%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU110+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 : n017.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 0.29s 1.09s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 13 unt; 2 def)
% Number of atoms : 225 ( 15 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 240 ( 96 ~; 102 |; 31 &)
% ( 6 <=>; 5 =>; 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 108 !; 7 ?; 38 :)
% 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(f26,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f27,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
? [X0,X1] :
( subset(X0,X1)
& ~ subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f69,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,[],[f52]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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))],[f70]) ).
fof(f72,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,[],[f53]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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))],[f74]) ).
fof(f86,plain,
( subset(sK12,sK13)
& ~ subset(finite_subsets(sK12),finite_subsets(sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f60]) ).
fof(f96,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f97,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f98,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ in(X3,X1)
| finite(X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f99,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f100,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f104,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f140,plain,
subset(sK12,sK13),
inference(cnf_transformation,[],[f86]) ).
fof(f141,plain,
~ subset(finite_subsets(sK12),finite_subsets(sK13)),
inference(cnf_transformation,[],[f86]) ).
fof(f150,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,finite_subsets(X0)) ),
inference(equality_resolution,[],[f100]) ).
fof(f151,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X3,finite_subsets(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f99]) ).
fof(f152,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X3,finite_subsets(X0))
| finite(X3) ),
inference(equality_resolution,[],[f98]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( in(X0,finite_subsets(X1))
| ~ finite(X0)
| ~ preboolean(finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ preboolean(finite_subsets(X1))
| ~ in(X0,finite_subsets(X1)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ preboolean(finite_subsets(X1))
| ~ in(X0,finite_subsets(X1)) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_65,plain,
! [X0: $i] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f104]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_101,negated_conjecture,
~ subset(finite_subsets(sK12),finite_subsets(sK13)),
inference(cnf_transformation,[],[f141]) ).
tcf(c_102,negated_conjecture,
subset(sK12,sK13),
inference(cnf_transformation,[],[f140]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ in(X0,finite_subsets(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_65]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i] :
( in(X0,finite_subsets(X1))
| ~ finite(X0)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_65]) ).
tcf(c_320,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_1178,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,finite_subsets(X1))
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_320]) ).
tcf(c_1179,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(renaming,[status(thm)],[c_1178]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,finite_subsets(X1))
| finite(X0) ),
inference(prop_impl_just,[status(thm)],[c_318]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ in(X0,finite_subsets(X1)) ),
inference(renaming,[status(thm)],[c_1184]) ).
tcf(c_2021,definition,
iPr_def_10 = finite_subsets(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2022,definition,
iPr_def_11 = finite_subsets(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2023,negated_conjecture,
subset(sK12,sK13),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_2024,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_101,c_2022,c_2021]) ).
tcf(c_2972,plain,
! [X0: $i] :
( finite(X0)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2021,c_1185]) ).
tcf(c_3001,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| finite(sK0(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_57,c_2972]) ).
tcf(c_3201,plain,
! [X0: $i] :
( subset(X0,sK13)
| ~ subset(X0,sK12) ),
inference(superposition,[status(thm)],[c_2023,c_100]) ).
tcf(c_3233,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ finite(X0)
| ~ subset(X0,sK13) ),
inference(superposition,[status(thm)],[c_2022,c_319]) ).
tcf(c_3722,plain,
! [X0: $i,X1: $i] :
( subset(finite_subsets(X0),X1)
| subset(sK0(finite_subsets(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_57,c_1179]) ).
tcf(c_4179,plain,
! [X0: $i] :
( subset(finite_subsets(sK12),X0)
| subset(sK0(finite_subsets(sK12),X0),sK13) ),
inference(superposition,[status(thm)],[c_3722,c_3201]) ).
tcf(c_4191,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| subset(sK0(iPr_def_10,X0),sK13) ),
inference(light_normalisation,[status(thm)],[c_4179,c_2021]) ).
tcf(c_12167,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),iPr_def_11)
| ~ finite(sK0(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_4191,c_3233]) ).
tcf(c_14205,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_12167,c_3001,c_12167]) ).
tcf(c_14216,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_14205,c_56]) ).
tcf(c_14219,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14216,c_2024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU110+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:41:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.29/1.09 % SZS status Started for theBenchmark.p
% 0.29/1.09 % SZS status Theorem for theBenchmark.p
% 0.29/1.09
% 0.29/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.29/1.09
% 0.29/1.09 % ------ iProver source info
% 0.29/1.09
% 0.29/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 0.29/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.29/1.09 % git: non_committed_changes: false
% 0.29/1.09
% 0.29/1.09 % ------ Parsing...
% 0.29/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.29/1.09
% 0.29/1.09 % ------ 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 %
% 0.29/1.09
% 0.29/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.29/1.09
% 0.29/1.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.29/1.09 % ------ Proving...
% 0.29/1.09 % ------ Problem Properties
% 0.29/1.09
% 0.29/1.09 %
% 0.29/1.09 % clauses 53
% 0.29/1.09 % conjectures 2
% 0.29/1.09 % EPR 22
% 0.29/1.09 % Horn 44
% 0.29/1.09 % unary 22
% 0.29/1.09 % binary 20
% 0.29/1.09 % lits 99
% 0.29/1.09 % lits eq 7
% 0.29/1.09 % fd_pure 0
% 0.29/1.09 % fd_pseudo 0
% 0.29/1.09 % fd_cond 1
% 0.29/1.09 % fd_pseudo_cond 4
% 0.29/1.09 % AC symbols 0
% 0.29/1.09
% 0.29/1.09 % ------ Schedule dynamic 5 is on
% 0.29/1.09
% 0.29/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.29/1.09
% 0.29/1.09
% 0.29/1.09 % ------
% 0.29/1.09 % Current options:
% 0.29/1.09 % ------
% 0.29/1.09
% 0.29/1.09
% 0.29/1.09 %
% 0.29/1.09
% 0.29/1.09 % ------ Proving...
% 0.29/1.09 %
% 0.29/1.09
% 0.29/1.09 % SZS status Theorem for theBenchmark.p
% 0.29/1.09
% 0.29/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.29/1.10
% 0.29/1.10
%------------------------------------------------------------------------------