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  
%------------------------------------------------------------------------------