TSTP Solution File: SET643+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 15:08:52 EDT 2023

% Result   : Theorem 0.90s 1.18s
% Output   : CNFRefutation 0.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   27 (   8 unt;   0 def)
%            Number of atoms       :   75 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   84 (  36   ~;  27   |;  10   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   48 (   1 sgn;  21   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ( subset(X0,cross_product(X1,X2))
               => ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f10,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => subset(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).

fof(f19,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).

fof(f20,conjecture,
    ! [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/sandbox2/benchmark/theBenchmark.p',prove_relset_1_5) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f23,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(X0,relation_type(X1,X2))
              | ~ subset(X0,cross_product(X1,X2))
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f24,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ilf_type(X0,relation_type(X1,X2))
              | ~ subset(X0,cross_product(X1,X2))
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f23]) ).

fof(f34,plain,
    ! [X0] :
      ( subset(X0,X0)
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f48,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,[],[f21]) ).

fof(f80,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ~ ilf_type(cross_product(X0,X1),relation_type(X0,X1))
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ~ ilf_type(cross_product(sK11,X1),relation_type(sK11,X1))
          & ilf_type(X1,set_type) )
      & ilf_type(sK11,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ( ? [X1] :
        ( ~ ilf_type(cross_product(sK11,X1),relation_type(sK11,X1))
        & ilf_type(X1,set_type) )
   => ( ~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12))
      & ilf_type(sK12,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ( ~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12))
    & ilf_type(sK12,set_type)
    & ilf_type(sK11,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f48,f81,f80]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X0,relation_type(X1,X2))
      | ~ subset(X0,cross_product(X1,X2))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f102,plain,
    ! [X0] :
      ( subset(X0,X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f123,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f19]) ).

fof(f126,plain,
    ~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12)),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_49,plain,
    ( ~ subset(X0,cross_product(X1,X2))
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,relation_type(X1,X2)) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_68,plain,
    ( ~ ilf_type(X0,set_type)
    | subset(X0,X0) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_89,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f123]) ).

cnf(c_90,negated_conjecture,
    ~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12)),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_129,plain,
    subset(X0,X0),
    inference(global_subsumption_just,[status(thm)],[c_68,c_89,c_68]) ).

cnf(c_217,plain,
    ( ~ subset(X0,cross_product(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,relation_type(X1,X2)) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_89,c_49]) ).

cnf(c_251,plain,
    ( ~ subset(X0,cross_product(X1,X2))
    | ~ ilf_type(X2,set_type)
    | ilf_type(X0,relation_type(X1,X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_217,c_89]) ).

cnf(c_351,plain,
    ( ~ subset(X0,cross_product(X1,X2))
    | ilf_type(X0,relation_type(X1,X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_251,c_89]) ).

cnf(c_671,plain,
    ( cross_product(X0,X1) != X2
    | X2 != X3
    | ilf_type(X3,relation_type(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_351,c_129]) ).

cnf(c_672,plain,
    ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
    inference(unflattening,[status(thm)],[c_671]) ).

cnf(c_690,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_90,c_672]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n031.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 11:02:38 EDT 2023
% 0.21/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.90/1.18  % SZS status Started for theBenchmark.p
% 0.90/1.18  % SZS status Theorem for theBenchmark.p
% 0.90/1.18  
% 0.90/1.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.90/1.18  
% 0.90/1.18  ------  iProver source info
% 0.90/1.18  
% 0.90/1.18  git: date: 2023-05-31 18:12:56 +0000
% 0.90/1.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.90/1.18  git: non_committed_changes: false
% 0.90/1.18  git: last_make_outside_of_git: false
% 0.90/1.18  
% 0.90/1.18  ------ Parsing...
% 0.90/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.90/1.18  
% 0.90/1.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s 
% 0.90/1.18  
% 0.90/1.18  % SZS status Theorem for theBenchmark.p
% 0.90/1.18  
% 0.90/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.90/1.18  
% 0.90/1.18  
%------------------------------------------------------------------------------