TSTP Solution File: PLA053_5 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : PLA053_5 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n002.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 : Mon May 22 15:41:23 EDT 2023

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   45 (  12 unt;  11 typ;   0 def)
%            Number of atoms       :  152 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  164 (  57   ~;  46   |;  41   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   11 (  11 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   14 (   8   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   2 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   78 (;  62   !;  16   ?;  47   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    '$ki_world': $tType ).

tff(func_def_0,type,
    '$ki_local_world': '$ki_world' ).

tff(func_def_1,type,
    sK0: '$ki_world' ).

tff(func_def_3,type,
    sK2: '$ki_world' > $i ).

tff(func_def_5,type,
    sK4: ( '$ki_world' * $i ) > $i ).

tff(func_def_6,type,
    sK5: '$ki_world' > $i ).

tff(pred_def_1,type,
    '$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).

tff(pred_def_2,type,
    h: ( '$ki_world' * $i ) > $o ).

tff(pred_def_3,type,
    bomb: ( '$ki_world' * $i ) > $o ).

tff(pred_def_4,type,
    defused: ( '$ki_world' * $i ) > $o ).

tff(pred_def_5,type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff(f69,plain,
    $false,
    inference(subsumption_resolution,[],[f66,f58]) ).

tff(f58,plain,
    ~ defused(sK0,sK1),
    inference(subsumption_resolution,[],[f38,f48]) ).

tff(f48,plain,
    ! [X0: $i,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
    inference(cnf_transformation,[],[f12]) ).

tff(f12,plain,
    ! [X0,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X2,X0: '$ki_world'] : '$ki_exists_in_world_$i'(X0,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(f38,plain,
    ! [X2: $i] :
      ( ~ defused(sK0,sK1)
      | ~ '$ki_exists_in_world_$i'(sK0,X2) ),
    inference(cnf_transformation,[],[f25]) ).

tff(f25,plain,
    ( '$ki_exists_in_world_$i'(sK0,sK1)
    & ! [X2] :
        ( ( ~ defused(sK0,sK1)
          & h(sK0,X2)
          & bomb(sK0,sK1) )
        | ~ '$ki_exists_in_world_$i'(sK0,X2) )
    & '$ki_accessible'('$ki_local_world',sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f24,f23]) ).

tff(f23,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
            & ! [X2] :
                ( ( ~ defused(X0,X1)
                  & h(X0,X2)
                  & bomb(X0,X1) )
                | ~ '$ki_exists_in_world_$i'(X0,X2) ) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ? [X1] :
          ( '$ki_exists_in_world_$i'(sK0,X1)
          & ! [X2] :
              ( ( ~ defused(sK0,X1)
                & h(sK0,X2)
                & bomb(sK0,X1) )
              | ~ '$ki_exists_in_world_$i'(sK0,X2) ) )
      & '$ki_accessible'('$ki_local_world',sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f24,plain,
    ( ? [X1] :
        ( '$ki_exists_in_world_$i'(sK0,X1)
        & ! [X2] :
            ( ( ~ defused(sK0,X1)
              & h(sK0,X2)
              & bomb(sK0,X1) )
            | ~ '$ki_exists_in_world_$i'(sK0,X2) ) )
   => ( '$ki_exists_in_world_$i'(sK0,sK1)
      & ! [X2] :
          ( ( ~ defused(sK0,sK1)
            & h(sK0,X2)
            & bomb(sK0,sK1) )
          | ~ '$ki_exists_in_world_$i'(sK0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
          & ! [X2] :
              ( ( ~ defused(X0,X1)
                & h(X0,X2)
                & bomb(X0,X1) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) ) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f18]) ).

tff(f18,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2] :
              ( ~ '$ki_exists_in_world_$i'(X0,X2)
              | ( ~ defused(X0,X1)
                & h(X0,X2)
                & bomb(X0,X1) ) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f13]) ).

tff(f13,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
           => ? [X2] :
                ( '$ki_exists_in_world_$i'(X0,X2)
                & ( ( h(X0,X2)
                    & bomb(X0,X1) )
                 => defused(X0,X1) ) ) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X2] :
            ( '$ki_exists_in_world_$i'(X0,X2)
           => ? [X6] :
                ( ( ( bomb(X0,X2)
                    & h(X0,X6) )
                 => defused(X0,X2) )
                & '$ki_exists_in_world_$i'(X0,X6) ) ) ),
    inference(negated_conjecture,[],[f7]) ).

tff(f7,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X2] :
          ( '$ki_exists_in_world_$i'(X0,X2)
         => ? [X6] :
              ( ( ( bomb(X0,X2)
                  & h(X0,X6) )
               => defused(X0,X2) )
              & '$ki_exists_in_world_$i'(X0,X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f66,plain,
    defused(sK0,sK1),
    inference(resolution,[],[f64,f59]) ).

tff(f59,plain,
    bomb(sK0,sK1),
    inference(subsumption_resolution,[],[f36,f48]) ).

tff(f36,plain,
    ! [X2: $i] :
      ( ~ '$ki_exists_in_world_$i'(sK0,X2)
      | bomb(sK0,sK1) ),
    inference(cnf_transformation,[],[f25]) ).

tff(f64,plain,
    ! [X0: $i] :
      ( ~ bomb(sK0,X0)
      | defused(sK0,X0) ),
    inference(subsumption_resolution,[],[f63,f48]) ).

tff(f63,plain,
    ! [X0: $i,X1: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X1,X0)
      | ~ bomb(sK0,X0)
      | defused(sK0,X0) ),
    inference(resolution,[],[f50,f57]) ).

tff(f57,plain,
    ! [X2: $i] : h(sK0,X2),
    inference(subsumption_resolution,[],[f37,f48]) ).

tff(f37,plain,
    ! [X2: $i] :
      ( ~ '$ki_exists_in_world_$i'(sK0,X2)
      | h(sK0,X2) ),
    inference(cnf_transformation,[],[f25]) ).

tff(f50,plain,
    ! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( ~ h(X3,sK4(X0,X1))
      | defused(X3,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ bomb(X3,X1) ),
    inference(subsumption_resolution,[],[f49,f45]) ).

tff(f45,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(rectify,[],[f14]) ).

tff(f14,plain,
    ! [X1: '$ki_world',X0: '$ki_world'] : '$ki_accessible'(X1,X0),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X1: '$ki_world',X0: '$ki_world'] : '$ki_accessible'(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).

tff(f49,plain,
    ! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( ~ bomb(X3,X1)
      | ~ h(X3,sK4(X0,X1))
      | ~ '$ki_accessible'(X0,X3)
      | defused(X3,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1) ),
    inference(subsumption_resolution,[],[f44,f45]) ).

tff(f44,plain,
    ! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( ~ bomb(X3,X1)
      | ~ h(X3,sK4(X0,X1))
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_accessible'(X0,X3)
      | defused(X3,X1) ),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ~ '$ki_exists_in_world_$i'(X0,X1)
          | ( ! [X3: '$ki_world'] :
                ( ~ bomb(X3,X1)
                | defused(X3,X1)
                | ~ h(X3,sK4(X0,X1))
                | ~ '$ki_accessible'(X0,X3) )
            & '$ki_exists_in_world_$i'(X0,sK4(X0,X1)) ) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f22,f30]) ).

tff(f30,plain,
    ! [X0: '$ki_world',X1] :
      ( ? [X2] :
          ( ! [X3: '$ki_world'] :
              ( ~ bomb(X3,X1)
              | defused(X3,X1)
              | ~ h(X3,X2)
              | ~ '$ki_accessible'(X0,X3) )
          & '$ki_exists_in_world_$i'(X0,X2) )
     => ( ! [X3: '$ki_world'] :
            ( ~ bomb(X3,X1)
            | defused(X3,X1)
            | ~ h(X3,sK4(X0,X1))
            | ~ '$ki_accessible'(X0,X3) )
        & '$ki_exists_in_world_$i'(X0,sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

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

tff(f21,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ? [X2] :
              ( ! [X3: '$ki_world'] :
                  ( defused(X3,X1)
                  | ~ bomb(X3,X1)
                  | ~ h(X3,X2)
                  | ~ '$ki_accessible'(X0,X3) )
              & '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f11]) ).

tff(f11,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ? [X2] :
              ( ! [X3: '$ki_world'] :
                  ( '$ki_accessible'(X0,X3)
                 => ( ( bomb(X3,X1)
                      & h(X3,X2) )
                   => defused(X3,X1) ) )
              & '$ki_exists_in_world_$i'(X0,X2) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X2] :
          ( '$ki_exists_in_world_$i'(X0,X2)
         => ? [X6] :
              ( '$ki_exists_in_world_$i'(X0,X6)
              & ! [X5: '$ki_world'] :
                  ( '$ki_accessible'(X0,X5)
                 => ( ( bomb(X5,X2)
                      & h(X5,X6) )
                   => defused(X5,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : PLA053_5 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n002.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   : Mon May 22 12:41:22 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (5119)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.50  % (5127)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.51  % (5135)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.51  % (5136)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.51  % (5127)First to succeed.
% 0.20/0.51  % (5127)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (5127)------------------------------
% 0.20/0.51  % (5127)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (5127)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (5127)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (5127)Memory used [KB]: 5884
% 0.20/0.51  % (5127)Time elapsed: 0.098 s
% 0.20/0.51  % (5127)Instructions burned: 2 (million)
% 0.20/0.51  % (5127)------------------------------
% 0.20/0.51  % (5127)------------------------------
% 0.20/0.51  % (5112)Success in time 0.163 s
%------------------------------------------------------------------------------