%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU114+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 : n004.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 02:55:27 PM UTC 2026
% Result : Theorem 4.38s 1.20s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 18 unt; 2 def)
% Number of atoms : 239 ( 28 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 245 ( 96 ~; 98 |; 37 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 102 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f10,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f26,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f27,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f28,axiom,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(f29,conjecture,
! [X0] :
( finite(X0)
=> finite_subsets(X0) = powerset(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( finite(X0)
=> finite_subsets(X0) = powerset(X0) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f59,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f60,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
? [X0] :
( finite(X0)
& powerset(X0) != finite_subsets(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f71,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f72,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f71]) ).
fof(f73,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,[],[f54]) ).
fof(f74,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,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( ( finite_subsets(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ finite(X2)
| ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f77,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( ( finite_subsets(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ finite(X2)
| ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( ( finite_subsets(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| ( finite(X3)
& subset(X3,X0) ) )
& ( ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( ( finite_subsets(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| ( finite(X3)
& subset(X3,X0) ) )
& ( ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| ( finite(sK1(X0,X1))
& subset(sK1(X0,X1),X0) ) )
& ( ~ in(sK1(X0,X1),X1)
| ~ finite(sK1(X0,X1))
| ~ subset(sK1(X0,X1),X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f78]) ).
fof(f90,plain,
( finite(sK12)
& powerset(sK12) != finite_subsets(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f62]) ).
fof(f91,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f101,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f103,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f104,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f107,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f111,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f145,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f146,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f147,plain,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f148,plain,
finite(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f149,plain,
powerset(sK12) != finite_subsets(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f151,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f160,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,finite_subsets(X0)) ),
inference(equality_resolution,[],[f107]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(X0,finite_subsets(X1))
| ~ finite(X0)
| ~ preboolean(finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_68,plain,
! [X0: $i] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f111]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_104,plain,
! [X0: $i] : subset(finite_subsets(X0),powerset(X0)),
inference(cnf_transformation,[],[f147]) ).
tcf(c_105,negated_conjecture,
powerset(sK12) != finite_subsets(sK12),
inference(cnf_transformation,[],[f149]) ).
tcf(c_106,negated_conjecture,
finite(sK12),
inference(cnf_transformation,[],[f148]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] :
( in(X0,finite_subsets(X1))
| ~ finite(X0)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_68]) ).
tcf(c_2033,definition,
iPr_def_10 = powerset(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2034,definition,
iPr_def_11 = finite_subsets(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2036,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_105,c_2034,c_2033]) ).
tcf(c_2927,plain,
subset(finite_subsets(sK12),iPr_def_10),
inference(superposition,[status(thm)],[c_2033,c_104]) ).
tcf(c_2928,plain,
subset(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_2927,c_2034]) ).
tcf(c_3076,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| element(sK0(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_60,c_103]) ).
tcf(c_3105,plain,
! [X0: $i] :
( subset(X0,sK12)
| ~ element(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2033,c_109]) ).
tcf(c_3293,plain,
! [X0: $i] :
( finite(X0)
| ~ finite(sK12)
| ~ subset(X0,sK12) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_3345,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ finite(X0)
| ~ subset(X0,sK12) ),
inference(superposition,[status(thm)],[c_2034,c_329]) ).
tcf(c_3386,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ subset(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2928,c_56]) ).
tcf(c_3391,plain,
~ subset(iPr_def_10,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_3386,c_2036]) ).
tcf(c_3812,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| subset(sK0(iPr_def_10,X0),sK12) ),
inference(superposition,[status(thm)],[c_3076,c_3105]) ).
tcf(c_4350,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ subset(X0,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_3345,c_106,c_3293,c_3345]) ).
tcf(c_4369,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3812,c_4350]) ).
tcf(c_4704,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_4369,c_59]) ).
tcf(c_4707,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4704,c_3391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU114+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:46:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 4.38/1.20 % SZS status Started for theBenchmark.p
% 4.38/1.20 % SZS status Theorem for theBenchmark.p
% 4.38/1.20
% 4.38/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.38/1.20
% 4.38/1.20 % ------ iProver source info
% 4.38/1.20
% 4.38/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 4.38/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.38/1.20 % git: non_committed_changes: false
% 4.38/1.20
% 4.38/1.20 % ------ Parsing...
% 4.38/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.38/1.20
% 4.38/1.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.38/1.20
% 4.38/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.38/1.20
% 4.38/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.38/1.20 % ------ Proving...
% 4.38/1.20 % ------ Problem Properties
% 4.38/1.20
% 4.38/1.20 %
% 4.38/1.20 % clauses 54
% 4.38/1.20 % conjectures 2
% 4.38/1.20 % EPR 22
% 4.38/1.20 % Horn 45
% 4.38/1.20 % unary 23
% 4.38/1.20 % binary 20
% 4.38/1.20 % lits 100
% 4.38/1.20 % lits eq 9
% 4.38/1.20 % fd_pure 0
% 4.38/1.20 % fd_pseudo 0
% 4.38/1.20 % fd_cond 1
% 4.38/1.20 % fd_pseudo_cond 5
% 4.38/1.20 % AC symbols 0
% 4.38/1.20
% 4.38/1.20 % ------ Schedule dynamic 5 is on
% 4.38/1.20
% 4.38/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.38/1.20
% 4.38/1.20
% 4.38/1.20 % ------
% 4.38/1.20 % Current options:
% 4.38/1.20 % ------
% 4.38/1.20
% 4.38/1.20
% 4.38/1.20 %
% 4.38/1.20
% 4.38/1.20 % ------ Proving...
% 4.38/1.20 %
% 4.38/1.20
% 4.38/1.20 % SZS status Theorem for theBenchmark.p
% 4.38/1.20
% 4.38/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.38/1.20
% 4.38/1.20
%------------------------------------------------------------------------------