TSTP Solution File: SEU275+1 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU275+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 : Thu Aug 31 17:05:24 EDT 2023

% Result   : Theorem 0.71s 1.16s
% Output   : CNFRefutation 0.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   42 (  19 unt;   0 def)
%            Number of atoms       :  115 (   0 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  123 (  50   ~;  43   |;  22   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   33 (   4 sgn;  21   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( relation(X0)
     => ( well_ordering(X0)
      <=> ( well_founded_relation(X0)
          & connected(X0)
          & antisymmetric(X0)
          & transitive(X0)
          & reflexive(X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).

fof(f4,axiom,
    ! [X0] : relation(inclusion_relation(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).

fof(f6,axiom,
    ! [X0] : reflexive(inclusion_relation(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).

fof(f7,axiom,
    ! [X0] : transitive(inclusion_relation(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).

fof(f8,axiom,
    ! [X0] :
      ( ordinal(X0)
     => connected(inclusion_relation(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).

fof(f9,axiom,
    ! [X0] : antisymmetric(inclusion_relation(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).

fof(f10,axiom,
    ! [X0] :
      ( ordinal(X0)
     => well_founded_relation(inclusion_relation(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_wellord2) ).

fof(f11,conjecture,
    ! [X0] :
      ( ordinal(X0)
     => well_ordering(inclusion_relation(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_wellord2) ).

fof(f12,negated_conjecture,
    ~ ! [X0] :
        ( ordinal(X0)
       => well_ordering(inclusion_relation(X0)) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f16,plain,
    ! [X0] :
      ( ( well_ordering(X0)
      <=> ( well_founded_relation(X0)
          & connected(X0)
          & antisymmetric(X0)
          & transitive(X0)
          & reflexive(X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f17,plain,
    ! [X0] :
      ( connected(inclusion_relation(X0))
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f18,plain,
    ! [X0] :
      ( well_founded_relation(inclusion_relation(X0))
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f19,plain,
    ? [X0] :
      ( ~ well_ordering(inclusion_relation(X0))
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f20,plain,
    ! [X0] :
      ( ( ( well_ordering(X0)
          | ~ well_founded_relation(X0)
          | ~ connected(X0)
          | ~ antisymmetric(X0)
          | ~ transitive(X0)
          | ~ reflexive(X0) )
        & ( ( well_founded_relation(X0)
            & connected(X0)
            & antisymmetric(X0)
            & transitive(X0)
            & reflexive(X0) )
          | ~ well_ordering(X0) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f21,plain,
    ! [X0] :
      ( ( ( well_ordering(X0)
          | ~ well_founded_relation(X0)
          | ~ connected(X0)
          | ~ antisymmetric(X0)
          | ~ transitive(X0)
          | ~ reflexive(X0) )
        & ( ( well_founded_relation(X0)
            & connected(X0)
            & antisymmetric(X0)
            & transitive(X0)
            & reflexive(X0) )
          | ~ well_ordering(X0) ) )
      | ~ relation(X0) ),
    inference(flattening,[],[f20]) ).

fof(f24,plain,
    ( ? [X0] :
        ( ~ well_ordering(inclusion_relation(X0))
        & ordinal(X0) )
   => ( ~ well_ordering(inclusion_relation(sK1))
      & ordinal(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ( ~ well_ordering(inclusion_relation(sK1))
    & ordinal(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f19,f24]) ).

fof(f34,plain,
    ! [X0] :
      ( well_ordering(X0)
      | ~ well_founded_relation(X0)
      | ~ connected(X0)
      | ~ antisymmetric(X0)
      | ~ transitive(X0)
      | ~ reflexive(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f35,plain,
    ! [X0] : relation(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f39,plain,
    ! [X0] : reflexive(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f40,plain,
    ! [X0] : transitive(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f7]) ).

fof(f41,plain,
    ! [X0] :
      ( connected(inclusion_relation(X0))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f42,plain,
    ! [X0] : antisymmetric(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f9]) ).

fof(f43,plain,
    ! [X0] :
      ( well_founded_relation(inclusion_relation(X0))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f44,plain,
    ordinal(sK1),
    inference(cnf_transformation,[],[f25]) ).

fof(f45,plain,
    ~ well_ordering(inclusion_relation(sK1)),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_52,plain,
    ( ~ well_founded_relation(X0)
    | ~ connected(X0)
    | ~ antisymmetric(X0)
    | ~ transitive(X0)
    | ~ reflexive(X0)
    | ~ relation(X0)
    | well_ordering(X0) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_58,plain,
    relation(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_62,plain,
    reflexive(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_63,plain,
    transitive(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_64,plain,
    ( ~ ordinal(X0)
    | connected(inclusion_relation(X0)) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_65,plain,
    antisymmetric(inclusion_relation(X0)),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_66,plain,
    ( ~ ordinal(X0)
    | well_founded_relation(inclusion_relation(X0)) ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_67,negated_conjecture,
    ~ well_ordering(inclusion_relation(sK1)),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_68,negated_conjecture,
    ordinal(sK1),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_175,plain,
    well_founded_relation(inclusion_relation(sK1)),
    inference(resolution,[status(thm)],[c_66,c_68]) ).

cnf(c_179,plain,
    connected(inclusion_relation(sK1)),
    inference(resolution,[status(thm)],[c_64,c_68]) ).

cnf(c_188,plain,
    ( ~ well_founded_relation(inclusion_relation(X0))
    | ~ connected(inclusion_relation(X0))
    | ~ transitive(inclusion_relation(X0))
    | ~ reflexive(inclusion_relation(X0))
    | ~ relation(inclusion_relation(X0))
    | well_ordering(inclusion_relation(X0)) ),
    inference(resolution,[status(thm)],[c_52,c_65]) ).

cnf(c_190,plain,
    ( ~ connected(inclusion_relation(X0))
    | ~ well_founded_relation(inclusion_relation(X0))
    | well_ordering(inclusion_relation(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_188,c_63,c_62,c_58,c_188]) ).

cnf(c_191,plain,
    ( ~ well_founded_relation(inclusion_relation(X0))
    | ~ connected(inclusion_relation(X0))
    | well_ordering(inclusion_relation(X0)) ),
    inference(renaming,[status(thm)],[c_190]) ).

cnf(c_230,plain,
    ( ~ connected(inclusion_relation(sK1))
    | well_ordering(inclusion_relation(sK1)) ),
    inference(resolution,[status(thm)],[c_191,c_175]) ).

cnf(c_231,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_230,c_179,c_67]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU275+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 23 13:58:36 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.71/1.16  % SZS status Started for theBenchmark.p
% 0.71/1.16  % SZS status Theorem for theBenchmark.p
% 0.71/1.16  
% 0.71/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.71/1.16  
% 0.71/1.16  ------  iProver source info
% 0.71/1.16  
% 0.71/1.16  git: date: 2023-05-31 18:12:56 +0000
% 0.71/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.71/1.16  git: non_committed_changes: false
% 0.71/1.16  git: last_make_outside_of_git: false
% 0.71/1.16  
% 0.71/1.16  ------ Parsing...
% 0.71/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.71/1.16  
% 0.71/1.16  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s
% 0.71/1.16  
% 0.71/1.16  % SZS status Theorem for theBenchmark.p
% 0.71/1.16  
% 0.71/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.71/1.16  
% 0.71/1.16  
%------------------------------------------------------------------------------