%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU337+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 : n001.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 7.85s 1.76s
% Output : CNFRefutation 7.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 6 unt; 0 def)
% Number of atoms : 106 ( 5 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 118 ( 47 ~; 46 |; 12 &)
% ( 4 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 38 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f169,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f260,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f404,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( closed_subsets(X1,X0)
<=> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tops_2) ).
fof(f410,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tops_2) ).
fof(f411,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f410]) ).
fof(f771,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f169]) ).
fof(f857,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f260]) ).
fof(f1027,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( closed_subsets(X1,X0)
<=> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f404]) ).
fof(f1036,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& ( open_subsets(X1,X0)
<~> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f411]) ).
fof(f1822,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( ( ~ closed_subsets(X1,X0)
| open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& ( ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| closed_subsets(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f1027]) ).
fof(f1825,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& ( open_subsets(X1,X0)
| closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& ( ~ open_subsets(X1,X0)
| ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(nnf_transformation,[],[f1036]) ).
fof(f1826,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& ( open_subsets(X1,X0)
| closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& ( ~ open_subsets(X1,X0)
| ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(flattening,[],[f1825]) ).
fof(f1827,plain,
( top_str(sK447)
& element(sK448,powerset(powerset(the_carrier(sK447))))
& ( open_subsets(sK448,sK447)
| closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) )
& ( ~ open_subsets(sK448,sK447)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK447,sK448]),skolemize(X0,sK447),skolemize(X1,sK448)],[f1826]) ).
fof(f2340,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f771]) ).
fof(f2508,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f857]) ).
fof(f3192,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subsets(X1,X0)
| open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f3193,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| closed_subsets(X1,X0) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f3201,plain,
top_str(sK447),
inference(cnf_transformation,[],[f1827]) ).
fof(f3202,plain,
element(sK448,powerset(powerset(the_carrier(sK447)))),
inference(cnf_transformation,[],[f1827]) ).
fof(f3203,plain,
( open_subsets(sK448,sK447)
| closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) ),
inference(cnf_transformation,[],[f1827]) ).
fof(f3204,plain,
( ~ open_subsets(sK448,sK447)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) ),
inference(cnf_transformation,[],[f1827]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2340]) ).
tcf(c_654,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2508]) ).
tcf(c_1338,plain,
! [X0: $i,X1: $i] :
( closed_subsets(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f3193]) ).
tcf(c_1339,plain,
! [X0: $i,X1: $i] :
( open_subsets(complements_of_subsets(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ closed_subsets(X0,X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f3192]) ).
tcf(c_1347,negated_conjecture,
( ~ open_subsets(sK448,sK447)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) ),
inference(cnf_transformation,[],[f3204]) ).
tcf(c_1348,negated_conjecture,
( open_subsets(sK448,sK447)
| closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) ),
inference(cnf_transformation,[],[f3203]) ).
tcf(c_1349,negated_conjecture,
element(sK448,powerset(powerset(the_carrier(sK447)))),
inference(cnf_transformation,[],[f3202]) ).
tcf(c_1350,negated_conjecture,
top_str(sK447),
inference(cnf_transformation,[],[f3201]) ).
tcf(c_1790,plain,
complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)) = sK448,
inference(superposition,[status(thm)],[c_1349,c_654]) ).
tcf(c_1807,plain,
! [X0: $i,X1: $i] :
( open_subsets(complements_of_subsets(the_carrier(X0),complements_of_subsets(the_carrier(X0),X1)),X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_486,c_1339]) ).
tcf(c_1820,plain,
! [X0: $i,X1: $i] :
( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ open_subsets(complements_of_subsets(the_carrier(X0),complements_of_subsets(the_carrier(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_486,c_1338]) ).
tcf(c_2073,plain,
( open_subsets(sK448,sK447)
| ~ top_str(sK447)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ element(sK448,powerset(powerset(the_carrier(sK447)))) ),
inference(superposition,[status(thm)],[c_1790,c_1807]) ).
tcf(c_2113,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ top_str(sK447)
| ~ open_subsets(sK448,sK447)
| ~ element(sK448,powerset(powerset(the_carrier(sK447)))) ),
inference(superposition,[status(thm)],[c_1790,c_1820]) ).
tcf(c_2176,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2113,c_2073,c_1347,c_1348,c_1349,c_1350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU337+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:51:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 7.85/1.76 % SZS status Started for theBenchmark.p
% 7.85/1.76 % SZS status Theorem for theBenchmark.p
% 7.85/1.76
% 7.85/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.85/1.76
% 7.85/1.76 % ------ iProver source info
% 7.85/1.76
% 7.85/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 7.85/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.85/1.76 % git: non_committed_changes: false
% 7.85/1.76
% 7.85/1.76 % ------ Parsing...
% 7.85/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.85/1.76 % ------ Proving...
% 7.85/1.76 % ------ Problem Properties
% 7.85/1.76
% 7.85/1.76 %
% 7.85/1.76 % clauses 1550
% 7.85/1.76 % conjectures 4
% 7.85/1.76 % EPR 229
% 7.85/1.76 % Horn 1169
% 7.85/1.76 % unary 182
% 7.85/1.76 % binary 472
% 7.85/1.76 % lits 4814
% 7.85/1.76 % lits eq 602
% 7.85/1.76 % fd_pure 0
% 7.85/1.76 % fd_pseudo 0
% 7.85/1.76 % fd_cond 48
% 7.85/1.76 % fd_pseudo_cond 120
% 7.85/1.76 % AC symbols 0
% 7.85/1.76
% 7.85/1.76 % ------ Input Options Time Limit: Unbounded
% 7.85/1.76
% 7.85/1.76
% 7.85/1.76 % ------
% 7.85/1.76 % Current options:
% 7.85/1.76 % ------
% 7.85/1.76
% 7.85/1.76
% 7.85/1.76 %
% 7.85/1.76
% 7.85/1.76 % ------ Proving...
% 7.85/1.76 %
% 7.85/1.76
% 7.85/1.76 % SZS status Theorem for theBenchmark.p
% 7.85/1.76
% 7.85/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.85/1.77
% 7.85/1.77
%------------------------------------------------------------------------------