%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU320+2 : 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 : n010.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 1.33s 1.85s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 114 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 48 ~; 45 |; 12 &)
% ( 4 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 42 !; 6 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f98,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f145,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f247,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f418,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f425,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
fof(f426,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f425]) ).
fof(f672,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(ennf_transformation,[],[f98]) ).
fof(f705,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f145]) ).
fof(f794,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f247]) ).
fof(f993,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f418]) ).
fof(f999,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( open_subset(X1,X0)
<~> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f426]) ).
fof(f1645,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f993]) ).
fof(f1648,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( open_subset(X1,X0)
| closed_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ open_subset(X1,X0)
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(nnf_transformation,[],[f999]) ).
fof(f1649,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( open_subset(X1,X0)
| closed_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ open_subset(X1,X0)
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(flattening,[],[f1648]) ).
fof(f1650,plain,
( top_str(sK374)
& element(sK375,powerset(the_carrier(sK374)))
& ( open_subset(sK375,sK374)
| closed_subset(subset_complement(the_carrier(sK374),sK375),sK374) )
& ( ~ open_subset(sK375,sK374)
| ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK374,sK375]),skolemize(X0,sK374),skolemize(X1,sK375)],[f1649]) ).
fof(f2041,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f672]) ).
fof(f2122,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f705]) ).
fof(f2295,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f794]) ).
fof(f2908,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1645]) ).
fof(f2909,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f1645]) ).
fof(f2918,plain,
top_str(sK374),
inference(cnf_transformation,[],[f1650]) ).
fof(f2919,plain,
element(sK375,powerset(the_carrier(sK374))),
inference(cnf_transformation,[],[f1650]) ).
fof(f2920,plain,
( open_subset(sK375,sK374)
| closed_subset(subset_complement(the_carrier(sK374),sK375),sK374) ),
inference(cnf_transformation,[],[f1650]) ).
fof(f2921,plain,
( ~ open_subset(sK375,sK374)
| ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374) ),
inference(cnf_transformation,[],[f1650]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2041]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2122]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2295]) ).
tcf(c_1246,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f2909]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_complement(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ closed_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2908]) ).
tcf(c_1256,negated_conjecture,
( ~ open_subset(sK375,sK374)
| ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374) ),
inference(cnf_transformation,[],[f2921]) ).
tcf(c_1257,negated_conjecture,
( open_subset(sK375,sK374)
| closed_subset(subset_complement(the_carrier(sK374),sK375),sK374) ),
inference(cnf_transformation,[],[f2920]) ).
tcf(c_1258,negated_conjecture,
element(sK375,powerset(the_carrier(sK374))),
inference(cnf_transformation,[],[f2919]) ).
tcf(c_1259,negated_conjecture,
top_str(sK374),
inference(cnf_transformation,[],[f2918]) ).
tcf(c_1619,plain,
subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) = sK375,
inference(superposition,[status(thm)],[c_1258,c_633]) ).
tcf(c_1628,plain,
set_difference(the_carrier(sK374),sK375) = subset_complement(the_carrier(sK374),sK375),
inference(superposition,[status(thm)],[c_1258,c_380]) ).
tcf(c_1802,plain,
( open_subset(sK375,sK374)
| ~ top_str(sK374)
| ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| ~ element(subset_complement(the_carrier(sK374),sK375),powerset(the_carrier(sK374))) ),
inference(superposition,[status(thm)],[c_1619,c_1247]) ).
tcf(c_1803,plain,
( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| ~ top_str(sK374)
| ~ open_subset(sK375,sK374)
| ~ element(subset_complement(the_carrier(sK374),sK375),powerset(the_carrier(sK374))) ),
inference(superposition,[status(thm)],[c_1619,c_1246]) ).
tcf(c_1868,plain,
( element(set_difference(the_carrier(sK374),sK375),powerset(the_carrier(sK374)))
| ~ element(sK375,powerset(the_carrier(sK374))) ),
inference(superposition,[status(thm)],[c_1628,c_460]) ).
tcf(c_2213,plain,
( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| ~ element(subset_complement(the_carrier(sK374),sK375),powerset(the_carrier(sK374))) ),
inference(global_subsumption_just,[status(thm)],[c_1803,c_1259,c_1257,c_1256,c_1803,c_1802]) ).
tcf(c_2215,plain,
~ element(subset_complement(the_carrier(sK374),sK375),powerset(the_carrier(sK374))),
inference(global_subsumption_just,[status(thm)],[c_2213,c_1259,c_1256,c_1802,c_2213]) ).
tcf(c_2217,plain,
~ element(set_difference(the_carrier(sK374),sK375),powerset(the_carrier(sK374))),
inference(light_normalisation,[status(thm)],[c_2215,c_1628]) ).
tcf(c_2345,plain,
element(set_difference(the_carrier(sK374),sK375),powerset(the_carrier(sK374))),
inference(global_subsumption_just,[status(thm)],[c_1868,c_1258,c_1868]) ).
tcf(c_2347,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2345,c_2217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 13:41:30 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 0.12/0.47
% 0.12/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.47
% 0.12/0.47 % Detected problem language: tptp
% 0.12/0.49 % Proving...
% 1.33/1.85 % SZS status Started for theBenchmark.p
% 1.33/1.85 % SZS status Theorem for theBenchmark.p
% 1.33/1.85
% 1.33/1.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.33/1.85
% 1.33/1.85 % ------ iProver source info
% 1.33/1.85
% 1.33/1.85 % git: date: 2026-07-19 20:42:38 +0200
% 1.33/1.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.33/1.85 % git: non_committed_changes: false
% 1.33/1.85
% 1.33/1.85 % ------ Parsing...
% 1.33/1.85 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.33/1.85 % ------ Proving...
% 1.33/1.85 % ------ Problem Properties
% 1.33/1.85
% 1.33/1.85 %
% 1.33/1.85 % clauses 1387
% 1.33/1.85 % conjectures 4
% 1.33/1.85 % EPR 229
% 1.33/1.85 % Horn 1065
% 1.33/1.85 % unary 182
% 1.33/1.85 % binary 451
% 1.33/1.85 % lits 4182
% 1.33/1.85 % lits eq 520
% 1.33/1.85 % fd_pure 0
% 1.33/1.85 % fd_pseudo 0
% 1.33/1.85 % fd_cond 45
% 1.33/1.85 % fd_pseudo_cond 118
% 1.33/1.85 % AC symbols 0
% 1.33/1.85
% 1.33/1.85 % ------ Input Options Time Limit: Unbounded
% 1.33/1.85
% 1.33/1.85
% 1.33/1.85 % ------
% 1.33/1.85 % Current options:
% 1.33/1.85 % ------
% 1.33/1.85
% 1.33/1.85
% 1.33/1.85 %
% 1.33/1.85
% 1.33/1.85 % ------ Proving...
% 1.33/1.85 %
% 1.33/1.85
% 1.33/1.85 % SZS status Theorem for theBenchmark.p
% 1.33/1.85
% 1.33/1.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.33/1.85
% 1.33/1.85
%------------------------------------------------------------------------------