%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU147+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 : 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 02:55:35 PM UTC 2026
% Result : Theorem 2.64s 1.31s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 18 unt; 2 def)
% Number of atoms : 200 ( 64 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 177 ( 68 ~; 81 |; 20 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 88 ( 1 sgn 82 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f12,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f14,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f15,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f16,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f12]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f14]) ).
fof(f20,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).
fof(f23,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,[],[f3]) ).
fof(f24,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,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| subset(sK1(X0,X1),X0) )
& ( ~ in(sK1(X0,X1),X1)
| ~ subset(sK1(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f24]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] :
( ( ( in(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1) )
& ( ~ in(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f28]) ).
fof(f31,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f43,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f44,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f46,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f47,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f32]) ).
fof(f48,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f47]) ).
fof(f49,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f31]) ).
fof(f50,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f36]) ).
fof(f51,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f35]) ).
tcf(c_52,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f48]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_61,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
tcf(c_62,negated_conjecture,
singleton(empty_set) != powerset(empty_set),
inference(cnf_transformation,[],[f43]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_370,definition,
iPr_def_10 = singleton(empty_set),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_371,definition,
iPr_def_11 = powerset(empty_set),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_372,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_62,c_371,c_370]) ).
tcf(c_750,plain,
in(empty_set,iPr_def_10),
inference(superposition,[status(thm)],[c_370,c_52]) ).
tcf(c_760,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_371,c_56]) ).
tcf(c_773,plain,
! [X0: $i] :
( subset(X0,empty_set)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_371,c_57]) ).
tcf(c_789,plain,
in(empty_set,iPr_def_11),
inference(superposition,[status(thm)],[c_61,c_760]) ).
tcf(c_801,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_370,c_53]) ).
tcf(c_841,plain,
! [X0: $i] :
( subset(sK4(X0,iPr_def_11),empty_set)
| in(sK4(X0,iPr_def_11),X0)
| ( X0 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_64,c_773]) ).
tcf(c_1039,plain,
( subset(sK4(iPr_def_10,iPr_def_11),empty_set)
| ( iPr_def_10 = iPr_def_11 )
| ( sK4(iPr_def_10,iPr_def_11) = empty_set ) ),
inference(superposition,[status(thm)],[c_841,c_801]) ).
tcf(c_1043,plain,
( subset(sK4(iPr_def_10,iPr_def_11),empty_set)
| ( sK4(iPr_def_10,iPr_def_11) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1039,c_372]) ).
tcf(c_1069,plain,
sK4(iPr_def_10,iPr_def_11) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_1043,c_65]) ).
tcf(c_1070,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ in(empty_set,iPr_def_11)
| ~ in(sK4(iPr_def_10,iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_1069,c_63]) ).
tcf(c_1076,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ in(empty_set,iPr_def_11)
| ~ in(empty_set,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_1070,c_1069]) ).
tcf(c_1077,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1076,c_372,c_789,c_750]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 12:59:20 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 0.10/0.44
% 0.10/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 2.64/1.31 % SZS status Started for theBenchmark.p
% 2.64/1.31 % SZS status Theorem for theBenchmark.p
% 2.64/1.31
% 2.64/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.64/1.31
% 2.64/1.31 % ------ iProver source info
% 2.64/1.31
% 2.64/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.64/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.64/1.31 % git: non_committed_changes: false
% 2.64/1.31
% 2.64/1.31 % ------ Parsing...
% 2.64/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.64/1.31
% 2.64/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.64/1.31
% 2.64/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.64/1.31
% 2.64/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.64/1.31 % ------ Proving...
% 2.64/1.31 % ------ Problem Properties
% 2.64/1.31
% 2.64/1.31 %
% 2.64/1.31 % clauses 19
% 2.64/1.31 % conjectures 1
% 2.64/1.31 % EPR 7
% 2.64/1.31 % Horn 16
% 2.64/1.31 % unary 8
% 2.64/1.31 % binary 5
% 2.64/1.31 % lits 36
% 2.64/1.31 % lits eq 13
% 2.64/1.31 % fd_pure 0
% 2.64/1.31 % fd_pseudo 0
% 2.64/1.31 % fd_cond 1
% 2.64/1.31 % fd_pseudo_cond 6
% 2.64/1.31 % AC symbols 0
% 2.64/1.31
% 2.64/1.31 % ------ Schedule dynamic 5 is on
% 2.64/1.31
% 2.64/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.64/1.31
% 2.64/1.31
% 2.64/1.31 % ------
% 2.64/1.31 % Current options:
% 2.64/1.31 % ------
% 2.64/1.31
% 2.64/1.31
% 2.64/1.31 %
% 2.64/1.31
% 2.64/1.31 % ------ Proving...
% 2.64/1.31 %
% 2.64/1.31
% 2.64/1.31 % SZS status Theorem for theBenchmark.p
% 2.64/1.31
% 2.64/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.64/1.31
% 2.64/1.31
%------------------------------------------------------------------------------