TSTP Solution File: SET606^3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET606^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n015.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 03:12:21 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   60 (  23 unt;  17 typ;   0 def)
%            Number of atoms       :  334 (  71 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :  266 (  38   ~;  28   |;  39   &; 160   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  85   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  18 usr;   3 con; 0-3 aty)
%            Number of variables   :   48 (  37   ^   6   !;   4   ?;  48   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_0,type,
    in: $i > ( $i > $o ) > $o ).

thf(func_def_2,type,
    is_a: $i > ( $i > $o ) > $o ).

thf(func_def_3,type,
    emptyset: $i > $o ).

thf(func_def_4,type,
    unord_pair: $i > $i > $i > $o ).

thf(func_def_5,type,
    singleton: $i > $i > $o ).

thf(func_def_6,type,
    union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_7,type,
    excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_8,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_9,type,
    setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_10,type,
    complement: ( $i > $o ) > $i > $o ).

thf(func_def_11,type,
    disjoint: ( $i > $o ) > ( $i > $o ) > $o ).

thf(func_def_12,type,
    subset: ( $i > $o ) > ( $i > $o ) > $o ).

thf(func_def_13,type,
    meets: ( $i > $o ) > ( $i > $o ) > $o ).

thf(func_def_14,type,
    misses: ( $i > $o ) > ( $i > $o ) > $o ).

thf(func_def_28,type,
    sK0: $i > $o ).

thf(func_def_29,type,
    sK1: $i > $o ).

thf(func_def_31,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(f82,plain,
    $false,
    inference(trivial_inequality_removal,[],[f81]) ).

thf(f81,plain,
    $true = $false,
    inference(forward_demodulation,[],[f80,f78]) ).

thf(f78,plain,
    ( ( sK1 @ sK4 )
    = $false ),
    inference(trivial_inequality_removal,[],[f77]) ).

thf(f77,plain,
    ( ( $true = $false )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(forward_demodulation,[],[f71,f76]) ).

thf(f76,plain,
    ( ( sK0 @ sK4 )
    = $true ),
    inference(duplicate_literal_removal,[],[f73]) ).

thf(f73,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f64]) ).

thf(f64,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f54]) ).

thf(f54,plain,
    ( ( $true
      = ( ~ ( ( sK1 @ sK4 )
            & ( sK0 @ sK4 ) )
        & ( sK0 @ sK4 ) ) )
    | ( ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f53]) ).

thf(f53,plain,
    ( ( ~ ( sK1 @ sK4 )
      & ( sK0 @ sK4 ) )
   != ( ~ ( ( sK1 @ sK4 )
          & ( sK0 @ sK4 ) )
      & ( sK0 @ sK4 ) ) ),
    inference(beta_eta_normalization,[],[f52]) ).

thf(f52,plain,
    ( ( ^ [Y0: $i] :
          ( ~ ( sK1 @ Y0 )
          & ( sK0 @ Y0 ) )
      @ sK4 )
   != ( ^ [Y0: $i] :
          ( ~ ( ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
          & ( sK0 @ Y0 ) )
      @ sK4 ) ),
    inference(negative_extensionality,[],[f51]) ).

thf(f51,plain,
    ( ( ^ [Y0: $i] :
          ( ~ ( sK1 @ Y0 )
          & ( sK0 @ Y0 ) ) )
   != ( ^ [Y0: $i] :
          ( ~ ( ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
          & ( sK0 @ Y0 ) ) ) ),
    inference(beta_eta_normalization,[],[f50]) ).

thf(f50,plain,
    ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ~ ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) )
      @ sK0
      @ sK1 )
   != ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ~ ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) )
      @ sK0
      @ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
            ( ( Y1 @ Y2 )
            & ( Y0 @ Y2 ) )
        @ sK0
        @ sK1 ) ) ),
    inference(definition_unfolding,[],[f48,f47,f47,f49]) ).

thf(f49,plain,
    ( intersection
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f42]) ).

thf(f42,plain,
    ( intersection
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f41]) ).

thf(f41,plain,
    ( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
          ( ( X0 @ X2 )
          & ( X1 @ X2 ) ) )
    = intersection ),
    inference(rectify,[],[f8]) ).

thf(f8,axiom,
    ( ( ^ [X0: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X0 @ X3 )
          & ( X2 @ X3 ) ) )
    = intersection ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).

thf(f47,plain,
    ( setminus
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ~ ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f24,plain,
    ( setminus
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ~ ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f23]) ).

thf(f23,plain,
    ( setminus
    = ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
          ( ( X0 @ X2 )
          & ~ ( X1 @ X2 ) ) ) ),
    inference(rectify,[],[f9]) ).

thf(f9,axiom,
    ( setminus
    = ( ^ [X0: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X0 @ X3 )
          & ~ ( X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminus) ).

thf(f48,plain,
    ( ( setminus @ sK0 @ sK1 )
   != ( setminus @ sK0 @ ( intersection @ sK0 @ sK1 ) ) ),
    inference(cnf_transformation,[],[f46]) ).

thf(f46,plain,
    ( ( setminus @ sK0 @ sK1 )
   != ( setminus @ sK0 @ ( intersection @ sK0 @ sK1 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f44,f45]) ).

thf(f45,plain,
    ( ? [X0: $i > $o,X1: $i > $o] :
        ( ( setminus @ X0 @ X1 )
       != ( setminus @ X0 @ ( intersection @ X0 @ X1 ) ) )
   => ( ( setminus @ sK0 @ sK1 )
     != ( setminus @ sK0 @ ( intersection @ sK0 @ sK1 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f44,plain,
    ? [X0: $i > $o,X1: $i > $o] :
      ( ( setminus @ X0 @ X1 )
     != ( setminus @ X0 @ ( intersection @ X0 @ X1 ) ) ),
    inference(ennf_transformation,[],[f43]) ).

thf(f43,plain,
    ~ ! [X0: $i > $o,X1: $i > $o] :
        ( ( setminus @ X0 @ X1 )
        = ( setminus @ X0 @ ( intersection @ X0 @ X1 ) ) ),
    inference(rectify,[],[f16]) ).

thf(f16,negated_conjecture,
    ~ ! [X0: $i > $o,X2: $i > $o] :
        ( ( setminus @ X0 @ ( intersection @ X0 @ X2 ) )
        = ( setminus @ X0 @ X2 ) ),
    inference(negated_conjecture,[],[f15]) ).

thf(f15,conjecture,
    ! [X0: $i > $o,X2: $i > $o] :
      ( ( setminus @ X0 @ ( intersection @ X0 @ X2 ) )
      = ( setminus @ X0 @ X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(f71,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f70]) ).

thf(f70,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f69]) ).

thf(f69,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( $true
      = ( ~ ( sK1 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f68]) ).

thf(f68,plain,
    ( ( ( ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $false )
    | ( $true
      = ( ~ ( sK1 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f66]) ).

thf(f66,plain,
    ( ( ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $true )
    | ( ( ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $false ) ),
    inference(not_proxy_clausification,[],[f65]) ).

thf(f65,plain,
    ( ( ( ~ ( ( sK1 @ sK4 )
            & ( sK0 @ sK4 ) ) )
      = $true )
    | ( ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f54]) ).

thf(f80,plain,
    ( ( sK1 @ sK4 )
    = $true ),
    inference(trivial_inequality_removal,[],[f79]) ).

thf(f79,plain,
    ( ( $true = $false )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(forward_demodulation,[],[f63,f76]) ).

thf(f63,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f62]) ).

thf(f62,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f60]) ).

thf(f60,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $false )
    | ( ( ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $true ) ),
    inference(not_proxy_clausification,[],[f59]) ).

thf(f59,plain,
    ( ( $false
      = ( ~ ( sK1 @ sK4 ) ) )
    | ( ( ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $true )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f58]) ).

thf(f58,plain,
    ( ( ( ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $true )
    | ( $false
      = ( ~ ( sK1 @ sK4 ) ) )
    | ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f57]) ).

thf(f57,plain,
    ( ( ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $false )
    | ( ( ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $true )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f56]) ).

thf(f56,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( ~ ( ( sK1 @ sK4 )
            & ( sK0 @ sK4 ) ) )
      = $false )
    | ( ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f55]) ).

thf(f55,plain,
    ( ( $false
      = ( ~ ( ( sK1 @ sK4 )
            & ( sK0 @ sK4 ) )
        & ( sK0 @ sK4 ) ) )
    | ( ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SET606^3 : TPTP v8.2.0. Released v3.6.0.
% 0.08/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36  % Computer : n015.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 20 12:09:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  This is a TH0_THM_EQU_NAR problem
% 0.14/0.37  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39  % (19264)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.39  % (19266)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.39  % (19267)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39  % (19265)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.39  % (19268)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39  % (19269)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.39  % (19271)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.39  % (19270)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.39  % (19267)Instruction limit reached!
% 0.14/0.39  % (19267)------------------------------
% 0.14/0.39  % (19267)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (19267)Termination reason: Unknown
% 0.14/0.39  % (19267)Termination phase: shuffling
% 0.14/0.39  
% 0.14/0.39  % (19267)Memory used [KB]: 895
% 0.14/0.39  % (19267)Time elapsed: 0.003 s
% 0.14/0.39  % (19267)Instructions burned: 2 (million)
% 0.14/0.39  % (19267)------------------------------
% 0.14/0.39  % (19267)------------------------------
% 0.14/0.39  % (19268)Instruction limit reached!
% 0.14/0.39  % (19268)------------------------------
% 0.14/0.39  % (19268)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (19268)Termination reason: Unknown
% 0.14/0.39  % (19268)Termination phase: shuffling
% 0.14/0.39  
% 0.14/0.39  % (19268)Memory used [KB]: 895
% 0.14/0.39  % (19268)Time elapsed: 0.003 s
% 0.14/0.39  % (19268)Instructions burned: 2 (million)
% 0.14/0.39  % (19268)------------------------------
% 0.14/0.39  % (19268)------------------------------
% 0.14/0.39  % (19271)Instruction limit reached!
% 0.14/0.39  % (19271)------------------------------
% 0.14/0.39  % (19271)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (19271)Termination reason: Unknown
% 0.14/0.39  % (19271)Termination phase: shuffling
% 0.14/0.39  
% 0.14/0.39  % (19271)Memory used [KB]: 1023
% 0.14/0.39  % (19271)Time elapsed: 0.004 s
% 0.14/0.39  % (19271)Instructions burned: 3 (million)
% 0.14/0.39  % (19271)------------------------------
% 0.14/0.39  % (19271)------------------------------
% 0.14/0.39  % (19265)Instruction limit reached!
% 0.14/0.39  % (19265)------------------------------
% 0.14/0.39  % (19265)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (19265)Termination reason: Unknown
% 0.14/0.39  % (19265)Termination phase: Saturation
% 0.14/0.39  
% 0.14/0.39  % (19265)Memory used [KB]: 5500
% 0.14/0.39  % (19265)Time elapsed: 0.005 s
% 0.14/0.39  % (19265)Instructions burned: 4 (million)
% 0.14/0.39  % (19265)------------------------------
% 0.14/0.39  % (19265)------------------------------
% 0.14/0.39  % (19269)First to succeed.
% 0.14/0.39  % (19264)Also succeeded, but the first one will report.
% 0.14/0.39  % (19269)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (19269)------------------------------
% 0.14/0.39  % (19269)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (19269)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (19269)Memory used [KB]: 5500
% 0.14/0.39  % (19269)Time elapsed: 0.006 s
% 0.14/0.39  % (19269)Instructions burned: 4 (million)
% 0.14/0.39  % (19269)------------------------------
% 0.14/0.39  % (19269)------------------------------
% 0.14/0.39  % (19263)Success in time 0.006 s
% 0.14/0.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------