%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:55:26 PM UTC 2026
% Result : Theorem 2.67s 1.17s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 17 unt; 2 def)
% Number of atoms : 184 ( 13 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 195 ( 75 ~; 81 |; 29 &)
% ( 7 <=>; 3 =>; 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 : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 89 !; 6 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f9,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f12,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f26,conjecture,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(f27,negated_conjecture,
~ ! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f52,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f57,plain,
? [X0] : ~ subset(finite_subsets(X0),powerset(X0)),
inference(ennf_transformation,[],[f27]) ).
fof(f58,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f59,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f58]) ).
fof(f66,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,[],[f51]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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))],[f67]) ).
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(nnf_transformation,[],[f52]) ).
fof(f70,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,[],[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) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(rectify,[],[f70]) ).
fof(f72,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))],[f71]) ).
fof(f83,plain,
~ subset(finite_subsets(sK12),powerset(sK12)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f57]) ).
fof(f84,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f93,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f94,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f96,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f101,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f107,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f136,plain,
~ subset(finite_subsets(sK12),powerset(sK12)),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f139,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f146,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X3,finite_subsets(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f96]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ preboolean(finite_subsets(X1))
| ~ in(X0,finite_subsets(X1)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_65,plain,
! [X0: $i] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f101]) ).
tcf(c_71,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f107]) ).
tcf(c_100,negated_conjecture,
~ subset(finite_subsets(sK12),powerset(sK12)),
inference(cnf_transformation,[],[f136]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_65]) ).
tcf(c_1780,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,finite_subsets(X1))
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_315]) ).
tcf(c_1781,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(renaming,[status(thm)],[c_1780]) ).
tcf(c_3206,definition,
iPr_def_10 = finite_subsets(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3207,definition,
iPr_def_11 = powerset(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3208,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_100,c_3207,c_3206]) ).
tcf(c_4252,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_102,c_101]) ).
tcf(c_4284,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4252,c_71]) ).
tcf(c_4835,plain,
! [X0: $i,X1: $i] :
( subset(finite_subsets(X0),X1)
| subset(sK0(finite_subsets(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_57,c_1781]) ).
tcf(c_4928,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ subset(X0,sK12) ),
inference(superposition,[status(thm)],[c_3207,c_4284]) ).
tcf(c_5004,plain,
! [X0: $i] :
( subset(finite_subsets(sK12),X0)
| in(sK0(finite_subsets(sK12),X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4835,c_4928]) ).
tcf(c_5009,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_5004,c_3206]) ).
tcf(c_5262,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_5009,c_56]) ).
tcf(c_5263,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5262,c_3208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 12:46:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 2.67/1.17 % SZS status Started for theBenchmark.p
% 2.67/1.17 % SZS status Theorem for theBenchmark.p
% 2.67/1.17
% 2.67/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.67/1.17
% 2.67/1.17 % ------ iProver source info
% 2.67/1.17
% 2.67/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.67/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.67/1.17 % git: non_committed_changes: false
% 2.67/1.17
% 2.67/1.17 % ------ Parsing...
% 2.67/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.67/1.17
% 2.67/1.17 % ------ 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 %
% 2.67/1.17
% 2.67/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.67/1.17
% 2.67/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.67/1.17 % ------ Proving...
% 2.67/1.17 % ------ Problem Properties
% 2.67/1.17
% 2.67/1.17 %
% 2.67/1.17 % clauses 51
% 2.67/1.17 % conjectures 1
% 2.67/1.17 % EPR 20
% 2.67/1.17 % Horn 42
% 2.67/1.17 % unary 21
% 2.67/1.17 % binary 20
% 2.67/1.17 % lits 95
% 2.67/1.17 % lits eq 7
% 2.67/1.17 % fd_pure 0
% 2.67/1.17 % fd_pseudo 0
% 2.67/1.17 % fd_cond 1
% 2.67/1.17 % fd_pseudo_cond 4
% 2.67/1.17 % AC symbols 0
% 2.67/1.17
% 2.67/1.17 % ------ Schedule dynamic 5 is on
% 2.67/1.17
% 2.67/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.67/1.17
% 2.67/1.17
% 2.67/1.17 % ------
% 2.67/1.17 % Current options:
% 2.67/1.17 % ------
% 2.67/1.17
% 2.67/1.17
% 2.67/1.17 %
% 2.67/1.17
% 2.67/1.17 % ------ Proving...
% 2.67/1.17 %
% 2.67/1.17
% 2.67/1.17 % SZS status Theorem for theBenchmark.p
% 2.67/1.17
% 2.67/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.57/1.17
%------------------------------------------------------------------------------