%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU164+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 : n015.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 02:55:42 PM UTC 2026
% Result : Theorem 36.87s 8.45s
% Output : CNFRefutation 36.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 14 unt; 0 def)
% Number of atoms : 177 ( 32 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 205 ( 77 ~; 90 |; 31 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 1 con; 0-2 aty)
% Number of variables : 101 ( 1 sgn 89 !; 12 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f15,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f49,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f93,conjecture,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f94,negated_conjecture,
~ ! [X0] : union(powerset(X0)) = X0,
inference(negated_conjecture,[status(cth)],[f93]) ).
fof(f99,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f49]) ).
fof(f105,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f144,plain,
? [X0] : union(powerset(X0)) != X0,
inference(ennf_transformation,[],[f94]) ).
fof(f154,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f155,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f154]) ).
fof(f156,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| subset(sK2(X0,X1),X0) )
& ( ~ in(sK2(X0,X1),X1)
| ~ subset(sK2(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f155]) ).
fof(f168,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f169,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f168]) ).
fof(f170,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK10(X0,X1),X0)
& ~ in(sK10(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f169]) ).
fof(f175,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f176,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f175]) ).
fof(f177,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK14(X0,X5),X0)
& in(X5,sK14(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK12(X0,X1),X1)
| ( in(sK13(X0,X1),X0)
& in(sK12(X0,X1),sK13(X0,X1)) ) )
& ( ~ in(sK12(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK12(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X2,sK12(X0,X1)),skolemize(X4,sK13(X0,X1)),skolemize(X7,sK14(X0,X5))],[f176]) ).
fof(f203,plain,
sK21 != union(powerset(sK21)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f144]) ).
fof(f218,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f219,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f156]) ).
fof(f242,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f254,plain,
! [X0,X1] :
( in(sK12(X0,X1),X1)
| in(sK13(X0,X1),X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f177]) ).
fof(f255,plain,
! [X0,X1] :
( in(sK12(X0,X1),X1)
| in(sK12(X0,X1),sK13(X0,X1))
| union(X0) = X1 ),
inference(cnf_transformation,[],[f177]) ).
fof(f256,plain,
! [X3,X0,X1] :
( ~ in(sK12(X0,X1),X1)
| ~ in(X3,X0)
| ~ in(sK12(X0,X1),X3)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f177]) ).
fof(f292,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f99]) ).
fof(f349,plain,
sK21 != union(powerset(sK21)),
inference(cnf_transformation,[],[f203]) ).
fof(f411,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f219]) ).
fof(f412,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f218]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f411]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f412]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( union(X0) = X1 )
| ~ in(X2,X0)
| ~ in(sK12(X0,X1),X2)
| ~ in(sK12(X0,X1),X1) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1),X1)
| in(sK12(X0,X1),sK13(X0,X1))
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X0)
| in(sK12(X0,X1),X1)
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_136,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f292]) ).
tcf(c_191,negated_conjecture,
union(powerset(sK21)) != sK21,
inference(cnf_transformation,[],[f349]) ).
tcf(c_5276,plain,
( in(sK12(powerset(sK21),sK21),sK21)
| in(sK13(powerset(sK21),sK21),powerset(sK21))
| ( union(powerset(sK21)) = sK21 ) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_5294,plain,
! [X0: $i] :
( ( union(powerset(sK21)) = sK21 )
| ~ in(X0,powerset(sK21))
| ~ in(sK12(powerset(sK21),sK21),sK21)
| ~ in(sK12(powerset(sK21),sK21),X0) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_6075,plain,
! [X0: $i] :
( in(X0,powerset(sK21))
| ~ subset(X0,sK21) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_16522,plain,
( in(sK21,powerset(sK21))
| ~ subset(sK21,sK21) ),
inference(instantiation,[status(thm)],[c_6075]) ).
tcf(c_16523,plain,
subset(sK21,sK21),
inference(instantiation,[status(thm)],[c_136]) ).
tcf(c_21177,plain,
( ( union(powerset(sK21)) = sK21 )
| ~ in(sK21,powerset(sK21))
| ~ in(sK12(powerset(sK21),sK21),sK21) ),
inference(instantiation,[status(thm)],[c_5294]) ).
tcf(c_23386,plain,
( in(sK12(powerset(sK21),sK21),sK21)
| in(sK13(powerset(sK21),sK21),powerset(sK21)) ),
inference(resolution,[status(thm)],[c_98,c_191]) ).
tcf(c_28574,plain,
in(sK13(powerset(sK21),sK21),powerset(sK21)),
inference(global_subsumption_just,[status(thm)],[c_23386,c_191,c_5276,c_16522,c_16523,c_21177]) ).
tcf(c_28587,plain,
subset(sK13(powerset(sK21),sK21),sK21),
inference(resolution,[status(thm)],[c_28574,c_66]) ).
tcf(c_28759,plain,
! [X0: $i] :
( in(X0,sK21)
| ~ in(X0,sK13(powerset(sK21),sK21)) ),
inference(resolution,[status(thm)],[c_28587,c_89]) ).
tcf(c_30452,plain,
( in(sK12(powerset(sK21),sK21),sK21)
| ( union(powerset(sK21)) = sK21 ) ),
inference(resolution,[status(thm)],[c_97,c_28759]) ).
tcf(c_30453,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_30452,c_21177,c_16523,c_16522,c_191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU164+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 13:03:42 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 36.87/8.45 % SZS status Started for theBenchmark.p
% 36.87/8.45 % SZS status Theorem for theBenchmark.p
% 36.87/8.45
% 36.87/8.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 36.87/8.45
% 36.87/8.45 % ------ iProver source info
% 36.87/8.45
% 36.87/8.45 % git: date: 2026-07-19 20:42:38 +0200
% 36.87/8.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 36.87/8.45 % git: non_committed_changes: false
% 36.87/8.45
% 36.87/8.45 % ------ Parsing...
% 36.87/8.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 36.87/8.45
% 36.87/8.45 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 36.87/8.45
% 36.87/8.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 36.87/8.45
% 36.87/8.45 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 36.87/8.45 % ------ Proving...
% 36.87/8.45 % ------ Problem Properties
% 36.87/8.45
% 36.87/8.45 %
% 36.87/8.45 % clauses 124
% 36.87/8.45 % conjectures 1
% 36.87/8.45 % EPR 21
% 36.87/8.45 % Horn 95
% 36.87/8.45 % unary 25
% 36.87/8.45 % binary 55
% 36.87/8.45 % lits 274
% 36.87/8.45 % lits eq 81
% 36.87/8.45 % fd_pure 0
% 36.87/8.45 % fd_pseudo 0
% 36.87/8.45 % fd_cond 3
% 36.87/8.45 % fd_pseudo_cond 35
% 36.87/8.45 % AC symbols 0
% 36.87/8.45
% 36.87/8.45 % ------ Input Options Time Limit: Unbounded
% 36.87/8.45
% 36.87/8.45
% 36.87/8.45 % ------
% 36.87/8.45 % Current options:
% 36.87/8.45 % ------
% 36.87/8.45
% 36.87/8.45
% 36.87/8.45 %
% 36.87/8.45
% 36.87/8.45 % ------ Proving...
% 36.87/8.45 %
% 36.87/8.45
% 36.87/8.45 % SZS status Theorem for theBenchmark.p
% 36.87/8.45
% 36.87/8.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 36.87/8.45
% 36.87/8.45
%------------------------------------------------------------------------------