TSTP Solution File: SET677+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET677+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 15:09:04 EDT 2023

% Result   : Theorem 2.88s 1.19s
% Output   : CNFRefutation 2.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   44 (   8 unt;   0 def)
%            Number of atoms       :  168 (  40 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  210 (  86   ~;  76   |;  28   &)
%                                         (   2 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   75 (   1 sgn;  38   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X1,X0))
             => ( subset(identity_relation_of(X1),X2)
               => ( subset(X1,range(X1,X0,X2))
                  & domain(X1,X0,X2) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ( subset(identity_relation_of(X1),X2)
               => ( range(X0,X1,X2) = X1
                  & subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f5,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ilf_type(X1,identity_relation_of_type(X0))
          <=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).

fof(f34,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).

fof(f35,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,identity_relation_of_type(X0))
         => ( subset(identity_relation_of(X0),X1)
           => ( range(X0,X0,X1) = X0
              & domain(X0,X0,X1) = X0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_44) ).

fof(f36,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,identity_relation_of_type(X0))
           => ( subset(identity_relation_of(X0),X1)
             => ( range(X0,X0,X1) = X0
                & domain(X0,X0,X1) = X0 ) ) ) ),
    inference(negated_conjecture,[],[f35]) ).

fof(f38,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( subset(X1,range(X1,X0,X2))
                & domain(X1,X0,X2) = X1 )
              | ~ subset(identity_relation_of(X1),X2)
              | ~ ilf_type(X2,relation_type(X1,X0)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f39,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( subset(X1,range(X1,X0,X2))
                & domain(X1,X0,X2) = X1 )
              | ~ subset(identity_relation_of(X1),X2)
              | ~ ilf_type(X2,relation_type(X1,X0)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f38]) ).

fof(f40,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( range(X0,X1,X2) = X1
                & subset(X1,domain(X0,X1,X2)) )
              | ~ subset(identity_relation_of(X1),X2)
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f41,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( range(X0,X1,X2) = X1
                & subset(X1,domain(X0,X1,X2)) )
              | ~ subset(identity_relation_of(X1),X2)
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f40]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X1,identity_relation_of_type(X0))
          <=> ilf_type(X1,relation_type(X0,X0)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f79,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( range(X0,X0,X1) != X0
            | domain(X0,X0,X1) != X0 )
          & subset(identity_relation_of(X0),X1)
          & ilf_type(X1,identity_relation_of_type(X0)) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f80,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( range(X0,X0,X1) != X0
            | domain(X0,X0,X1) != X0 )
          & subset(identity_relation_of(X0),X1)
          & ilf_type(X1,identity_relation_of_type(X0)) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f79]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X1,identity_relation_of_type(X0))
              | ~ ilf_type(X1,relation_type(X0,X0)) )
            & ( ilf_type(X1,relation_type(X0,X0))
              | ~ ilf_type(X1,identity_relation_of_type(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f123,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( range(X0,X0,X1) != X0
              | domain(X0,X0,X1) != X0 )
            & subset(identity_relation_of(X0),X1)
            & ilf_type(X1,identity_relation_of_type(X0)) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ( sK13 != range(sK13,sK13,X1)
            | sK13 != domain(sK13,sK13,X1) )
          & subset(identity_relation_of(sK13),X1)
          & ilf_type(X1,identity_relation_of_type(sK13)) )
      & ilf_type(sK13,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ( ? [X1] :
        ( ( sK13 != range(sK13,sK13,X1)
          | sK13 != domain(sK13,sK13,X1) )
        & subset(identity_relation_of(sK13),X1)
        & ilf_type(X1,identity_relation_of_type(sK13)) )
   => ( ( sK13 != range(sK13,sK13,sK14)
        | sK13 != domain(sK13,sK13,sK14) )
      & subset(identity_relation_of(sK13),sK14)
      & ilf_type(sK14,identity_relation_of_type(sK13)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ( ( sK13 != range(sK13,sK13,sK14)
      | sK13 != domain(sK13,sK13,sK14) )
    & subset(identity_relation_of(sK13),sK14)
    & ilf_type(sK14,identity_relation_of_type(sK13))
    & ilf_type(sK13,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f80,f124,f123]) ).

fof(f126,plain,
    ! [X2,X0,X1] :
      ( domain(X1,X0,X2) = X1
      | ~ subset(identity_relation_of(X1),X2)
      | ~ ilf_type(X2,relation_type(X1,X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f129,plain,
    ! [X2,X0,X1] :
      ( range(X0,X1,X2) = X1
      | ~ subset(identity_relation_of(X1),X2)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ilf_type(X1,relation_type(X0,X0))
      | ~ ilf_type(X1,identity_relation_of_type(X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f189,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f34]) ).

fof(f191,plain,
    ilf_type(sK14,identity_relation_of_type(sK13)),
    inference(cnf_transformation,[],[f125]) ).

fof(f192,plain,
    subset(identity_relation_of(sK13),sK14),
    inference(cnf_transformation,[],[f125]) ).

fof(f193,plain,
    ( sK13 != range(sK13,sK13,sK14)
    | sK13 != domain(sK13,sK13,sK14) ),
    inference(cnf_transformation,[],[f125]) ).

cnf(c_50,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X1),X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | domain(X1,X2,X0) = X1 ),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_51,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X2),X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | range(X1,X2,X0) = X2 ),
    inference(cnf_transformation,[],[f129]) ).

cnf(c_58,plain,
    ( ~ ilf_type(X0,identity_relation_of_type(X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,relation_type(X1,X1)) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_111,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f189]) ).

cnf(c_112,negated_conjecture,
    ( range(sK13,sK13,sK14) != sK13
    | domain(sK13,sK13,sK14) != sK13 ),
    inference(cnf_transformation,[],[f193]) ).

cnf(c_113,negated_conjecture,
    subset(identity_relation_of(sK13),sK14),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_114,negated_conjecture,
    ilf_type(sK14,identity_relation_of_type(sK13)),
    inference(cnf_transformation,[],[f191]) ).

cnf(c_262,plain,
    ( ~ ilf_type(X0,identity_relation_of_type(X1))
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,relation_type(X1,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_58,c_111,c_58]) ).

cnf(c_458,plain,
    ( ~ ilf_type(X0,identity_relation_of_type(X1))
    | ilf_type(X0,relation_type(X1,X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_262,c_111]) ).

cnf(c_467,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X1),X0)
    | ~ ilf_type(X2,set_type)
    | domain(X1,X2,X0) = X1 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_50,c_111]) ).

cnf(c_468,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X2),X0)
    | ~ ilf_type(X2,set_type)
    | range(X1,X2,X0) = X2 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_51,c_111]) ).

cnf(c_783,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X1),X0)
    | domain(X1,X2,X0) = X1 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_467,c_111]) ).

cnf(c_798,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(identity_relation_of(X2),X0)
    | range(X1,X2,X0) = X2 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_468,c_111]) ).

cnf(c_1391,plain,
    ( ~ ilf_type(X0,identity_relation_of_type(X1))
    | ilf_type(X0,relation_type(X1,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_458]) ).

cnf(c_3571,plain,
    ( ~ ilf_type(sK14,identity_relation_of_type(sK13))
    | ilf_type(sK14,relation_type(sK13,sK13)) ),
    inference(instantiation,[status(thm)],[c_1391]) ).

cnf(c_3796,plain,
    ( ~ ilf_type(sK14,relation_type(sK13,X0))
    | ~ subset(identity_relation_of(sK13),sK14)
    | domain(sK13,X0,sK14) = sK13 ),
    inference(instantiation,[status(thm)],[c_783]) ).

cnf(c_3854,plain,
    ( ~ ilf_type(sK14,relation_type(X0,sK13))
    | ~ subset(identity_relation_of(sK13),sK14)
    | range(X0,sK13,sK14) = sK13 ),
    inference(instantiation,[status(thm)],[c_798]) ).

cnf(c_4094,plain,
    ( ~ ilf_type(sK14,relation_type(sK13,sK13))
    | ~ subset(identity_relation_of(sK13),sK14)
    | domain(sK13,sK13,sK14) = sK13 ),
    inference(instantiation,[status(thm)],[c_3796]) ).

cnf(c_4133,plain,
    ( ~ ilf_type(sK14,relation_type(sK13,sK13))
    | ~ subset(identity_relation_of(sK13),sK14)
    | range(sK13,sK13,sK14) = sK13 ),
    inference(instantiation,[status(thm)],[c_3854]) ).

cnf(c_4134,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_4133,c_4094,c_3571,c_112,c_113,c_114]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET677+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n023.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 : Sat Aug 26 10:23:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.88/1.19  % SZS status Started for theBenchmark.p
% 2.88/1.19  % SZS status Theorem for theBenchmark.p
% 2.88/1.19  
% 2.88/1.19  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.88/1.19  
% 2.88/1.19  ------  iProver source info
% 2.88/1.19  
% 2.88/1.19  git: date: 2023-05-31 18:12:56 +0000
% 2.88/1.19  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.88/1.19  git: non_committed_changes: false
% 2.88/1.19  git: last_make_outside_of_git: false
% 2.88/1.19  
% 2.88/1.19  ------ Parsing...
% 2.88/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.88/1.19  
% 2.88/1.19  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.88/1.19  
% 2.88/1.19  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.88/1.19  
% 2.88/1.19  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.88/1.19  ------ Proving...
% 2.88/1.19  ------ Problem Properties 
% 2.88/1.19  
% 2.88/1.19  
% 2.88/1.19  clauses                                 49
% 2.88/1.19  conjectures                             3
% 2.88/1.19  EPR                                     9
% 2.88/1.19  Horn                                    42
% 2.88/1.19  unary                                   10
% 2.88/1.19  binary                                  28
% 2.88/1.19  lits                                    101
% 2.88/1.19  lits eq                                 10
% 2.88/1.19  fd_pure                                 0
% 2.88/1.19  fd_pseudo                               0
% 2.88/1.19  fd_cond                                 0
% 2.88/1.19  fd_pseudo_cond                          2
% 2.88/1.19  AC symbols                              0
% 2.88/1.19  
% 2.88/1.19  ------ Schedule dynamic 5 is on 
% 2.88/1.19  
% 2.88/1.19  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.88/1.19  
% 2.88/1.19  
% 2.88/1.19  ------ 
% 2.88/1.19  Current options:
% 2.88/1.19  ------ 
% 2.88/1.19  
% 2.88/1.19  
% 2.88/1.19  
% 2.88/1.19  
% 2.88/1.19  ------ Proving...
% 2.88/1.19  
% 2.88/1.19  
% 2.88/1.19  % SZS status Theorem for theBenchmark.p
% 2.88/1.19  
% 2.88/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.88/1.19  
% 2.88/1.19  
%------------------------------------------------------------------------------