TSTP Solution File: PUZ149_13 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : PUZ149_13 : 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 : n023.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 08:50:53 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   59 (   7 unt;  21 typ;   0 def)
%            Number of atoms       :  113 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  127 (  52   ~;  35   |;  28   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   12 (  10   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-1 aty)
%            Number of variables   :   52 (  33   !;  19   ?;  52   :)

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

tff(type_def_6,type,
    '$ki_index': $tType ).

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

tff(func_def_1,type,
    '#idx(make_c)': '$ki_index' ).

tff(func_def_2,type,
    '#idx(pour_b)': '$ki_index' ).

tff(func_def_3,type,
    '#idx(pour_a)': '$ki_index' ).

tff(func_def_4,type,
    sK4: '$ki_world' > '$ki_world' ).

tff(func_def_5,type,
    sK5: '$ki_world' ).

tff(func_def_6,type,
    sK6: '$ki_world' > '$ki_world' ).

tff(func_def_7,type,
    sK7: '$ki_world' ).

tff(func_def_8,type,
    sK8: '$ki_world' > '$ki_world' ).

tff(func_def_9,type,
    sK9: '$ki_world' ).

tff(func_def_10,type,
    sK10: '$ki_world' > '$ki_world' ).

tff(func_def_11,type,
    sK11: '$ki_world' ).

tff(func_def_12,type,
    sK12: '$ki_world' ).

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

tff(pred_def_2,type,
    acid: '$ki_world' > $o ).

tff(pred_def_3,type,
    sP0: '$ki_world' > $o ).

tff(pred_def_4,type,
    sP1: '$ki_world' > $o ).

tff(pred_def_5,type,
    sP2: '$ki_world' > $o ).

tff(pred_def_6,type,
    sP3: '$ki_world' > $o ).

tff(f93,plain,
    $false,
    inference(subsumption_resolution,[],[f92,f73]) ).

tff(f73,plain,
    acid(sK12),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,plain,
    ( acid(sK12)
    & '$ki_accessible'('#idx(make_c)','$ki_local_world',sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f6,f52]) ).

tff(f52,plain,
    ( ? [X0: '$ki_world'] :
        ( acid(X0)
        & '$ki_accessible'('#idx(make_c)','$ki_local_world',X0) )
   => ( acid(sK12)
      & '$ki_accessible'('#idx(make_c)','$ki_local_world',sK12) ) ),
    introduced(choice_axiom,[]) ).

tff(f6,axiom,
    ? [X0: '$ki_world'] :
      ( acid(X0)
      & '$ki_accessible'('#idx(make_c)','$ki_local_world',X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',make_c_acid) ).

tff(f92,plain,
    ~ acid(sK12),
    inference(resolution,[],[f91,f72]) ).

tff(f72,plain,
    '$ki_accessible'('#idx(make_c)','$ki_local_world',sK12),
    inference(cnf_transformation,[],[f53]) ).

tff(f91,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(make_c)','$ki_local_world',X0)
      | ~ acid(X0) ),
    inference(subsumption_resolution,[],[f65,f85]) ).

tff(f85,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',sK9)
      | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f84,f83]) ).

tff(f83,plain,
    acid(sK8(sK9)),
    inference(resolution,[],[f81,f64]) ).

tff(f64,plain,
    ! [X0: '$ki_world'] :
      ( ~ sP2(X0)
      | acid(sK8(X0)) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X0: '$ki_world'] :
      ( ( acid(sK8(X0))
        & '$ki_accessible'('#idx(pour_b)',X0,sK8(X0)) )
      | ~ sP2(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f40,f41]) ).

tff(f41,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1: '$ki_world'] :
          ( acid(X1)
          & '$ki_accessible'('#idx(pour_b)',X0,X1) )
     => ( acid(sK8(X0))
        & '$ki_accessible'('#idx(pour_b)',X0,sK8(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f40,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1: '$ki_world'] :
          ( acid(X1)
          & '$ki_accessible'('#idx(pour_b)',X0,X1) )
      | ~ sP2(X0) ),
    inference(nnf_transformation,[],[f24]) ).

tff(f24,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1: '$ki_world'] :
          ( acid(X1)
          & '$ki_accessible'('#idx(pour_b)',X0,X1) )
      | ~ sP2(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

tff(f81,plain,
    sP2(sK9),
    inference(subsumption_resolution,[],[f80,f73]) ).

tff(f80,plain,
    ( ~ acid(sK12)
    | sP2(sK9) ),
    inference(resolution,[],[f66,f72]) ).

tff(f66,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(make_c)','$ki_local_world',X0)
      | ~ acid(X0)
      | sP2(sK9) ),
    inference(cnf_transformation,[],[f45]) ).

tff(f45,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ acid(X0)
        | ~ '$ki_accessible'('#idx(make_c)','$ki_local_world',X0) )
    | ( sP2(sK9)
      & '$ki_accessible'('#idx(pour_a)','$ki_local_world',sK9) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f43,f44]) ).

tff(f44,plain,
    ( ? [X1: '$ki_world'] :
        ( sP2(X1)
        & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X1) )
   => ( sP2(sK9)
      & '$ki_accessible'('#idx(pour_a)','$ki_local_world',sK9) ) ),
    introduced(choice_axiom,[]) ).

tff(f43,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ acid(X0)
        | ~ '$ki_accessible'('#idx(make_c)','$ki_local_world',X0) )
    | ? [X1: '$ki_world'] :
        ( sP2(X1)
        & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X1) ) ),
    inference(rectify,[],[f25]) ).

tff(f25,plain,
    ( ! [X2: '$ki_world'] :
        ( ~ acid(X2)
        | ~ '$ki_accessible'('#idx(make_c)','$ki_local_world',X2) )
    | ? [X0: '$ki_world'] :
        ( sP2(X0)
        & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) ) ),
    inference(definition_folding,[],[f17,f24]) ).

tff(f17,plain,
    ( ! [X2: '$ki_world'] :
        ( ~ acid(X2)
        | ~ '$ki_accessible'('#idx(make_c)','$ki_local_world',X2) )
    | ? [X0: '$ki_world'] :
        ( ? [X1: '$ki_world'] :
            ( acid(X1)
            & '$ki_accessible'('#idx(pour_b)',X0,X1) )
        & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) ) ),
    inference(ennf_transformation,[],[f12]) ).

tff(f12,plain,
    ( ! [X0: '$ki_world'] :
        ( '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0)
       => ! [X1: '$ki_world'] :
            ( '$ki_accessible'('#idx(pour_b)',X0,X1)
           => ~ acid(X1) ) )
   => ! [X2: '$ki_world'] :
        ( '$ki_accessible'('#idx(make_c)','$ki_local_world',X2)
       => ~ acid(X2) ) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ( ! [X0: '$ki_world'] :
        ( '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0)
       => ! [X1: '$ki_world'] :
            ( '$ki_accessible'('#idx(pour_b)',X0,X1)
           => ~ acid(X1) ) )
   => ! [X0: '$ki_world'] :
        ( '$ki_accessible'('#idx(make_c)','$ki_local_world',X0)
       => ~ acid(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pour_ab_make_axiom_2) ).

tff(f84,plain,
    ! [X0: '$ki_world'] :
      ( ~ acid(sK8(sK9))
      | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',sK9)
      | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) ),
    inference(resolution,[],[f82,f74]) ).

tff(f74,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(pour_b)',X0,X1)
      | ~ acid(X1)
      | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0)
      | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X2) ),
    inference(subsumption_resolution,[],[f54,f71]) ).

tff(f71,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0)
      | ~ acid(X0) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ! [X0: '$ki_world'] :
      ( ~ acid(X0)
      | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f5]) ).

tff(f5,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0)
     => ~ acid(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pour_a_acid) ).

tff(f54,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
      ( ~ acid(X1)
      | ~ '$ki_accessible'('#idx(pour_b)',X0,X1)
      | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0)
      | acid(X2)
      | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X2) ),
    inference(cnf_transformation,[],[f14]) ).

tff(f14,plain,
    ( ! [X0: '$ki_world'] :
        ( ! [X1: '$ki_world'] :
            ( ~ acid(X1)
            | ~ '$ki_accessible'('#idx(pour_b)',X0,X1) )
        | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) )
    | ! [X2: '$ki_world'] :
        ( acid(X2)
        | ~ '$ki_accessible'('#idx(pour_a)','$ki_local_world',X2) ) ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,plain,
    ~ ( ? [X0: '$ki_world'] :
          ( ? [X1: '$ki_world'] :
              ( acid(X1)
              & '$ki_accessible'('#idx(pour_b)',X0,X1) )
          & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) )
      & ? [X2: '$ki_world'] :
          ( ~ acid(X2)
          & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X2) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,negated_conjecture,
    ~ ( ? [X0: '$ki_world'] :
          ( ? [X1: '$ki_world'] :
              ( acid(X1)
              & '$ki_accessible'('#idx(pour_b)',X0,X1) )
          & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) )
      & ? [X0: '$ki_world'] :
          ( ~ acid(X0)
          & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) ) ),
    inference(negated_conjecture,[],[f7]) ).

tff(f7,conjecture,
    ( ? [X0: '$ki_world'] :
        ( ? [X1: '$ki_world'] :
            ( acid(X1)
            & '$ki_accessible'('#idx(pour_b)',X0,X1) )
        & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) )
    & ? [X0: '$ki_world'] :
        ( ~ acid(X0)
        & '$ki_accessible'('#idx(pour_a)','$ki_local_world',X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f82,plain,
    '$ki_accessible'('#idx(pour_b)',sK9,sK8(sK9)),
    inference(resolution,[],[f81,f63]) ).

tff(f63,plain,
    ! [X0: '$ki_world'] :
      ( ~ sP2(X0)
      | '$ki_accessible'('#idx(pour_b)',X0,sK8(X0)) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f65,plain,
    ! [X0: '$ki_world'] :
      ( ~ acid(X0)
      | ~ '$ki_accessible'('#idx(make_c)','$ki_local_world',X0)
      | '$ki_accessible'('#idx(pour_a)','$ki_local_world',sK9) ),
    inference(cnf_transformation,[],[f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12  % Problem    : PUZ149_13 : TPTP v8.2.0. Released v8.2.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n023.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 18:07:08 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (14307)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (14312)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (14308)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  % (14309)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (14311)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38  % (14310)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)
% 0.14/0.38  % (14313)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  % (14314)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)
% 0.14/0.38  % (14312)First to succeed.
% 0.14/0.38  Detected minimum model sizes of [1,1]
% 0.14/0.38  Detected maximum model sizes of [max,3]
% 0.14/0.38  TRYING [1,1]
% 0.14/0.38  % (14313)Also succeeded, but the first one will report.
% 0.14/0.38  Detected minimum model sizes of [1,1]
% 0.14/0.38  Detected maximum model sizes of [10,3]
% 0.14/0.38  Detected minimum model sizes of [1,1]
% 0.14/0.38  Detected minimum model sizes of [1,1]
% 0.14/0.38  TRYING [1,1]
% 0.14/0.38  Detected maximum model sizes of [max,3]
% 0.14/0.38  Detected maximum model sizes of [10,3]
% 0.14/0.38  TRYING [1,1]
% 0.14/0.38  TRYING [1,1]
% 0.14/0.38  % (14310)Also succeeded, but the first one will report.
% 0.14/0.38  TRYING [2,1]
% 0.14/0.38  TRYING [2,1]
% 0.14/0.38  % (14312)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14307"
% 0.14/0.38  TRYING [2,1]
% 0.14/0.38  TRYING [2,1]
% 0.14/0.38  TRYING [1,2]
% 0.14/0.38  TRYING [1,2]
% 0.14/0.38  TRYING [1,2]
% 0.14/0.38  % (14312)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (14312)------------------------------
% 0.14/0.38  % (14312)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (14312)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (14312)Memory used [KB]: 756
% 0.14/0.38  % (14312)Time elapsed: 0.004 s
% 0.14/0.38  % (14312)Instructions burned: 4 (million)
% 0.14/0.38  % (14307)Success in time 0.02 s
%------------------------------------------------------------------------------