%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET933+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:49:09 PM UTC 2026
% Result : Theorem 1.61s 1.16s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 79 ( 18 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 86 ( 39 ~; 34 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 1 sgn 42 !; 3 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f7,conjecture,
! [X0] : subset(singleton(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0] : subset(singleton(X0),powerset(X0)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f6]) ).
fof(f11,plain,
? [X0] : ~ subset(singleton(X0),powerset(X0)),
inference(ennf_transformation,[],[f8]) ).
fof(f12,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,[],[f2]) ).
fof(f13,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,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| subset(sK0(X0,X1),X0) )
& ( ~ in(sK0(X0,X1),X1)
| ~ subset(sK0(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
~ subset(singleton(sK3),powerset(sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f11]) ).
fof(f21,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f29,plain,
~ subset(singleton(sK3),powerset(sK3)),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_58,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,negated_conjecture,
~ subset(singleton(sK3),powerset(sK3)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,plain,
subset(sK3,sK3),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_63,plain,
( in(sK3,powerset(sK3))
| ~ subset(sK3,sK3) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ( powerset(sK3) != X1 )
| ( singleton(X0) != singleton(sK3) ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_59]) ).
tcf(c_326,plain,
! [X0: $i] :
( ~ in(X0,powerset(sK3))
| ( singleton(X0) != singleton(sK3) ) ),
inference(unflattening,[status(thm)],[c_325]) ).
tcf(c_327,plain,
( ~ in(sK3,powerset(sK3))
| ( singleton(sK3) != singleton(sK3) ) ),
inference(instantiation,[status(thm)],[c_326]) ).
tcf(c_672,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_678,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_680,plain,
( ( singleton(sK3) = singleton(sK3) )
| ( sK3 != sK3 ) ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_681,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_672]) ).
tcf(c_682,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_681,c_680,c_327,c_63,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET933+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:23:48 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 1.61/1.16 % SZS status Started for theBenchmark.p
% 1.61/1.16 % SZS status Theorem for theBenchmark.p
% 1.61/1.16
% 1.61/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.16
% 1.61/1.16 % ------ iProver source info
% 1.61/1.16
% 1.61/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.16 % git: non_committed_changes: false
% 1.61/1.16
% 1.61/1.16 % ------ Parsing...
% 1.61/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/1.16
% 1.61/1.16 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.61/1.16
% 1.61/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.61/1.16
% 1.61/1.16 % ------ Preprocessing...%
% 1.61/1.16
% 1.61/1.16 % SZS status Theorem for theBenchmark.p
% 1.61/1.16
% 1.61/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.16
% 1.61/1.16
%------------------------------------------------------------------------------