TSTP Solution File: PLA053_4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n016.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 02:53:59 EDT 2024

% Result   : Theorem 0.77s 1.15s
% Output   : CNFRefutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   45 (  15 unt;   0 typ;   0 def)
%            Number of atoms       :  224 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  197 (  77   ~;  59   |;  41   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   59 (  59 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   5 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   79 (   5 sgn  46   !;  16   ?;  31   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f1,axiom,
    ! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

tff(f3,axiom,
    ! [X0: '$ki_world',X3] : '$ki_exists_in_world_$i'(X0,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(f7,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X3] :
          ( '$ki_exists_in_world_$i'(X0,X3)
         => ? [X7] :
              ( ! [X6: '$ki_world'] :
                  ( '$ki_accessible'(X0,X6)
                 => ( ( h(X6,X7)
                      & bomb(X6,X3) )
                   => defused(X6,X3) ) )
              & '$ki_exists_in_world_$i'(X0,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

tff(f8,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X3] :
          ( '$ki_exists_in_world_$i'(X0,X3)
         => ? [X7] :
              ( ( ( h(X0,X7)
                  & bomb(X0,X3) )
               => defused(X0,X3) )
              & '$ki_exists_in_world_$i'(X0,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f9,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X3] :
            ( '$ki_exists_in_world_$i'(X0,X3)
           => ? [X7] :
                ( ( ( h(X0,X7)
                    & bomb(X0,X3) )
                 => defused(X0,X3) )
                & '$ki_exists_in_world_$i'(X0,X7) ) ) ),
    inference(negated_conjecture,[],[f8]) ).

tff(f10,plain,
    ! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
    inference(rectify,[],[f3]) ).

tff(f14,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ? [X2] :
              ( ! [X3: '$ki_world'] :
                  ( '$ki_accessible'(X0,X3)
                 => ( ( h(X3,X2)
                      & bomb(X3,X1) )
                   => defused(X3,X1) ) )
              & '$ki_exists_in_world_$i'(X0,X2) ) ) ),
    inference(rectify,[],[f7]) ).

tff(f15,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
           => ? [X2] :
                ( ( ( h(X0,X2)
                    & bomb(X0,X1) )
                 => defused(X0,X1) )
                & '$ki_exists_in_world_$i'(X0,X2) ) ) ),
    inference(rectify,[],[f9]) ).

tff(f21,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ? [X2] :
              ( ! [X3: '$ki_world'] :
                  ( defused(X3,X1)
                  | ~ h(X3,X2)
                  | ~ bomb(X3,X1)
                  | ~ '$ki_accessible'(X0,X3) )
              & '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f14]) ).

tff(f22,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ? [X2] :
              ( ! [X3: '$ki_world'] :
                  ( defused(X3,X1)
                  | ~ h(X3,X2)
                  | ~ bomb(X3,X1)
                  | ~ '$ki_accessible'(X0,X3) )
              & '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f21]) ).

tff(f23,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2] :
              ( ( ~ defused(X0,X1)
                & h(X0,X2)
                & bomb(X0,X1) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f15]) ).

tff(f24,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2] :
              ( ( ~ defused(X0,X1)
                & h(X0,X2)
                & bomb(X0,X1) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f23]) ).

tff(f31,plain,
    ! [X0: '$ki_world',X1] :
      ( ? [X2] :
          ( ! [X3: '$ki_world'] :
              ( defused(X3,X1)
              | ~ h(X3,X2)
              | ~ bomb(X3,X1)
              | ~ '$ki_accessible'(X0,X3) )
          & '$ki_exists_in_world_$i'(X0,X2) )
     => ( ! [X3: '$ki_world'] :
            ( defused(X3,X1)
            | ~ h(X3,sK3(X0,X1))
            | ~ bomb(X3,X1)
            | ~ '$ki_accessible'(X0,X3) )
        & '$ki_exists_in_world_$i'(X0,sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f32,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ( ! [X3: '$ki_world'] :
                ( defused(X3,X1)
                | ~ h(X3,sK3(X0,X1))
                | ~ bomb(X3,X1)
                | ~ '$ki_accessible'(X0,X3) )
            & '$ki_exists_in_world_$i'(X0,sK3(X0,X1)) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f22,f31]) ).

tff(f33,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1] :
            ( ! [X2] :
                ( ( ~ defused(X0,X1)
                  & h(X0,X2)
                  & bomb(X0,X1) )
                | ~ '$ki_exists_in_world_$i'(X0,X2) )
            & '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ? [X1] :
          ( ! [X2] :
              ( ( ~ defused(sK4,X1)
                & h(sK4,X2)
                & bomb(sK4,X1) )
              | ~ '$ki_exists_in_world_$i'(sK4,X2) )
          & '$ki_exists_in_world_$i'(sK4,X1) )
      & '$ki_accessible'('$ki_local_world',sK4) ) ),
    introduced(choice_axiom,[]) ).

tff(f34,plain,
    ( ? [X1] :
        ( ! [X2] :
            ( ( ~ defused(sK4,X1)
              & h(sK4,X2)
              & bomb(sK4,X1) )
            | ~ '$ki_exists_in_world_$i'(sK4,X2) )
        & '$ki_exists_in_world_$i'(sK4,X1) )
   => ( ! [X2] :
          ( ( ~ defused(sK4,sK5)
            & h(sK4,X2)
            & bomb(sK4,sK5) )
          | ~ '$ki_exists_in_world_$i'(sK4,X2) )
      & '$ki_exists_in_world_$i'(sK4,sK5) ) ),
    introduced(choice_axiom,[]) ).

tff(f35,plain,
    ( ! [X2] :
        ( ( ~ defused(sK4,sK5)
          & h(sK4,X2)
          & bomb(sK4,sK5) )
        | ~ '$ki_exists_in_world_$i'(sK4,X2) )
    & '$ki_exists_in_world_$i'(sK4,sK5)
    & '$ki_accessible'('$ki_local_world',sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f24,f34,f33]) ).

tff(f36,plain,
    ! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

tff(f38,plain,
    ! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
    inference(cnf_transformation,[],[f10]) ).

tff(f45,plain,
    ! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( defused(X3,X1)
      | ~ h(X3,sK3(X0,X1))
      | ~ bomb(X3,X1)
      | ~ '$ki_accessible'(X0,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f46,plain,
    '$ki_accessible'('$ki_local_world',sK4),
    inference(cnf_transformation,[],[f35]) ).

tff(f47,plain,
    '$ki_exists_in_world_$i'(sK4,sK5),
    inference(cnf_transformation,[],[f35]) ).

tff(f48,plain,
    ! [X2: $i] :
      ( bomb(sK4,sK5)
      | ~ '$ki_exists_in_world_$i'(sK4,X2) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f49,plain,
    ! [X2: $i] :
      ( h(sK4,X2)
      | ~ '$ki_exists_in_world_$i'(sK4,X2) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f50,plain,
    ! [X2: $i] :
      ( ~ defused(sK4,sK5)
      | ~ '$ki_exists_in_world_$i'(sK4,X2) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_49,plain,
    '$ki_accessible'(X0_13,X0_13),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_51,plain,
    '$ki_exists_in_world_$i'(X0_13,X0),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_57,plain,
    ( ~ h(X0_13,sK3(X1_13,X0))
    | ~ '$ki_accessible'(X1_13,X0_13)
    | ~ bomb(X0_13,X0)
    | ~ '$ki_exists_in_world_$i'(X1_13,X0)
    | ~ '$ki_accessible'('$ki_local_world',X1_13)
    | defused(X0_13,X0) ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_59,negated_conjecture,
    ( ~ '$ki_exists_in_world_$i'(sK4,X0)
    | ~ defused(sK4,sK5) ),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_60,negated_conjecture,
    ( ~ '$ki_exists_in_world_$i'(sK4,X0)
    | h(sK4,X0) ),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_61,negated_conjecture,
    ( ~ '$ki_exists_in_world_$i'(sK4,X0)
    | bomb(sK4,sK5) ),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_62,negated_conjecture,
    '$ki_exists_in_world_$i'(sK4,sK5),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_63,negated_conjecture,
    '$ki_accessible'('$ki_local_world',sK4),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_64,plain,
    '$ki_accessible'(sK4,sK4),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_66,plain,
    ( ~ '$ki_exists_in_world_$i'(sK4,sK5)
    | bomb(sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_68,plain,
    ( ~ defused(sK4,sK5)
    | ~ '$ki_exists_in_world_$i'(sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_75,negated_conjecture,
    ~ defused(sK4,sK5),
    inference(global_subsumption_just,[status(thm)],[c_59,c_62,c_68]) ).

cnf(c_86,plain,
    h(sK4,X0),
    inference(backward_subsumption_resolution,[status(thm)],[c_60,c_51]) ).

cnf(c_87,plain,
    ( ~ h(X0_13,sK3(X1_13,X0))
    | ~ '$ki_accessible'(X1_13,X0_13)
    | ~ bomb(X0_13,X0)
    | ~ '$ki_accessible'('$ki_local_world',X1_13)
    | defused(X0_13,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_57,c_51]) ).

cnf(c_128,plain,
    ( ~ h(sK4,sK3(X0_13,sK5))
    | ~ '$ki_accessible'(X0_13,sK4)
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | ~ bomb(sK4,sK5) ),
    inference(resolution,[status(thm)],[c_87,c_75]) ).

cnf(c_130,plain,
    ( ~ '$ki_accessible'('$ki_local_world',X0_13)
    | ~ '$ki_accessible'(X0_13,sK4)
    | ~ h(sK4,sK3(X0_13,sK5)) ),
    inference(global_subsumption_just,[status(thm)],[c_128,c_62,c_66,c_128]) ).

cnf(c_131,plain,
    ( ~ h(sK4,sK3(X0_13,sK5))
    | ~ '$ki_accessible'(X0_13,sK4)
    | ~ '$ki_accessible'('$ki_local_world',X0_13) ),
    inference(renaming,[status(thm)],[c_130]) ).

cnf(c_139,plain,
    ( ~ '$ki_accessible'(X0_13,sK4)
    | ~ '$ki_accessible'('$ki_local_world',X0_13) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_131,c_86]) ).

cnf(c_142,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK4)
    | ~ '$ki_accessible'(sK4,sK4) ),
    inference(instantiation,[status(thm)],[c_139]) ).

cnf(c_143,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_142,c_64,c_63]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n016.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May  2 22:06:45 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  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
% 0.77/1.15  % SZS status Started for theBenchmark.p
% 0.77/1.15  % SZS status Theorem for theBenchmark.p
% 0.77/1.15  
% 0.77/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.77/1.15  
% 0.77/1.15  ------  iProver source info
% 0.77/1.15  
% 0.77/1.15  git: date: 2024-05-02 19:28:25 +0000
% 0.77/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.77/1.15  git: non_committed_changes: false
% 0.77/1.15  
% 0.77/1.15  ------ Parsing...
% 0.77/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 0.77/1.15  
% 0.77/1.15  
% 0.77/1.15  ------ Preprocessing... pe_s  pe:1:0s
% 0.77/1.15  
% 0.77/1.15  % SZS status Theorem for theBenchmark.p
% 0.77/1.15  
% 0.77/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.77/1.15  
% 0.77/1.15  
%------------------------------------------------------------------------------