%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU354+2 : 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 : n014.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 02:57:01 PM UTC 2026
% Result : Theorem 7.11s 1.78s
% Output : CNFRefutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 83 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 80 ( 36 ~; 28 |; 8 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 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 : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 26 !; 6 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f102,axiom,
! [X0,X1] :
( element(X1,X0)
=> ( proper_element(X1,X0)
<=> X1 != union(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
fof(f398,axiom,
! [X0] : k1_pcomps_1(X0) = powerset(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
fof(f627,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
fof(f628,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
inference(negated_conjecture,[status(cth)],[f627]) ).
fof(f668,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f860,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ( proper_element(X1,X0)
<=> X1 != union(X0) ) ),
inference(ennf_transformation,[],[f102]) ).
fof(f1465,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& ( proper_element(X1,powerset(X0))
<~> X1 != X0 ) ),
inference(ennf_transformation,[],[f628]) ).
fof(f1723,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ( ( ~ proper_element(X1,X0)
| X1 != union(X0) )
& ( union(X0) = X1
| proper_element(X1,X0) ) ) ),
inference(nnf_transformation,[],[f860]) ).
fof(f2241,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& ( proper_element(X1,powerset(X0))
| X1 != X0 )
& ( ~ proper_element(X1,powerset(X0))
| X0 = X1 ) ),
inference(nnf_transformation,[],[f1465]) ).
fof(f2242,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& ( proper_element(X1,powerset(X0))
| X1 != X0 )
& ( ~ proper_element(X1,powerset(X0))
| X0 = X1 ) ),
inference(flattening,[],[f2241]) ).
fof(f2243,plain,
( element(sK499,powerset(sK498))
& ( proper_element(sK499,powerset(sK498))
| sK498 != sK499 )
& ( ~ proper_element(sK499,powerset(sK498))
| sK498 = sK499 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK498,sK499]),skolemize(X0,sK498),skolemize(X1,sK499)],[f2242]) ).
fof(f2569,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ proper_element(X1,X0)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f1723]) ).
fof(f2570,plain,
! [X0,X1] :
( ~ element(X1,X0)
| union(X0) = X1
| proper_element(X1,X0) ),
inference(cnf_transformation,[],[f1723]) ).
fof(f3260,plain,
! [X0] : powerset(X0) = k1_pcomps_1(X0),
inference(cnf_transformation,[],[f398]) ).
fof(f4042,plain,
element(sK499,powerset(sK498)),
inference(cnf_transformation,[],[f2243]) ).
fof(f4043,plain,
( proper_element(sK499,powerset(sK498))
| sK498 != sK499 ),
inference(cnf_transformation,[],[f2243]) ).
fof(f4044,plain,
( ~ proper_element(sK499,powerset(sK498))
| sK498 = sK499 ),
inference(cnf_transformation,[],[f2243]) ).
fof(f4104,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f668]) ).
fof(f4792,plain,
( ~ proper_element(sK499,k1_pcomps_1(sK498))
| sK498 = sK499 ),
inference(definition_unfolding,[],[f4044,f3260]) ).
fof(f4793,plain,
( proper_element(sK499,k1_pcomps_1(sK498))
| sK498 != sK499 ),
inference(definition_unfolding,[],[f4043,f3260]) ).
fof(f4794,plain,
element(sK499,k1_pcomps_1(sK498)),
inference(definition_unfolding,[],[f4042,f3260]) ).
fof(f4815,plain,
! [X0] : union(k1_pcomps_1(X0)) = X0,
inference(definition_unfolding,[],[f4104,f3260]) ).
fof(f4902,plain,
! [X0] :
( ~ element(union(X0),X0)
| ~ proper_element(union(X0),X0) ),
inference(equality_resolution,[],[f2569]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( proper_element(X0,X1)
| ( union(X1) = X0 )
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2570]) ).
tcf(c_339,plain,
! [X0: $i] :
( ~ proper_element(union(X0),X0)
| ~ element(union(X0),X0) ),
inference(cnf_transformation,[],[f4902]) ).
tcf(c_1807,negated_conjecture,
( ( sK498 = sK499 )
| ~ proper_element(sK499,k1_pcomps_1(sK498)) ),
inference(cnf_transformation,[],[f4792]) ).
tcf(c_1808,negated_conjecture,
( proper_element(sK499,k1_pcomps_1(sK498))
| ( sK498 != sK499 ) ),
inference(cnf_transformation,[],[f4793]) ).
tcf(c_1809,negated_conjecture,
element(sK499,k1_pcomps_1(sK498)),
inference(cnf_transformation,[],[f4794]) ).
tcf(c_1868,plain,
! [X0: $i] : union(k1_pcomps_1(X0)) = X0,
inference(cnf_transformation,[],[f4815]) ).
tcf(c_2303,plain,
! [X0: $i] :
( ~ proper_element(X0,k1_pcomps_1(X0))
| ~ element(union(k1_pcomps_1(X0)),k1_pcomps_1(X0)) ),
inference(superposition,[status(thm)],[c_1868,c_339]) ).
tcf(c_2343,plain,
( proper_element(sK499,k1_pcomps_1(sK498))
| ( union(k1_pcomps_1(sK498)) = sK499 ) ),
inference(superposition,[status(thm)],[c_1809,c_338]) ).
tcf(c_2366,plain,
! [X0: $i] :
( ~ proper_element(X0,k1_pcomps_1(X0))
| ~ element(X0,k1_pcomps_1(X0)) ),
inference(demodulation,[status(thm)],[c_2303,c_1868]) ).
tcf(c_2393,plain,
( proper_element(sK499,k1_pcomps_1(sK498))
| ( sK498 = sK499 ) ),
inference(demodulation,[status(thm)],[c_2343,c_1868]) ).
tcf(c_2396,plain,
proper_element(sK499,k1_pcomps_1(sK498)),
inference(forward_subsumption_resolution,[status(thm)],[c_2393,c_1808]) ).
tcf(c_2397,plain,
sK498 = sK499,
inference(superposition,[status(thm)],[c_2396,c_1807]) ).
tcf(c_2399,plain,
proper_element(sK498,k1_pcomps_1(sK498)),
inference(demodulation,[status(thm)],[c_2396,c_2397]) ).
tcf(c_2402,plain,
element(sK498,k1_pcomps_1(sK498)),
inference(demodulation,[status(thm)],[c_1809,c_2397]) ).
tcf(c_2413,plain,
~ element(sK498,k1_pcomps_1(sK498)),
inference(superposition,[status(thm)],[c_2399,c_2366]) ).
tcf(c_2414,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2402,c_2413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU354+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.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 13:49:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 7.11/1.78 % SZS status Started for theBenchmark.p
% 7.11/1.78 % SZS status Theorem for theBenchmark.p
% 7.11/1.78
% 7.11/1.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.11/1.78
% 7.11/1.78 % ------ iProver source info
% 7.11/1.78
% 7.11/1.78 % git: date: 2026-07-19 20:42:38 +0200
% 7.11/1.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.11/1.78 % git: non_committed_changes: false
% 7.11/1.78
% 7.11/1.78 % ------ Parsing...
% 7.11/1.78 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.11/1.78 % ------ Proving...
% 7.11/1.78 % ------ Problem Properties
% 7.11/1.78
% 7.11/1.78 %
% 7.11/1.78 % clauses 1830
% 7.11/1.78 % conjectures 3
% 7.11/1.78 % EPR 272
% 7.11/1.78 % Horn 1308
% 7.11/1.78 % unary 246
% 7.11/1.78 % binary 484
% 7.11/1.78 % lits 5923
% 7.11/1.78 % lits eq 674
% 7.11/1.78 % fd_pure 0
% 7.11/1.78 % fd_pseudo 0
% 7.11/1.78 % fd_cond 53
% 7.11/1.78 % fd_pseudo_cond 133
% 7.11/1.78 % AC symbols 0
% 7.11/1.78
% 7.11/1.78 % ------ Input Options Time Limit: Unbounded
% 7.11/1.78
% 7.11/1.78
% 7.11/1.78 % ------
% 7.11/1.78 % Current options:
% 7.11/1.78 % ------
% 7.11/1.78
% 7.11/1.78
% 7.11/1.78 %
% 7.11/1.78
% 7.11/1.78 % ------ Proving...
% 7.11/1.78 %
% 7.11/1.78
% 7.11/1.78 % ------ Proving...
% 7.11/1.78 %
% 7.11/1.78
% 7.11/1.78 % ------ Proving...
% 7.11/1.78 %
% 7.11/1.78
% 7.11/1.78 % SZS status Theorem for theBenchmark.p
% 7.11/1.78
% 7.11/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.11/1.78
% 7.11/1.78
%------------------------------------------------------------------------------