TSTP Solution File: SET676+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n009.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 2.23s 1.13s
% Output   : CNFRefutation 2.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (   9 unt;   0 def)
%            Number of atoms       :   68 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   71 (  32   ~;  25   |;   5   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (   1 sgn;  18   !;   2   ?)

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

fof(f4,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',p4) ).

fof(f19,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).

fof(f20,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_41) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f23,plain,
    ! [X0] :
      ( ! [X1] :
          ( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f26,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,[],[f4]) ).

fof(f46,plain,
    ? [X0] :
      ( ~ ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f52,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,[],[f26]) ).

fof(f77,plain,
    ( ? [X0] :
        ( ~ ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
        & ilf_type(X0,set_type) )
   => ( ~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11))
      & ilf_type(sK11,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ( ~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11))
    & ilf_type(sK11,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f46,f77]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f88,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(cnf_transformation,[],[f52]) ).

fof(f117,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f19]) ).

fof(f119,plain,
    ~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11)),
    inference(cnf_transformation,[],[f78]) ).

cnf(c_49,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_57,plain,
    ( ~ ilf_type(X0,relation_type(X1,X1))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,identity_relation_of_type(X1)) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_87,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_88,negated_conjecture,
    ~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11)),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_175,plain,
    ( ~ ilf_type(X1,set_type)
    | ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_87,c_49]) ).

cnf(c_176,plain,
    ( ~ ilf_type(X0,set_type)
    | ilf_type(cross_product(X1,X0),relation_type(X1,X0)) ),
    inference(renaming,[status(thm)],[c_175]) ).

cnf(c_177,plain,
    ilf_type(cross_product(X1,X0),relation_type(X1,X0)),
    inference(global_subsumption_just,[status(thm)],[c_176,c_87,c_176]) ).

cnf(c_178,plain,
    ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
    inference(renaming,[status(thm)],[c_177]) ).

cnf(c_203,plain,
    ( ~ ilf_type(X0,relation_type(X1,X1))
    | ~ ilf_type(X1,set_type)
    | ilf_type(X0,identity_relation_of_type(X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_57,c_87,c_57]) ).

cnf(c_246,plain,
    ( ~ ilf_type(X0,relation_type(X1,X1))
    | ilf_type(X0,identity_relation_of_type(X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_203,c_87]) ).

cnf(c_690,plain,
    ( ilf_type(X0,identity_relation_of_type(X1))
    | ~ ilf_type(X0,relation_type(X1,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_246]) ).

cnf(c_691,plain,
    ( ~ ilf_type(X0,relation_type(X1,X1))
    | ilf_type(X0,identity_relation_of_type(X1)) ),
    inference(renaming,[status(thm)],[c_690]) ).

cnf(c_1874,plain,
    ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)),
    inference(superposition,[status(thm)],[c_178,c_691]) ).

cnf(c_1876,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_88,c_1874]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 12:09:05 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.23/1.13  % SZS status Started for theBenchmark.p
% 2.23/1.13  % SZS status Theorem for theBenchmark.p
% 2.23/1.13  
% 2.23/1.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.23/1.13  
% 2.23/1.13  ------  iProver source info
% 2.23/1.13  
% 2.23/1.13  git: date: 2023-05-31 18:12:56 +0000
% 2.23/1.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.23/1.13  git: non_committed_changes: false
% 2.23/1.13  git: last_make_outside_of_git: false
% 2.23/1.13  
% 2.23/1.13  ------ Parsing...
% 2.23/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.23/1.13  
% 2.23/1.13  ------ 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 
% 2.23/1.13  
% 2.23/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.23/1.13  
% 2.23/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.23/1.13  ------ Proving...
% 2.23/1.13  ------ Problem Properties 
% 2.23/1.13  
% 2.23/1.13  
% 2.23/1.13  clauses                                 30
% 2.23/1.13  conjectures                             1
% 2.23/1.13  EPR                                     3
% 2.23/1.13  Horn                                    25
% 2.23/1.13  unary                                   7
% 2.23/1.13  binary                                  19
% 2.23/1.13  lits                                    57
% 2.23/1.13  lits eq                                 3
% 2.23/1.13  fd_pure                                 0
% 2.23/1.13  fd_pseudo                               0
% 2.23/1.13  fd_cond                                 0
% 2.23/1.13  fd_pseudo_cond                          0
% 2.23/1.13  AC symbols                              0
% 2.23/1.13  
% 2.23/1.13  ------ Schedule dynamic 5 is on 
% 2.23/1.13  
% 2.23/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.23/1.13  
% 2.23/1.13  
% 2.23/1.13  ------ 
% 2.23/1.13  Current options:
% 2.23/1.13  ------ 
% 2.23/1.13  
% 2.23/1.13  
% 2.23/1.13  
% 2.23/1.13  
% 2.23/1.13  ------ Proving...
% 2.23/1.13  
% 2.23/1.13  
% 2.23/1.13  % SZS status Theorem for theBenchmark.p
% 2.23/1.13  
% 2.23/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.23/1.13  
% 2.23/1.13  
%------------------------------------------------------------------------------