TSTP Solution File: SEU864^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU864^5 : 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 : n018.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 03:51:58 EDT 2024

% Result   : Theorem 0.11s 0.28s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   24 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :  146 (  74 equ;   2 cnn)
%            Maximal formula atoms :   10 (   7 avg)
%            Number of connectives :  142 (  24   ~;  28   |;  14   &;  63   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   3 usr;   4 con; 0-2 aty)
%            Number of variables   :   66 (  37   ^  25   !;   3   ?;  66   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_1,type,
    t: a ).

thf(func_def_9,type,
    sK0: ( a > $o ) > $o ).

thf(func_def_12,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(f20,plain,
    $false,
    inference(subsumption_resolution,[],[f19,f14]) ).

thf(f14,plain,
    ( $true
   != ( sK0 @ ( (=) @ t ) ) ),
    inference(beta_eta_normalization,[],[f11]) ).

thf(f11,plain,
    ( ( sK0
      @ ^ [Y0: a] : ( t = Y0 ) )
   != $true ),
    inference(cnf_transformation,[],[f9]) ).

thf(f9,plain,
    ( ( ( sK0
        @ ^ [Y0: a] : $false )
      = $true )
    & ( ( sK0
        @ ^ [Y0: a] : ( t = Y0 ) )
     != $true )
    & ! [X1: a > $o] :
        ( ( $true
         != ( sK0 @ X1 ) )
        | ! [X2: a] :
            ( ( $true
              = ( sK0
                @ ^ [Y0: a] :
                    ( ( X2 = Y0 )
                    | ( X1 @ Y0 ) ) ) )
            | ( t != X2 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).

thf(f8,plain,
    ( ? [X0: ( a > $o ) > $o] :
        ( ( ( X0
            @ ^ [Y0: a] : $false )
          = $true )
        & ( ( X0
            @ ^ [Y0: a] : ( t = Y0 ) )
         != $true )
        & ! [X1: a > $o] :
            ( ( ( X0 @ X1 )
             != $true )
            | ! [X2: a] :
                ( ( ( X0
                    @ ^ [Y0: a] :
                        ( ( X2 = Y0 )
                        | ( X1 @ Y0 ) ) )
                  = $true )
                | ( t != X2 ) ) ) )
   => ( ( ( sK0
          @ ^ [Y0: a] : $false )
        = $true )
      & ( ( sK0
          @ ^ [Y0: a] : ( t = Y0 ) )
       != $true )
      & ! [X1: a > $o] :
          ( ( $true
           != ( sK0 @ X1 ) )
          | ! [X2: a] :
              ( ( $true
                = ( sK0
                  @ ^ [Y0: a] :
                      ( ( X2 = Y0 )
                      | ( X1 @ Y0 ) ) ) )
              | ( t != X2 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

thf(f6,plain,
    ? [X0: ( a > $o ) > $o] :
      ( ( ( X0
          @ ^ [Y0: a] : ( t = Y0 ) )
       != $true )
      & ( ( X0
          @ ^ [Y0: a] : $false )
        = $true )
      & ! [X1: a > $o] :
          ( ( ( X0 @ X1 )
           != $true )
          | ! [X2: a] :
              ( ( ( X0
                  @ ^ [Y0: a] :
                      ( ( X2 = Y0 )
                      | ( X1 @ Y0 ) ) )
                = $true )
              | ( t != X2 ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

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

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

thf(f2,negated_conjecture,
    ~ ! [X0: ( a > $o ) > $o] :
        ( ( ! [X2: a > $o] :
              ( ( X0 @ X2 )
             => ! [X3: a] :
                  ( ( t = X3 )
                 => ( X0
                    @ ^ [X4: a] :
                        ( ( X2 @ X4 )
                        | ( X3 = X4 ) ) ) ) )
          & ( X0
            @ ^ [X1: a] : $false ) )
       => ( X0
          @ ^ [X1: a] : ( t = X1 ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: ( a > $o ) > $o] :
      ( ( ! [X2: a > $o] :
            ( ( X0 @ X2 )
           => ! [X3: a] :
                ( ( t = X3 )
               => ( X0
                  @ ^ [X4: a] :
                      ( ( X2 @ X4 )
                      | ( X3 = X4 ) ) ) ) )
        & ( X0
          @ ^ [X1: a] : $false ) )
     => ( X0
        @ ^ [X1: a] : ( t = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDOMLEMMA1_pme) ).

thf(f19,plain,
    ( $true
    = ( sK0 @ ( (=) @ t ) ) ),
    inference(beta_eta_normalization,[],[f18]) ).

thf(f18,plain,
    ( ( sK0
      @ ^ [Y0: a] : ( t = Y0 ) )
    = $true ),
    inference(boolean_simplification,[],[f17]) ).

thf(f17,plain,
    ( ( sK0
      @ ^ [Y0: a] :
          ( ( t = Y0 )
          | $false ) )
    = $true ),
    inference(beta_eta_normalization,[],[f16]) ).

thf(f16,plain,
    ( ( sK0
      @ ^ [Y0: a] :
          ( ( t = Y0 )
          | ( ^ [Y1: a] : $false
            @ Y0 ) ) )
    = $true ),
    inference(trivial_inequality_removal,[],[f15]) ).

thf(f15,plain,
    ( ( $true != $true )
    | ( ( sK0
        @ ^ [Y0: a] :
            ( ( t = Y0 )
            | ( ^ [Y1: a] : $false
              @ Y0 ) ) )
      = $true ) ),
    inference(superposition,[],[f13,f12]) ).

thf(f12,plain,
    ( ( sK0
      @ ^ [Y0: a] : $false )
    = $true ),
    inference(cnf_transformation,[],[f9]) ).

thf(f13,plain,
    ! [X1: a > $o] :
      ( ( $true
       != ( sK0 @ X1 ) )
      | ( ( sK0
          @ ^ [Y0: a] :
              ( ( t = Y0 )
              | ( X1 @ Y0 ) ) )
        = $true ) ),
    inference(equality_resolution,[],[f10]) ).

thf(f10,plain,
    ! [X2: a,X1: a > $o] :
      ( ( $true
       != ( sK0 @ X1 ) )
      | ( $true
        = ( sK0
          @ ^ [Y0: a] :
              ( ( X2 = Y0 )
              | ( X1 @ Y0 ) ) ) )
      | ( t != X2 ) ),
    inference(cnf_transformation,[],[f9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem    : SEU864^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.08  % 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
% 0.08/0.27  % Computer : n018.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit   : 300
% 0.08/0.27  % WCLimit    : 300
% 0.08/0.27  % DateTime   : Sun May 19 15:46:37 EDT 2024
% 0.08/0.27  % CPUTime    : 
% 0.08/0.27  This is a TH0_THM_EQU_NAR problem
% 0.08/0.27  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
% 0.11/0.28  % (9179)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.11/0.28  % (9181)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)
% 0.11/0.28  % (9180)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)
% 0.11/0.28  % (9183)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)
% 0.11/0.28  % (9182)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.28  % (9184)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)
% 0.11/0.28  % (9185)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.11/0.28  % (9186)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)
% 0.11/0.28  % (9182)First to succeed.
% 0.11/0.28  % (9184)Refutation not found, incomplete strategy
% 0.11/0.28  % (9184)------------------------------
% 0.11/0.28  % (9184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.28  % (9184)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.28  
% 0.11/0.28  
% 0.11/0.28  % (9184)Memory used [KB]: 5500
% 0.11/0.28  % (9184)Time elapsed: 0.002 s
% 0.11/0.28  % (9184)Instructions burned: 1 (million)
% 0.11/0.28  % (9184)------------------------------
% 0.11/0.28  % (9184)------------------------------
% 0.11/0.28  % (9183)Instruction limit reached!
% 0.11/0.28  % (9183)------------------------------
% 0.11/0.28  % (9183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.28  % (9183)Termination reason: Unknown
% 0.11/0.28  % (9183)Termination phase: Saturation
% 0.11/0.28  
% 0.11/0.28  % (9183)Memory used [KB]: 5500
% 0.11/0.28  % (9183)Time elapsed: 0.003 s
% 0.11/0.28  % (9183)Instructions burned: 3 (million)
% 0.11/0.28  % (9183)------------------------------
% 0.11/0.28  % (9183)------------------------------
% 0.11/0.28  % (9181)Also succeeded, but the first one will report.
% 0.11/0.28  % (9186)Also succeeded, but the first one will report.
% 0.11/0.28  % (9182)Refutation found. Thanks to Tanya!
% 0.11/0.28  % SZS status Theorem for theBenchmark
% 0.11/0.28  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.28  % (9182)------------------------------
% 0.11/0.28  % (9182)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.28  % (9182)Termination reason: Refutation
% 0.11/0.28  
% 0.11/0.28  % (9182)Memory used [KB]: 5500
% 0.11/0.28  % (9182)Time elapsed: 0.003 s
% 0.11/0.28  % (9182)Instructions burned: 1 (million)
% 0.11/0.28  % (9182)------------------------------
% 0.11/0.28  % (9182)------------------------------
% 0.11/0.28  % (9178)Success in time 0.002 s
% 0.11/0.28  % Vampire---4.8 exiting
%------------------------------------------------------------------------------