TSTP Solution File: SET027^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET027^5 : 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/sandbox2/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 03:07:57 EDT 2024

% Result   : Theorem 0.21s 0.37s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   25 (   5 unt;   6 typ;   0 def)
%            Number of atoms       :  145 (  58 equ;   0 cnn)
%            Maximal formula atoms :   12 (   7 avg)
%            Number of connectives :  164 (  32   ~;  16   |;  24   &;  74   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   56 (   0   ^  38   !;  18   ?;  56   :)

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

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

thf(func_def_4,type,
    sK0: a > $o ).

thf(func_def_5,type,
    sK1: a > $o ).

thf(func_def_6,type,
    sK2: a > $o ).

thf(func_def_7,type,
    sK3: a ).

thf(f20,plain,
    $false,
    inference(subsumption_resolution,[],[f19,f12]) ).

thf(f12,plain,
    ( $true
    = ( sK1 @ sK3 ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ( ! [X3: a] :
        ( ( ( sK1 @ X3 )
         != $true )
        | ( ( sK0 @ X3 )
          = $true ) )
    & ! [X4: a] :
        ( ( ( sK2 @ X4 )
          = $true )
        | ( ( sK0 @ X4 )
         != $true ) )
    & ( ( sK2 @ sK3 )
     != $true )
    & ( $true
      = ( sK1 @ sK3 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).

thf(f9,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ! [X3: a] :
            ( ( ( X1 @ X3 )
             != $true )
            | ( ( X0 @ X3 )
              = $true ) )
        & ! [X4: a] :
            ( ( ( X2 @ X4 )
              = $true )
            | ( ( X0 @ X4 )
             != $true ) )
        & ? [X5: a] :
            ( ( ( X2 @ X5 )
             != $true )
            & ( $true
              = ( X1 @ X5 ) ) ) )
   => ( ! [X3: a] :
          ( ( ( sK1 @ X3 )
           != $true )
          | ( ( sK0 @ X3 )
            = $true ) )
      & ! [X4: a] :
          ( ( ( sK2 @ X4 )
            = $true )
          | ( ( sK0 @ X4 )
           != $true ) )
      & ? [X5: a] :
          ( ( ( sK2 @ X5 )
           != $true )
          & ( $true
            = ( sK1 @ X5 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ( ? [X5: a] :
        ( ( ( sK2 @ X5 )
         != $true )
        & ( $true
          = ( sK1 @ X5 ) ) )
   => ( ( ( sK2 @ sK3 )
       != $true )
      & ( $true
        = ( sK1 @ sK3 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ! [X3: a] :
          ( ( ( X1 @ X3 )
           != $true )
          | ( ( X0 @ X3 )
            = $true ) )
      & ! [X4: a] :
          ( ( ( X2 @ X4 )
            = $true )
          | ( ( X0 @ X4 )
           != $true ) )
      & ? [X5: a] :
          ( ( ( X2 @ X5 )
           != $true )
          & ( $true
            = ( X1 @ X5 ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ? [X1: a > $o,X2: a > $o,X0: a > $o] :
      ( ! [X4: a] :
          ( ( ( X2 @ X4 )
           != $true )
          | ( $true
            = ( X1 @ X4 ) ) )
      & ! [X3: a] :
          ( ( ( X0 @ X3 )
            = $true )
          | ( ( X1 @ X3 )
           != $true ) )
      & ? [X5: a] :
          ( ( ( X0 @ X5 )
           != $true )
          & ( ( X2 @ X5 )
            = $true ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ? [X2: a > $o,X1: a > $o,X0: a > $o] :
      ( ? [X5: a] :
          ( ( ( X0 @ X5 )
           != $true )
          & ( ( X2 @ X5 )
            = $true ) )
      & ! [X3: a] :
          ( ( ( X0 @ X3 )
            = $true )
          | ( ( X1 @ X3 )
           != $true ) )
      & ! [X4: a] :
          ( ( ( X2 @ X4 )
           != $true )
          | ( $true
            = ( X1 @ X4 ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
        ( ( ! [X3: a] :
              ( ( ( X1 @ X3 )
                = $true )
             => ( ( X0 @ X3 )
                = $true ) )
          & ! [X4: a] :
              ( ( ( X2 @ X4 )
                = $true )
             => ( $true
                = ( X1 @ X4 ) ) ) )
       => ! [X5: a] :
            ( ( ( X2 @ X5 )
              = $true )
           => ( ( X0 @ X5 )
              = $true ) ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ! [X2: a > $o,X1: a > $o,X0: a > $o] :
      ( ( ! [X3: a] :
            ( ( X1 @ X3 )
           => ( X2 @ X3 ) )
        & ! [X3: a] :
            ( ( X0 @ X3 )
           => ( X1 @ X3 ) ) )
     => ! [X3: a] :
          ( ( X0 @ X3 )
         => ( X2 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_29_pme) ).

thf(f19,plain,
    ( $true
   != ( sK1 @ sK3 ) ),
    inference(trivial_inequality_removal,[],[f18]) ).

thf(f18,plain,
    ( ( $true != $true )
    | ( $true
     != ( sK1 @ sK3 ) ) ),
    inference(superposition,[],[f17,f15]) ).

thf(f15,plain,
    ! [X3: a] :
      ( ( ( sK0 @ X3 )
        = $true )
      | ( ( sK1 @ X3 )
       != $true ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f17,plain,
    ( ( sK0 @ sK3 )
   != $true ),
    inference(trivial_inequality_removal,[],[f16]) ).

thf(f16,plain,
    ( ( $true != $true )
    | ( ( sK0 @ sK3 )
     != $true ) ),
    inference(superposition,[],[f13,f14]) ).

thf(f14,plain,
    ! [X4: a] :
      ( ( ( sK2 @ X4 )
        = $true )
      | ( ( sK0 @ X4 )
       != $true ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f13,plain,
    ( ( sK2 @ sK3 )
   != $true ),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET027^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14  % 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
% 0.14/0.34  % Computer : n018.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon May 20 12:20:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TH0_THM_NEQ_NAR problem
% 0.14/0.35  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
% 0.14/0.37  % (31247)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)
% 0.14/0.37  % (31248)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)
% 0.14/0.37  % (31245)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)
% 0.21/0.37  % (31244)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)
% 0.21/0.37  % (31243)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.21/0.37  % (31247)Instruction limit reached!
% 0.21/0.37  % (31247)------------------------------
% 0.21/0.37  % (31247)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37  % (31247)Termination reason: Unknown
% 0.21/0.37  % (31247)Termination phase: Saturation
% 0.21/0.37  
% 0.21/0.37  % (31247)Memory used [KB]: 5373
% 0.21/0.37  % (31247)Time elapsed: 0.003 s
% 0.21/0.37  % (31247)Instructions burned: 2 (million)
% 0.21/0.37  % (31247)------------------------------
% 0.21/0.37  % (31247)------------------------------
% 0.21/0.37  % (31249)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.21/0.37  % (31248)First to succeed.
% 0.21/0.37  % (31246)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.21/0.37  % (31243)Also succeeded, but the first one will report.
% 0.21/0.37  % (31246)Instruction limit reached!
% 0.21/0.37  % (31246)------------------------------
% 0.21/0.37  % (31246)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37  % (31248)Refutation found. Thanks to Tanya!
% 0.21/0.37  % SZS status Theorem for theBenchmark
% 0.21/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.37  % (31248)------------------------------
% 0.21/0.37  % (31248)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37  % (31248)Termination reason: Refutation
% 0.21/0.37  
% 0.21/0.37  % (31248)Memory used [KB]: 5500
% 0.21/0.37  % (31248)Time elapsed: 0.004 s
% 0.21/0.37  % (31248)Instructions burned: 1 (million)
% 0.21/0.37  % (31248)------------------------------
% 0.21/0.37  % (31248)------------------------------
% 0.21/0.37  % (31242)Success in time 0.005 s
% 0.21/0.37  % Vampire---4.8 exiting
%------------------------------------------------------------------------------