%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU315+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 : n007.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 02:56:46 PM UTC 2026
% Result : Theorem 3.15s 1.18s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 8
% Syntax : Number of formulae : 178 ( 19 unt; 2 def)
% Number of atoms : 842 ( 74 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 932 ( 390 ~; 422 |; 100 &)
% ( 9 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 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 : 12 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 285 ( 0 sgn 248 !; 37 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f29,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f30,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(f31,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f35,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f39,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f58,plain,
? [X0,X1] :
( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
<~> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f59,plain,
? [X0,X1] :
( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
<~> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(flattening,[],[f58]) ).
fof(f74,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f75,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( element(X1,X0)
<=> empty(X1) ) )
& ( empty(X0)
| ( element(X1,X0)
<=> in(X1,X0) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f35]) ).
fof(f79,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f81,plain,
? [X0,X1] :
( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
| ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f82,plain,
? [X0,X1] :
( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
| ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
? [X0,X1] :
( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
| ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
( element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0)
& topological_space(sK0)
& ! [X2] :
( ( element(sK2(X2),powerset(the_carrier(sK0)))
& ( in(sK2(X2),X2)
| ( subset(sK1,sK2(X2))
& closed_subset(sK3(X2),sK0)
& sK2(X2) = sK3(X2)
& element(sK3(X2),powerset(the_carrier(sK0))) ) )
& ( ~ in(sK2(X2),X2)
| ! [X4] :
( ~ subset(sK1,sK2(X2))
| ~ closed_subset(X4,sK0)
| sK2(X2) != X4
| ~ element(X4,powerset(the_carrier(sK0))) ) ) )
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2)),skolemize(X5,sK3(X2))],[f83]) ).
fof(f89,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f90,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ! [X3] :
( ( ~ in(X3,sK8(X0,X1))
| ( subset(X1,X3)
& closed_subset(sK9(X0,X1,X3),X0)
& sK9(X0,X1,X3) = X3
& element(sK9(X0,X1,X3),powerset(the_carrier(X0)))
& in(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK8(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X2,sK8(X0,X1)),skolemize(X5,sK9(X0,X1,X3))],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( ( ~ element(X1,X0)
| empty(X1) )
& ( ~ empty(X1)
| element(X1,X0) ) ) )
& ( empty(X0)
| ( ( ~ element(X1,X0)
| in(X1,X0) )
& ( ~ in(X1,X0)
| element(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f95,plain,
! [X0,X1] :
( ( in(sK11(X0,X1),X0)
& ~ in(sK11(X0,X1),X1) )
| element(X0,powerset(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f77]) ).
fof(f98,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f84]) ).
fof(f99,plain,
top_str(sK0),
inference(cnf_transformation,[],[f84]) ).
fof(f100,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f84]) ).
fof(f101,plain,
! [X2] :
( element(sK2(X2),powerset(the_carrier(sK0)))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f102,plain,
! [X2] :
( in(sK2(X2),X2)
| subset(sK1,sK2(X2))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f103,plain,
! [X2] :
( in(sK2(X2),X2)
| closed_subset(sK3(X2),sK0)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f104,plain,
! [X2] :
( in(sK2(X2),X2)
| sK2(X2) = sK3(X2)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f105,plain,
! [X2] :
( in(sK2(X2),X2)
| element(sK3(X2),powerset(the_carrier(sK0)))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f106,plain,
! [X2,X4] :
( ~ in(sK2(X2),X2)
| ~ subset(sK1,sK2(X2))
| ~ closed_subset(X4,sK0)
| sK2(X2) != X4
| ~ element(X4,powerset(the_carrier(sK0)))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f145,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f146,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK8(X0,X1))
| subset(X1,X3) ),
inference(cnf_transformation,[],[f92]) ).
fof(f147,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK8(X0,X1))
| closed_subset(sK9(X0,X1,X3),X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f148,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK8(X0,X1))
| sK9(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f92]) ).
fof(f149,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK8(X0,X1))
| element(sK9(X0,X1,X3),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f150,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK8(X0,X1))
| in(X3,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f151,plain,
! [X3,X0,X1,X4] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK8(X0,X1)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f154,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f155,plain,
! [X0,X1] :
( empty(X0)
| ~ in(X1,X0)
| element(X1,X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f158,plain,
! [X0,X1] :
( in(sK11(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f159,plain,
! [X0,X1] :
( ~ in(sK11(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f163,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f165,plain,
! [X2] :
( ~ in(sK2(X2),X2)
| ~ subset(sK1,sK2(X2))
| ~ closed_subset(sK2(X2),sK0)
| ~ element(sK2(X2),powerset(the_carrier(sK0)))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(equality_resolution,[],[f106]) ).
fof(f166,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,powerset(the_carrier(X0)))
| in(X4,sK8(X0,X1)) ),
inference(equality_resolution,[],[f151]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ subset(sK1,sK2(X0))
| ~ closed_subset(sK2(X0),sK0)
| ~ in(sK2(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ element(sK2(X0),powerset(the_carrier(sK0))) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(sK2(X0),X0)
| element(sK3(X0),powerset(the_carrier(sK0)))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( in(sK2(X0),X0)
| ( sK2(X0) = sK3(X0) )
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( closed_subset(sK3(X0),sK0)
| in(sK2(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( subset(sK1,sK2(X0))
| in(sK2(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( element(sK2(X0),powerset(the_carrier(sK0)))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_55,negated_conjecture,
topological_space(sK0),
inference(cnf_transformation,[],[f100]) ).
tcf(c_56,negated_conjecture,
top_str(sK0),
inference(cnf_transformation,[],[f99]) ).
tcf(c_57,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f98]) ).
tcf(c_96,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f145]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK8(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,X2)
| ~ closed_subset(X2,X1)
| ~ in(X2,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK8(X1,X2)) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK9(X1,X2,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK8(X1,X2)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK9(X1,X2,X0) = X0 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK8(X1,X2)) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK9(X1,X2,X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK8(X1,X2)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK8(X1,X2)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ in(sK11(X0,X1),X1) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_103,c_114,c_103]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_159]) ).
tcf(c_161,negated_conjecture,
! [X0: $i] :
( ~ subset(sK1,sK2(X0))
| ~ closed_subset(sK2(X0),sK0)
| ~ in(sK2(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_54,c_49]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK8(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,X2)
| ~ closed_subset(X2,X1)
| ~ in(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_97,c_160]) ).
tcf(c_802,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK8(X0,X1))
| ~ top_str(X0)
| ~ subset(X1,X2)
| ~ closed_subset(X2,X0)
| ~ in(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_254]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i] :
( in(X1,sK8(sK0,X0))
| ~ top_str(sK0)
| ~ closed_subset(X1,sK0)
| ~ subset(X0,X1)
| ~ in(X1,powerset(the_carrier(sK0)))
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(unflattening,[status(thm)],[c_802]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i] :
( in(X1,sK8(sK0,X0))
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ in(X1,powerset(the_carrier(sK0)))
| ~ subset(X0,X1)
| ~ closed_subset(X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_803,c_56,c_803]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i] :
( in(X1,sK8(sK0,X0))
| ~ closed_subset(X1,sK0)
| ~ subset(X0,X1)
| ~ in(X1,powerset(the_carrier(sK0)))
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(renaming,[status(thm)],[c_805]) ).
tcf(c_823,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK8(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_102]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ top_str(sK0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_823]) ).
tcf(c_825,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_824,c_56,c_824]) ).
tcf(c_826,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(renaming,[status(thm)],[c_825]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK9(X0,X2,X1),X0)
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK8(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_101]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK9(sK0,X1,X0),sK0)
| ~ top_str(sK0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_836]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK9(sK0,X1,X0),sK0)
| ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_837,c_56,c_837]) ).
tcf(c_840,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK9(sK0,X1,X0),sK0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(renaming,[status(thm)],[c_839]) ).
tcf(c_851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK9(X0,X2,X1) = X1 )
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK8(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_100]) ).
tcf(c_852,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK0,X1,X0) = X0 )
| ~ top_str(sK0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_851]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK0,X1,X0) = X0 )
| ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_852,c_56,c_852]) ).
tcf(c_855,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK0,X1,X0) = X0 )
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(renaming,[status(thm)],[c_854]) ).
tcf(c_866,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK9(X0,X2,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK8(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_99]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i] :
( element(sK9(sK0,X1,X0),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_866]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i] :
( element(sK9(sK0,X1,X0),powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_867,c_56,c_867]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i] :
( element(sK9(sK0,X1,X0),powerset(the_carrier(sK0)))
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(renaming,[status(thm)],[c_869]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK8(X0,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_98]) ).
tcf(c_882,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(unflattening,[status(thm)],[c_881]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_882,c_56,c_882]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK0)))
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1)) ),
inference(renaming,[status(thm)],[c_884]) ).
tcf(c_1762,definition,
iPr_def_12 = powerset(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1763,definition,
iPr_def_13 = powerset(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1766,plain,
! [X0: $i,X1: $i] :
( in(X0,iPr_def_12)
| ~ element(X1,iPr_def_12)
| ~ in(X0,sK8(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_885]) ).
tcf(c_1767,plain,
! [X0: $i,X1: $i] :
( element(sK9(sK0,X1,X0),iPr_def_12)
| ~ element(X1,iPr_def_12)
| ~ in(X0,sK8(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_870]) ).
tcf(c_1768,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK0,X1,X0) = X0 )
| ~ element(X1,iPr_def_12)
| ~ in(X0,sK8(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_855]) ).
tcf(c_1769,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK9(sK0,X1,X0),sK0)
| ~ element(X1,iPr_def_12)
| ~ in(X0,sK8(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_840]) ).
tcf(c_1770,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ element(X1,iPr_def_12)
| ~ in(X0,sK8(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_826]) ).
tcf(c_1771,plain,
! [X0: $i,X1: $i] :
( in(X1,sK8(sK0,X0))
| ~ in(X1,iPr_def_12)
| ~ closed_subset(X1,sK0)
| ~ element(X0,iPr_def_12)
| ~ subset(X0,X1) ),
inference(demodulation,[status(thm)],[c_806]) ).
tcf(c_1772,negated_conjecture,
! [X0: $i] :
( ~ element(X0,iPr_def_13)
| ~ subset(sK1,sK2(X0))
| ~ closed_subset(sK2(X0),sK0)
| ~ in(sK2(X0),X0) ),
inference(demodulation,[status(thm)],[c_161,c_1763]) ).
tcf(c_1773,negated_conjecture,
element(sK1,iPr_def_12),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_1775,negated_conjecture,
! [X0: $i] :
( subset(sK1,sK2(X0))
| in(sK2(X0),X0)
| ~ element(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_1776,negated_conjecture,
! [X0: $i] :
( closed_subset(sK3(X0),sK0)
| in(sK2(X0),X0)
| ~ element(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_1777,negated_conjecture,
! [X0: $i] :
( in(sK2(X0),X0)
| ( sK2(X0) = sK3(X0) )
| ~ element(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_1778,negated_conjecture,
! [X0: $i] :
( element(sK3(X0),iPr_def_12)
| in(sK2(X0),X0)
| ~ element(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_2377,plain,
! [X0: $i] :
( subset(sK1,sK2(sK8(sK0,X0)))
| subset(X0,sK2(sK8(sK0,X0)))
| ~ element(X0,iPr_def_12)
| ~ element(sK8(sK0,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_1775,c_1770]) ).
tcf(c_2415,plain,
~ empty(iPr_def_12),
inference(superposition,[status(thm)],[c_1762,c_96]) ).
tcf(c_2426,plain,
( subset(sK1,sK2(sK8(sK0,sK1)))
| ~ element(sK1,iPr_def_12)
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(equality_factoring,[status(thm)],[c_2377]) ).
tcf(c_2428,plain,
( subset(sK1,sK2(sK8(sK0,sK1)))
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2426,c_1773]) ).
tcf(c_2461,plain,
! [X0: $i] :
( ( sK2(sK8(sK0,X0)) = sK3(sK8(sK0,X0)) )
| ( sK9(sK0,X0,sK2(sK8(sK0,X0))) = sK2(sK8(sK0,X0)) )
| ~ element(X0,iPr_def_12)
| ~ element(sK8(sK0,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_1777,c_1768]) ).
tcf(c_2462,plain,
! [X0: $i] :
( element(sK3(sK8(sK0,X0)),iPr_def_12)
| ( sK9(sK0,X0,sK2(sK8(sK0,X0))) = sK2(sK8(sK0,X0)) )
| ~ element(X0,iPr_def_12)
| ~ element(sK8(sK0,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_1778,c_1768]) ).
tcf(c_2506,plain,
! [X0: $i] :
( element(sK3(X0),iPr_def_12)
| element(sK2(X0),X0)
| ~ element(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_1778,c_160]) ).
tcf(c_2569,plain,
! [X0: $i] :
( element(sK3(X0),iPr_def_12)
| ~ empty(X0)
| ~ element(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_1778,c_114]) ).
tcf(c_2718,plain,
! [X0: $i,X1: $i] :
( empty(iPr_def_12)
| in(sK9(sK0,X1,X0),iPr_def_12)
| ~ element(X1,iPr_def_12)
| ~ in(X0,sK8(sK0,X1)) ),
inference(superposition,[status(thm)],[c_1767,c_104]) ).
tcf(c_2721,plain,
! [X0: $i] :
( empty(iPr_def_12)
| in(sK3(X0),iPr_def_12)
| element(sK2(X0),X0)
| ~ element(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2506,c_104]) ).
tcf(c_2722,plain,
! [X0: $i] :
( empty(iPr_def_12)
| in(sK3(X0),iPr_def_12)
| ~ empty(X0)
| ~ element(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2569,c_104]) ).
tcf(c_2723,plain,
! [X0: $i] :
( empty(iPr_def_12)
| in(sK3(sK8(sK0,X0)),iPr_def_12)
| ( sK9(sK0,X0,sK2(sK8(sK0,X0))) = sK2(sK8(sK0,X0)) )
| ~ element(X0,iPr_def_12)
| ~ element(sK8(sK0,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_2462,c_104]) ).
tcf(c_2744,plain,
! [X0: $i] :
( in(sK3(X0),iPr_def_12)
| ~ empty(X0)
| ~ element(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2722,c_2415]) ).
tcf(c_2748,plain,
! [X0: $i] :
( in(sK3(X0),iPr_def_12)
| element(sK2(X0),X0)
| ~ element(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2721,c_2415]) ).
tcf(c_2752,plain,
! [X0: $i,X1: $i] :
( in(sK9(sK0,X1,X0),iPr_def_12)
| ~ element(X1,iPr_def_12)
| ~ in(X0,sK8(sK0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2718,c_2415]) ).
tcf(c_2756,plain,
! [X0: $i] :
( in(sK3(sK8(sK0,X0)),iPr_def_12)
| ( sK9(sK0,X0,sK2(sK8(sK0,X0))) = sK2(sK8(sK0,X0)) )
| ~ element(X0,iPr_def_12)
| ~ element(sK8(sK0,X0),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2723,c_2415]) ).
tcf(c_2894,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_110,c_114]) ).
tcf(c_2898,plain,
! [X0: $i,X1: $i] :
( element(sK8(sK0,X0),powerset(X1))
| in(sK11(sK8(sK0,X0),X1),iPr_def_12)
| ~ element(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_110,c_1766]) ).
tcf(c_3025,plain,
! [X0: $i,X1: $i] :
( ( sK9(sK0,X0,X1) = X1 )
| ~ in(X1,iPr_def_12)
| ~ closed_subset(X1,sK0)
| ~ element(X0,iPr_def_12)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1771,c_1768]) ).
tcf(c_3130,plain,
! [X0: $i] :
( empty(X0)
| in(sK3(X0),iPr_def_12)
| in(sK2(X0),X0)
| ~ element(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2748,c_104]) ).
tcf(c_3156,plain,
! [X0: $i] :
( element(sK8(sK0,X0),powerset(iPr_def_12))
| ~ element(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_2898,c_109]) ).
tcf(c_3157,plain,
! [X0: $i] :
( element(sK8(sK0,X0),iPr_def_13)
| ~ element(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_3156,c_1763]) ).
tcf(c_3279,plain,
( ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) )
| ~ element(sK1,iPr_def_12)
| ~ element(sK8(sK0,sK1),iPr_def_13)
| ~ in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ~ closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(superposition,[status(thm)],[c_2428,c_3025]) ).
tcf(c_3304,plain,
( ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) )
| ~ element(sK8(sK0,sK1),iPr_def_13)
| ~ in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ~ closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3279,c_1773]) ).
tcf(c_3517,plain,
! [X0: $i] :
( element(X0,iPr_def_13)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1763,c_2894]) ).
tcf(c_3742,plain,
! [X0: $i] :
( in(sK3(sK8(sK0,X0)),iPr_def_12)
| ( sK9(sK0,X0,sK2(sK8(sK0,X0))) = sK2(sK8(sK0,X0)) )
| ~ element(X0,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_2756,c_2756,c_3157]) ).
tcf(c_3780,plain,
! [X0: $i] :
( in(sK3(X0),iPr_def_12)
| ~ empty(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2744,c_3517]) ).
tcf(c_3807,plain,
! [X0: $i] :
( ( sK2(sK8(sK0,X0)) = sK3(sK8(sK0,X0)) )
| ( sK9(sK0,X0,sK2(sK8(sK0,X0))) = sK2(sK8(sK0,X0)) )
| ~ element(X0,iPr_def_12)
| ~ empty(sK8(sK0,X0)) ),
inference(superposition,[status(thm)],[c_3517,c_2461]) ).
tcf(c_3970,plain,
! [X0: $i] :
( ( sK2(sK8(sK0,X0)) = sK3(sK8(sK0,X0)) )
| ( sK9(sK0,X0,sK2(sK8(sK0,X0))) = sK2(sK8(sK0,X0)) )
| ~ element(X0,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_3807,c_2461,c_3157]) ).
tcf(c_3984,plain,
( ( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) )
| ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) ) ),
inference(superposition,[status(thm)],[c_1773,c_3970]) ).
tcf(c_4100,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) )
| ~ element(sK1,iPr_def_12)
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_3984,c_1769]) ).
tcf(c_4106,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) )
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4100,c_1773]) ).
tcf(c_4123,plain,
! [X0: $i] :
( subset(sK1,sK2(sK8(sK0,X0)))
| subset(X0,sK2(sK8(sK0,X0)))
| ~ element(X0,iPr_def_12)
| ~ element(sK8(sK0,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_1775,c_1770]) ).
tcf(c_4221,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) )
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_1777,c_4106]) ).
tcf(c_4242,plain,
( ( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) )
| ~ element(sK8(sK0,sK1),iPr_def_13)
| ~ subset(sK1,sK2(sK8(sK0,sK1)))
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_4221,c_1772]) ).
tcf(c_4349,plain,
! [X0: $i] :
( subset(sK1,sK2(sK8(sK0,X0)))
| subset(X0,sK2(sK8(sK0,X0)))
| ~ element(X0,iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2377,c_3157]) ).
tcf(c_4499,plain,
( ( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) )
| ~ element(sK8(sK0,sK1),iPr_def_13)
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_4242,c_2428,c_4242]) ).
tcf(c_4504,plain,
( ( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) )
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4499,c_1777]) ).
tcf(c_4513,plain,
( ( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) )
| ~ element(sK1,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3157,c_4504]) ).
tcf(c_4514,plain,
sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_4513,c_1773]) ).
tcf(c_4522,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_4514,c_1776]) ).
tcf(c_4523,plain,
( in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) )
| ~ element(sK1,iPr_def_12) ),
inference(superposition,[status(thm)],[c_4514,c_3742]) ).
tcf(c_4544,plain,
( in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4523,c_1773]) ).
tcf(c_4569,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) )
| ~ element(sK1,iPr_def_12)
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_4522,c_1768]) ).
tcf(c_4583,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) )
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4569,c_1773]) ).
tcf(c_4659,plain,
! [X0: $i] :
( subset(sK1,sK2(sK8(sK0,X0)))
| subset(X0,sK2(sK8(sK0,X0)))
| ~ element(X0,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_4123,c_4349]) ).
tcf(c_4667,plain,
( subset(sK1,sK2(sK8(sK0,sK1)))
| ~ element(sK1,iPr_def_12) ),
inference(equality_factoring,[status(thm)],[c_4659]) ).
tcf(c_4669,plain,
subset(sK1,sK2(sK8(sK0,sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_4667,c_1773]) ).
tcf(c_4750,plain,
( ~ element(sK8(sK0,sK1),iPr_def_13)
| ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_4583,c_3304,c_4544,c_4583]) ).
tcf(c_4751,plain,
( ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) )
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(renaming,[status(thm)],[c_4750]) ).
tcf(c_4758,plain,
( ( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)) )
| ~ element(sK1,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3157,c_4751]) ).
tcf(c_4759,plain,
sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_4758,c_1773]) ).
tcf(c_4760,plain,
( in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ~ element(sK1,iPr_def_12)
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_4759,c_2752]) ).
tcf(c_4761,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ~ element(sK1,iPr_def_12)
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_4759,c_1769]) ).
tcf(c_4766,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4761,c_1773]) ).
tcf(c_4769,plain,
( in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4760,c_1773]) ).
tcf(c_4807,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4522,c_4766]) ).
tcf(c_4884,plain,
! [X0: $i] :
( ~ element(X0,iPr_def_13)
| in(sK2(X0),X0)
| in(sK3(X0),iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_3130,c_3130,c_3780]) ).
tcf(c_4885,plain,
! [X0: $i] :
( in(sK3(X0),iPr_def_12)
| in(sK2(X0),X0)
| ~ element(X0,iPr_def_13) ),
inference(renaming,[status(thm)],[c_4884]) ).
tcf(c_4905,plain,
( in(sK3(sK8(sK0,sK1)),iPr_def_12)
| in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_4885,c_4769]) ).
tcf(c_4915,plain,
( in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ~ element(sK8(sK0,sK1),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_4905,c_4514]) ).
tcf(c_5026,plain,
( ~ element(sK8(sK0,sK1),iPr_def_13)
| ~ subset(sK1,sK2(sK8(sK0,sK1)))
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_4807,c_1772]) ).
tcf(c_5037,plain,
( ~ element(sK8(sK0,sK1),iPr_def_13)
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_5026,c_4669,c_5026]) ).
tcf(c_5048,plain,
( ~ element(sK1,iPr_def_12)
| ~ element(sK8(sK0,sK1),iPr_def_13)
| ~ in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ~ subset(sK1,sK2(sK8(sK0,sK1)))
| ~ closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(superposition,[status(thm)],[c_1771,c_5037]) ).
tcf(c_5052,plain,
( ~ element(sK8(sK0,sK1),iPr_def_13)
| ~ in(sK2(sK8(sK0,sK1)),iPr_def_12)
| ~ subset(sK1,sK2(sK8(sK0,sK1)))
| ~ closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5048,c_1773]) ).
tcf(c_5057,plain,
~ element(sK8(sK0,sK1),iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_5052,c_4669,c_4807,c_4915,c_5052]) ).
tcf(c_5061,plain,
~ element(sK1,iPr_def_12),
inference(superposition,[status(thm)],[c_3157,c_5057]) ).
tcf(c_5062,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5061,c_1773]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU315+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 13:37:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.15/1.18 % SZS status Started for theBenchmark.p
% 3.15/1.18 % SZS status Theorem for theBenchmark.p
% 3.15/1.18
% 3.15/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.15/1.18
% 3.15/1.18 % ------ iProver source info
% 3.15/1.18
% 3.15/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.15/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.15/1.18 % git: non_committed_changes: false
% 3.15/1.18
% 3.15/1.18 % ------ Parsing...
% 3.15/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.15/1.18
% 3.15/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 35 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e %
% 3.15/1.18
% 3.15/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.15/1.18
% 3.15/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.15/1.18 % ------ Proving...
% 3.15/1.18 % ------ Problem Properties
% 3.15/1.18
% 3.15/1.18 %
% 3.15/1.18 % clauses 40
% 3.15/1.18 % conjectures 7
% 3.15/1.18 % EPR 16
% 3.15/1.18 % Horn 33
% 3.15/1.18 % unary 16
% 3.15/1.18 % binary 9
% 3.15/1.18 % lits 82
% 3.15/1.18 % lits eq 8
% 3.15/1.18 % fd_pure 0
% 3.15/1.18 % fd_pseudo 0
% 3.15/1.18 % fd_cond 1
% 3.15/1.18 % fd_pseudo_cond 1
% 3.15/1.18 % AC symbols 0
% 3.15/1.18
% 3.15/1.18 % ------ Schedule dynamic 5 is on
% 3.15/1.18
% 3.15/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.15/1.18
% 3.15/1.18
% 3.15/1.18 % ------
% 3.15/1.18 % Current options:
% 3.15/1.18 % ------
% 3.15/1.18
% 3.15/1.18
% 3.15/1.18 %
% 3.15/1.18
% 3.15/1.18 % ------ Proving...
% 3.15/1.18 %
% 3.15/1.18
% 3.15/1.18 % SZS status Theorem for theBenchmark.p
% 3.15/1.18
% 3.15/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.15/1.19
% 3.15/1.19
%------------------------------------------------------------------------------