TSTP Solution File: SET143^3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET143^3 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n021.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 03:09:13 EDT 2024

% Result   : Theorem 0.14s 0.32s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   59 (  20 unt;  18 typ;   0 def)
%            Number of atoms       :  382 (  74 equ;   0 cnn)
%            Maximal formula atoms :    5 (   9 avg)
%            Number of connectives :  278 (  11   ~;  33   |;  45   &; 188   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  85   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;   3 con; 0-3 aty)
%            Number of variables   :   44 (  28   ^   9   !;   6   ?;  44   :)
%                                         (   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_30,type,
    sK2: $i > $o ).

thf(func_def_32,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(f86,plain,
    $false,
    inference(trivial_inequality_removal,[],[f85]) ).

thf(f85,plain,
    $false = $true,
    inference(superposition,[],[f83,f79]) ).

thf(f79,plain,
    ( $true
    = ( sK2 @ sK5 ) ),
    inference(duplicate_literal_removal,[],[f77]) ).

thf(f77,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ( $true
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f75]) ).

thf(f75,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ( $true
      = ( ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f61]) ).

thf(f61,plain,
    ( ( $true
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $true
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f53]) ).

thf(f53,plain,
    ( ( $true
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $true
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f52]) ).

thf(f52,plain,
    ( ( ( sK0 @ sK5 )
      & ( sK1 @ sK5 )
      & ( sK2 @ sK5 ) )
   != ( ( sK0 @ sK5 )
      & ( sK1 @ sK5 )
      & ( sK2 @ sK5 ) ) ),
    inference(beta_eta_normalization,[],[f51]) ).

thf(f51,plain,
    ( ( ^ [Y0: $i] :
          ( ( sK0 @ Y0 )
          & ( sK1 @ Y0 )
          & ( sK2 @ Y0 ) )
      @ sK5 )
   != ( ^ [Y0: $i] :
          ( ( sK0 @ Y0 )
          & ( sK1 @ Y0 )
          & ( sK2 @ Y0 ) )
      @ sK5 ) ),
    inference(negative_extensionality,[],[f50]) ).

thf(f50,plain,
    ( ( ^ [Y0: $i] :
          ( ( sK0 @ Y0 )
          & ( sK1 @ Y0 )
          & ( sK2 @ Y0 ) ) )
   != ( ^ [Y0: $i] :
          ( ( sK0 @ Y0 )
          & ( sK1 @ Y0 )
          & ( sK2 @ Y0 ) ) ) ),
    inference(beta_eta_normalization,[],[f49]) ).

thf(f49,plain,
    ( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) )
      @ sK2
      @ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
            ( ( Y1 @ Y2 )
            & ( Y0 @ Y2 ) )
        @ sK1
        @ sK0 ) )
   != ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) )
      @ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
            ( ( Y1 @ Y2 )
            & ( Y0 @ Y2 ) )
        @ sK2
        @ sK1 )
      @ sK0 ) ),
    inference(definition_unfolding,[],[f47,f48,f48,f48,f48]) ).

thf(f48,plain,
    ( intersection
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f21]) ).

thf(f21,plain,
    ( intersection
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f20]) ).

thf(f20,plain,
    ( intersection
    = ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
          ( ( X0 @ X2 )
          & ( X1 @ X2 ) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,axiom,
    ( intersection
    = ( ^ [X0: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X0 @ X3 )
          & ( X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).

thf(f47,plain,
    ( ( intersection @ ( intersection @ sK2 @ sK1 ) @ sK0 )
   != ( intersection @ sK2 @ ( intersection @ sK1 @ sK0 ) ) ),
    inference(cnf_transformation,[],[f46]) ).

thf(f46,plain,
    ( ( intersection @ ( intersection @ sK2 @ sK1 ) @ sK0 )
   != ( intersection @ sK2 @ ( intersection @ sK1 @ sK0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f44,f45]) ).

thf(f45,plain,
    ( ? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
        ( ( intersection @ ( intersection @ X2 @ X1 ) @ X0 )
       != ( intersection @ X2 @ ( intersection @ X1 @ X0 ) ) )
   => ( ( intersection @ ( intersection @ sK2 @ sK1 ) @ sK0 )
     != ( intersection @ sK2 @ ( intersection @ sK1 @ sK0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f44,plain,
    ? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
      ( ( intersection @ ( intersection @ X2 @ X1 ) @ X0 )
     != ( intersection @ X2 @ ( intersection @ X1 @ X0 ) ) ),
    inference(ennf_transformation,[],[f43]) ).

thf(f43,plain,
    ~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
        ( ( intersection @ ( intersection @ X2 @ X1 ) @ X0 )
        = ( intersection @ X2 @ ( intersection @ X1 @ X0 ) ) ),
    inference(rectify,[],[f16]) ).

thf(f16,negated_conjecture,
    ~ ! [X4: $i > $o,X2: $i > $o,X0: $i > $o] :
        ( ( intersection @ ( intersection @ X0 @ X2 ) @ X4 )
        = ( intersection @ X0 @ ( intersection @ X2 @ X4 ) ) ),
    inference(negated_conjecture,[],[f15]) ).

thf(f15,conjecture,
    ! [X4: $i > $o,X2: $i > $o,X0: $i > $o] :
      ( ( intersection @ ( intersection @ X0 @ X2 ) @ X4 )
      = ( intersection @ X0 @ ( intersection @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(f83,plain,
    ( $false
    = ( sK2 @ sK5 ) ),
    inference(trivial_inequality_removal,[],[f82]) ).

thf(f82,plain,
    ( ( $false
      = ( sK2 @ sK5 ) )
    | ( $false = $true ) ),
    inference(forward_demodulation,[],[f81,f67]) ).

thf(f67,plain,
    ( $true
    = ( sK0 @ sK5 ) ),
    inference(duplicate_literal_removal,[],[f66]) ).

thf(f66,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( sK0 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f64]) ).

thf(f64,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f62]) ).

thf(f62,plain,
    ( ( $true
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $true
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f53]) ).

thf(f81,plain,
    ( ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( sK0 @ sK5 ) ) ),
    inference(trivial_inequality_removal,[],[f80]) ).

thf(f80,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( $false = $true ) ),
    inference(forward_demodulation,[],[f60,f74]) ).

thf(f74,plain,
    ( $true
    = ( sK1 @ sK5 ) ),
    inference(duplicate_literal_removal,[],[f73]) ).

thf(f73,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( $true
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f68]) ).

thf(f68,plain,
    ( ( $true
      = ( ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $true
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f63]) ).

thf(f63,plain,
    ( ( $true
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( $true
      = ( ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f62]) ).

thf(f60,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( sK0 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f59]) ).

thf(f59,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ( $false
      = ( sK0 @ sK5 ) )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f58]) ).

thf(f58,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( sK0 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f57]) ).

thf(f57,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( $false
      = ( sK0 @ sK5 ) )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f56]) ).

thf(f56,plain,
    ( ( $false
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $false
      = ( sK0 @ sK5 ) )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f55]) ).

thf(f55,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ( $false
      = ( ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f54]) ).

thf(f54,plain,
    ( ( $false
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem    : SET143^3 : TPTP v8.2.0. Released v3.6.0.
% 0.04/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.09/0.30  % Computer : n021.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Mon May 20 12:26:38 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.09/0.30  This is a TH0_THM_EQU_NAR problem
% 0.09/0.30  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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.31  % (32429)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)
% 0.14/0.31  % (32428)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.31  % (32426)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)
% 0.14/0.31  % (32427)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)
% 0.14/0.31  % (32425)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.31  % (32430)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)
% 0.14/0.32  % (32431)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.32  % (32428)Instruction limit reached!
% 0.14/0.32  % (32428)------------------------------
% 0.14/0.32  % (32428)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32  % (32428)Termination reason: Unknown
% 0.14/0.32  % (32428)Termination phase: Preprocessing 3
% 0.14/0.32  
% 0.14/0.32  % (32428)Memory used [KB]: 1023
% 0.14/0.32  % (32428)Time elapsed: 0.003 s
% 0.14/0.32  % (32428)Instructions burned: 3 (million)
% 0.14/0.32  % (32428)------------------------------
% 0.14/0.32  % (32428)------------------------------
% 0.14/0.32  % (32429)Instruction limit reached!
% 0.14/0.32  % (32429)------------------------------
% 0.14/0.32  % (32429)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32  % (32429)Termination reason: Unknown
% 0.14/0.32  % (32429)Termination phase: Property scanning
% 0.14/0.32  
% 0.14/0.32  % (32429)Memory used [KB]: 1023
% 0.14/0.32  % (32429)Time elapsed: 0.003 s
% 0.14/0.32  % (32429)Instructions burned: 3 (million)
% 0.14/0.32  % (32429)------------------------------
% 0.14/0.32  % (32429)------------------------------
% 0.14/0.32  % (32432)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)
% 0.14/0.32  % (32426)Instruction limit reached!
% 0.14/0.32  % (32426)------------------------------
% 0.14/0.32  % (32426)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32  % (32426)Termination reason: Unknown
% 0.14/0.32  % (32426)Termination phase: Saturation
% 0.14/0.32  
% 0.14/0.32  % (32426)Memory used [KB]: 5500
% 0.14/0.32  % (32426)Time elapsed: 0.004 s
% 0.14/0.32  % (32426)Instructions burned: 4 (million)
% 0.14/0.32  % (32426)------------------------------
% 0.14/0.32  % (32426)------------------------------
% 0.14/0.32  % (32432)Instruction limit reached!
% 0.14/0.32  % (32432)------------------------------
% 0.14/0.32  % (32432)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32  % (32432)Termination reason: Unknown
% 0.14/0.32  % (32432)Termination phase: Clausification
% 0.14/0.32  
% 0.14/0.32  % (32432)Memory used [KB]: 1023
% 0.14/0.32  % (32432)Time elapsed: 0.003 s
% 0.14/0.32  % (32432)Instructions burned: 3 (million)
% 0.14/0.32  % (32432)------------------------------
% 0.14/0.32  % (32432)------------------------------
% 0.14/0.32  % (32430)First to succeed.
% 0.14/0.32  % (32425)Also succeeded, but the first one will report.
% 0.14/0.32  % (32430)Refutation found. Thanks to Tanya!
% 0.14/0.32  % SZS status Theorem for theBenchmark
% 0.14/0.32  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.32  % (32430)------------------------------
% 0.14/0.32  % (32430)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32  % (32430)Termination reason: Refutation
% 0.14/0.32  
% 0.14/0.32  % (32430)Memory used [KB]: 5500
% 0.14/0.32  % (32430)Time elapsed: 0.005 s
% 0.14/0.32  % (32430)Instructions burned: 4 (million)
% 0.14/0.32  % (32430)------------------------------
% 0.14/0.32  % (32430)------------------------------
% 0.14/0.32  % (32424)Success in time 0.005 s
% 0.14/0.32  % Vampire---4.8 exiting
%------------------------------------------------------------------------------