TSTP Solution File: SYO891_16 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 1.61s 1.19s
% Output   : CNFRefutation 1.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (   7 unt;   0 typ;   0 def)
%            Number of atoms       :  189 (   0 equ)
%            Maximal formula atoms :   10 (   6 avg)
%            Number of connectives :  144 (  46   ~;  36   |;  45   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   62 (  62 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; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   78 (   0 sgn  41   !;  29   ?;  37   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f3,axiom,
    ! [X0: '$ki_world',X1: '$ki_world',X3] :
      ( ( '$ki_accessible'(X0,X1)
        & '$ki_exists_in_world_$i'(X0,X3) )
     => '$ki_exists_in_world_$i'(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).

tff(f9,conjecture,
    ( ! [X3] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
       => ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ? [X4] :
                ( qmltpeq(X0,X3,X4)
                & '$ki_exists_in_world_$i'(X0,X4) ) ) )
   => ( ? [X3] :
          ( ? [X0: '$ki_world'] :
              ( p(X0,X3)
              & '$ki_accessible'('$ki_local_world',X0) )
          & '$ki_exists_in_world_$i'('$ki_local_world',X3) )
     => ? [X0: '$ki_world'] :
          ( ? [X3] :
              ( p(X0,X3)
              & '$ki_exists_in_world_$i'(X0,X3) )
          & '$ki_accessible'('$ki_local_world',X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f10,negated_conjecture,
    ~ ( ! [X3] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
         => ! [X0: '$ki_world'] :
              ( '$ki_accessible'('$ki_local_world',X0)
             => ? [X4] :
                  ( qmltpeq(X0,X3,X4)
                  & '$ki_exists_in_world_$i'(X0,X4) ) ) )
     => ( ? [X3] :
            ( ? [X0: '$ki_world'] :
                ( p(X0,X3)
                & '$ki_accessible'('$ki_local_world',X0) )
            & '$ki_exists_in_world_$i'('$ki_local_world',X3) )
       => ? [X0: '$ki_world'] :
            ( ? [X3] :
                ( p(X0,X3)
                & '$ki_exists_in_world_$i'(X0,X3) )
            & '$ki_accessible'('$ki_local_world',X0) ) ) ),
    inference(negated_conjecture,[],[f9]) ).

tff(f11,plain,
    ! [X0: '$ki_world',X1: '$ki_world',X2] :
      ( ( '$ki_accessible'(X0,X1)
        & '$ki_exists_in_world_$i'(X0,X2) )
     => '$ki_exists_in_world_$i'(X1,X2) ),
    inference(rectify,[],[f3]) ).

tff(f17,plain,
    ~ ( ! [X0] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X0)
         => ! [X1: '$ki_world'] :
              ( '$ki_accessible'('$ki_local_world',X1)
             => ? [X2] :
                  ( qmltpeq(X1,X0,X2)
                  & '$ki_exists_in_world_$i'(X1,X2) ) ) )
     => ( ? [X3] :
            ( ? [X4: '$ki_world'] :
                ( p(X4,X3)
                & '$ki_accessible'('$ki_local_world',X4) )
            & '$ki_exists_in_world_$i'('$ki_local_world',X3) )
       => ? [X5: '$ki_world'] :
            ( ? [X6] :
                ( p(X5,X6)
                & '$ki_exists_in_world_$i'(X5,X6) )
            & '$ki_accessible'('$ki_local_world',X5) ) ) ),
    inference(rectify,[],[f10]) ).

tff(f20,plain,
    ! [X0: '$ki_world',X1: '$ki_world',X2] :
      ( '$ki_exists_in_world_$i'(X1,X2)
      | ~ '$ki_accessible'(X0,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X2) ),
    inference(ennf_transformation,[],[f11]) ).

tff(f21,plain,
    ! [X0: '$ki_world',X1: '$ki_world',X2] :
      ( '$ki_exists_in_world_$i'(X1,X2)
      | ~ '$ki_accessible'(X0,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X2) ),
    inference(flattening,[],[f20]) ).

tff(f29,plain,
    ( ! [X5: '$ki_world'] :
        ( ! [X6] :
            ( ~ p(X5,X6)
            | ~ '$ki_exists_in_world_$i'(X5,X6) )
        | ~ '$ki_accessible'('$ki_local_world',X5) )
    & ? [X3] :
        ( ? [X4: '$ki_world'] :
            ( p(X4,X3)
            & '$ki_accessible'('$ki_local_world',X4) )
        & '$ki_exists_in_world_$i'('$ki_local_world',X3) )
    & ! [X0] :
        ( ! [X1: '$ki_world'] :
            ( ? [X2] :
                ( qmltpeq(X1,X0,X2)
                & '$ki_exists_in_world_$i'(X1,X2) )
            | ~ '$ki_accessible'('$ki_local_world',X1) )
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
    inference(ennf_transformation,[],[f17]) ).

tff(f30,plain,
    ( ! [X5: '$ki_world'] :
        ( ! [X6] :
            ( ~ p(X5,X6)
            | ~ '$ki_exists_in_world_$i'(X5,X6) )
        | ~ '$ki_accessible'('$ki_local_world',X5) )
    & ? [X3] :
        ( ? [X4: '$ki_world'] :
            ( p(X4,X3)
            & '$ki_accessible'('$ki_local_world',X4) )
        & '$ki_exists_in_world_$i'('$ki_local_world',X3) )
    & ! [X0] :
        ( ! [X1: '$ki_world'] :
            ( ? [X2] :
                ( qmltpeq(X1,X0,X2)
                & '$ki_exists_in_world_$i'(X1,X2) )
            | ~ '$ki_accessible'('$ki_local_world',X1) )
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
    inference(flattening,[],[f29]) ).

tff(f33,plain,
    ( ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ~ p(X0,X1)
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X2] :
        ( ? [X3: '$ki_world'] :
            ( p(X3,X2)
            & '$ki_accessible'('$ki_local_world',X3) )
        & '$ki_exists_in_world_$i'('$ki_local_world',X2) )
    & ! [X4] :
        ( ! [X5: '$ki_world'] :
            ( ? [X6] :
                ( qmltpeq(X5,X4,X6)
                & '$ki_exists_in_world_$i'(X5,X6) )
            | ~ '$ki_accessible'('$ki_local_world',X5) )
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
    inference(rectify,[],[f30]) ).

tff(f34,plain,
    ( ? [X2] :
        ( ? [X3: '$ki_world'] :
            ( p(X3,X2)
            & '$ki_accessible'('$ki_local_world',X3) )
        & '$ki_exists_in_world_$i'('$ki_local_world',X2) )
   => ( ? [X3: '$ki_world'] :
          ( p(X3,sK1)
          & '$ki_accessible'('$ki_local_world',X3) )
      & '$ki_exists_in_world_$i'('$ki_local_world',sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f35,plain,
    ( ? [X3: '$ki_world'] :
        ( p(X3,sK1)
        & '$ki_accessible'('$ki_local_world',X3) )
   => ( p(sK2,sK1)
      & '$ki_accessible'('$ki_local_world',sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f36,plain,
    ! [X4,X5: '$ki_world'] :
      ( ? [X6] :
          ( qmltpeq(X5,X4,X6)
          & '$ki_exists_in_world_$i'(X5,X6) )
     => ( qmltpeq(X5,X4,sK3(X4,X5))
        & '$ki_exists_in_world_$i'(X5,sK3(X4,X5)) ) ),
    introduced(choice_axiom,[]) ).

tff(f37,plain,
    ( ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ~ p(X0,X1)
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & p(sK2,sK1)
    & '$ki_accessible'('$ki_local_world',sK2)
    & '$ki_exists_in_world_$i'('$ki_local_world',sK1)
    & ! [X4] :
        ( ! [X5: '$ki_world'] :
            ( ( qmltpeq(X5,X4,sK3(X4,X5))
              & '$ki_exists_in_world_$i'(X5,sK3(X4,X5)) )
            | ~ '$ki_accessible'('$ki_local_world',X5) )
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f33,f36,f35,f34]) ).

tff(f40,plain,
    ! [X2: $i,X0: '$ki_world',X1: '$ki_world'] :
      ( '$ki_exists_in_world_$i'(X1,X2)
      | ~ '$ki_accessible'(X0,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X2) ),
    inference(cnf_transformation,[],[f21]) ).

tff(f48,plain,
    '$ki_exists_in_world_$i'('$ki_local_world',sK1),
    inference(cnf_transformation,[],[f37]) ).

tff(f49,plain,
    '$ki_accessible'('$ki_local_world',sK2),
    inference(cnf_transformation,[],[f37]) ).

tff(f50,plain,
    p(sK2,sK1),
    inference(cnf_transformation,[],[f37]) ).

tff(f51,plain,
    ! [X0: '$ki_world',X1: $i] :
      ( ~ p(X0,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_51,plain,
    ( ~ '$ki_accessible'(X0_13,X1_13)
    | ~ '$ki_exists_in_world_$i'(X0_13,X0)
    | '$ki_exists_in_world_$i'(X1_13,X0) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_57,negated_conjecture,
    ( ~ p(X0_13,X0)
    | ~ '$ki_exists_in_world_$i'(X0_13,X0)
    | ~ '$ki_accessible'('$ki_local_world',X0_13) ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_58,negated_conjecture,
    p(sK2,sK1),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_59,negated_conjecture,
    '$ki_accessible'('$ki_local_world',sK2),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_60,negated_conjecture,
    '$ki_exists_in_world_$i'('$ki_local_world',sK1),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_148,negated_conjecture,
    ( ~ p(X0_13,X0)
    | ~ '$ki_exists_in_world_$i'(X0_13,X0)
    | ~ '$ki_accessible'('$ki_local_world',X0_13) ),
    inference(demodulation,[status(thm)],[c_57]) ).

cnf(c_149,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK2)
    | ~ p(sK2,sK1)
    | ~ '$ki_exists_in_world_$i'(sK2,sK1) ),
    inference(instantiation,[status(thm)],[c_148]) ).

cnf(c_150,plain,
    ( ~ '$ki_accessible'(X0_13,sK2)
    | ~ '$ki_exists_in_world_$i'(X0_13,sK1)
    | '$ki_exists_in_world_$i'(sK2,sK1) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_151,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK2)
    | ~ '$ki_exists_in_world_$i'('$ki_local_world',sK1)
    | '$ki_exists_in_world_$i'(sK2,sK1) ),
    inference(instantiation,[status(thm)],[c_150]) ).

cnf(c_152,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_151,c_149,c_58,c_59,c_60]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% 0.04/0.14  % Command  : run_iprover %s %d THM
% 0.15/0.35  % Computer : n018.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May  2 20:27:01 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.22/0.49  Running first-order theorem proving
% 0.22/0.49  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
% 1.61/1.19  % SZS status Started for theBenchmark.p
% 1.61/1.19  % SZS status Theorem for theBenchmark.p
% 1.61/1.19  
% 1.61/1.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.61/1.19  
% 1.61/1.19  ------  iProver source info
% 1.61/1.19  
% 1.61/1.19  git: date: 2024-05-02 19:28:25 +0000
% 1.61/1.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.61/1.19  git: non_committed_changes: false
% 1.61/1.19  
% 1.61/1.19  ------ Parsing...
% 1.61/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.61/1.19  
% 1.61/1.19  
% 1.61/1.19  ------ Preprocessing... pe_s  pe_e 
% 1.61/1.19  
% 1.61/1.19  ------ Preprocessing...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.61/1.19   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.61/1.19  ------ Proving...
% 1.61/1.19  ------ Problem Properties 
% 1.61/1.19  
% 1.61/1.19  
% 1.61/1.19  clauses                                 14
% 1.61/1.19  conjectures                             6
% 1.61/1.19  EPR                                     11
% 1.61/1.19  Horn                                    14
% 1.61/1.19  unary                                   5
% 1.61/1.19  binary                                  1
% 1.61/1.19  lits                                    37
% 1.61/1.19  lits eq                                 0
% 1.61/1.19  fd_pure                                 0
% 1.61/1.19  fd_pseudo                               0
% 1.61/1.19  fd_cond                                 0
% 1.61/1.19  fd_pseudo_cond                          0
% 1.61/1.19  AC symbols                              0
% 1.61/1.19  
% 1.61/1.19  ------ Schedule dynamic 5 is on 
% 1.61/1.19  
% 1.61/1.19  ------ no equalities: superposition off 
% 1.61/1.19  
% 1.61/1.19  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/1.19  
% 1.61/1.19  
% 1.61/1.19  ------ 
% 1.61/1.19  Current options:
% 1.61/1.19  ------ 
% 1.61/1.19  
% 1.61/1.19  
% 1.61/1.19  
% 1.61/1.19  
% 1.61/1.19  ------ Proving...
% 1.61/1.19  
% 1.61/1.19  
% 1.61/1.19  % SZS status Theorem for theBenchmark.p
% 1.61/1.19  
% 1.61/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.19  
% 1.61/1.19  
%------------------------------------------------------------------------------