TSTP Solution File: DAT334_23 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT334_23 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.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 : Sun May  5 05:06:25 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   35 (   9 unt;   9 typ;   0 def)
%            Number of atoms       :  115 (   0 equ)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   66 (  20   ~;  12   |;  27   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   43 (  43 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   7 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :   42 (  31   !;  11   ?;  27   :)

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

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

tff(func_def_7,type,
    sK1: '$ki_world' ).

tff(func_def_8,type,
    sK2: '$ki_world' > $i ).

tff(func_def_9,type,
    sK3: '$ki_world' > $i ).

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

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

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

tff(pred_def_4,type,
    sP0: '$ki_world' > $o ).

tff(f36,plain,
    $false,
    inference(resolution,[],[f35,f34]) ).

tff(f34,plain,
    ! [X1: $i] : ~ teach(sK1,X1,cs),
    inference(subsumption_resolution,[],[f23,f32]) ).

tff(f32,plain,
    ! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
    inference(cnf_transformation,[],[f10]) ).

tff(f10,plain,
    ! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X0: '$ki_world',X2] : '$ki_exists_in_world_$i'(X0,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(f23,plain,
    ! [X1: $i] :
      ( ~ teach(sK1,X1,cs)
      | ~ '$ki_exists_in_world_$i'(sK1,X1) ),
    inference(cnf_transformation,[],[f16]) ).

tff(f16,plain,
    ( ! [X1] :
        ( ~ teach(sK1,X1,cs)
        | ~ '$ki_exists_in_world_$i'(sK1,X1) )
    & '$ki_accessible'('$ki_local_world',sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f15]) ).

tff(f15,plain,
    ( ? [X0: '$ki_world'] :
        ( ! [X1] :
            ( ~ teach(X0,X1,cs)
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ! [X1] :
          ( ~ teach(sK1,X1,cs)
          | ~ '$ki_exists_in_world_$i'(sK1,X1) )
      & '$ki_accessible'('$ki_local_world',sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f11,plain,
    ? [X0: '$ki_world'] :
      ( ! [X1] :
          ( ~ teach(X0,X1,cs)
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f7]) ).

tff(f7,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X1] :
            ( teach(X0,X1,cs)
            & '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X2] :
            ( teach(X0,X2,cs)
            & '$ki_exists_in_world_$i'(X0,X2) ) ),
    inference(negated_conjecture,[],[f5]) ).

tff(f5,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ? [X2] :
          ( teach(X0,X2,cs)
          & '$ki_exists_in_world_$i'(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f35,plain,
    ! [X0: '$ki_world'] : teach(X0,sK2(X0),cs),
    inference(subsumption_resolution,[],[f25,f33]) ).

tff(f33,plain,
    ! [X0: '$ki_world'] : sP0(X0),
    inference(subsumption_resolution,[],[f27,f31]) ).

tff(f31,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).

tff(f27,plain,
    ! [X0: '$ki_world'] :
      ( sP0(X0)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f14]) ).

tff(f14,plain,
    ! [X0: '$ki_world'] :
      ( ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & sP0(X0)
        & teach(X0,john,math) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(definition_folding,[],[f12,f13]) ).

tff(f13,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( teach(X0,X1,cs)
          & '$ki_exists_in_world_$i'(X0,X1) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f12,plain,
    ! [X0: '$ki_world'] :
      ( ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & ? [X1] :
            ( teach(X0,X1,cs)
            & '$ki_exists_in_world_$i'(X0,X1) )
        & teach(X0,john,math) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & ? [X1] :
            ( teach(X0,X1,cs)
            & '$ki_exists_in_world_$i'(X0,X1) )
        & teach(X0,john,math) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & ? [X2] :
            ( teach(X0,X2,cs)
            & '$ki_exists_in_world_$i'(X0,X2) )
        & teach(X0,john,math) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',db) ).

tff(f25,plain,
    ! [X0: '$ki_world'] :
      ( teach(X0,sK2(X0),cs)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ! [X0: '$ki_world'] :
      ( ( teach(X0,sK2(X0),cs)
        & '$ki_exists_in_world_$i'(X0,sK2(X0)) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f18]) ).

tff(f18,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( teach(X0,X1,cs)
          & '$ki_exists_in_world_$i'(X0,X1) )
     => ( teach(X0,sK2(X0),cs)
        & '$ki_exists_in_world_$i'(X0,sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f17,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( teach(X0,X1,cs)
          & '$ki_exists_in_world_$i'(X0,X1) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : DAT334_23 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n025.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 13:15:59 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (548)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37  % (552)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.37  % (551)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.21/0.37  % (550)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37  % (553)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.37  % (549)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.37  % (554)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.37  % (555)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.37  Detected minimum model sizes of [1,1,1,1]
% 0.21/0.37  Detected minimum model sizes of [1,1]
% 0.21/0.37  Detected maximum model sizes of [1,max,1,max]
% 0.21/0.37  Detected maximum model sizes of [2,max]
% 0.21/0.37  TRYING [1,1]
% 0.21/0.37  TRYING [1,1,1,1]
% 0.21/0.37  % (553)Also succeeded, but the first one will report.
% 0.21/0.37  % (554)First to succeed.
% 0.21/0.37  Detected minimum model sizes of [1,1,1,1]
% 0.21/0.37  Detected maximum model sizes of [1,max,1,max]
% 0.21/0.37  TRYING [1,1,1,1]
% 0.21/0.37  TRYING [1,2]
% 0.21/0.37  TRYING [1,2,1,2]
% 0.21/0.37  TRYING [1,2,1,2]
% 0.21/0.37  Cannot enumerate next child to try in an incomplete setup
% 0.21/0.37  % (552)Refutation not found, incomplete strategy% (552)------------------------------
% 0.21/0.37  % (552)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.37  % (552)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.37  
% 0.21/0.37  % (552)Memory used [KB]: 728
% 0.21/0.37  % (552)Time elapsed: 0.003 s
% 0.21/0.37  Detected minimum model sizes of [1,1]
% 0.21/0.37  Detected maximum model sizes of [2,max]
% 0.21/0.37  % (552)Instructions burned: 3 (million)
% 0.21/0.37  TRYING [1,3]
% 0.21/0.37  % (551)Also succeeded, but the first one will report.
% 0.21/0.37  TRYING [1,1]
% 0.21/0.37  Cannot enumerate next child to try in an incomplete setup
% 0.21/0.37  % (550)Refutation not found, incomplete strategy% (550)------------------------------
% 0.21/0.37  % (550)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.37  % (550)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.37  
% 0.21/0.37  % (550)Memory used [KB]: 728
% 0.21/0.37  % (550)Time elapsed: 0.004 s
% 0.21/0.37  % (550)Instructions burned: 3 (million)
% 0.21/0.38  TRYING [1,2]
% 0.21/0.38  TRYING [1,4]
% 0.21/0.38  % (552)------------------------------
% 0.21/0.38  % (552)------------------------------
% 0.21/0.38  % (554)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-548"
% 0.21/0.38  TRYING [1,3]
% 0.21/0.38  Cannot enumerate next child to try in an incomplete setup
% 0.21/0.38  % (550)------------------------------
% 0.21/0.38  % (550)------------------------------
% 0.21/0.38  % (549)Refutation not found, incomplete strategy% (549)------------------------------
% 0.21/0.38  % (549)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (549)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38  
% 0.21/0.38  % (549)Memory used [KB]: 725
% 0.21/0.38  % (549)Time elapsed: 0.004 s
% 0.21/0.38  % (549)Instructions burned: 4 (million)
% 0.21/0.38  TRYING [1,4]
% 0.21/0.38  % (549)------------------------------
% 0.21/0.38  % (549)------------------------------
% 0.21/0.38  TRYING [1,5]
% 0.21/0.38  % (554)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (554)------------------------------
% 0.21/0.38  % (554)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (554)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (554)Memory used [KB]: 733
% 0.21/0.38  % (554)Time elapsed: 0.004 s
% 0.21/0.38  % (554)Instructions burned: 3 (million)
% 0.21/0.38  % (548)Success in time 0.019 s
%------------------------------------------------------------------------------