TSTP Solution File: SYO889_16 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.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 03:39:05 EDT 2024

% Result   : Theorem 1.58s 1.15s
% Output   : CNFRefutation 1.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   29 (   5 unt;   0 typ;   0 def)
%            Number of atoms       :  217 (   0 equ)
%            Maximal formula atoms :   13 (   7 avg)
%            Number of connectives :  217 (  81   ~;  69   |;  52   &)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   52 (  52 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   9 usr;   5 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   94 (   0 sgn  47   !;  32   ?;  55   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f5,conjecture,
    ( ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ! [X3] :
              ( '$ki_exists_in_world_$i'(X0,X3)
             => ? [X4: '$ki_world'] :
                  ( b(X4,X3)
                  & '$ki_accessible'(X0,X4) ) ) )
      & ? [X0: '$ki_world'] :
          ( ? [X3] :
              ( ! [X4: '$ki_world'] :
                  ( '$ki_accessible'(X0,X4)
                 => a(X4,X3) )
              & '$ki_exists_in_world_$i'(X0,X3) )
          & '$ki_accessible'('$ki_local_world',X0) ) )
   => ? [X0: '$ki_world'] :
        ( ? [X3] :
            ( ? [X4: '$ki_world'] :
                ( b(X4,X3)
                & a(X4,X3)
                & '$ki_accessible'(X0,X4) )
            & '$ki_exists_in_world_$i'(X0,X3) )
        & '$ki_accessible'('$ki_local_world',X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f6,negated_conjecture,
    ~ ( ( ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ! [X3] :
                ( '$ki_exists_in_world_$i'(X0,X3)
               => ? [X4: '$ki_world'] :
                    ( b(X4,X3)
                    & '$ki_accessible'(X0,X4) ) ) )
        & ? [X0: '$ki_world'] :
            ( ? [X3] :
                ( ! [X4: '$ki_world'] :
                    ( '$ki_accessible'(X0,X4)
                   => a(X4,X3) )
                & '$ki_exists_in_world_$i'(X0,X3) )
            & '$ki_accessible'('$ki_local_world',X0) ) )
     => ? [X0: '$ki_world'] :
          ( ? [X3] :
              ( ? [X4: '$ki_world'] :
                  ( b(X4,X3)
                  & a(X4,X3)
                  & '$ki_accessible'(X0,X4) )
              & '$ki_exists_in_world_$i'(X0,X3) )
          & '$ki_accessible'('$ki_local_world',X0) ) ),
    inference(negated_conjecture,[],[f5]) ).

tff(f9,plain,
    ~ ( ( ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ! [X1] :
                ( '$ki_exists_in_world_$i'(X0,X1)
               => ? [X2: '$ki_world'] :
                    ( b(X2,X1)
                    & '$ki_accessible'(X0,X2) ) ) )
        & ? [X3: '$ki_world'] :
            ( ? [X4] :
                ( ! [X5: '$ki_world'] :
                    ( '$ki_accessible'(X3,X5)
                   => a(X5,X4) )
                & '$ki_exists_in_world_$i'(X3,X4) )
            & '$ki_accessible'('$ki_local_world',X3) ) )
     => ? [X6: '$ki_world'] :
          ( ? [X7] :
              ( ? [X8: '$ki_world'] :
                  ( b(X8,X7)
                  & a(X8,X7)
                  & '$ki_accessible'(X6,X8) )
              & '$ki_exists_in_world_$i'(X6,X7) )
          & '$ki_accessible'('$ki_local_world',X6) ) ),
    inference(rectify,[],[f6]) ).

tff(f14,plain,
    ( ! [X6: '$ki_world'] :
        ( ! [X7] :
            ( ! [X8: '$ki_world'] :
                ( ~ b(X8,X7)
                | ~ a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) )
            | ~ '$ki_exists_in_world_$i'(X6,X7) )
        | ~ '$ki_accessible'('$ki_local_world',X6) )
    & ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ? [X2: '$ki_world'] :
                ( b(X2,X1)
                & '$ki_accessible'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( ? [X4] :
            ( ! [X5: '$ki_world'] :
                ( a(X5,X4)
                | ~ '$ki_accessible'(X3,X5) )
            & '$ki_exists_in_world_$i'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    inference(ennf_transformation,[],[f9]) ).

tff(f15,plain,
    ( ! [X6: '$ki_world'] :
        ( ! [X7] :
            ( ! [X8: '$ki_world'] :
                ( ~ b(X8,X7)
                | ~ a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) )
            | ~ '$ki_exists_in_world_$i'(X6,X7) )
        | ~ '$ki_accessible'('$ki_local_world',X6) )
    & ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ? [X2: '$ki_world'] :
                ( b(X2,X1)
                & '$ki_accessible'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( ? [X4] :
            ( ! [X5: '$ki_world'] :
                ( a(X5,X4)
                | ~ '$ki_accessible'(X3,X5) )
            & '$ki_exists_in_world_$i'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    inference(flattening,[],[f14]) ).

tff(f18,plain,
    ( ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ! [X2: '$ki_world'] :
                ( ~ b(X2,X1)
                | ~ a(X2,X1)
                | ~ '$ki_accessible'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ! [X3: '$ki_world'] :
        ( ! [X4] :
            ( ? [X5: '$ki_world'] :
                ( b(X5,X4)
                & '$ki_accessible'(X3,X5) )
            | ~ '$ki_exists_in_world_$i'(X3,X4) )
        | ~ '$ki_accessible'('$ki_local_world',X3) )
    & ? [X6: '$ki_world'] :
        ( ? [X7] :
            ( ! [X8: '$ki_world'] :
                ( a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) )
            & '$ki_exists_in_world_$i'(X6,X7) )
        & '$ki_accessible'('$ki_local_world',X6) ) ),
    inference(rectify,[],[f15]) ).

tff(f19,plain,
    ! [X3: '$ki_world',X4] :
      ( ? [X5: '$ki_world'] :
          ( b(X5,X4)
          & '$ki_accessible'(X3,X5) )
     => ( b(sK1(X3,X4),X4)
        & '$ki_accessible'(X3,sK1(X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f20,plain,
    ( ? [X6: '$ki_world'] :
        ( ? [X7] :
            ( ! [X8: '$ki_world'] :
                ( a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) )
            & '$ki_exists_in_world_$i'(X6,X7) )
        & '$ki_accessible'('$ki_local_world',X6) )
   => ( ? [X7] :
          ( ! [X8: '$ki_world'] :
              ( a(X8,X7)
              | ~ '$ki_accessible'(sK2,X8) )
          & '$ki_exists_in_world_$i'(sK2,X7) )
      & '$ki_accessible'('$ki_local_world',sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f21,plain,
    ( ? [X7] :
        ( ! [X8: '$ki_world'] :
            ( a(X8,X7)
            | ~ '$ki_accessible'(sK2,X8) )
        & '$ki_exists_in_world_$i'(sK2,X7) )
   => ( ! [X8: '$ki_world'] :
          ( a(X8,sK3)
          | ~ '$ki_accessible'(sK2,X8) )
      & '$ki_exists_in_world_$i'(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

tff(f22,plain,
    ( ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ! [X2: '$ki_world'] :
                ( ~ b(X2,X1)
                | ~ a(X2,X1)
                | ~ '$ki_accessible'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ! [X3: '$ki_world'] :
        ( ! [X4] :
            ( ( b(sK1(X3,X4),X4)
              & '$ki_accessible'(X3,sK1(X3,X4)) )
            | ~ '$ki_exists_in_world_$i'(X3,X4) )
        | ~ '$ki_accessible'('$ki_local_world',X3) )
    & ! [X8: '$ki_world'] :
        ( a(X8,sK3)
        | ~ '$ki_accessible'(sK2,X8) )
    & '$ki_exists_in_world_$i'(sK2,sK3)
    & '$ki_accessible'('$ki_local_world',sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f18,f21,f20,f19]) ).

tff(f27,plain,
    '$ki_accessible'('$ki_local_world',sK2),
    inference(cnf_transformation,[],[f22]) ).

tff(f28,plain,
    '$ki_exists_in_world_$i'(sK2,sK3),
    inference(cnf_transformation,[],[f22]) ).

tff(f29,plain,
    ! [X8: '$ki_world'] :
      ( a(X8,sK3)
      | ~ '$ki_accessible'(sK2,X8) ),
    inference(cnf_transformation,[],[f22]) ).

tff(f30,plain,
    ! [X3: '$ki_world',X4: $i] :
      ( '$ki_accessible'(X3,sK1(X3,X4))
      | ~ '$ki_exists_in_world_$i'(X3,X4)
      | ~ '$ki_accessible'('$ki_local_world',X3) ),
    inference(cnf_transformation,[],[f22]) ).

tff(f31,plain,
    ! [X3: '$ki_world',X4: $i] :
      ( b(sK1(X3,X4),X4)
      | ~ '$ki_exists_in_world_$i'(X3,X4)
      | ~ '$ki_accessible'('$ki_local_world',X3) ),
    inference(cnf_transformation,[],[f22]) ).

tff(f32,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
      ( ~ b(X2,X1)
      | ~ a(X2,X1)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f22]) ).

cnf(c_53,negated_conjecture,
    ( ~ '$ki_accessible'(X0_13,X1_13)
    | ~ a(X1_13,X0)
    | ~ b(X1_13,X0)
    | ~ '$ki_exists_in_world_$i'(X0_13,X0)
    | ~ '$ki_accessible'('$ki_local_world',X0_13) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_54,negated_conjecture,
    ( ~ '$ki_exists_in_world_$i'(X0_13,X0)
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | b(sK1(X0_13,X0),X0) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_55,negated_conjecture,
    ( ~ '$ki_exists_in_world_$i'(X0_13,X0)
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | '$ki_accessible'(X0_13,sK1(X0_13,X0)) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_56,negated_conjecture,
    ( ~ '$ki_accessible'(sK2,X0_13)
    | a(X0_13,sK3) ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_57,negated_conjecture,
    '$ki_exists_in_world_$i'(sK2,sK3),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_58,negated_conjecture,
    '$ki_accessible'('$ki_local_world',sK2),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_111,plain,
    ( ~ '$ki_accessible'(X0_13,X1_13)
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | ~ '$ki_accessible'(sK2,X1_13)
    | ~ b(X1_13,sK3)
    | ~ '$ki_exists_in_world_$i'(X0_13,sK3) ),
    inference(resolution,[status(thm)],[c_53,c_56]) ).

cnf(c_133,plain,
    ( ~ '$ki_accessible'(X0_13,sK1(X1_13,sK3))
    | ~ '$ki_accessible'(sK2,sK1(X1_13,sK3))
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | ~ '$ki_accessible'('$ki_local_world',X1_13)
    | ~ '$ki_exists_in_world_$i'(X0_13,sK3)
    | ~ '$ki_exists_in_world_$i'(X1_13,sK3) ),
    inference(resolution,[status(thm)],[c_54,c_111]) ).

cnf(c_199,negated_conjecture,
    ( ~ '$ki_exists_in_world_$i'(X0_13,X0)
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | '$ki_accessible'(X0_13,sK1(X0_13,X0)) ),
    inference(demodulation,[status(thm)],[c_55]) ).

cnf(c_200,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK2)
    | ~ '$ki_exists_in_world_$i'(sK2,sK3)
    | '$ki_accessible'(sK2,sK1(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_199]) ).

cnf(c_201,plain,
    ( ~ '$ki_accessible'(sK2,sK1(X0_13,sK3))
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | ~ '$ki_exists_in_world_$i'(X0_13,sK3)
    | ~ '$ki_accessible'('$ki_local_world',sK2)
    | ~ '$ki_exists_in_world_$i'(sK2,sK3) ),
    inference(instantiation,[status(thm)],[c_133]) ).

cnf(c_211,plain,
    ( ~ '$ki_accessible'(sK2,sK1(sK2,sK3))
    | ~ '$ki_accessible'('$ki_local_world',sK2)
    | ~ '$ki_exists_in_world_$i'(sK2,sK3) ),
    inference(instantiation,[status(thm)],[c_201]) ).

cnf(c_212,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_211,c_200,c_57,c_58]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem  : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% 0.05/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n004.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 : Thu May  2 20:03:18 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.58/1.15  % SZS status Started for theBenchmark.p
% 1.58/1.15  % SZS status Theorem for theBenchmark.p
% 1.58/1.15  
% 1.58/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.58/1.15  
% 1.58/1.15  ------  iProver source info
% 1.58/1.15  
% 1.58/1.15  git: date: 2024-05-02 19:28:25 +0000
% 1.58/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.58/1.15  git: non_committed_changes: false
% 1.58/1.15  
% 1.58/1.15  ------ Parsing...
% 1.58/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.58/1.15  
% 1.58/1.15  
% 1.58/1.15  ------ Preprocessing... pe_s  pe:1:0s pe:2:0s pe_e  pe_s  pe_e 
% 1.58/1.15  
% 1.58/1.15  ------ Preprocessing...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.58/1.15   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.58/1.15  ------ Proving...
% 1.58/1.15  ------ Problem Properties 
% 1.58/1.15  
% 1.58/1.15  
% 1.58/1.15  clauses                                 8
% 1.58/1.15  conjectures                             3
% 1.58/1.15  EPR                                     5
% 1.58/1.15  Horn                                    8
% 1.58/1.15  unary                                   4
% 1.58/1.15  binary                                  0
% 1.58/1.15  lits                                    19
% 1.58/1.15  lits eq                                 0
% 1.58/1.15  fd_pure                                 0
% 1.58/1.15  fd_pseudo                               0
% 1.58/1.15  fd_cond                                 0
% 1.58/1.15  fd_pseudo_cond                          0
% 1.58/1.15  AC symbols                              0
% 1.58/1.15  
% 1.58/1.15  ------ Schedule dynamic 5 is on 
% 1.58/1.15  
% 1.58/1.15  ------ no equalities: superposition off 
% 1.58/1.15  
% 1.58/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.58/1.15  
% 1.58/1.15  
% 1.58/1.15  ------ 
% 1.58/1.15  Current options:
% 1.58/1.15  ------ 
% 1.58/1.15  
% 1.58/1.15  
% 1.58/1.15  
% 1.58/1.15  
% 1.58/1.15  ------ Proving...
% 1.58/1.15  
% 1.58/1.15  
% 1.58/1.15  % SZS status Theorem for theBenchmark.p
% 1.58/1.15  
% 1.58/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.58/1.15  
% 1.58/1.15  
%------------------------------------------------------------------------------