TSTP Solution File: LCL962_16 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL962_16 : 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 : n028.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 : Tue May 21 00:37:05 EDT 2024

% Result   : Theorem 0.10s 0.34s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   43 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :   94 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  104 (  44   ~;  33   |;   9   &)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   38 (  33   !;   5   ?;  38   :)

% 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(a)': '$ki_index' ).

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

tff(func_def_3,type,
    sK0: '$ki_world' ).

tff(func_def_4,type,
    sK1: '$ki_world' > '$ki_world' ).

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

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

tff(f54,plain,
    $false,
    inference(subsumption_resolution,[],[f53,f25]) ).

tff(f25,plain,
    '$ki_accessible'('#idx(a)','$ki_local_world',sK0),
    inference(cnf_transformation,[],[f21]) ).

tff(f21,plain,
    ( p(sK0)
    & '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f20]) ).

tff(f20,plain,
    ( ? [X0: '$ki_world'] :
        ( p(X0)
        & '$ki_accessible'('#idx(a)','$ki_local_world',X0) )
   => ( p(sK0)
      & '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f12,plain,
    ? [X0: '$ki_world'] :
      ( p(X0)
      & '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
       => ~ p(X0) ),
    inference(negated_conjecture,[],[f8]) ).

tff(f8,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
     => ~ p(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f53,plain,
    ~ '$ki_accessible'('#idx(a)','$ki_local_world',sK0),
    inference(subsumption_resolution,[],[f52,f26]) ).

tff(f26,plain,
    p(sK0),
    inference(cnf_transformation,[],[f21]) ).

tff(f52,plain,
    ( ~ p(sK0)
    | ~ '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ),
    inference(subsumption_resolution,[],[f51,f43]) ).

tff(f43,plain,
    ~ p(sK1(sK0)),
    inference(subsumption_resolution,[],[f42,f27]) ).

tff(f27,plain,
    ~ p('$ki_local_world'),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    ~ p('$ki_local_world'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_a_axiom_1) ).

tff(f42,plain,
    ( p('$ki_local_world')
    | ~ p(sK1(sK0)) ),
    inference(resolution,[],[f40,f31]) ).

tff(f31,plain,
    ! [X0: '$ki_world'] : '$ki_accessible'('#idx(b)',X0,X0),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    ! [X0: '$ki_world'] : '$ki_accessible'('#idx(b)',X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_reflexive_#idx(b)') ).

tff(f40,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
      | p(X0)
      | ~ p(sK1(sK0)) ),
    inference(resolution,[],[f29,f25]) ).

tff(f29,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
      | ~ p(sK1(X0))
      | p(X2)
      | ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f24,plain,
    ( ! [X0: '$ki_world'] :
        ( ( ~ p(sK1(X0))
          & '$ki_accessible'('#idx(b)',X0,sK1(X0)) )
        | ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) )
    | ! [X2: '$ki_world'] :
        ( p(X2)
        | ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).

tff(f23,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1: '$ki_world'] :
          ( ~ p(X1)
          & '$ki_accessible'('#idx(b)',X0,X1) )
     => ( ~ p(sK1(X0))
        & '$ki_accessible'('#idx(b)',X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f22,plain,
    ( ! [X0: '$ki_world'] :
        ( ? [X1: '$ki_world'] :
            ( ~ p(X1)
            & '$ki_accessible'('#idx(b)',X0,X1) )
        | ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) )
    | ! [X2: '$ki_world'] :
        ( p(X2)
        | ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ) ),
    inference(rectify,[],[f13]) ).

tff(f13,plain,
    ( ! [X1: '$ki_world'] :
        ( ? [X2: '$ki_world'] :
            ( ~ p(X2)
            & '$ki_accessible'('#idx(b)',X1,X2) )
        | ~ '$ki_accessible'('#idx(a)','$ki_local_world',X1) )
    | ! [X0: '$ki_world'] :
        ( p(X0)
        | ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0) ) ),
    inference(ennf_transformation,[],[f10]) ).

tff(f10,plain,
    ( ~ ! [X0: '$ki_world'] :
          ( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
         => p(X0) )
   => ! [X1: '$ki_world'] :
        ( '$ki_accessible'('#idx(a)','$ki_local_world',X1)
       => ~ ! [X2: '$ki_world'] :
              ( '$ki_accessible'('#idx(b)',X1,X2)
             => p(X2) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ( ~ ! [X0: '$ki_world'] :
          ( '$ki_accessible'('#idx(b)','$ki_local_world',X0)
         => p(X0) )
   => ! [X0: '$ki_world'] :
        ( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
       => ~ ! [X3: '$ki_world'] :
              ( '$ki_accessible'('#idx(b)',X0,X3)
             => p(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_2) ).

tff(f51,plain,
    ( p(sK1(sK0))
    | ~ p(sK0)
    | ~ '$ki_accessible'('#idx(a)','$ki_local_world',sK0) ),
    inference(resolution,[],[f49,f32]) ).

tff(f32,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(b)',X0,X1)
      | p(X1)
      | ~ p(X0)
      | ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f15]) ).

tff(f15,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1: '$ki_world'] :
          ( p(X1)
          | ~ '$ki_accessible'('#idx(b)',X0,X1) )
      | ~ p(X0)
      | ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
    inference(flattening,[],[f14]) ).

tff(f14,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1: '$ki_world'] :
          ( p(X1)
          | ~ '$ki_accessible'('#idx(b)',X0,X1) )
      | ~ p(X0)
      | ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f11]) ).

tff(f11,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
     => ( p(X0)
       => ! [X1: '$ki_world'] :
            ( '$ki_accessible'('#idx(b)',X0,X1)
           => p(X1) ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('#idx(a)','$ki_local_world',X0)
     => ( p(X0)
       => ! [X3: '$ki_world'] :
            ( '$ki_accessible'('#idx(b)',X0,X3)
           => p(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_1) ).

tff(f49,plain,
    '$ki_accessible'('#idx(b)',sK0,sK1(sK0)),
    inference(subsumption_resolution,[],[f48,f27]) ).

tff(f48,plain,
    ( p('$ki_local_world')
    | '$ki_accessible'('#idx(b)',sK0,sK1(sK0)) ),
    inference(resolution,[],[f46,f31]) ).

tff(f46,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(b)','$ki_local_world',X0)
      | p(X0)
      | '$ki_accessible'('#idx(b)',sK0,sK1(sK0)) ),
    inference(resolution,[],[f28,f25]) ).

tff(f28,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( ~ '$ki_accessible'('#idx(a)','$ki_local_world',X0)
      | '$ki_accessible'('#idx(b)',X0,sK1(X0))
      | p(X2)
      | ~ '$ki_accessible'('#idx(b)','$ki_local_world',X2) ),
    inference(cnf_transformation,[],[f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : LCL962_16 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32  % Computer : n028.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Mon May 20 01:32:22 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  % (2163)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33  % (2165)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.33  Detected minimum model sizes of [1,1]
% 0.10/0.33  Detected maximum model sizes of [max,2]
% 0.10/0.33  TRYING [1,1]
% 0.10/0.33  TRYING [2,1]
% 0.10/0.33  TRYING [3,1]
% 0.10/0.33  TRYING [2,2]
% 0.10/0.33  TRYING [3,2]
% 0.10/0.33  TRYING [4,1]
% 0.10/0.33  TRYING [4,2]
% 0.10/0.33  % (2168)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.10/0.33  % (2167)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.10/0.33  % (2169)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.10/0.34  % (2166)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)
% 0.10/0.34  Cannot enumerate next child to try in an incomplete setup
% 0.10/0.34  % (2165)Refutation not found, incomplete strategy% (2165)------------------------------
% 0.10/0.34  % (2165)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.34  % (2165)Termination reason: Refutation not found, incomplete strategy
% 0.10/0.34  
% 0.10/0.34  % (2165)Memory used [KB]: 785
% 0.10/0.34  % (2165)Time elapsed: 0.007 s
% 0.10/0.34  % (2165)Instructions burned: 19 (million)
% 0.10/0.34  % (2164)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.34  % (2170)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)
% 0.10/0.34  % (2165)------------------------------
% 0.10/0.34  % (2165)------------------------------
% 0.10/0.34  Detected minimum model sizes of [1,1]
% 0.10/0.34  Detected maximum model sizes of [max,2]
% 0.10/0.34  TRYING [1,1]
% 0.10/0.34  % (2169)Also succeeded, but the first one will report.
% 0.10/0.34  % (2168)First to succeed.
% 0.10/0.34  TRYING [2,1]
% 0.10/0.34  % (2166)Also succeeded, but the first one will report.
% 0.10/0.34  Detected minimum model sizes of [1,1]
% 0.10/0.34  Detected maximum model sizes of [max,2]
% 0.10/0.34  TRYING [3,1]
% 0.10/0.34  TRYING [1,1]
% 0.10/0.34  Detected minimum model sizes of [1,1]
% 0.10/0.34  Detected maximum model sizes of [max,2]
% 0.10/0.34  % (2168)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2163"
% 0.10/0.34  TRYING [1,1]
% 0.10/0.34  TRYING [2,1]
% 0.10/0.34  TRYING [2,1]
% 0.10/0.34  TRYING [3,1]
% 0.10/0.34  % (2168)Refutation found. Thanks to Tanya!
% 0.10/0.34  % SZS status Theorem for theBenchmark
% 0.10/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.34  % (2168)------------------------------
% 0.10/0.34  % (2168)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.34  % (2168)Termination reason: Refutation
% 0.10/0.34  
% 0.10/0.34  % (2168)Memory used [KB]: 749
% 0.10/0.34  % (2168)Time elapsed: 0.003 s
% 0.10/0.34  % (2168)Instructions burned: 3 (million)
% 0.10/0.34  % (2163)Success in time 0.015 s
%------------------------------------------------------------------------------