TSTP Solution File: NUM409+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM409+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 12:51:49 EDT 2024
% Result : Theorem 0.45s 1.11s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 18 unt; 0 def)
% Number of atoms : 174 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 193 ( 80 ~; 68 |; 32 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 49 ( 2 sgn 31 !; 2 ?)
% 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,[],[f45]) ).
fof(f50,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f58,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(f61,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,[],[f58]) ).
fof(f72,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f74,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f75,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f77,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f76]) ).
fof(f83,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f84,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f88,plain,
? [X0] : ~ transfinite_sequence_of(empty_set,X0),
inference(ennf_transformation,[],[f46]) ).
fof(f93,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f102,plain,
! [X0] :
( ( ( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0)) )
& ( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f103,plain,
! [X0,X1] :
( ( ( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0) )
& ( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f137,plain,
( ? [X0] : ~ transfinite_sequence_of(empty_set,X0)
=> ~ transfinite_sequence_of(empty_set,sK19) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
~ transfinite_sequence_of(empty_set,sK19),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f88,f137]) ).
fof(f150,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f158,plain,
! [X0] :
( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f160,plain,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f171,plain,
function(empty_set),
inference(cnf_transformation,[],[f61]) ).
fof(f176,plain,
empty(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f177,plain,
relation(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f180,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f182,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f221,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f224,plain,
~ transfinite_sequence_of(empty_set,sK19),
inference(cnf_transformation,[],[f138]) ).
fof(f229,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_55,plain,
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_63,plain,
( ~ ordinal(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| transfinite_sequence(X0) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_65,plain,
( ~ subset(relation_rng(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ transfinite_sequence(X0)
| transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_80,plain,
function(empty_set),
inference(cnf_transformation,[],[f171]) ).
cnf(c_82,plain,
relation(empty_set),
inference(cnf_transformation,[],[f177]) ).
cnf(c_83,plain,
empty(empty_set),
inference(cnf_transformation,[],[f176]) ).
cnf(c_87,plain,
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f180]) ).
cnf(c_89,plain,
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_127,plain,
subset(empty_set,X0),
inference(cnf_transformation,[],[f221]) ).
cnf(c_130,negated_conjecture,
~ transfinite_sequence_of(empty_set,sK19),
inference(cnf_transformation,[],[f224]) ).
cnf(c_135,plain,
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f229]) ).
cnf(c_143,plain,
( ~ empty(empty_set)
| empty(relation_dom(empty_set)) ),
inference(instantiation,[status(thm)],[c_87]) ).
cnf(c_182,plain,
( ~ empty(X0)
| ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
cnf(c_993,plain,
( relation_dom(X0) != X1
| ~ function(X0)
| ~ empty(X1)
| ~ relation(X0)
| transfinite_sequence(X0) ),
inference(resolution_lifted,[status(thm)],[c_182,c_63]) ).
cnf(c_994,plain,
( ~ empty(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| transfinite_sequence(X0) ),
inference(unflattening,[status(thm)],[c_993]) ).
cnf(c_995,plain,
( ~ empty(relation_dom(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set)
| transfinite_sequence(empty_set) ),
inference(instantiation,[status(thm)],[c_994]) ).
cnf(c_1122,plain,
( X0 != empty_set
| X1 != sK19
| ~ subset(relation_rng(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ transfinite_sequence(X0) ),
inference(resolution_lifted,[status(thm)],[c_65,c_130]) ).
cnf(c_1123,plain,
( ~ subset(relation_rng(empty_set),sK19)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ transfinite_sequence(empty_set) ),
inference(unflattening,[status(thm)],[c_1122]) ).
cnf(c_1124,plain,
~ subset(relation_rng(empty_set),sK19),
inference(global_subsumption_just,[status(thm)],[c_1123,c_83,c_82,c_80,c_143,c_995,c_1123]) ).
cnf(c_1198,plain,
( relation_rng(empty_set) != empty_set
| X0 != sK19 ),
inference(resolution_lifted,[status(thm)],[c_127,c_1124]) ).
cnf(c_1199,plain,
relation_rng(empty_set) != empty_set,
inference(unflattening,[status(thm)],[c_1198]) ).
cnf(c_5205,plain,
( ~ empty(X0)
| relation_rng(X0) = empty_set ),
inference(superposition,[status(thm)],[c_89,c_135]) ).
cnf(c_5222,plain,
( ~ empty(empty_set)
| relation_rng(empty_set) = empty_set ),
inference(instantiation,[status(thm)],[c_5205]) ).
cnf(c_5223,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5222,c_1199,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM409+1 : TPTP v8.2.0. Released v3.2.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Jun 23 03:46:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.45/1.11 % SZS status Started for theBenchmark.p
% 0.45/1.11 % SZS status Theorem for theBenchmark.p
% 0.45/1.11
% 0.45/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.11
% 0.45/1.11 ------ iProver source info
% 0.45/1.11
% 0.45/1.11 git: date: 2024-06-12 09:56:46 +0000
% 0.45/1.11 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 0.45/1.11 git: non_committed_changes: false
% 0.45/1.11
% 0.45/1.11 ------ Parsing...
% 0.45/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.45/1.11
% 0.45/1.11 ------ 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
% 0.45/1.11
% 0.45/1.11 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.45/1.11
% 0.45/1.11 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.11 ------ Proving...
% 0.45/1.11 ------ Problem Properties
% 0.45/1.11
% 0.45/1.11
% 0.45/1.11 clauses 51
% 0.45/1.11 conjectures 0
% 0.45/1.11 EPR 30
% 0.45/1.11 Horn 49
% 0.45/1.11 unary 28
% 0.45/1.11 binary 11
% 0.45/1.11 lits 88
% 0.45/1.11 lits eq 10
% 0.45/1.11 fd_pure 0
% 0.45/1.11 fd_pseudo 0
% 0.45/1.11 fd_cond 1
% 0.45/1.11 fd_pseudo_cond 3
% 0.45/1.11 AC symbols 0
% 0.45/1.11
% 0.45/1.11 ------ Schedule dynamic 5 is on
% 0.45/1.11
% 0.45/1.11 ------ no conjectures: strip conj schedule
% 0.45/1.11
% 0.45/1.11 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.45/1.11
% 0.45/1.11
% 0.45/1.11 ------
% 0.45/1.11 Current options:
% 0.45/1.11 ------
% 0.45/1.11
% 0.45/1.11
% 0.45/1.11
% 0.45/1.11
% 0.45/1.11 ------ Proving...
% 0.45/1.11
% 0.45/1.11
% 0.45/1.11 % SZS status Theorem for theBenchmark.p
% 0.45/1.11
% 0.45/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.11
% 0.45/1.11
%------------------------------------------------------------------------------