TSTP Solution File: SEV451^1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV451^1 : TPTP v8.1.2. Released v7.0.0.
% 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 : n009.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 09:43:14 EDT 2024

% Result   : Theorem 0.11s 0.35s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   49 (  12 unt;   9 typ;   0 def)
%            Number of atoms       :  176 (  42 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  233 (  17   ~;  23   |;   0   &; 190   @)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   40 (  40   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   5 con; 0-4 aty)
%            Number of variables   :   70 (   0   ^  60   !;   4   ?;  70   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_6,type,
    sK0: $tType ).

thf(func_def_0,type,
    'const/sets/UNIV': 
      !>[X0: $tType] : ( X0 > $o ) ).

thf(func_def_1,type,
    'const/sets/UNION': 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).

thf(func_def_2,type,
    'const/sets/IN': 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).

thf(func_def_4,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_12,type,
    sK1: sK0 > $o ).

thf(func_def_14,type,
    sK3: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_15,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(func_def_16,type,
    sK5: sK0 ).

thf(f163,plain,
    $false,
    inference(avatar_sat_refutation,[],[f64,f78,f160]) ).

thf(f160,plain,
    ~ spl2_4,
    inference(avatar_contradiction_clause,[],[f159]) ).

thf(f159,plain,
    ( $false
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f148]) ).

thf(f148,plain,
    ( ( $false = $true )
    | ~ spl2_4 ),
    inference(superposition,[],[f144,f19]) ).

thf(f19,plain,
    ! [X0: $tType,X1: X0] :
      ( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
      = $true ),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ! [X0: $tType,X1: X0] :
      ( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
      = $true ),
    inference(fool_elimination,[],[f12]) ).

thf(f12,plain,
    ! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
    file('/export/starexec/sandbox/tmp/tmp.IMdPW78gU3/Vampire---4.8_26839','thm/sets/IN_UNIV_') ).

thf(f144,plain,
    ( ( $false
      = ( 'const/sets/IN' @ sK0 @ sK5 @ 'const/sets/UNIV' @ sK0 ) )
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f143]) ).

thf(f143,plain,
    ( ( $false
      = ( 'const/sets/IN' @ sK0 @ sK5 @ 'const/sets/UNIV' @ sK0 ) )
    | ( $false = $true )
    | ~ spl2_4 ),
    inference(superposition,[],[f63,f118]) ).

thf(f118,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
      ( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
        = $true )
      | ( $false
        = ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
    inference(trivial_inequality_removal,[],[f114]) ).

thf(f114,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
      ( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
        = $true )
      | ( $false = $true )
      | ( $false
        = ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
    inference(superposition,[],[f25,f43]) ).

thf(f43,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( $false
        = ( 'const/sets/IN' @ X0 @ X2 @ X1 ) )
      | ( ( X1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f22,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
      = ( X1 @ X2 ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ! [X0: $tType,X1: X0 > $o,X2: X0] :
      ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
      = ( X1 @ X2 ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X0: $tType,X2: X0 > $o,X1: X0] :
      ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
      = ( X2 @ X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.IMdPW78gU3/Vampire---4.8_26839','thm/sets/IN_') ).

thf(f25,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
        = $true )
      | ( $false
        = ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f24]) ).

thf(f24,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
      ( ( $false
        = ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
          | ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
      | ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f20]) ).

thf(f20,plain,
    ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
        | ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
      = ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
      ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
        | ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
      = ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ),
    inference(fool_elimination,[],[f10]) ).

thf(f10,plain,
    ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
      ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
      | ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
        = ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X4: X0] :
      ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
      | ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
        = ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.IMdPW78gU3/Vampire---4.8_26839','thm/sets/IN_UNION_') ).

thf(f63,plain,
    ( ( $false
      = ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) )
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f61]) ).

thf(f61,plain,
    ( spl2_4
  <=> ( $false
      = ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

thf(f78,plain,
    ~ spl2_3,
    inference(avatar_contradiction_clause,[],[f77]) ).

thf(f77,plain,
    ( $false
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f73]) ).

thf(f73,plain,
    ( ( $false = $true )
    | ~ spl2_3 ),
    inference(superposition,[],[f69,f59]) ).

thf(f59,plain,
    ( ( $false
      = ( 'const/sets/UNIV' @ sK0 @ sK5 ) )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f57]) ).

thf(f57,plain,
    ( spl2_3
  <=> ( $false
      = ( 'const/sets/UNIV' @ sK0 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f69,plain,
    ! [X0: $tType,X1: X0] :
      ( ( 'const/sets/UNIV' @ X0 @ X1 )
      = $true ),
    inference(trivial_inequality_removal,[],[f65]) ).

thf(f65,plain,
    ! [X0: $tType,X1: X0] :
      ( ( $false = $true )
      | ( ( 'const/sets/UNIV' @ X0 @ X1 )
        = $true ) ),
    inference(superposition,[],[f43,f19]) ).

thf(f64,plain,
    ( spl2_3
    | spl2_4 ),
    inference(avatar_split_clause,[],[f46,f61,f57]) ).

thf(f46,plain,
    ( ( $false
      = ( 'const/sets/UNIV' @ sK0 @ sK5 ) )
    | ( $false
      = ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f44]) ).

thf(f44,plain,
    ( ( 'const/sets/UNIV' @ sK0 @ sK5 )
   != ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) ),
    inference(negative_extensionality,[],[f21]) ).

thf(f21,plain,
    ( 'const/sets/UNIV'
    @ ( sK0
     != ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ),
    inference(cnf_transformation,[],[f17]) ).

thf(f17,plain,
    ( 'const/sets/UNIV'
    @ ( sK0
     != ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).

thf(f16,plain,
    ( ? [X0: $tType,X1: X0 > $o] :
        ( 'const/sets/UNIV'
        @ ( X0
         != ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) )
   => ( 'const/sets/UNIV'
      @ ( sK0
       != ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f15,plain,
    ? [X0: $tType,X1: X0 > $o] :
      ( 'const/sets/UNIV'
      @ ( X0
       != ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,negated_conjecture,
    ~ ! [X0: $tType,X1: X0 > $o] :
        ( 'const/sets/UNIV'
        @ ( X0
          = ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
    inference(negated_conjecture,[],[f5]) ).

thf(f5,conjecture,
    ! [X0: $tType,X1: X0 > $o] :
      ( 'const/sets/UNIV'
      @ ( X0
        = ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.IMdPW78gU3/Vampire---4.8_26839','thm/sets/UNION_UNIV_1') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : SEV451^1 : TPTP v8.1.2. Released v7.0.0.
% 0.09/0.12  % 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
% 0.11/0.32  % Computer : n009.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 11:50:55 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  This is a TH1_THM_EQU_NAR problem
% 0.11/0.32  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/tmp/tmp.IMdPW78gU3/Vampire---4.8_26839
% 0.11/0.34  % (26954)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (3000ds/18Mi)
% 0.11/0.34  % (26953)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (3000ds/275Mi)
% 0.11/0.34  % (26955)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (3000ds/3Mi)
% 0.11/0.34  % (26951)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.11/0.34  % (26949)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 Vampire---4 for (3000ds/4Mi)
% 0.11/0.34  % (26948)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (3000ds/183Mi)
% 0.11/0.34  % (26950)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 Vampire---4 for (3000ds/27Mi)
% 0.11/0.34  % (26952)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.11/0.34  % Exception at run slice level
% 0.11/0.34  User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.11/0.34  % (26955)Instruction limit reached!
% 0.11/0.34  % (26955)------------------------------
% 0.11/0.34  % (26955)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (26955)Termination reason: Unknown
% 0.11/0.34  % (26955)Termination phase: Saturation
% 0.11/0.34  
% 0.11/0.34  % (26955)Memory used [KB]: 5500
% 0.11/0.34  % (26955)Time elapsed: 0.003 s
% 0.11/0.34  % (26955)Instructions burned: 3 (million)
% 0.11/0.34  % (26955)------------------------------
% 0.11/0.34  % (26955)------------------------------
% 0.11/0.34  % (26953)Refutation not found, incomplete strategy
% 0.11/0.34  % (26953)------------------------------
% 0.11/0.34  % (26953)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (26953)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.34  
% 0.11/0.34  
% 0.11/0.34  % (26951)Instruction limit reached!
% 0.11/0.34  % (26951)------------------------------
% 0.11/0.34  % (26951)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (26953)Memory used [KB]: 5500
% 0.11/0.34  % (26953)Time elapsed: 0.003 s
% 0.11/0.34  % (26953)Instructions burned: 3 (million)
% 0.11/0.34  % (26953)------------------------------
% 0.11/0.34  % (26953)------------------------------
% 0.11/0.34  % (26951)Termination reason: Unknown
% 0.11/0.34  % (26951)Termination phase: Saturation
% 0.11/0.34  
% 0.11/0.34  % (26951)Memory used [KB]: 5500
% 0.11/0.34  % (26951)Time elapsed: 0.003 s
% 0.11/0.34  % (26951)Instructions burned: 3 (million)
% 0.11/0.34  % (26951)------------------------------
% 0.11/0.34  % (26951)------------------------------
% 0.11/0.34  % (26949)Instruction limit reached!
% 0.11/0.34  % (26949)------------------------------
% 0.11/0.34  % (26949)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34  % (26949)Termination reason: Unknown
% 0.11/0.34  % (26949)Termination phase: Saturation
% 0.11/0.34  
% 0.11/0.34  % (26949)Memory used [KB]: 5500
% 0.11/0.34  % (26949)Time elapsed: 0.004 s
% 0.11/0.34  % (26949)Instructions burned: 5 (million)
% 0.11/0.34  % (26949)------------------------------
% 0.11/0.34  % (26949)------------------------------
% 0.11/0.35  % (26954)Instruction limit reached!
% 0.11/0.35  % (26954)------------------------------
% 0.11/0.35  % (26954)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (26954)Termination reason: Unknown
% 0.11/0.35  % (26954)Termination phase: Saturation
% 0.11/0.35  
% 0.11/0.35  % (26954)Memory used [KB]: 5628
% 0.11/0.35  % (26954)Time elapsed: 0.011 s
% 0.11/0.35  % (26954)Instructions burned: 19 (million)
% 0.11/0.35  % (26954)------------------------------
% 0.11/0.35  % (26954)------------------------------
% 0.11/0.35  % (26950)First to succeed.
% 0.11/0.35  % (26950)Refutation found. Thanks to Tanya!
% 0.11/0.35  % SZS status Theorem for Vampire---4
% 0.11/0.35  % SZS output start Proof for Vampire---4
% See solution above
% 0.11/0.35  % (26950)------------------------------
% 0.11/0.35  % (26950)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35  % (26950)Termination reason: Refutation
% 0.11/0.35  
% 0.11/0.35  % (26950)Memory used [KB]: 5628
% 0.11/0.35  % (26950)Time elapsed: 0.012 s
% 0.11/0.35  % (26950)Instructions burned: 17 (million)
% 0.11/0.35  % (26950)------------------------------
% 0.11/0.35  % (26950)------------------------------
% 0.11/0.35  % (26947)Success in time 0.012 s
% 0.11/0.35  % Vampire---4.8 exiting
%------------------------------------------------------------------------------