%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU174+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 : n002.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 02:55:45 PM UTC 2026
% Result : Theorem 3.81s 1.19s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 15 unt; 0 def)
% Number of atoms : 181 ( 42 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 221 ( 95 ~; 85 |; 28 &)
% ( 5 <=>; 8 =>; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 103 ( 0 sgn 94 !; 9 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f21,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f34,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(f45,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(f98,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f99,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f98]) ).
fof(f103,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f140,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( ~ element(X3,powerset(X0))
| ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f144,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f34]) ).
fof(f148,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f45]) ).
fof(f182,plain,
? [X0,X1] :
( element(X1,powerset(powerset(X0)))
& complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ),
inference(ennf_transformation,[],[f99]) ).
fof(f183,plain,
? [X0,X1] :
( element(X1,powerset(powerset(X0)))
& complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ),
inference(flattening,[],[f182]) ).
fof(f185,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f103]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f185]) ).
fof(f212,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f213,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f212]) ).
fof(f214,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK1(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f213]) ).
fof(f245,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f140]) ).
fof(f246,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(flattening,[],[f245]) ).
fof(f247,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(rectify,[],[f246]) ).
fof(f248,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ( element(sK16(X0,X1,X2),powerset(X0))
& ( in(sK16(X0,X1,X2),X2)
| in(subset_complement(X0,sK16(X0,X1,X2)),X1) )
& ( ~ in(sK16(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK16(X0,X1,X2)),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X3,sK16(X0,X1,X2))],[f247]) ).
fof(f275,plain,
( element(sK27,powerset(powerset(sK26)))
& empty_set = complements_of_subsets(sK26,sK27)
& empty_set != sK27 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26,sK27]),skolemize(X0,sK26),skolemize(X1,sK27)],[f183]) ).
fof(f292,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f293,plain,
! [X0] :
( in(sK1(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f214]) ).
fof(f347,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f354,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f144]) ).
fof(f364,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f148]) ).
fof(f443,plain,
element(sK27,powerset(powerset(sK26))),
inference(cnf_transformation,[],[f275]) ).
fof(f444,plain,
empty_set = complements_of_subsets(sK26,sK27),
inference(cnf_transformation,[],[f275]) ).
fof(f445,plain,
empty_set != sK27,
inference(cnf_transformation,[],[f275]) ).
fof(f449,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f538,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f292]) ).
fof(f564,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(X4,complements_of_subsets(X0,X1))
| in(subset_complement(X0,X4),X1) ),
inference(equality_resolution,[],[f347]) ).
tcf(c_61,plain,
! [X0: $i] :
( in(sK1(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_62,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f538]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X0,X2),X1)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X2,complements_of_subsets(X0,X1))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f564]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f364]) ).
tcf(c_211,negated_conjecture,
empty_set != sK27,
inference(cnf_transformation,[],[f445]) ).
tcf(c_212,negated_conjecture,
complements_of_subsets(sK26,sK27) = empty_set,
inference(cnf_transformation,[],[f444]) ).
tcf(c_213,negated_conjecture,
element(sK27,powerset(powerset(sK26))),
inference(cnf_transformation,[],[f443]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f449]) ).
tcf(c_368,plain,
( element(empty_set,powerset(powerset(sK26)))
| ~ element(sK27,powerset(powerset(sK26))) ),
inference(superposition,[status(thm)],[c_212,c_122]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(X1))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(superposition,[status(thm)],[c_122,c_216]) ).
tcf(c_382,plain,
complements_of_subsets(sK26,complements_of_subsets(sK26,sK27)) = sK27,
inference(superposition,[status(thm)],[c_213,c_132]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ element(X0,powerset(X1))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_119,c_122]) ).
tcf(c_603,plain,
element(empty_set,powerset(powerset(sK26))),
inference(global_subsumption_just,[status(thm)],[c_368,c_213,c_368]) ).
tcf(c_610,plain,
! [X0: $i] :
( in(subset_complement(sK26,X0),empty_set)
| ~ element(X0,powerset(sK26))
| ~ in(X0,complements_of_subsets(sK26,empty_set)) ),
inference(superposition,[status(thm)],[c_603,c_400]) ).
tcf(c_641,plain,
! [X0: $i] :
( element(X0,powerset(sK26))
| ~ in(X0,complements_of_subsets(sK26,empty_set)) ),
inference(superposition,[status(thm)],[c_603,c_370]) ).
tcf(c_682,plain,
complements_of_subsets(sK26,empty_set) = sK27,
inference(light_normalisation,[status(thm)],[c_382,c_212]) ).
tcf(c_1267,plain,
! [X0: $i] :
( in(subset_complement(sK26,X0),empty_set)
| ~ in(X0,complements_of_subsets(sK26,empty_set)) ),
inference(global_subsumption_just,[status(thm)],[c_610,c_610,c_641]) ).
tcf(c_1272,plain,
! [X0: $i] : ~ in(X0,complements_of_subsets(sK26,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_1267,c_62]) ).
tcf(c_1273,plain,
! [X0: $i] : ~ in(X0,sK27),
inference(light_normalisation,[status(thm)],[c_1272,c_682]) ).
tcf(c_1274,plain,
empty_set = sK27,
inference(superposition,[status(thm)],[c_61,c_1273]) ).
tcf(c_1277,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_211,c_1274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:05:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.81/1.19 % SZS status Started for theBenchmark.p
% 3.81/1.19 % SZS status Theorem for theBenchmark.p
% 3.81/1.19
% 3.81/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.81/1.19
% 3.81/1.19 % ------ iProver source info
% 3.81/1.19
% 3.81/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.81/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.81/1.19 % git: non_committed_changes: false
% 3.81/1.19
% 3.81/1.19 % ------ Parsing...
% 3.81/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.81/1.19 % ------ Proving...
% 3.81/1.19 % ------ Problem Properties
% 3.81/1.19
% 3.81/1.19 %
% 3.81/1.19 % clauses 193
% 3.81/1.19 % conjectures 3
% 3.81/1.19 % EPR 30
% 3.81/1.19 % Horn 155
% 3.81/1.19 % unary 43
% 3.81/1.19 % binary 82
% 3.81/1.19 % lits 431
% 3.81/1.19 % lits eq 97
% 3.81/1.19 % fd_pure 0
% 3.81/1.19 % fd_pseudo 0
% 3.81/1.19 % fd_cond 4
% 3.81/1.19 % fd_pseudo_cond 39
% 3.81/1.19 % AC symbols 0
% 3.81/1.19
% 3.81/1.19 % ------ Input Options Time Limit: Unbounded
% 3.81/1.20
% 3.81/1.20
% 3.81/1.20 % ------
% 3.81/1.20 % Current options:
% 3.81/1.20 % ------
% 3.81/1.20
% 3.81/1.20
% 3.81/1.20 %
% 3.81/1.20
% 3.81/1.20 % ------ Proving...
% 3.81/1.20 %
% 3.81/1.20
% 3.81/1.20 % SZS status Theorem for theBenchmark.p
% 3.81/1.20
% 3.81/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.81/1.20
% 3.81/1.20
%------------------------------------------------------------------------------