%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU117+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 : n018.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 3.15s 1.31s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 18 unt; 2 def)
% Number of atoms : 158 ( 13 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 163 ( 63 ~; 63 |; 28 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 61 !; 5 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f11,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f13,axiom,
! [X0] :
( preboolean(finite_subsets(X0))
& diff_closed(finite_subsets(X0))
& cup_closed(finite_subsets(X0))
& ~ empty(finite_subsets(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finsub_1) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f31,conjecture,
! [X0,X1] :
( element(X1,finite_subsets(X0))
=> element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1] :
( element(X1,finite_subsets(X0))
=> element(X1,powerset(X0)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,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(f46,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f47,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f46]) ).
fof(f62,plain,
? [X0,X1] :
( element(X1,finite_subsets(X0))
& ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f32]) ).
fof(f63,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f74,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f75,plain,
( element(sK11,finite_subsets(sK10))
& ~ element(sK11,powerset(sK10)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f62]) ).
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,[],[f63]) ).
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(sK12(X0,X1),X1)
| ( finite(sK12(X0,X1))
& subset(sK12(X0,X1),X0) ) )
& ( ~ in(sK12(X0,X1),X1)
| ~ finite(sK12(X0,X1))
| ~ subset(sK12(X0,X1),X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f78]) ).
fof(f83,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f90,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f98,plain,
! [X0] : ~ empty(finite_subsets(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f127,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f130,plain,
element(sK11,finite_subsets(sK10)),
inference(cnf_transformation,[],[f75]) ).
fof(f131,plain,
~ element(sK11,powerset(sK10)),
inference(cnf_transformation,[],[f75]) ).
fof(f133,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f139,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X3,finite_subsets(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f133]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_59,plain,
! [X0: $i] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f90]) ).
tcf(c_64,plain,
! [X0: $i] : ~ empty(finite_subsets(X0)),
inference(cnf_transformation,[],[f98]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_99,negated_conjecture,
~ element(sK11,powerset(sK10)),
inference(cnf_transformation,[],[f131]) ).
tcf(c_100,negated_conjecture,
element(sK11,finite_subsets(sK10)),
inference(cnf_transformation,[],[f130]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ preboolean(finite_subsets(X1))
| ~ in(X0,finite_subsets(X1)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_105,c_59]) ).
tcf(c_1600,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,finite_subsets(X1))
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_304]) ).
tcf(c_1601,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(renaming,[status(thm)],[c_1600]) ).
tcf(c_2832,definition,
iPr_def_10 = finite_subsets(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2833,definition,
iPr_def_11 = powerset(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2834,negated_conjecture,
element(sK11,iPr_def_10),
inference(demodulation,[status(thm)],[c_100,c_2832]) ).
tcf(c_2835,negated_conjecture,
~ element(sK11,iPr_def_11),
inference(demodulation,[status(thm)],[c_99,c_2833]) ).
tcf(c_3631,plain,
~ empty(iPr_def_10),
inference(superposition,[status(thm)],[c_2832,c_64]) ).
tcf(c_3768,plain,
( empty(iPr_def_10)
| in(sK11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2834,c_52]) ).
tcf(c_3775,plain,
in(sK11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3768,c_3631]) ).
tcf(c_3802,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| ~ subset(X0,sK10) ),
inference(superposition,[status(thm)],[c_2833,c_95]) ).
tcf(c_4130,plain,
! [X0: $i] :
( subset(X0,sK10)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2832,c_1601]) ).
tcf(c_4170,plain,
subset(sK11,sK10),
inference(superposition,[status(thm)],[c_3775,c_4130]) ).
tcf(c_4180,plain,
element(sK11,iPr_def_11),
inference(superposition,[status(thm)],[c_4170,c_3802]) ).
tcf(c_4181,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4180,c_2835]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU117+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:49:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 3.15/1.31 % SZS status Started for theBenchmark.p
% 3.15/1.31 % SZS status Theorem for theBenchmark.p
% 3.15/1.31
% 3.15/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.15/1.31
% 3.15/1.31 % ------ iProver source info
% 3.15/1.31
% 3.15/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.15/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.15/1.31 % git: non_committed_changes: false
% 3.15/1.31
% 3.15/1.31 % ------ Parsing...
% 3.15/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.15/1.31
% 3.15/1.31 % ------ 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 %
% 3.15/1.31
% 3.15/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.15/1.31
% 3.15/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.15/1.31 % ------ Proving...
% 3.15/1.31 % ------ Problem Properties
% 3.15/1.31
% 3.15/1.31 %
% 3.15/1.31 % clauses 49
% 3.15/1.31 % conjectures 2
% 3.15/1.31 % EPR 20
% 3.15/1.31 % Horn 41
% 3.15/1.31 % unary 22
% 3.15/1.31 % binary 18
% 3.15/1.31 % lits 89
% 3.15/1.31 % lits eq 7
% 3.15/1.31 % fd_pure 0
% 3.15/1.31 % fd_pseudo 0
% 3.15/1.31 % fd_cond 1
% 3.15/1.31 % fd_pseudo_cond 4
% 3.15/1.31 % AC symbols 0
% 3.15/1.31
% 3.15/1.31 % ------ Schedule dynamic 5 is on
% 3.15/1.31
% 3.15/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.15/1.31
% 3.15/1.31
% 3.15/1.31 % ------
% 3.15/1.31 % Current options:
% 3.15/1.31 % ------
% 3.15/1.31
% 3.15/1.31
% 3.15/1.31 %
% 3.15/1.31
% 3.15/1.31 % ------ Proving...
% 3.15/1.31 %
% 3.15/1.31
% 3.15/1.31 % SZS status Theorem for theBenchmark.p
% 3.15/1.31
% 3.15/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.15/1.31
% 3.15/1.31
%------------------------------------------------------------------------------