TSTP Solution File: SET654+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET654+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n006.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 : Fri May  3 03:01:08 EDT 2024

% Result   : Theorem 3.85s 1.12s
% Output   : CNFRefutation 3.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   47 (  13 unt;   0 def)
%            Number of atoms       :  193 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  236 (  90   ~;  74   |;  46   &)
%                                         (   0 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  113 (   5 sgn  47   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ( ( subset(X1,X2)
                  & subset(X0,X1) )
               => subset(X0,X2) ) ) ) ),
    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(range_of(X2),X1)
                & subset(domain_of(X2),X0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f3,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X2,X0))
                 => ( subset(range_of(X3),X1)
                   => ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

fof(f22,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).

fof(f23,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X2,X0))
                 => ( subset(X0,X1)
                   => ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_16) ).

fof(f24,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,set_type)
               => ! [X3] :
                    ( ilf_type(X3,relation_type(X2,X0))
                   => ( subset(X0,X1)
                     => ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f26,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( subset(X0,X2)
              | ~ subset(X1,X2)
              | ~ subset(X0,X1)
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f27,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( subset(X0,X2)
              | ~ subset(X1,X2)
              | ~ subset(X0,X1)
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f26]) ).

fof(f28,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( subset(range_of(X2),X1)
                & subset(domain_of(X2),X0) )
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f29,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ilf_type(X3,relation_type(X2,X1))
                  | ~ subset(range_of(X3),X1)
                  | ~ ilf_type(X3,relation_type(X2,X0)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f30,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ilf_type(X3,relation_type(X2,X1))
                  | ~ subset(range_of(X3),X1)
                  | ~ ilf_type(X3,relation_type(X2,X0)) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f29]) ).

fof(f55,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X3,relation_type(X2,X1))
                  & subset(X0,X1)
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f56,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X3,relation_type(X2,X1))
                  & subset(X0,X1)
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f55]) ).

fof(f83,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ~ ilf_type(X3,relation_type(X2,X1))
                    & subset(X0,X1)
                    & ilf_type(X3,relation_type(X2,X0)) )
                & ilf_type(X2,set_type) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(X3,relation_type(X2,X1))
                  & subset(sK9,X1)
                  & ilf_type(X3,relation_type(X2,sK9)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK9,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ~ ilf_type(X3,relation_type(X2,X1))
                & subset(sK9,X1)
                & ilf_type(X3,relation_type(X2,sK9)) )
            & ilf_type(X2,set_type) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ~ ilf_type(X3,relation_type(X2,sK10))
              & subset(sK9,sK10)
              & ilf_type(X3,relation_type(X2,sK9)) )
          & ilf_type(X2,set_type) )
      & ilf_type(sK10,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ ilf_type(X3,relation_type(X2,sK10))
            & subset(sK9,sK10)
            & ilf_type(X3,relation_type(X2,sK9)) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( ~ ilf_type(X3,relation_type(sK11,sK10))
          & subset(sK9,sK10)
          & ilf_type(X3,relation_type(sK11,sK9)) )
      & ilf_type(sK11,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ( ? [X3] :
        ( ~ ilf_type(X3,relation_type(sK11,sK10))
        & subset(sK9,sK10)
        & ilf_type(X3,relation_type(sK11,sK9)) )
   => ( ~ ilf_type(sK12,relation_type(sK11,sK10))
      & subset(sK9,sK10)
      & ilf_type(sK12,relation_type(sK11,sK9)) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ( ~ ilf_type(sK12,relation_type(sK11,sK10))
    & subset(sK9,sK10)
    & ilf_type(sK12,relation_type(sK11,sK9))
    & ilf_type(sK11,set_type)
    & ilf_type(sK10,set_type)
    & ilf_type(sK9,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f56,f86,f85,f84,f83]) ).

fof(f88,plain,
    ! [X2,X0,X1] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f90,plain,
    ! [X2,X0,X1] :
      ( subset(range_of(X2),X1)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f91,plain,
    ! [X2,X3,X0,X1] :
      ( ilf_type(X3,relation_type(X2,X1))
      | ~ subset(range_of(X3),X1)
      | ~ ilf_type(X3,relation_type(X2,X0))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f127,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f22]) ).

fof(f131,plain,
    ilf_type(sK12,relation_type(sK11,sK9)),
    inference(cnf_transformation,[],[f87]) ).

fof(f132,plain,
    subset(sK9,sK10),
    inference(cnf_transformation,[],[f87]) ).

fof(f133,plain,
    ~ ilf_type(sK12,relation_type(sK11,sK10)),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_49,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X2)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | subset(X0,X2) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_50,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | subset(range_of(X0),X2) ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_52,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(range_of(X0),X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ilf_type(X0,relation_type(X1,X3)) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_88,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f127]) ).

cnf(c_89,negated_conjecture,
    ~ ilf_type(sK12,relation_type(sK11,sK10)),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_90,negated_conjecture,
    subset(sK9,sK10),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_91,negated_conjecture,
    ilf_type(sK12,relation_type(sK11,sK9)),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_216,plain,
    ( ~ subset(X1,X2)
    | ~ subset(X0,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | subset(X0,X2) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_88,c_49]) ).

cnf(c_217,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | subset(X0,X2) ),
    inference(renaming,[status(thm)],[c_216]) ).

cnf(c_228,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X2)
    | ~ ilf_type(X2,set_type)
    | subset(X0,X2) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_217,c_88]) ).

cnf(c_229,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X2,set_type)
    | subset(range_of(X0),X2) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_50,c_88]) ).

cnf(c_231,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(range_of(X0),X3)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ilf_type(X0,relation_type(X1,X3)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_52,c_88]) ).

cnf(c_340,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | subset(range_of(X0),X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_229,c_88]) ).

cnf(c_405,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X2)
    | subset(X0,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_228,c_88]) ).

cnf(c_434,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | ~ subset(range_of(X0),X3)
    | ilf_type(X0,relation_type(X1,X3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_231,c_88,c_88]) ).

cnf(c_612,plain,
    ( ~ ilf_type(X0,relation_type(X1,X2))
    | subset(range_of(X0),X2) ),
    inference(prop_impl_just,[status(thm)],[c_340]) ).

cnf(c_2173,plain,
    subset(range_of(sK12),sK9),
    inference(superposition,[status(thm)],[c_91,c_612]) ).

cnf(c_2212,plain,
    ( ~ subset(range_of(sK12),X0)
    | ilf_type(sK12,relation_type(sK11,X0)) ),
    inference(superposition,[status(thm)],[c_91,c_434]) ).

cnf(c_2226,plain,
    ~ subset(range_of(sK12),sK10),
    inference(superposition,[status(thm)],[c_2212,c_89]) ).

cnf(c_2397,plain,
    ( ~ subset(sK9,X0)
    | subset(range_of(sK12),X0) ),
    inference(superposition,[status(thm)],[c_2173,c_405]) ).

cnf(c_2867,plain,
    ~ subset(sK9,sK10),
    inference(superposition,[status(thm)],[c_2397,c_2226]) ).

cnf(c_2868,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_2867,c_90]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET654+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n006.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 20:08:34 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.18/0.44  Running first-order theorem proving
% 0.18/0.44  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
% 3.85/1.12  % SZS status Started for theBenchmark.p
% 3.85/1.12  % SZS status Theorem for theBenchmark.p
% 3.85/1.12  
% 3.85/1.12  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.85/1.12  
% 3.85/1.12  ------  iProver source info
% 3.85/1.12  
% 3.85/1.12  git: date: 2024-05-02 19:28:25 +0000
% 3.85/1.12  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.85/1.12  git: non_committed_changes: false
% 3.85/1.12  
% 3.85/1.12  ------ Parsing...
% 3.85/1.12  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.85/1.12  
% 3.85/1.12  ------ 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 
% 3.85/1.12  
% 3.85/1.12  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.85/1.12  
% 3.85/1.12  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.85/1.12  ------ Proving...
% 3.85/1.12  ------ Problem Properties 
% 3.85/1.12  
% 3.85/1.12  
% 3.85/1.12  clauses                                 32
% 3.85/1.12  conjectures                             3
% 3.85/1.12  EPR                                     7
% 3.85/1.12  Horn                                    26
% 3.85/1.12  unary                                   8
% 3.85/1.12  binary                                  18
% 3.85/1.12  lits                                    62
% 3.85/1.12  lits eq                                 2
% 3.85/1.12  fd_pure                                 0
% 3.85/1.12  fd_pseudo                               0
% 3.85/1.12  fd_cond                                 0
% 3.85/1.12  fd_pseudo_cond                          0
% 3.85/1.12  AC symbols                              0
% 3.85/1.12  
% 3.85/1.12  ------ Input Options Time Limit: Unbounded
% 3.85/1.12  
% 3.85/1.12  
% 3.85/1.12  ------ 
% 3.85/1.12  Current options:
% 3.85/1.12  ------ 
% 3.85/1.12  
% 3.85/1.12  
% 3.85/1.12  
% 3.85/1.12  
% 3.85/1.12  ------ Proving...
% 3.85/1.12  
% 3.85/1.12  
% 3.85/1.12  % SZS status Theorem for theBenchmark.p
% 3.85/1.12  
% 3.85/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.85/1.12  
% 3.85/1.12  
%------------------------------------------------------------------------------