%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU354+1 : 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 : n008.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 1.16s 1.50s
% Output : CNFRefutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 17 unt; 0 def)
% Number of atoms : 126 ( 50 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 130 ( 61 ~; 51 |; 8 &)
% ( 5 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 59 ( 1 sgn 53 !; 6 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] :
( element(X1,X0)
=> ( proper_element(X1,X0)
<=> X1 != union(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
fof(f31,axiom,
! [X0] : k1_pcomps_1(X0) = powerset(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
fof(f33,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f39,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(f40,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f44,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f45,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f33]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f36]) ).
fof(f73,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ( proper_element(X1,X0)
<=> X1 != union(X0) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f80,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f84,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& ( proper_element(X1,powerset(X0))
<~> X1 != X0 ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f88,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ( ( ~ proper_element(X1,X0)
| X1 != union(X0) )
& ( union(X0) = X1
| proper_element(X1,X0) ) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f94,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& ( proper_element(X1,powerset(X0))
| X1 != X0 )
& ( ~ proper_element(X1,powerset(X0))
| X0 = X1 ) ),
inference(nnf_transformation,[],[f84]) ).
fof(f95,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& ( proper_element(X1,powerset(X0))
| X1 != X0 )
& ( ~ proper_element(X1,powerset(X0))
| X0 = X1 ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
( element(sK6,powerset(sK5))
& ( proper_element(sK6,powerset(sK5))
| sK5 != sK6 )
& ( ~ proper_element(sK6,powerset(sK5))
| sK5 = sK6 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f95]) ).
fof(f122,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ proper_element(X1,X0)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f88]) ).
fof(f123,plain,
! [X0,X1] :
( ~ element(X1,X0)
| union(X0) = X1
| proper_element(X1,X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f146,plain,
! [X0] : powerset(X0) = k1_pcomps_1(X0),
inference(cnf_transformation,[],[f31]) ).
fof(f148,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f45]) ).
fof(f151,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f154,plain,
element(sK6,powerset(sK5)),
inference(cnf_transformation,[],[f96]) ).
fof(f155,plain,
( proper_element(sK6,powerset(sK5))
| sK5 != sK6 ),
inference(cnf_transformation,[],[f96]) ).
fof(f156,plain,
( ~ proper_element(sK6,powerset(sK5))
| sK5 = sK6 ),
inference(cnf_transformation,[],[f96]) ).
fof(f160,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f184,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,k1_pcomps_1(X1)) ),
inference(definition_unfolding,[],[f151,f146]) ).
fof(f187,plain,
( ~ proper_element(sK6,k1_pcomps_1(sK5))
| sK5 = sK6 ),
inference(definition_unfolding,[],[f156,f146]) ).
fof(f188,plain,
( proper_element(sK6,k1_pcomps_1(sK5))
| sK5 != sK6 ),
inference(definition_unfolding,[],[f155,f146]) ).
fof(f189,plain,
element(sK6,k1_pcomps_1(sK5)),
inference(definition_unfolding,[],[f154,f146]) ).
fof(f190,plain,
! [X0] : union(k1_pcomps_1(X0)) = X0,
inference(definition_unfolding,[],[f160,f146]) ).
fof(f191,plain,
! [X0] :
( ~ element(union(X0),X0)
| ~ proper_element(union(X0),X0) ),
inference(equality_resolution,[],[f122]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( proper_element(X0,X1)
| ( union(X1) = X0 )
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_75,plain,
! [X0: $i] :
( ~ proper_element(union(X0),X0)
| ~ element(union(X0),X0) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_99,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f148]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( element(X0,k1_pcomps_1(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_105,negated_conjecture,
( ( sK5 = sK6 )
| ~ proper_element(sK6,k1_pcomps_1(sK5)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_106,negated_conjecture,
( proper_element(sK6,k1_pcomps_1(sK5))
| ( sK5 != sK6 ) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_107,negated_conjecture,
element(sK6,k1_pcomps_1(sK5)),
inference(cnf_transformation,[],[f189]) ).
tcf(c_111,plain,
! [X0: $i] : union(k1_pcomps_1(X0)) = X0,
inference(cnf_transformation,[],[f190]) ).
tcf(c_130,plain,
( ( sK5 != sK6 )
| proper_element(sK6,k1_pcomps_1(sK5)) ),
inference(prop_impl_just,[status(thm)],[c_106]) ).
tcf(c_131,plain,
( proper_element(sK6,k1_pcomps_1(sK5))
| ( sK5 != sK6 ) ),
inference(renaming,[status(thm)],[c_130]) ).
tcf(c_132,plain,
( ( sK5 = sK6 )
| ~ proper_element(sK6,k1_pcomps_1(sK5)) ),
inference(prop_impl_just,[status(thm)],[c_105]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( ~ subset(X0,X1)
| element(X0,k1_pcomps_1(X1)) ),
inference(prop_impl_just,[status(thm)],[c_102]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( element(X0,k1_pcomps_1(X1))
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_168]) ).
tcf(c_186,plain,
! [X0: $i] :
( ~ proper_element(union(X0),X0)
| ~ element(union(X0),X0) ),
inference(prop_impl_just,[status(thm)],[c_75]) ).
tcf(c_740,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X1,k1_pcomps_1(X2))
| ( X0 != X2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_99,c_169]) ).
tcf(c_741,plain,
! [X0: $i] : element(X0,k1_pcomps_1(X0)),
inference(unflattening,[status(thm)],[c_740]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i] :
( ( sK5 = sK6 )
| ( union(X1) = X0 )
| ~ element(X0,X1)
| ( X0 != sK6 )
| ( k1_pcomps_1(sK5) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_132]) ).
tcf(c_760,plain,
( ( sK5 = sK6 )
| ( union(k1_pcomps_1(sK5)) = sK6 )
| ~ element(sK6,k1_pcomps_1(sK5)) ),
inference(unflattening,[status(thm)],[c_759]) ).
tcf(c_761,plain,
( ( sK5 = sK6 )
| ( union(k1_pcomps_1(sK5)) = sK6 ) ),
inference(global_subsumption_just,[status(thm)],[c_760,c_107,c_760]) ).
tcf(c_769,plain,
! [X0: $i] :
( ~ element(union(X0),X0)
| ( sK5 != sK6 )
| ( k1_pcomps_1(sK5) != X0 )
| ( union(X0) != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_186,c_131]) ).
tcf(c_770,plain,
( ~ element(union(k1_pcomps_1(sK5)),k1_pcomps_1(sK5))
| ( sK5 != sK6 )
| ( union(k1_pcomps_1(sK5)) != sK6 ) ),
inference(unflattening,[status(thm)],[c_769]) ).
tcf(c_924,plain,
sK5 = sK6,
inference(demodulation,[status(thm)],[c_761,c_111]) ).
tcf(c_961,plain,
( ~ element(union(k1_pcomps_1(sK5)),k1_pcomps_1(sK5))
| ( sK5 != sK6 )
| ( union(k1_pcomps_1(sK5)) != sK5 ) ),
inference(light_normalisation,[status(thm)],[c_770,c_924]) ).
tcf(c_962,plain,
( ~ element(sK5,k1_pcomps_1(sK5))
| ( sK5 != sK5 ) ),
inference(demodulation,[status(thm)],[c_961,c_111,c_924]) ).
tcf(c_963,plain,
~ element(sK5,k1_pcomps_1(sK5)),
inference(equality_resolution_simp,[status(thm)],[c_962]) ).
tcf(c_964,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_963,c_741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.44 % Computer : n008.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Thu Sep 24 13:49:54 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 0.17/0.51
% 0.17/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.51
% 0.24/0.51 % Detected problem language: tptp
% 0.24/0.53 % Proving...
% 1.16/1.50 % SZS status Started for theBenchmark.p
% 1.16/1.50 % SZS status Theorem for theBenchmark.p
% 1.16/1.50
% 1.16/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.16/1.50
% 1.16/1.50 % ------ iProver source info
% 1.16/1.50
% 1.16/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 1.16/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.16/1.50 % git: non_committed_changes: false
% 1.16/1.50
% 1.16/1.50 % ------ Parsing...
% 1.16/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.16/1.50
% 1.16/1.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 40 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 1.16/1.50
% 1.16/1.50 % SZS status Theorem for theBenchmark.p
% 1.16/1.50
% 1.16/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.69/1.50
% 2.69/1.50
%------------------------------------------------------------------------------