X1,X6),X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ is_eventually_in(X0,X1,X2)
| element(sK1(X0,X1,X2),the_carrier(X1)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| element(sK2(X0,X1,X2),the_carrier(X1))
| is_often_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f126]) ).
fof(f165,plain,
! [X2,X0,X1,X4] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,sK2(X0,X1,X2),X4)
| ~ element(X4,the_carrier(X1))
| is_often_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f126]) ).
fof(f166,plain,
! [X0,X4,X5] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ~ directed_relstr(X0)
| ~ element(X4,the_carrier(X0))
| ~ element(X5,the_carrier(X0))
| related(X0,X5,sK6(X0,X4,X5)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f167,plain,
! [X0,X4,X5] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ~ directed_relstr(X0)
| ~ element(X4,the_carrier(X0))
| ~ element(X5,the_carrier(X0))
| related(X0,X4,sK6(X0,X4,X5)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f168,plain,
! [X0,X4,X5] :
( ~ rel_str(X0)
| empty_carrier(X0)
| ~ directed_relstr(X0)
| ~ element(X4,the_carrier(X0))
| ~ element(X5,the_carrier(X0))
| element(sK6(X0,X4,X5),the_carrier(X0)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f176,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| rel_str(X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f227,plain,
one_sorted_str(sK25),
inference(cnf_transformation,[],[f149]) ).
fof(f228,plain,
~ empty_carrier(sK25),
inference(cnf_transformation,[],[f149]) ).
fof(f229,plain,
net_str(sK26,sK25),
inference(cnf_transformation,[],[f149]) ).
fof(f230,plain,
directed_relstr(sK26),
inference(cnf_transformation,[],[f149]) ).
fof(f231,plain,
~ empty_carrier(sK26),
inference(cnf_transformation,[],[f149]) ).
fof(f232,plain,
is_eventually_in(sK25,sK26,sK27),
inference(cnf_transformation,[],[f149]) ).
fof(f233,plain,
~ is_often_in(sK25,sK26,sK27),
inference(cnf_transformation,[],[f149]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| element(sK1(X0,X1,X2),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ is_eventually_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| in(apply_netmap(X1,X0,X3),X2)
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1)
| ~ element(X3,the_carrier(X0))
| ~ is_eventually_in(X1,X0,X2)
| ~ related(X0,sK1(X1,X0,X2),X3) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_often_in(X1,X0,X2)
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1)
| ~ element(X3,the_carrier(X0))
| ~ in(apply_netmap(X1,X0,X3),X2)
| ~ related(X0,sK2(X1,X0,X2),X3) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_often_in(X1,X0,X2)
| element(sK2(X1,X0,X2),the_carrier(X0))
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| element(sK6(X1,X0,X2),the_carrier(X1))
| ~ rel_str(X1)
| ~ directed_relstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| related(X1,X0,sK6(X1,X0,X2))
| ~ rel_str(X1)
| ~ directed_relstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| related(X1,X2,sK6(X1,X0,X2))
| ~ rel_str(X1)
| ~ directed_relstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( rel_str(X0)
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_124,negated_conjecture,
~ is_often_in(sK25,sK26,sK27),
inference(cnf_transformation,[],[f233]) ).
tcf(c_125,negated_conjecture,
is_eventually_in(sK25,sK26,sK27),
inference(cnf_transformation,[],[f232]) ).
tcf(c_126,negated_conjecture,
~ empty_carrier(sK26),
inference(cnf_transformation,[],[f231]) ).
tcf(c_127,negated_conjecture,
directed_relstr(sK26),
inference(cnf_transformation,[],[f230]) ).
tcf(c_128,negated_conjecture,
net_str(sK26,sK25),
inference(cnf_transformation,[],[f229]) ).
tcf(c_129,negated_conjecture,
~ empty_carrier(sK25),
inference(cnf_transformation,[],[f228]) ).
tcf(c_130,negated_conjecture,
one_sorted_str(sK25),
inference(cnf_transformation,[],[f227]) ).
tcf(c_3018,plain,
! [X0: $i,X1: $i] :
( rel_str(X0)
| ~ one_sorted_str(X1)
| ( X1 != sK25 )
| ( X0 != sK26 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_128]) ).
tcf(c_3019,plain,
( rel_str(sK26)
| ~ one_sorted_str(sK25) ),
inference(unflattening,[status(thm)],[c_3018]) ).
tcf(c_3025,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_often_in(X1,X0,X2)
| element(sK2(X1,X0,X2),the_carrier(X0))
| ~ one_sorted_str(X1)
| ( X1 != sK25 )
| ( X0 != sK26 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_128]) ).
tcf(c_3026,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| is_often_in(sK25,sK26,X0)
| element(sK2(sK25,sK26,X0),the_carrier(sK26))
| ~ one_sorted_str(sK25) ),
inference(unflattening,[status(thm)],[c_3025]) ).
tcf(c_3028,plain,
! [X0: $i] :
( is_often_in(sK25,sK26,X0)
| element(sK2(sK25,sK26,X0),the_carrier(sK26)) ),
inference(global_subsumption_just,[status(thm)],[c_3026,c_130,c_129,c_126,c_3026]) ).
tcf(c_3037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| is_often_in(X1,X0,X2)
| ~ one_sorted_str(X1)
| ~ element(X3,the_carrier(X0))
| ~ in(apply_netmap(X1,X0,X3),X2)
| ~ related(X0,sK2(X1,X0,X2),X3)
| ( X1 != sK25 )
| ( X0 != sK26 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_128]) ).
tcf(c_3038,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| is_often_in(sK25,sK26,X0)
| ~ one_sorted_str(sK25)
| ~ element(X1,the_carrier(sK26))
| ~ in(apply_netmap(sK25,sK26,X1),X0)
| ~ related(sK26,sK2(sK25,sK26,X0),X1) ),
inference(unflattening,[status(thm)],[c_3037]) ).
tcf(c_3040,plain,
! [X0: $i,X1: $i] :
( is_often_in(sK25,sK26,X0)
| ~ related(sK26,sK2(sK25,sK26,X0),X1)
| ~ in(apply_netmap(sK25,sK26,X1),X0)
| ~ element(X1,the_carrier(sK26)) ),
inference(global_subsumption_just,[status(thm)],[c_3038,c_130,c_129,c_126,c_3038]) ).
tcf(c_3041,plain,
! [X0: $i,X1: $i] :
( is_often_in(sK25,sK26,X0)
| ~ element(X1,the_carrier(sK26))
| ~ in(apply_netmap(sK25,sK26,X1),X0)
| ~ related(sK26,sK2(sK25,sK26,X0),X1) ),
inference(renaming,[status(thm)],[c_3040]) ).
tcf(c_3055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| in(apply_netmap(X1,X0,X3),X2)
| ~ one_sorted_str(X1)
| ~ element(X3,the_carrier(X0))
| ~ is_eventually_in(X1,X0,X2)
| ~ related(X0,sK1(X1,X0,X2),X3)
| ( X1 != sK25 )
| ( X0 != sK26 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_128]) ).
tcf(c_3056,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| in(apply_netmap(sK25,sK26,X1),X0)
| ~ one_sorted_str(sK25)
| ~ is_eventually_in(sK25,sK26,X0)
| ~ element(X1,the_carrier(sK26))
| ~ related(sK26,sK1(sK25,sK26,X0),X1) ),
inference(unflattening,[status(thm)],[c_3055]) ).
tcf(c_3058,plain,
! [X0: $i,X1: $i] :
( in(apply_netmap(sK25,sK26,X1),X0)
| ~ related(sK26,sK1(sK25,sK26,X0),X1)
| ~ element(X1,the_carrier(sK26))
| ~ is_eventually_in(sK25,sK26,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3056,c_130,c_129,c_126,c_3056]) ).
tcf(c_3059,plain,
! [X0: $i,X1: $i] :
( in(apply_netmap(sK25,sK26,X1),X0)
| ~ is_eventually_in(sK25,sK26,X0)
| ~ element(X1,the_carrier(sK26))
| ~ related(sK26,sK1(sK25,sK26,X0),X1) ),
inference(renaming,[status(thm)],[c_3058]) ).
tcf(c_3242,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| empty_carrier(X0)
| element(sK1(X0,X1,X2),the_carrier(X1))
| ~ one_sorted_str(X0)
| ~ is_eventually_in(X0,X1,X2)
| ( X1 != sK26 )
| ( X0 != sK25 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_128]) ).
tcf(c_3243,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| element(sK1(sK25,sK26,X0),the_carrier(sK26))
| ~ one_sorted_str(sK25)
| ~ is_eventually_in(sK25,sK26,X0) ),
inference(unflattening,[status(thm)],[c_3242]) ).
tcf(c_3245,plain,
! [X0: $i] :
( element(sK1(sK25,sK26,X0),the_carrier(sK26))
| ~ is_eventually_in(sK25,sK26,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3243,c_130,c_129,c_126,c_3243]) ).
tcf(c_4313,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK26)
| is_often_in(sK25,sK26,X0)
| ~ rel_str(sK26)
| ~ directed_relstr(sK26)
| ~ element(X1,the_carrier(sK26))
| ~ element(sK2(sK25,sK26,X0),the_carrier(sK26))
| ~ element(sK6(sK26,sK2(sK25,sK26,X0),X1),the_carrier(sK26))
| ~ in(apply_netmap(sK25,sK26,sK6(sK26,sK2(sK25,sK26,X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_67,c_3041]) ).
tcf(c_4324,plain,
! [X0: $i,X1: $i] :
( ~ element(sK6(sK26,sK2(sK25,sK26,X0),X1),the_carrier(sK26))
| ~ in(apply_netmap(sK25,sK26,sK6(sK26,sK2(sK25,sK26,X0),X1)),X0)
| ~ element(X1,the_carrier(sK26))
| is_often_in(sK25,sK26,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4313,c_130,c_127,c_126,c_3019,c_3028,c_4313]) ).
tcf(c_4325,plain,
! [X0: $i,X1: $i] :
( is_often_in(sK25,sK26,X0)
| ~ element(X1,the_carrier(sK26))
| ~ element(sK6(sK26,sK2(sK25,sK26,X0),X1),the_carrier(sK26))
| ~ in(apply_netmap(sK25,sK26,sK6(sK26,sK2(sK25,sK26,X0),X1)),X0) ),
inference(renaming,[status(thm)],[c_4324]) ).
tcf(c_4350,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK26)
| in(apply_netmap(sK25,sK26,sK6(sK26,X0,sK1(sK25,sK26,X1))),X1)
| ~ rel_str(sK26)
| ~ directed_relstr(sK26)
| ~ is_eventually_in(sK25,sK26,X1)
| ~ element(X0,the_carrier(sK26))
| ~ element(sK1(sK25,sK26,X1),the_carrier(sK26))
| ~ element(sK6(sK26,X0,sK1(sK25,sK26,X1)),the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_68,c_3059]) ).
tcf(c_4352,plain,
! [X0: $i,X1: $i] :
( ~ element(sK6(sK26,X0,sK1(sK25,sK26,X1)),the_carrier(sK26))
| ~ element(sK1(sK25,sK26,X1),the_carrier(sK26))
| ~ element(X0,the_carrier(sK26))
| ~ is_eventually_in(sK25,sK26,X1)
| in(apply_netmap(sK25,sK26,sK6(sK26,X0,sK1(sK25,sK26,X1))),X1) ),
inference(global_subsumption_just,[status(thm)],[c_4350,c_130,c_127,c_126,c_3019,c_4350]) ).
tcf(c_4353,plain,
! [X0: $i,X1: $i] :
( in(apply_netmap(sK25,sK26,sK6(sK26,X0,sK1(sK25,sK26,X1))),X1)
| ~ is_eventually_in(sK25,sK26,X1)
| ~ element(X0,the_carrier(sK26))
| ~ element(sK1(sK25,sK26,X1),the_carrier(sK26))
| ~ element(sK6(sK26,X0,sK1(sK25,sK26,X1)),the_carrier(sK26)) ),
inference(renaming,[status(thm)],[c_4352]) ).
tcf(c_4360,plain,
! [X0: $i,X1: $i] :
( in(apply_netmap(sK25,sK26,sK6(sK26,X0,sK1(sK25,sK26,X1))),X1)
| ~ is_eventually_in(sK25,sK26,X1)
| ~ element(X0,the_carrier(sK26))
| ~ element(sK6(sK26,X0,sK1(sK25,sK26,X1)),the_carrier(sK26)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4353,c_3245]) ).
tcf(c_4397,plain,
! [X0: $i] :
( is_often_in(sK25,sK26,X0)
| ~ is_eventually_in(sK25,sK26,X0)
| ~ element(sK2(sK25,sK26,X0),the_carrier(sK26))
| ~ element(sK1(sK25,sK26,X0),the_carrier(sK26))
| ~ element(sK6(sK26,sK2(sK25,sK26,X0),sK1(sK25,sK26,X0)),the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_4360,c_4325]) ).
tcf(c_4404,plain,
! [X0: $i] :
( is_often_in(sK25,sK26,X0)
| ~ is_eventually_in(sK25,sK26,X0)
| ~ element(sK6(sK26,sK2(sK25,sK26,X0),sK1(sK25,sK26,X0)),the_carrier(sK26)) ),
inference(global_subsumption_just,[status(thm)],[c_4397,c_3028,c_3245,c_4397]) ).
tcf(c_4429,plain,
! [X0: $i] :
( empty_carrier(sK26)
| is_often_in(sK25,sK26,X0)
| ~ rel_str(sK26)
| ~ directed_relstr(sK26)
| ~ is_eventually_in(sK25,sK26,X0)
| ~ element(sK2(sK25,sK26,X0),the_carrier(sK26))
| ~ element(sK1(sK25,sK26,X0),the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_66,c_4404]) ).
tcf(c_4431,plain,
! [X0: $i] :
( ~ is_eventually_in(sK25,sK26,X0)
| is_often_in(sK25,sK26,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4429,c_130,c_127,c_126,c_3019,c_3028,c_3245,c_4429]) ).
tcf(c_4432,plain,
! [X0: $i] :
( is_often_in(sK25,sK26,X0)
| ~ is_eventually_in(sK25,sK26,X0) ),
inference(renaming,[status(thm)],[c_4431]) ).
tcf(c_4441,plain,
is_often_in(sK25,sK26,sK27),
inference(superposition,[status(thm)],[c_125,c_4432]) ).
tcf(c_4442,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4441,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU376+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.43 % Computer : n011.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8046.5625MB
% 0.14/0.43 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Thu Sep 24 13:54:13 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.49 Running first-order theorem proving
% 0.14/0.49 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
% 0.22/0.51
% 0.22/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.51
% 0.22/0.51 % Detected problem language: tptp
% 0.22/0.53 % Proving...
% 8.52/1.99 % SZS status Started for theBenchmark.p
% 8.52/1.99 % SZS status Theorem for theBenchmark.p
% 8.52/1.99
% 8.52/1.99 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.52/1.99
% 8.52/1.99 % ------ iProver source info
% 8.52/1.99
% 8.52/1.99 % git: date: 2026-07-19 20:42:38 +0200
% 8.52/1.99 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.52/1.99 % git: non_committed_changes: false
% 8.52/1.99
% 8.52/1.99 % ------ Parsing...
% 8.52/1.99 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.52/1.99
% 8.52/1.99 % ------ Preprocessing... sup_sim: 0 sf_s rm: 14 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 8.52/1.99
% 8.52/1.99 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.52/1.99
% 8.52/1.99 % ------ Preprocessing... sf_s rm: 1 0s sf_e
% 8.52/1.99 % ------ Proving...
% 8.52/1.99 % ------ Problem Properties
% 8.52/1.99
% 8.52/1.99 %
% 8.52/1.99 % clauses 88
% 8.52/1.99 % conjectures 6
% 8.52/1.99 % EPR 28
% 8.52/1.99 % Horn 60
% 8.52/1.99 % unary 33
% 8.52/1.99 % binary 18
% 8.52/1.99 % lits 243
% 8.52/1.99 % lits eq 5
% 8.52/1.99 % fd_pure 0
% 8.52/1.99 % fd_pseudo 0
% 8.52/1.99 % fd_cond 1
% 8.52/1.99 % fd_pseudo_cond 1
% 8.52/1.99 % AC symbols 0
% 8.52/1.99
% 8.52/1.99 % ------ Input Options Time Limit: Unbounded
% 8.52/1.99
% 8.52/1.99
% 8.52/1.99 % ------
% 8.52/1.99 % Current options:
% 8.52/1.99 % ------
% 8.52/1.99
% 8.52/1.99
% 8.52/1.99 %
% 8.52/1.99
% 8.52/1.99 % ------ Proving...
% 8.52/1.99 %
% 8.52/1.99
% 8.52/1.99 % SZS status Theorem for theBenchmark.p
% 8.52/1.99
% 8.52/1.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.52/1.99
% 8.52/1.99
%------------------------------------------------------------------------------