%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM409+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 : n013.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 02:24:10 PM UTC 2026
% Result : Theorem 2.75s 1.17s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 22 unt; 1 def)
% Number of atoms : 178 ( 9 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 185 ( 75 ~; 66 |; 32 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 14 ( 12 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 47 ( 0 sgn 46 !; 1 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f11,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( ( transfinite_sequence(X1)
& function(X1)
& relation(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f19,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f20,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f24,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f25,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f43,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f45,conjecture,
! [X0] : transfinite_sequence_of(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_ordinal1) ).
fof(f46,negated_conjecture,
~ ! [X0] : transfinite_sequence_of(empty_set,X0),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f50,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f59,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f19]) ).
fof(f63,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f59]) ).
fof(f72,plain,
! [X0] :
( ~ empty(X0)
| ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f74,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f75,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f77,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
inference(flattening,[],[f76]) ).
fof(f83,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f84,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f88,plain,
? [X0] : ~ transfinite_sequence_of(empty_set,X0),
inference(ennf_transformation,[],[f46]) ).
fof(f93,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f50]) ).
fof(f99,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ transfinite_sequence(X0)
| ordinal(relation_dom(X0)) )
& ( ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f100,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ( ( ~ transfinite_sequence_of(X1,X0)
| subset(relation_rng(X1),X0) )
& ( ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0) ) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f118,plain,
~ transfinite_sequence_of(empty_set,sK19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f88]) ).
fof(f128,plain,
! [X0] :
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f138,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f140,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f154,plain,
function(empty_set),
inference(cnf_transformation,[],[f63]) ).
fof(f156,plain,
relation(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f157,plain,
empty(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f161,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f163,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f201,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f204,plain,
~ transfinite_sequence_of(empty_set,sK19),
inference(cnf_transformation,[],[f118]) ).
fof(f209,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_57,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_63,plain,
! [X0: $i] :
( transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ subset(relation_rng(X0),X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_77,plain,
function(empty_set),
inference(cnf_transformation,[],[f154]) ).
tcf(c_82,plain,
empty(empty_set),
inference(cnf_transformation,[],[f157]) ).
tcf(c_83,plain,
relation(empty_set),
inference(cnf_transformation,[],[f156]) ).
tcf(c_86,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_88,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_127,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f201]) ).
tcf(c_130,negated_conjecture,
~ transfinite_sequence_of(empty_set,sK19),
inference(cnf_transformation,[],[f204]) ).
tcf(c_135,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_144,plain,
( empty(relation_dom(empty_set))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_182,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(X0) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_993,plain,
! [X0: $i,X1: $i] :
( transfinite_sequence(X0)
| ~ relation(X0)
| ~ empty(X1)
| ~ function(X0)
| ( relation_dom(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_182,c_63]) ).
tcf(c_994,plain,
! [X0: $i] :
( transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ empty(relation_dom(X0)) ),
inference(unflattening,[status(thm)],[c_993]) ).
tcf(c_995,plain,
( transfinite_sequence(empty_set)
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ empty(relation_dom(empty_set)) ),
inference(instantiation,[status(thm)],[c_994]) ).
tcf(c_1122,plain,
! [X0: $i,X1: $i] :
( ~ transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ subset(relation_rng(X0),X1)
| ( X1 != sK19 )
| ( X0 != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_130]) ).
tcf(c_1123,plain,
( ~ transfinite_sequence(empty_set)
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ subset(relation_rng(empty_set),sK19) ),
inference(unflattening,[status(thm)],[c_1122]) ).
tcf(c_1124,plain,
~ subset(relation_rng(empty_set),sK19),
inference(global_subsumption_just,[status(thm)],[c_1123,c_83,c_82,c_77,c_144,c_995,c_1123]) ).
tcf(c_4397,definition,
iPr_def_11 = relation_rng(empty_set),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4399,plain,
~ subset(iPr_def_11,sK19),
inference(demodulation,[status(thm)],[c_1124,c_4397]) ).
tcf(c_5204,plain,
( empty(iPr_def_11)
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_4397,c_88]) ).
tcf(c_5206,plain,
empty(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_5204,c_82]) ).
tcf(c_5228,plain,
empty_set = iPr_def_11,
inference(superposition,[status(thm)],[c_5206,c_135]) ).
tcf(c_5243,plain,
! [X0: $i] : subset(iPr_def_11,X0),
inference(demodulation,[status(thm)],[c_127,c_5228]) ).
tcf(c_5247,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_4399,c_5243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 03:51:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.75/1.17 % SZS status Started for theBenchmark.p
% 2.75/1.17 % SZS status Theorem for theBenchmark.p
% 2.75/1.17
% 2.75/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.75/1.17
% 2.75/1.17 % ------ iProver source info
% 2.75/1.17
% 2.75/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.75/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.75/1.17 % git: non_committed_changes: false
% 2.75/1.17
% 2.75/1.17 % ------ Parsing...
% 2.75/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.75/1.17
% 2.75/1.17 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 2.75/1.17
% 2.75/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.75/1.17
% 2.75/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.75/1.17 % ------ Proving...
% 2.75/1.17 % ------ Problem Properties
% 2.75/1.17
% 2.75/1.17 %
% 2.75/1.17 % clauses 53
% 2.75/1.17 % conjectures 0
% 2.75/1.17 % EPR 32
% 2.75/1.17 % Horn 51
% 2.75/1.17 % unary 30
% 2.75/1.17 % binary 11
% 2.75/1.17 % lits 90
% 2.75/1.17 % lits eq 12
% 2.75/1.17 % fd_pure 0
% 2.75/1.17 % fd_pseudo 0
% 2.75/1.17 % fd_cond 1
% 2.75/1.17 % fd_pseudo_cond 3
% 2.75/1.17 % AC symbols 0
% 2.75/1.17
% 2.75/1.17 % ------ Schedule dynamic 5 is on
% 2.75/1.17
% 2.75/1.17 % ------ no conjectures: strip conj schedule
% 2.75/1.17
% 2.75/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.75/1.17
% 2.75/1.17
% 2.75/1.17 % ------
% 2.75/1.17 % Current options:
% 2.75/1.17 % ------
% 2.75/1.17
% 2.75/1.17
% 2.75/1.17 %
% 2.75/1.17
% 2.75/1.17 % ------ Proving...
% 2.75/1.17 %
% 2.75/1.17
% 2.75/1.17 % SZS status Theorem for theBenchmark.p
% 2.75/1.17
% 2.75/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.75/1.17
% 2.75/1.17
%------------------------------------------------------------------------------