TSTP Solution File: SET592^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET592^5 : TPTP v8.2.0. Released v4.0.0.
% 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 : n020.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 03:12:15 EDT 2024

% Result   : Theorem 0.16s 0.34s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   38 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :  222 (  86 equ;   0 cnn)
%            Maximal formula atoms :   12 (   7 avg)
%            Number of connectives :  210 (  31   ~;  24   |;  42   &;  97   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   98 (  39   ^  46   !;  12   ?;  98   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    a: $tType ).

thf(func_def_0,type,
    a: $tType ).

thf(func_def_7,type,
    sK0: a > $o ).

thf(func_def_8,type,
    sK1: a > $o ).

thf(func_def_9,type,
    sK2: a > $o ).

thf(func_def_11,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(func_def_12,type,
    sK5: a ).

thf(f49,plain,
    $false,
    inference(trivial_inequality_removal,[],[f48]) ).

thf(f48,plain,
    $true = $false,
    inference(backward_demodulation,[],[f32,f47]) ).

thf(f47,plain,
    ( $false
    = ( sK1 @ sK5 ) ),
    inference(trivial_inequality_removal,[],[f44]) ).

thf(f44,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(superposition,[],[f39,f25]) ).

thf(f25,plain,
    ! [X1: a] :
      ( ( $false
        = ( sK2 @ X1 ) )
      | ( ( sK1 @ X1 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f24]) ).

thf(f24,plain,
    ! [X1: a] :
      ( $false
      = ( ( sK1 @ X1 )
        & ( sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f23]) ).

thf(f23,plain,
    ! [X1: a] :
      ( ( ^ [Y0: a] :
            ( ( sK1 @ Y0 )
            & ( sK2 @ Y0 ) )
        @ X1 )
      = ( ^ [Y0: a] : $false
        @ X1 ) ),
    inference(argument_congruence,[],[f12]) ).

thf(f12,plain,
    ( ( ^ [Y0: a] :
          ( ( sK1 @ Y0 )
          & ( sK2 @ Y0 ) ) )
    = ( ^ [Y0: a] : $false ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ( ! [X3: a] :
        ( ( $true
          = ( sK2 @ X3 ) )
        | ( $true
         != ( sK0 @ X3 ) ) )
    & ! [X4: a] :
        ( ( ( sK1 @ X4 )
          = $true )
        | ( $true
         != ( sK0 @ X4 ) ) )
    & ( ( ^ [Y0: a] : $false )
     != sK0 )
    & ( ( ^ [Y0: a] :
            ( ( sK1 @ Y0 )
            & ( sK2 @ Y0 ) ) )
      = ( ^ [Y0: a] : $false ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10]) ).

thf(f10,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ! [X3: a] :
            ( ( ( X2 @ X3 )
              = $true )
            | ( ( X0 @ X3 )
             != $true ) )
        & ! [X4: a] :
            ( ( $true
              = ( X1 @ X4 ) )
            | ( $true
             != ( X0 @ X4 ) ) )
        & ( ( ^ [Y0: a] : $false )
         != X0 )
        & ( ( ^ [Y0: a] :
                ( ( X1 @ Y0 )
                & ( X2 @ Y0 ) ) )
          = ( ^ [Y0: a] : $false ) ) )
   => ( ! [X3: a] :
          ( ( $true
            = ( sK2 @ X3 ) )
          | ( $true
           != ( sK0 @ X3 ) ) )
      & ! [X4: a] :
          ( ( ( sK1 @ X4 )
            = $true )
          | ( $true
           != ( sK0 @ X4 ) ) )
      & ( ( ^ [Y0: a] : $false )
       != sK0 )
      & ( ( ^ [Y0: a] :
              ( ( sK1 @ Y0 )
              & ( sK2 @ Y0 ) ) )
        = ( ^ [Y0: a] : $false ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ! [X3: a] :
          ( ( ( X2 @ X3 )
            = $true )
          | ( ( X0 @ X3 )
           != $true ) )
      & ! [X4: a] :
          ( ( $true
            = ( X1 @ X4 ) )
          | ( $true
           != ( X0 @ X4 ) ) )
      & ( ( ^ [Y0: a] : $false )
       != X0 )
      & ( ( ^ [Y0: a] :
              ( ( X1 @ Y0 )
              & ( X2 @ Y0 ) ) )
        = ( ^ [Y0: a] : $false ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ! [X4: a] :
          ( ( $true
            = ( X2 @ X4 ) )
          | ( $true
           != ( X0 @ X4 ) ) )
      & ! [X3: a] :
          ( ( ( X1 @ X3 )
            = $true )
          | ( ( X0 @ X3 )
           != $true ) )
      & ( ( ^ [Y0: a] : $false )
       != X0 )
      & ( ( ^ [Y0: a] :
              ( ( X1 @ Y0 )
              & ( X2 @ Y0 ) ) )
        = ( ^ [Y0: a] : $false ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ( ^ [Y0: a] : $false )
       != X0 )
      & ! [X4: a] :
          ( ( $true
            = ( X2 @ X4 ) )
          | ( $true
           != ( X0 @ X4 ) ) )
      & ! [X3: a] :
          ( ( ( X1 @ X3 )
            = $true )
          | ( ( X0 @ X3 )
           != $true ) )
      & ( ( ^ [Y0: a] :
              ( ( X1 @ Y0 )
              & ( X2 @ Y0 ) ) )
        = ( ^ [Y0: a] : $false ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ! [X4: a] :
              ( ( $true
                = ( X0 @ X4 ) )
             => ( $true
                = ( X2 @ X4 ) ) )
          & ! [X3: a] :
              ( ( ( X0 @ X3 )
                = $true )
             => ( ( X1 @ X3 )
                = $true ) )
          & ( ( ^ [Y0: a] :
                  ( ( X1 @ Y0 )
                  & ( X2 @ Y0 ) ) )
            = ( ^ [Y0: a] : $false ) ) )
       => ( ( ^ [Y0: a] : $false )
          = X0 ) ),
    inference(rectify,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ( ( ^ [Y0: a] :
                  ( ( X1 @ Y0 )
                  & ( X2 @ Y0 ) ) )
            = ( ^ [Y0: a] : $false ) )
          & ! [X5: a] :
              ( ( $true
                = ( X0 @ X5 ) )
             => ( $true
                = ( X1 @ X5 ) ) )
          & ! [X6: a] :
              ( ( $true
                = ( X0 @ X6 ) )
             => ( $true
                = ( X2 @ X6 ) ) ) )
       => ( ( ^ [Y0: a] : $false )
          = X0 ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ( ( ^ [X3: a] : $false )
            = ( ^ [X4: a] :
                  ( ( X2 @ X4 )
                  & ( X1 @ X4 ) ) ) )
          & ! [X5: a] :
              ( ( X0 @ X5 )
             => ( X1 @ X5 ) )
          & ! [X6: a] :
              ( ( X0 @ X6 )
             => ( X2 @ X6 ) ) )
       => ( ( ^ [X7: a] : $false )
          = X0 ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
        ( ( ( ( ^ [X3: a] : $false )
            = ( ^ [X3: a] :
                  ( ( X1 @ X3 )
                  & ( X2 @ X3 ) ) ) )
          & ! [X3: a] :
              ( ( X0 @ X3 )
             => ( X2 @ X3 ) )
          & ! [X3: a] :
              ( ( X0 @ X3 )
             => ( X1 @ X3 ) ) )
       => ( ( ^ [X3: a] : $false )
          = X0 ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > $o,X2: a > $o,X1: a > $o] :
      ( ( ( ( ^ [X3: a] : $false )
          = ( ^ [X3: a] :
                ( ( X1 @ X3 )
                & ( X2 @ X3 ) ) ) )
        & ! [X3: a] :
            ( ( X0 @ X3 )
           => ( X2 @ X3 ) )
        & ! [X3: a] :
            ( ( X0 @ X3 )
           => ( X1 @ X3 ) ) )
     => ( ( ^ [X3: a] : $false )
        = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_51_pme) ).

thf(f39,plain,
    ( $true
    = ( sK2 @ sK5 ) ),
    inference(trivial_inequality_removal,[],[f34]) ).

thf(f34,plain,
    ( ( $false != $false )
    | ( $true
      = ( sK2 @ sK5 ) ) ),
    inference(superposition,[],[f17,f22]) ).

thf(f22,plain,
    ! [X3: a] :
      ( ( $false
        = ( sK0 @ X3 ) )
      | ( $true
        = ( sK2 @ X3 ) ) ),
    inference(trivial_inequality_removal,[],[f21]) ).

thf(f21,plain,
    ! [X3: a] :
      ( ( $true
        = ( sK2 @ X3 ) )
      | ( $true != $true )
      | ( $false
        = ( sK0 @ X3 ) ) ),
    inference(fool_paramodulation,[],[f15]) ).

thf(f15,plain,
    ! [X3: a] :
      ( ( $true
       != ( sK0 @ X3 ) )
      | ( $true
        = ( sK2 @ X3 ) ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f17,plain,
    ( ( sK0 @ sK5 )
   != $false ),
    inference(beta_eta_normalization,[],[f16]) ).

thf(f16,plain,
    ( ( sK0 @ sK5 )
   != ( ^ [Y0: a] : $false
      @ sK5 ) ),
    inference(negative_extensionality,[],[f13]) ).

thf(f13,plain,
    ( ( ^ [Y0: a] : $false )
   != sK0 ),
    inference(cnf_transformation,[],[f11]) ).

thf(f32,plain,
    ( $true
    = ( sK1 @ sK5 ) ),
    inference(trivial_inequality_removal,[],[f27]) ).

thf(f27,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( $false != $false ) ),
    inference(superposition,[],[f17,f20]) ).

thf(f20,plain,
    ! [X4: a] :
      ( ( $false
        = ( sK0 @ X4 ) )
      | ( ( sK1 @ X4 )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f19]) ).

thf(f19,plain,
    ! [X4: a] :
      ( ( $true != $true )
      | ( ( sK1 @ X4 )
        = $true )
      | ( $false
        = ( sK0 @ X4 ) ) ),
    inference(fool_paramodulation,[],[f14]) ).

thf(f14,plain,
    ! [X4: a] :
      ( ( $true
       != ( sK0 @ X4 ) )
      | ( ( sK1 @ X4 )
        = $true ) ),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET592^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.12  % 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
% 0.11/0.31  % Computer : n020.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon May 20 12:05:23 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.11/0.31  This is a TH0_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/benchmark/theBenchmark.p
% 0.16/0.33  % (4853)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 (3000ds/2Mi)
% 0.16/0.33  % (4854)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 (3000ds/275Mi)
% 0.16/0.33  % (4853)Instruction limit reached!
% 0.16/0.33  % (4853)------------------------------
% 0.16/0.33  % (4853)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (4853)Termination reason: Unknown
% 0.16/0.33  % (4853)Termination phase: Saturation
% 0.16/0.33  
% 0.16/0.33  % (4853)Memory used [KB]: 5500
% 0.16/0.33  % (4853)Time elapsed: 0.002 s
% 0.16/0.33  % (4853)Instructions burned: 2 (million)
% 0.16/0.33  % (4853)------------------------------
% 0.16/0.33  % (4853)------------------------------
% 0.16/0.33  % (4854)Refutation not found, incomplete strategy
% 0.16/0.33  % (4854)------------------------------
% 0.16/0.33  % (4854)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (4854)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.33  
% 0.16/0.33  
% 0.16/0.33  % (4854)Memory used [KB]: 5500
% 0.16/0.33  % (4854)Time elapsed: 0.003 s
% 0.16/0.33  % (4854)Instructions burned: 3 (million)
% 0.16/0.33  % (4854)------------------------------
% 0.16/0.33  % (4854)------------------------------
% 0.16/0.33  % (4849)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.16/0.34  % (4851)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 (3000ds/27Mi)
% 0.16/0.34  % (4852)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.16/0.34  % (4850)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 (3000ds/4Mi)
% 0.16/0.34  % (4855)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.16/0.34  % (4856)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.16/0.34  % (4852)Instruction limit reached!
% 0.16/0.34  % (4852)------------------------------
% 0.16/0.34  % (4852)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34  % (4852)Termination reason: Unknown
% 0.16/0.34  % (4852)Termination phase: Saturation
% 0.16/0.34  
% 0.16/0.34  % (4852)Memory used [KB]: 5500
% 0.16/0.34  % (4852)Time elapsed: 0.004 s
% 0.16/0.34  % (4852)Instructions burned: 2 (million)
% 0.16/0.34  % (4852)------------------------------
% 0.16/0.34  % (4852)------------------------------
% 0.16/0.34  % (4851)Refutation not found, incomplete strategy
% 0.16/0.34  % (4851)------------------------------
% 0.16/0.34  % (4851)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34  % (4851)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.34  
% 0.16/0.34  
% 0.16/0.34  % (4851)Memory used [KB]: 5500
% 0.16/0.34  % (4851)Time elapsed: 0.004 s
% 0.16/0.34  % (4851)Instructions burned: 2 (million)
% 0.16/0.34  % (4851)------------------------------
% 0.16/0.34  % (4851)------------------------------
% 0.16/0.34  % (4849)Refutation not found, incomplete strategy
% 0.16/0.34  % (4849)------------------------------
% 0.16/0.34  % (4849)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34  % (4849)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.34  
% 0.16/0.34  
% 0.16/0.34  % (4849)Memory used [KB]: 5500
% 0.16/0.34  % (4849)Time elapsed: 0.004 s
% 0.16/0.34  % (4855)Refutation not found, incomplete strategy
% 0.16/0.34  % (4855)------------------------------
% 0.16/0.34  % (4855)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34  % (4855)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.34  
% 0.16/0.34  
% 0.16/0.34  % (4855)Memory used [KB]: 5500
% 0.16/0.34  % (4855)Time elapsed: 0.004 s
% 0.16/0.34  % (4855)Instructions burned: 2 (million)
% 0.16/0.34  % (4855)------------------------------
% 0.16/0.34  % (4855)------------------------------
% 0.16/0.34  % (4849)Instructions burned: 2 (million)
% 0.16/0.34  % (4856)Refutation not found, incomplete strategy
% 0.16/0.34  % (4856)------------------------------
% 0.16/0.34  % (4856)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34  % (4856)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.34  
% 0.16/0.34  
% 0.16/0.34  % (4856)Memory used [KB]: 5500
% 0.16/0.34  % (4856)Time elapsed: 0.004 s
% 0.16/0.34  % (4856)Instructions burned: 2 (million)
% 0.16/0.34  % (4856)------------------------------
% 0.16/0.34  % (4856)------------------------------
% 0.16/0.34  % (4849)------------------------------
% 0.16/0.34  % (4849)------------------------------
% 0.16/0.34  % (4857)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.16/0.34  % (4850)First to succeed.
% 0.16/0.34  % (4858)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.16/0.34  % (4857)Also succeeded, but the first one will report.
% 0.16/0.34  % (4850)Refutation found. Thanks to Tanya!
% 0.16/0.34  % SZS status Theorem for theBenchmark
% 0.16/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.34  % (4850)------------------------------
% 0.16/0.34  % (4850)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34  % (4850)Termination reason: Refutation
% 0.16/0.34  
% 0.16/0.34  % (4850)Memory used [KB]: 5500
% 0.16/0.34  % (4850)Time elapsed: 0.007 s
% 0.16/0.34  % (4850)Instructions burned: 3 (million)
% 0.16/0.34  % (4850)------------------------------
% 0.16/0.34  % (4850)------------------------------
% 0.16/0.34  % (4848)Success in time 0.009 s
% 0.16/0.34  % Vampire---4.8 exiting
%------------------------------------------------------------------------------