%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU118+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 : n016.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 2.97s 11.54s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 17 unt; 2 def)
% Number of atoms : 170 ( 13 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 185 ( 73 ~; 70 |; 30 &)
% ( 5 <=>; 7 =>; 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; 2 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 64 !; 7 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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(f8,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f24,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f25,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f27,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ( finite(X0)
=> element(X1,finite_subsets(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ( finite(X0)
=> element(X1,finite_subsets(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f51,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f55,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f56,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f60,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& finite(X0)
& ~ element(X1,finite_subsets(X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f61,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& finite(X0)
& ~ element(X1,finite_subsets(X0)) ),
inference(flattening,[],[f60]) ).
fof(f68,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,[],[f51]) ).
fof(f69,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,[],[f68]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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(sK0(X0,X1),X1)
| ( finite(sK0(X0,X1))
& subset(sK0(X0,X1),X0) ) )
& ( ~ in(sK0(X0,X1),X1)
| ~ finite(sK0(X0,X1))
| ~ subset(sK0(X0,X1),X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f70]) ).
fof(f82,plain,
( element(sK12,powerset(sK11))
& finite(sK11)
& ~ element(sK12,finite_subsets(sK11)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f61]) ).
fof(f83,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f93,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f97,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f131,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f132,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f134,plain,
element(sK12,powerset(sK11)),
inference(cnf_transformation,[],[f82]) ).
fof(f135,plain,
finite(sK11),
inference(cnf_transformation,[],[f82]) ).
fof(f136,plain,
~ element(sK12,finite_subsets(sK11)),
inference(cnf_transformation,[],[f82]) ).
fof(f137,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f144,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,finite_subsets(X0)) ),
inference(equality_resolution,[],[f93]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( in(X0,finite_subsets(X1))
| ~ finite(X0)
| ~ preboolean(finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_62,plain,
! [X0: $i] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f97]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_99,negated_conjecture,
~ element(sK12,finite_subsets(sK11)),
inference(cnf_transformation,[],[f136]) ).
tcf(c_100,negated_conjecture,
finite(sK11),
inference(cnf_transformation,[],[f135]) ).
tcf(c_101,negated_conjecture,
element(sK12,powerset(sK11)),
inference(cnf_transformation,[],[f134]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i] :
( in(X0,finite_subsets(X1))
| ~ finite(X0)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_59,c_62]) ).
tcf(c_2837,definition,
iPr_def_10 = powerset(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2838,definition,
iPr_def_11 = finite_subsets(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2839,negated_conjecture,
element(sK12,iPr_def_10),
inference(demodulation,[status(thm)],[c_101,c_2837]) ).
tcf(c_2841,negated_conjecture,
~ element(sK12,iPr_def_11),
inference(demodulation,[status(thm)],[c_99,c_2838]) ).
tcf(c_3795,plain,
! [X0: $i] :
( subset(X0,sK11)
| ~ element(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2837,c_103]) ).
tcf(c_3912,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ finite(X0)
| ~ subset(X0,sK11) ),
inference(superposition,[status(thm)],[c_2838,c_307]) ).
tcf(c_4059,plain,
! [X0: $i] :
( finite(X0)
| ~ finite(sK11)
| ~ subset(X0,sK11) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_4183,plain,
subset(sK12,sK11),
inference(superposition,[status(thm)],[c_2839,c_3795]) ).
tcf(c_4366,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ subset(X0,sK11) ),
inference(global_subsumption_just,[status(thm)],[c_3912,c_100,c_3912,c_4059]) ).
tcf(c_4378,plain,
in(sK12,iPr_def_11),
inference(superposition,[status(thm)],[c_4183,c_4366]) ).
tcf(c_4418,plain,
element(sK12,iPr_def_11),
inference(superposition,[status(thm)],[c_4378,c_97]) ).
tcf(c_4421,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4418,c_2841]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.62 % Computer : n016.cluster.edu
% 0.12/10.62 % Model : x86_64 x86_64
% 0.12/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.62 % Memory : 8046.5625MB
% 0.12/10.62 % OS : Linux 6.8.0-71-generic
% 0.12/10.62 % CPULimit : 300
% 0.12/10.62 % WCLimit : 300
% 0.12/10.62 % DateTime : Thu Sep 24 12:52:25 UTC 2026
% 0.12/10.62 % CPUTime :
% 0.12/10.62 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.66 Running first-order theorem proving
% 0.12/10.66 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
% 0.12/10.67
% 0.12/10.67 % ======== iProver multi-core TPTP/SMT =========
% 0.12/10.67
% 0.12/10.67 % Detected problem language: tptp
% 0.12/10.68 % Proving...
% 2.97/11.54 % SZS status Started for theBenchmark.p
% 2.97/11.54 % SZS status Theorem for theBenchmark.p
% 2.97/11.54
% 2.97/11.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.97/11.54
% 2.97/11.54 % ------ iProver source info
% 2.97/11.54
% 2.97/11.54 % git: date: 2026-07-19 20:42:38 +0200
% 2.97/11.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.97/11.54 % git: non_committed_changes: false
% 2.97/11.54
% 2.97/11.54 % ------ Parsing...
% 2.97/11.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.97/11.54
% 2.97/11.54 % ------ 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 %
% 2.97/11.54
% 2.97/11.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.97/11.54
% 2.97/11.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.97/11.54 % ------ Proving...
% 2.97/11.54 % ------ Problem Properties
% 2.97/11.54
% 2.97/11.54 %
% 2.97/11.54 % clauses 50
% 2.97/11.54 % conjectures 3
% 2.97/11.54 % EPR 21
% 2.97/11.54 % Horn 42
% 2.97/11.54 % unary 23
% 2.97/11.54 % binary 18
% 2.97/11.54 % lits 90
% 2.97/11.54 % lits eq 7
% 2.97/11.54 % fd_pure 0
% 2.97/11.54 % fd_pseudo 0
% 2.97/11.54 % fd_cond 1
% 2.97/11.54 % fd_pseudo_cond 4
% 2.97/11.54 % AC symbols 0
% 2.97/11.54
% 2.97/11.54 % ------ Schedule dynamic 5 is on
% 2.97/11.54
% 2.97/11.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.97/11.54
% 2.97/11.54
% 2.97/11.54 % ------
% 2.97/11.54 % Current options:
% 2.97/11.54 % ------
% 2.97/11.54
% 2.97/11.54
% 2.97/11.54 %
% 2.97/11.54
% 2.97/11.54 % ------ Proving...
% 2.97/11.54 %
% 2.97/11.54
% 2.97/11.54 % SZS status Theorem for theBenchmark.p
% 2.97/11.54
% 2.97/11.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.97/11.54
% 2.97/11.54
%------------------------------------------------------------------------------