TSTP Solution File: DAT334_19 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT334_19 : 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 : 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 : Sun May  5 05:06:25 EDT 2024

% Result   : Theorem 0.12s 0.36s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   38 (   7 unt;  10 typ;   0 def)
%            Number of atoms       :  129 (   0 equ)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   77 (  24   ~;  16   |;  30   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   48 (  48 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  11 usr;   7 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :   33 (  22   !;  11   ?;  20   :)

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

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

tff(func_def_7,type,
    sK2: '$ki_world' ).

tff(func_def_8,type,
    sK3: '$ki_world' > $i ).

tff(func_def_9,type,
    sK4: '$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(pred_def_5,type,
    sP1: '$ki_world' > $o ).

tff(f43,plain,
    $false,
    inference(subsumption_resolution,[],[f42,f40]) ).

tff(f40,plain,
    '$ki_exists_in_world_$i'(sK2,sK3(sK2)),
    inference(resolution,[],[f30,f36]) ).

tff(f36,plain,
    sP0(sK2),
    inference(resolution,[],[f35,f27]) ).

tff(f27,plain,
    ! [X0: '$ki_world'] :
      ( ~ sP1(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,plain,
    ! [X0: '$ki_world'] :
      ( ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & sP0(X0)
        & teach(X0,john,math) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f14]) ).

tff(f14,plain,
    ! [X0: '$ki_world'] :
      ( ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & sP0(X0)
        & teach(X0,john,math) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f35,plain,
    sP1(sK2),
    inference(resolution,[],[f32,f24]) ).

tff(f24,plain,
    '$ki_accessible'('$ki_local_world',sK2),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ( ! [X1] :
        ( ~ teach(sK2,X1,cs)
        | ~ '$ki_exists_in_world_$i'(sK2,X1) )
    & '$ki_accessible'('$ki_local_world',sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f9,f16]) ).

tff(f16,plain,
    ( ? [X0: '$ki_world'] :
        ( ! [X1] :
            ( ~ teach(X0,X1,cs)
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ! [X1] :
          ( ~ teach(sK2,X1,cs)
          | ~ '$ki_exists_in_world_$i'(sK2,X1) )
      & '$ki_accessible'('$ki_local_world',sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f9,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,[],[f6]) ).

tff(f6,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X1] :
            ( teach(X0,X1,cs)
            & '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,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,[],[f4]) ).

tff(f4,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(f32,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | sP1(X0) ),
    inference(cnf_transformation,[],[f15]) ).

tff(f15,plain,
    ! [X0: '$ki_world'] :
      ( sP1(X0)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(definition_folding,[],[f10,f14,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(f10,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,[],[f7]) ).

tff(f7,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,[],[f3]) ).

tff(f3,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(f30,plain,
    ! [X0: '$ki_world'] :
      ( ~ sP0(X0)
      | '$ki_exists_in_world_$i'(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f21]) ).

tff(f21,plain,
    ! [X0: '$ki_world'] :
      ( ( teach(X0,sK3(X0),cs)
        & '$ki_exists_in_world_$i'(X0,sK3(X0)) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f19,f20]) ).

tff(f20,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( teach(X0,X1,cs)
          & '$ki_exists_in_world_$i'(X0,X1) )
     => ( teach(X0,sK3(X0),cs)
        & '$ki_exists_in_world_$i'(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( teach(X0,X1,cs)
          & '$ki_exists_in_world_$i'(X0,X1) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f13]) ).

tff(f42,plain,
    ~ '$ki_exists_in_world_$i'(sK2,sK3(sK2)),
    inference(resolution,[],[f41,f25]) ).

tff(f25,plain,
    ! [X1: $i] :
      ( ~ teach(sK2,X1,cs)
      | ~ '$ki_exists_in_world_$i'(sK2,X1) ),
    inference(cnf_transformation,[],[f17]) ).

tff(f41,plain,
    teach(sK2,sK3(sK2),cs),
    inference(resolution,[],[f31,f36]) ).

tff(f31,plain,
    ! [X0: '$ki_world'] :
      ( ~ sP0(X0)
      | teach(X0,sK3(X0),cs) ),
    inference(cnf_transformation,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : DAT334_19 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri May  3 13:10:17 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  % (7186)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36  % (7187)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.36  % (7188)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.36  % (7191)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.36  % (7190)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.36  % (7192)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.36  % (7189)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)
% 0.12/0.36  % (7193)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)
% 0.12/0.36  % (7192)Also succeeded, but the first one will report.
% 0.12/0.36  % (7191)First to succeed.
% 0.12/0.36  % (7189)Also succeeded, but the first one will report.
% 0.12/0.36  Detected minimum model sizes of [1,1]
% 0.12/0.36  Detected maximum model sizes of [2,max]
% 0.12/0.36  TRYING [1,1]
% 0.12/0.36  Detected minimum model sizes of [1,1,1]
% 0.12/0.36  Detected maximum model sizes of [2,max,max]
% 0.12/0.36  Detected minimum model sizes of [1,1,1]
% 0.12/0.36  Detected maximum model sizes of [2,max,max]
% 0.12/0.36  TRYING [1,1,1]
% 0.12/0.36  TRYING [1,1,1]
% 0.12/0.36  % (7191)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7186"
% 0.12/0.36  TRYING [2,1]
% 0.12/0.36  Detected minimum model sizes of [1,1]
% 0.12/0.36  TRYING [2,1,1]
% 0.12/0.36  Detected maximum model sizes of [2,max]
% 0.12/0.36  TRYING [2,1,1]
% 0.12/0.36  TRYING [1,1]
% 0.12/0.36  TRYING [1,2]
% 0.12/0.36  TRYING [1,2,2]
% 0.12/0.36  TRYING [2,1]
% 0.12/0.36  TRYING [1,2,2]
% 0.12/0.36  TRYING [2,2]
% 0.12/0.36  TRYING [2,2,2]
% 0.12/0.36  TRYING [2,2,2]
% 0.12/0.36  TRYING [1,2]
% 0.12/0.36  TRYING [2,2]
% 0.12/0.36  % (7191)Refutation found. Thanks to Tanya!
% 0.12/0.36  % SZS status Theorem for theBenchmark
% 0.12/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36  % (7191)------------------------------
% 0.12/0.36  % (7191)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36  % (7191)Termination reason: Refutation
% 0.12/0.36  
% 0.12/0.36  % (7191)Memory used [KB]: 735
% 0.12/0.36  % (7191)Time elapsed: 0.003 s
% 0.12/0.36  % (7191)Instructions burned: 3 (million)
% 0.12/0.36  % (7186)Success in time 0.019 s
%------------------------------------------------------------------------------