%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU322+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 : 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 02:56:51 PM UTC 2026
% Result : Theorem 29.64s 4.83s
% Output : CNFRefutation 29.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 148 ( 16 unt; 0 def)
% Number of atoms : 417 ( 30 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 494 ( 225 ~; 221 |; 20 &)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 244 ( 0 sgn 240 !; 4 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ( empty_carrier(X0)
<=> empty(the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
fof(f18,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f19,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f20,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f23,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f24,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f25,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f35,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f40,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f43,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f44,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f47,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f48,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f79,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ( empty_carrier(X0)
<=> empty(the_carrier(X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f80,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f81,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f82,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f83,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f85,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f24]) ).
fof(f86,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f91,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f92,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(flattening,[],[f91]) ).
fof(f95,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f98,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ~ subset(interior(X0,X1),X1) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f99,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f108,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ( ( ~ empty_carrier(X0)
| empty(the_carrier(X0)) )
& ( ~ empty(the_carrier(X0))
| empty_carrier(X0) ) ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f109,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,[],[f81]) ).
fof(f110,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,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f110]) ).
fof(f115,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ in(X2,subset_complement(the_carrier(X0),X1))
| ~ in(X2,X1) )
& ( in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) ) ) ) ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f119,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f120,plain,
( top_str(sK7)
& element(sK8,powerset(the_carrier(sK7)))
& ~ subset(interior(sK7,sK8),sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f98]) ).
fof(f146,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ~ empty_carrier(X0)
| empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f148,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f149,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f150,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f151,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f152,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f83]) ).
fof(f153,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f154,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f86]) ).
fof(f155,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,the_carrier(X0))
| in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f180,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f182,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f183,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f184,plain,
top_str(sK7),
inference(cnf_transformation,[],[f120]) ).
fof(f185,plain,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f120]) ).
fof(f186,plain,
~ subset(interior(sK7,sK8),sK8),
inference(cnf_transformation,[],[f120]) ).
fof(f187,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_75,plain,
! [X0: $i] :
( empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ empty_carrier(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))) = interior(X1,X0) )
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( element(interior(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_83,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| in(X2,X0)
| in(X2,subset_complement(the_carrier(X1),X0))
| ~ one_sorted_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_112,negated_conjecture,
~ subset(interior(sK7,sK8),sK8),
inference(cnf_transformation,[],[f186]) ).
tcf(c_113,negated_conjecture,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f185]) ).
tcf(c_114,negated_conjecture,
top_str(sK7),
inference(cnf_transformation,[],[f184]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( subset(X0,topstr_closure(X1,X0))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ element(X2,powerset(X1))
| ~ in(X0,subset_complement(X1,X2)) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_110]) ).
tcf(c_189,plain,
! [X0: $i] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
tcf(c_190,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(renaming,[status(thm)],[c_189]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_77]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_110,c_81]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_78]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_203]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_116,c_143]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_118,c_143]) ).
tcf(c_685,plain,
! [X0: $i,X1: $i] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_115,c_114]) ).
tcf(c_686,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK7,X0))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(unflattening,[status(thm)],[c_685]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_114]) ).
tcf(c_695,plain,
! [X0: $i] :
( element(topstr_closure(sK7,X0),powerset(the_carrier(sK7)))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(unflattening,[status(thm)],[c_694]) ).
tcf(c_703,plain,
! [X0: $i,X1: $i] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_114]) ).
tcf(c_704,plain,
! [X0: $i] :
( element(interior(sK7,X0),powerset(the_carrier(sK7)))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(unflattening,[status(thm)],[c_703]) ).
tcf(c_712,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) = interior(X0,X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_114]) ).
tcf(c_713,plain,
! [X0: $i] :
( ( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),X0))) = interior(sK7,X0) )
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(unflattening,[status(thm)],[c_712]) ).
tcf(c_726,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_190,c_114]) ).
tcf(c_727,plain,
one_sorted_str(sK7),
inference(unflattening,[status(thm)],[c_726]) ).
tcf(c_906,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_95,c_727]) ).
tcf(c_907,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK7)
| in(X1,X0)
| in(X1,subset_complement(the_carrier(sK7),X0))
| ~ element(X1,the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(unflattening,[status(thm)],[c_906]) ).
tcf(c_1027,plain,
! [X0: $i] :
( empty(the_carrier(X0))
| ~ empty_carrier(X0)
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_727]) ).
tcf(c_1028,plain,
( empty(the_carrier(sK7))
| ~ empty_carrier(sK7) ),
inference(unflattening,[status(thm)],[c_1027]) ).
tcf(c_1274,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X0)
| ( X1 != sK8 )
| ( interior(sK7,sK8) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_204,c_112]) ).
tcf(c_1275,plain,
in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8)),
inference(unflattening,[status(thm)],[c_1274]) ).
tcf(c_1279,plain,
! [X0: $i,X1: $i] :
( ~ in(sK0(X0,X1),X1)
| ( X1 != sK8 )
| ( interior(sK7,sK8) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_191,c_112]) ).
tcf(c_1280,plain,
~ in(sK0(interior(sK7,sK8),sK8),sK8),
inference(unflattening,[status(thm)],[c_1279]) ).
tcf(c_2202,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_193]) ).
tcf(c_2236,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK7,X0))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(prop_impl_just,[status(thm)],[c_686]) ).
tcf(c_2238,plain,
! [X0: $i] :
( element(topstr_closure(sK7,X0),powerset(the_carrier(sK7)))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(prop_impl_just,[status(thm)],[c_695]) ).
tcf(c_2240,plain,
! [X0: $i] :
( element(interior(sK7,X0),powerset(the_carrier(sK7)))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(prop_impl_just,[status(thm)],[c_704]) ).
tcf(c_2242,plain,
! [X0: $i] :
( ( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),X0))) = interior(sK7,X0) )
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(prop_impl_just,[status(thm)],[c_713]) ).
tcf(c_3642,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4685,plain,
! [X0: $i,X1: $i] :
( element(X1,the_carrier(sK7))
| ~ in(X1,X0)
| ~ subset(X0,the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_317]) ).
tcf(c_4730,plain,
( element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7))
| ~ subset(interior(sK7,sK8),the_carrier(sK7))
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8)) ),
inference(instantiation,[status(thm)],[c_4685]) ).
tcf(c_4731,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(interior(sK7,sK8),X0)
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8)) ),
inference(instantiation,[status(thm)],[c_318]) ).
tcf(c_4764,plain,
( subset(interior(sK7,sK8),the_carrier(sK7))
| ~ element(interior(sK7,sK8),powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_4793,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| ( X1 != interior(sK7,sK8) )
| ( X0 != sK0(interior(sK7,sK8),sK8) ) ),
inference(instantiation,[status(thm)],[c_3645]) ).
tcf(c_4960,plain,
( element(interior(sK7,sK8),powerset(the_carrier(sK7)))
| ~ element(sK8,powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_2240]) ).
tcf(c_5060,plain,
! [X0: $i] :
( empty_carrier(sK7)
| in(sK0(interior(sK7,sK8),sK8),X0)
| in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0))
| ~ element(X0,powerset(the_carrier(sK7)))
| ~ element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_907]) ).
tcf(c_5099,plain,
( ~ empty(the_carrier(sK7))
| ~ subset(interior(sK7,sK8),the_carrier(sK7))
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8)) ),
inference(instantiation,[status(thm)],[c_4731]) ).
tcf(c_5123,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ element(X1,powerset(the_carrier(sK7)))
| ~ in(X0,subset_complement(the_carrier(sK7),X1)) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_5170,plain,
! [X0: $i] :
( in(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))))
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| ( X0 != sK0(interior(sK7,sK8),sK8) )
| ( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) != interior(sK7,sK8) ) ),
inference(instantiation,[status(thm)],[c_4793]) ).
tcf(c_5172,plain,
! [X0: $i,X1: $i] :
( ~ element(X0,powerset(the_carrier(sK7)))
| ~ element(X1,the_carrier(sK7))
| in(X1,subset_complement(the_carrier(sK7),X0))
| in(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_907,c_113,c_907,c_1028,c_1275,c_4764,c_4960,c_5099]) ).
tcf(c_5173,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X1,subset_complement(the_carrier(sK7),X0))
| ~ element(X1,the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7))) ),
inference(renaming,[status(thm)],[c_5172]) ).
tcf(c_5266,plain,
subset(sK8,the_carrier(sK7)),
inference(superposition,[status(thm)],[c_113,c_111]) ).
tcf(c_5336,plain,
! [X0: $i,X1: $i] :
( subset(X0,subset_complement(the_carrier(sK7),X1))
| in(sK0(X0,subset_complement(the_carrier(sK7),X1)),X1)
| ~ element(X1,powerset(the_carrier(sK7)))
| ~ element(sK0(X0,subset_complement(the_carrier(sK7),X1)),the_carrier(sK7)) ),
inference(superposition,[status(thm)],[c_5173,c_77]) ).
tcf(c_5539,plain,
! [X0: $i] :
( element(subset_complement(the_carrier(sK7),X0),powerset(the_carrier(sK7)))
| ~ subset(X0,the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_2202]) ).
tcf(c_6532,plain,
( ( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) = interior(sK7,sK8) )
| ~ element(sK8,powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_2242]) ).
tcf(c_8350,plain,
! [X0: $i,X1: $i] :
( in(sK0(interior(sK7,sK8),sK8),X1)
| ~ subset(subset_complement(the_carrier(sK7),X0),X1)
| ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_8371,plain,
! [X0: $i] :
( ~ element(X0,powerset(the_carrier(sK7)))
| ~ in(sK0(interior(sK7,sK8),sK8),X0)
| ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0)) ),
inference(instantiation,[status(thm)],[c_5123]) ).
tcf(c_9707,plain,
( in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))))
| ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
| ( sK0(interior(sK7,sK8),sK8) != sK0(interior(sK7,sK8),sK8) )
| ( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) != interior(sK7,sK8) ) ),
inference(instantiation,[status(thm)],[c_5170]) ).
tcf(c_9884,plain,
( subset(subset_complement(the_carrier(sK7),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
| ~ element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7))) ),
inference(instantiation,[status(thm)],[c_2236]) ).
tcf(c_9977,plain,
( element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7)))
| ~ subset(sK8,the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_5539]) ).
tcf(c_14702,plain,
! [X0: $i] :
( in(sK0(interior(sK7,sK8),sK8),X0)
| ~ subset(subset_complement(the_carrier(sK7),sK8),X0)
| ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8)) ),
inference(instantiation,[status(thm)],[c_8350]) ).
tcf(c_15257,plain,
sK0(interior(sK7,sK8),sK8) = sK0(interior(sK7,sK8),sK8),
inference(instantiation,[status(thm)],[c_3642]) ).
tcf(c_29079,plain,
( empty_carrier(sK7)
| in(sK0(interior(sK7,sK8),sK8),sK8)
| in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8))
| ~ element(sK8,powerset(the_carrier(sK7)))
| ~ element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7)) ),
inference(instantiation,[status(thm)],[c_5060]) ).
tcf(c_42482,plain,
subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) = interior(sK7,sK8),
inference(superposition,[status(thm)],[c_113,c_2242]) ).
tcf(c_42504,plain,
! [X0: $i] :
( subset(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))))
| in(sK0(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
| ~ element(sK0(X0,interior(sK7,sK8)),the_carrier(sK7))
| ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7))) ),
inference(superposition,[status(thm)],[c_42482,c_5336]) ).
tcf(c_42607,plain,
! [X0: $i] :
( subset(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))))
| element(sK0(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
| ~ element(sK0(X0,interior(sK7,sK8)),the_carrier(sK7))
| ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7))) ),
inference(superposition,[status(thm)],[c_42504,c_108]) ).
tcf(c_52373,plain,
( in(sK0(interior(sK7,sK8),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
| ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8))
| ~ subset(subset_complement(the_carrier(sK7),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) ),
inference(instantiation,[status(thm)],[c_14702]) ).
tcf(c_56675,plain,
( ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7)))
| ~ in(sK0(interior(sK7,sK8),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
| ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
inference(instantiation,[status(thm)],[c_8371]) ).
tcf(c_57091,plain,
~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7))),
inference(global_subsumption_just,[status(thm)],[c_42607,c_113,c_1028,c_1275,c_1280,c_4730,c_4764,c_4960,c_5099,c_5266,c_6532,c_9707,c_9884,c_9977,c_15257,c_29079,c_52373,c_56675]) ).
tcf(c_57094,plain,
~ element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7))),
inference(superposition,[status(thm)],[c_2238,c_57091]) ).
tcf(c_57095,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_57094,c_9977,c_5266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU322+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 : n008.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 13:42:29 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 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...
% 29.64/4.83 % SZS status Started for theBenchmark.p
% 29.64/4.83 % SZS status Theorem for theBenchmark.p
% 29.64/4.83
% 29.64/4.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.64/4.83
% 29.64/4.83 % ------ iProver source info
% 29.64/4.83
% 29.64/4.83 % git: date: 2026-07-19 20:42:38 +0200
% 29.64/4.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.64/4.83 % git: non_committed_changes: false
% 29.64/4.83
% 29.64/4.83 % ------ Parsing...
% 29.64/4.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 29.64/4.83
% 29.64/4.83 % ------ Preprocessing... sup_sim: 0 sf_s rm: 40 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 %
% 29.64/4.83
% 29.64/4.83 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 29.64/4.83
% 29.64/4.83 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 29.64/4.83 % ------ Proving...
% 29.64/4.83 % ------ Problem Properties
% 29.64/4.83
% 29.64/4.83 %
% 29.64/4.83 % clauses 50
% 29.64/4.83 % conjectures 2
% 29.64/4.83 % EPR 13
% 29.64/4.83 % Horn 41
% 29.64/4.83 % unary 10
% 29.64/4.83 % binary 30
% 29.64/4.83 % lits 107
% 29.64/4.83 % lits eq 5
% 29.64/4.83 % fd_pure 0
% 29.64/4.83 % fd_pseudo 0
% 29.64/4.83 % fd_cond 1
% 29.64/4.83 % fd_pseudo_cond 1
% 29.64/4.83 % AC symbols 0
% 29.64/4.83
% 29.64/4.83 % ------ Input Options Time Limit: Unbounded
% 29.64/4.83
% 29.64/4.83
% 29.64/4.83 % ------
% 29.64/4.83 % Current options:
% 29.64/4.83 % ------
% 29.64/4.83
% 29.64/4.83
% 29.64/4.83 %
% 29.64/4.83
% 29.64/4.83 % ------ Proving...
% 29.64/4.83 %
% 29.64/4.83
% 29.64/4.83 % SZS status Theorem for theBenchmark.p
% 29.64/4.83
% 29.64/4.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.64/4.83
% 29.64/4.83
%------------------------------------------------------------------------------