%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 02:56:58 PM UTC 2026
% Result : Theorem 3.10s 1.44s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 24 unt; 1 def)
% Number of atoms : 215 ( 25 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 269 ( 114 ~; 101 |; 34 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 68 !; 6 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f40,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( ( interior(X0,X2) = X2
=> open_subset(X2,X0) )
& ( open_subset(X3,X1)
=> interior(X1,X3) = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
fof(f41,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( in(X2,X1)
& open_subset(X1,X0) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( in(X2,X1)
& open_subset(X1,X0) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f77,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f78,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
inference(flattening,[],[f77]) ).
fof(f92,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| ( ( interior(X0,X2) != X2
| open_subset(X2,X0) )
& ( ~ open_subset(X3,X1)
| interior(X1,X3) = X3 ) ) ) ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f93,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| ( ( interior(X0,X2) != X2
| open_subset(X2,X0) )
& ( ~ open_subset(X3,X1)
| interior(X1,X3) = X3 ) ) ) ) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& in(X2,X1)
& open_subset(X1,X0)
& ~ point_neighbourhood(X1,X0,X2) ) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f95,plain,
? [X0] :
( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& in(X2,X1)
& open_subset(X1,X0)
& ~ point_neighbourhood(X1,X0,X2) ) ) ),
inference(flattening,[],[f94]) ).
fof(f100,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( ( ~ point_neighbourhood(X2,X0,X1)
| in(X1,interior(X0,X2)) )
& ( ~ in(X1,interior(X0,X2))
| point_neighbourhood(X2,X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f107,plain,
( top_str(sK6)
& topological_space(sK6)
& ~ empty_carrier(sK6)
& element(sK7,powerset(the_carrier(sK6)))
& element(sK8,the_carrier(sK6))
& in(sK8,sK7)
& open_subset(sK7,sK6)
& ~ point_neighbourhood(sK7,sK6,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f95]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,interior(X0,X2))
| point_neighbourhood(X2,X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ open_subset(X3,X1)
| interior(X1,X3) = X3 ),
inference(cnf_transformation,[],[f93]) ).
fof(f164,plain,
top_str(sK6),
inference(cnf_transformation,[],[f107]) ).
fof(f165,plain,
topological_space(sK6),
inference(cnf_transformation,[],[f107]) ).
fof(f166,plain,
~ empty_carrier(sK6),
inference(cnf_transformation,[],[f107]) ).
fof(f167,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(cnf_transformation,[],[f107]) ).
fof(f168,plain,
element(sK8,the_carrier(sK6)),
inference(cnf_transformation,[],[f107]) ).
fof(f169,plain,
in(sK8,sK7),
inference(cnf_transformation,[],[f107]) ).
fof(f170,plain,
open_subset(sK7,sK6),
inference(cnf_transformation,[],[f107]) ).
fof(f171,plain,
~ point_neighbourhood(sK7,sK6,sK8),
inference(cnf_transformation,[],[f107]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| point_neighbourhood(X2,X1,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,the_carrier(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,interior(X1,X2)) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( interior(X3,X2) = X2 )
| ~ top_str(X3)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ open_subset(X2,X3)
| ~ element(X2,powerset(the_carrier(X3)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_105,negated_conjecture,
~ point_neighbourhood(sK7,sK6,sK8),
inference(cnf_transformation,[],[f171]) ).
tcf(c_106,negated_conjecture,
open_subset(sK7,sK6),
inference(cnf_transformation,[],[f170]) ).
tcf(c_107,negated_conjecture,
in(sK8,sK7),
inference(cnf_transformation,[],[f169]) ).
tcf(c_108,negated_conjecture,
element(sK8,the_carrier(sK6)),
inference(cnf_transformation,[],[f168]) ).
tcf(c_109,negated_conjecture,
element(sK7,powerset(the_carrier(sK6))),
inference(cnf_transformation,[],[f167]) ).
tcf(c_110,negated_conjecture,
~ empty_carrier(sK6),
inference(cnf_transformation,[],[f166]) ).
tcf(c_111,negated_conjecture,
topological_space(sK6),
inference(cnf_transformation,[],[f165]) ).
tcf(c_112,negated_conjecture,
top_str(sK6),
inference(cnf_transformation,[],[f164]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( interior(X1,X0) = X0 )
| ~ top_str(X3)
| ~ top_str(X1)
| ~ topological_space(X3)
| ~ element(X2,powerset(the_carrier(X3)))
| ~ element(X0,powerset(the_carrier(X1)))
| ( X1 != sK6 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_103,c_106]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i] :
( ( interior(sK6,sK7) = sK7 )
| ~ top_str(sK6)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(unflattening,[status(thm)],[c_734]) ).
tcf(c_737,plain,
! [X0: $i,X1: $i] :
( ( interior(sK6,sK7) = sK7 )
| ~ element(X0,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(global_subsumption_just,[status(thm)],[c_735,c_112,c_109,c_735]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i] :
( ( interior(sK6,sK7) = sK7 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(renaming,[status(thm)],[c_737]) ).
tcf(c_798,plain,
! [X0: $i,X1: $i,X2: $i] :
( point_neighbourhood(X2,X0,X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,interior(X0,X2))
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_110]) ).
tcf(c_799,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(X1,sK6,X0)
| ~ top_str(sK6)
| ~ topological_space(sK6)
| ~ element(X0,the_carrier(sK6))
| ~ element(X1,powerset(the_carrier(sK6)))
| ~ in(X0,interior(sK6,X1)) ),
inference(unflattening,[status(thm)],[c_798]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i] :
( point_neighbourhood(X1,sK6,X0)
| ~ element(X0,the_carrier(sK6))
| ~ element(X1,powerset(the_carrier(sK6)))
| ~ in(X0,interior(sK6,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_799,c_112,c_111,c_799]) ).
tcf(c_828,plain,
! [X0: $i,X1: $i] :
( ( interior(sK6,sK7) = sK7 )
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_738,c_111]) ).
tcf(c_829,plain,
! [X0: $i] :
( ( interior(sK6,sK7) = sK7 )
| ~ top_str(sK6)
| ~ element(X0,powerset(the_carrier(sK6))) ),
inference(unflattening,[status(thm)],[c_828]) ).
tcf(c_831,plain,
! [X0: $i] :
( ( interior(sK6,sK7) = sK7 )
| ~ element(X0,powerset(the_carrier(sK6))) ),
inference(global_subsumption_just,[status(thm)],[c_829,c_112,c_829]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK6))
| ~ element(X0,powerset(the_carrier(sK6)))
| ~ in(X1,interior(sK6,X0))
| ( sK6 != sK6 )
| ( X1 != sK8 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_105,c_801]) ).
tcf(c_872,plain,
( ~ element(sK8,the_carrier(sK6))
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ in(sK8,interior(sK6,sK7)) ),
inference(unflattening,[status(thm)],[c_871]) ).
tcf(c_873,plain,
~ in(sK8,interior(sK6,sK7)),
inference(global_subsumption_just,[status(thm)],[c_872,c_108,c_109,c_872]) ).
tcf(c_1076,definition,
iPr_def_12 = interior(sK6,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1080,plain,
~ in(sK8,iPr_def_12),
inference(demodulation,[status(thm)],[c_873,c_1076]) ).
tcf(c_1083,plain,
! [X0: $i] :
( ( iPr_def_12 = sK7 )
| ~ element(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_831]) ).
tcf(c_1084,negated_conjecture,
element(sK7,iPr_def_11),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_1086,negated_conjecture,
in(sK8,sK7),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_1411,plain,
sK7 = iPr_def_12,
inference(superposition,[status(thm)],[c_1084,c_1083]) ).
tcf(c_1414,plain,
in(sK8,iPr_def_12),
inference(demodulation,[status(thm)],[c_1086,c_1411]) ).
tcf(c_1416,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1414,c_1080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 % Computer : n015.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Thu Sep 24 13:48:56 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.45
% 0.14/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.45
% 0.14/0.45 % Detected problem language: tptp
% 0.14/0.47 % Proving...
% 3.10/1.44 % SZS status Started for theBenchmark.p
% 3.10/1.44 % SZS status Theorem for theBenchmark.p
% 3.10/1.44
% 3.10/1.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.10/1.44
% 3.10/1.44 % ------ iProver source info
% 3.10/1.44
% 3.10/1.44 % git: date: 2026-07-19 20:42:38 +0200
% 3.10/1.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.10/1.44 % git: non_committed_changes: false
% 3.10/1.44
% 3.10/1.44 % ------ Parsing...
% 3.10/1.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.10/1.44
% 3.10/1.44 % ------ Preprocessing... sup_sim: 0 sf_s rm: 40 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 11 0s sf_e pe_s pe_e %
% 3.10/1.44
% 3.10/1.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.10/1.44
% 3.10/1.44 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.10/1.44 % ------ Proving...
% 3.10/1.44 % ------ Problem Properties
% 3.10/1.44
% 3.10/1.44 %
% 3.10/1.44 % clauses 31
% 3.10/1.44 % conjectures 3
% 3.10/1.44 % EPR 14
% 3.10/1.44 % Horn 29
% 3.10/1.44 % unary 16
% 3.10/1.44 % binary 11
% 3.10/1.44 % lits 50
% 3.10/1.44 % lits eq 8
% 3.10/1.44 % fd_pure 0
% 3.10/1.44 % fd_pseudo 0
% 3.10/1.44 % fd_cond 1
% 3.10/1.44 % fd_pseudo_cond 1
% 3.10/1.44 % AC symbols 0
% 3.10/1.44
% 3.10/1.44 % ------ Schedule dynamic 5 is on
% 3.10/1.44
% 3.10/1.44 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.10/1.44
% 3.10/1.44
% 3.10/1.44 % ------
% 3.10/1.44 % Current options:
% 3.10/1.44 % ------
% 3.10/1.44
% 3.10/1.44
% 3.10/1.44 %
% 3.10/1.44
% 3.10/1.44 % ------ Proving...
% 3.10/1.44 %
% 3.10/1.44
% 3.10/1.44 % SZS status Theorem for theBenchmark.p
% 3.10/1.44
% 3.10/1.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.10/1.44
% 3.10/1.44
%------------------------------------------------------------------------------