TSTP Solution File: SEV097^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV097^5 : 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 : n023.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 04:11:58 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   27 (   4 unt;  11 typ;   0 def)
%            Number of atoms       :  346 ( 101 equ;   0 cnn)
%            Maximal formula atoms :   14 (  21 avg)
%            Number of connectives :  468 (  51   ~;  37   |;  63   &; 289   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  143 (   0   ^ 119   !;  24   ?; 143   :)

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

thf(type_def_7,type,
    b: $tType ).

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

thf(func_def_1,type,
    b: $tType ).

thf(func_def_2,type,
    z: a ).

thf(func_def_3,type,
    cR: a > a > $o ).

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

thf(func_def_5,type,
    cS: b > b > $o ).

thf(func_def_9,type,
    sK0: a > b ).

thf(func_def_10,type,
    sK1: a ).

thf(func_def_11,type,
    sK2: b > a ).

thf(f30,plain,
    $false,
    inference(trivial_inequality_removal,[],[f29]) ).

thf(f29,plain,
    $true != $true,
    inference(superposition,[],[f15,f20]) ).

thf(f20,plain,
    ! [X0: a] :
      ( ( f @ X0 @ ( sK0 @ X0 ) )
      = $true ),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ( ! [X0: a] :
        ( ( f @ X0 @ ( sK0 @ X0 ) )
        = $true )
    & ! [X2: a,X3: b,X4: a] :
        ( ( ( f @ X2 @ X3 )
         != $true )
        | ( ( cR @ X2 @ X4 )
          = $true )
        | ( ( f @ X4 @ X3 )
         != $true ) )
    & ! [X5: a,X6: a,X7: a] :
        ( ( $true
         != ( cR @ X6 @ X5 ) )
        | ( ( cR @ X6 @ X7 )
          = $true )
        | ( $true
         != ( cR @ X7 @ X5 ) ) )
    & ! [X8: b,X9: b,X10: a] :
        ( ( ( f @ X10 @ X9 )
         != $true )
        | ( ( cS @ X9 @ X8 )
          = $true )
        | ( ( f @ X10 @ X8 )
         != $true ) )
    & ! [X11: a] :
        ( $true
        = ( cR @ X11 @ X11 ) )
    & ! [X13: b] :
        ( ( ( f @ sK1 @ X13 )
         != $true )
        & ( ( $true
            = ( f @ ( sK2 @ X13 ) @ X13 ) )
          | ( ( cR @ sK1 @ z )
           != $true ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).

thf(f10,plain,
    ! [X0: a] :
      ( ? [X1: b] :
          ( ( f @ X0 @ X1 )
          = $true )
     => ( ( f @ X0 @ ( sK0 @ X0 ) )
        = $true ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X12: a] :
      ! [X13: b] :
      ? [X14: a] :
        ( ( $true
         != ( f @ X12 @ X13 ) )
        & ( ( $true
            = ( f @ X14 @ X13 ) )
          | ( $true
           != ( cR @ X12 @ z ) ) ) )
   => ! [X13: b] :
      ? [X14: a] :
        ( ( ( f @ sK1 @ X13 )
         != $true )
        & ( ( $true
            = ( f @ X14 @ X13 ) )
          | ( ( cR @ sK1 @ z )
           != $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X13: b] :
      ( ? [X14: a] :
          ( ( ( f @ sK1 @ X13 )
           != $true )
          & ( ( $true
              = ( f @ X14 @ X13 ) )
            | ( ( cR @ sK1 @ z )
             != $true ) ) )
     => ( ( ( f @ sK1 @ X13 )
         != $true )
        & ( ( $true
            = ( f @ ( sK2 @ X13 ) @ X13 ) )
          | ( ( cR @ sK1 @ z )
           != $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ( ! [X0: a] :
      ? [X1: b] :
        ( ( f @ X0 @ X1 )
        = $true )
    & ! [X2: a,X3: b,X4: a] :
        ( ( ( f @ X2 @ X3 )
         != $true )
        | ( ( cR @ X2 @ X4 )
          = $true )
        | ( ( f @ X4 @ X3 )
         != $true ) )
    & ! [X5: a,X6: a,X7: a] :
        ( ( $true
         != ( cR @ X6 @ X5 ) )
        | ( ( cR @ X6 @ X7 )
          = $true )
        | ( $true
         != ( cR @ X7 @ X5 ) ) )
    & ! [X8: b,X9: b,X10: a] :
        ( ( ( f @ X10 @ X9 )
         != $true )
        | ( ( cS @ X9 @ X8 )
          = $true )
        | ( ( f @ X10 @ X8 )
         != $true ) )
    & ! [X11: a] :
        ( $true
        = ( cR @ X11 @ X11 ) )
    & ? [X12: a] :
      ! [X13: b] :
      ? [X14: a] :
        ( ( $true
         != ( f @ X12 @ X13 ) )
        & ( ( $true
            = ( f @ X14 @ X13 ) )
          | ( $true
           != ( cR @ X12 @ z ) ) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,plain,
    ( ! [X7: a] :
      ? [X8: b] :
        ( ( f @ X7 @ X8 )
        = $true )
    & ! [X10: a,X11: b,X9: a] :
        ( ( $true
         != ( f @ X10 @ X11 ) )
        | ( ( cR @ X10 @ X9 )
          = $true )
        | ( ( f @ X9 @ X11 )
         != $true ) )
    & ! [X2: a,X1: a,X3: a] :
        ( ( $true
         != ( cR @ X1 @ X2 ) )
        | ( ( cR @ X1 @ X3 )
          = $true )
        | ( ( cR @ X3 @ X2 )
         != $true ) )
    & ! [X5: b,X6: b,X4: a] :
        ( ( ( f @ X4 @ X6 )
         != $true )
        | ( ( cS @ X6 @ X5 )
          = $true )
        | ( $true
         != ( f @ X4 @ X5 ) ) )
    & ! [X0: a] :
        ( $true
        = ( cR @ X0 @ X0 ) )
    & ? [X12: a] :
      ! [X13: b] :
      ? [X14: a] :
        ( ( $true
         != ( f @ X12 @ X13 ) )
        & ( ( $true
            = ( f @ X14 @ X13 ) )
          | ( $true
           != ( cR @ X12 @ z ) ) ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ( ? [X12: a] :
      ! [X13: b] :
      ? [X14: a] :
        ( ( $true
         != ( f @ X12 @ X13 ) )
        & ( ( $true
            = ( f @ X14 @ X13 ) )
          | ( $true
           != ( cR @ X12 @ z ) ) ) )
    & ! [X10: a,X11: b,X9: a] :
        ( ( ( cR @ X10 @ X9 )
          = $true )
        | ( $true
         != ( f @ X10 @ X11 ) )
        | ( ( f @ X9 @ X11 )
         != $true ) )
    & ! [X5: b,X6: b,X4: a] :
        ( ( ( cS @ X6 @ X5 )
          = $true )
        | ( ( f @ X4 @ X6 )
         != $true )
        | ( $true
         != ( f @ X4 @ X5 ) ) )
    & ! [X7: a] :
      ? [X8: b] :
        ( ( f @ X7 @ X8 )
        = $true )
    & ! [X0: a] :
        ( $true
        = ( cR @ X0 @ X0 ) )
    & ! [X2: a,X1: a,X3: a] :
        ( ( ( cR @ X1 @ X3 )
          = $true )
        | ( ( cR @ X3 @ X2 )
         != $true )
        | ( $true
         != ( cR @ X1 @ X2 ) ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ( ( ! [X0: a] :
            ( $true
            = ( cR @ X0 @ X0 ) )
        & ! [X2: a,X1: a,X3: a] :
            ( ( ( ( cR @ X3 @ X2 )
                = $true )
              & ( $true
                = ( cR @ X1 @ X2 ) ) )
           => ( ( cR @ X1 @ X3 )
              = $true ) ) )
     => ( ( ! [X10: a,X11: b,X9: a] :
              ( ( ( $true
                  = ( f @ X10 @ X11 ) )
                & ( ( f @ X9 @ X11 )
                  = $true ) )
             => ( ( cR @ X10 @ X9 )
                = $true ) )
          & ! [X5: b,X6: b,X4: a] :
              ( ( ( ( f @ X4 @ X6 )
                  = $true )
                & ( $true
                  = ( f @ X4 @ X5 ) ) )
             => ( ( cS @ X6 @ X5 )
                = $true ) )
          & ! [X7: a] :
            ? [X8: b] :
              ( ( f @ X7 @ X8 )
              = $true ) )
       => ! [X12: a] :
          ? [X13: b] :
          ! [X14: a] :
            ( ( ( $true
               != ( f @ X14 @ X13 ) )
              & ( $true
                = ( cR @ X12 @ z ) ) )
            | ( $true
              = ( f @ X12 @ X13 ) ) ) ) ),
    inference(flattening,[],[f5]) ).

thf(f5,plain,
    ~ ( ( ! [X0: a] :
            ( $true
            = ( cR @ X0 @ X0 ) )
        & ! [X2: a,X1: a,X3: a] :
            ( ( ( ( cR @ X3 @ X2 )
                = $true )
              & ( $true
                = ( cR @ X1 @ X2 ) ) )
           => ( ( cR @ X1 @ X3 )
              = $true ) ) )
     => ( ( ! [X10: a,X11: b,X9: a] :
              ( ( ( $true
                  = ( f @ X10 @ X11 ) )
                & ( ( f @ X9 @ X11 )
                  = $true ) )
             => ( ( cR @ X10 @ X9 )
                = $true ) )
          & ! [X5: b,X6: b,X4: a] :
              ( ( ( ( f @ X4 @ X6 )
                  = $true )
                & ( $true
                  = ( f @ X4 @ X5 ) ) )
             => ( ( cS @ X6 @ X5 )
                = $true ) )
          & ! [X7: a] :
            ? [X8: b] :
              ( ( f @ X7 @ X8 )
              = $true ) )
       => ! [X12: a] :
          ? [X13: b] :
          ! [X14: a] :
            ( ( $true
              = ( f @ X12 @ X13 ) )
            | ( ( $true
                = ( cR @ X12 @ z ) )
              & ( $true
               != ( f @ X14 @ X13 ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ( ! [X0: a] : ( cR @ X0 @ X0 )
        & ! [X1: a,X2: a,X3: a] :
            ( ( ( cR @ X3 @ X2 )
              & ( cR @ X1 @ X2 ) )
           => ( cR @ X1 @ X3 ) ) )
     => ( ( ! [X4: a,X5: b,X6: b] :
              ( ( ( f @ X4 @ X6 )
                & ( f @ X4 @ X5 ) )
             => ( cS @ X6 @ X5 ) )
          & ! [X7: a] :
            ? [X8: b] : ( f @ X7 @ X8 )
          & ! [X9: a,X10: a,X11: b] :
              ( ( ( f @ X10 @ X11 )
                & ( f @ X9 @ X11 ) )
             => ( cR @ X10 @ X9 ) ) )
       => ! [X12: a] :
          ? [X13: b] :
          ! [X14: a] :
            ( ( f @ X12 @ X13 )
            | ( ( cR @ X12 @ z )
              & ~ ( f @ X14 @ X13 ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ( ! [X3: a] : ( cR @ X3 @ X3 )
        & ! [X0: a,X1: a,X2: a] :
            ( ( ( cR @ X2 @ X1 )
              & ( cR @ X0 @ X1 ) )
           => ( cR @ X0 @ X2 ) ) )
     => ( ( ! [X3: a,X6: b,X5: b] :
              ( ( ( f @ X3 @ X5 )
                & ( f @ X3 @ X6 ) )
             => ( cS @ X5 @ X6 ) )
          & ! [X3: a] :
            ? [X4: b] : ( f @ X3 @ X4 )
          & ! [X8: a,X7: a,X4: b] :
              ( ( ( f @ X7 @ X4 )
                & ( f @ X8 @ X4 ) )
             => ( cR @ X7 @ X8 ) ) )
       => ! [X3: a] :
          ? [X4: b] :
          ! [X2: a] :
            ( ( f @ X3 @ X4 )
            | ( ( cR @ X3 @ z )
              & ~ ( f @ X2 @ X4 ) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ( ! [X3: a] : ( cR @ X3 @ X3 )
      & ! [X0: a,X1: a,X2: a] :
          ( ( ( cR @ X2 @ X1 )
            & ( cR @ X0 @ X1 ) )
         => ( cR @ X0 @ X2 ) ) )
   => ( ( ! [X3: a,X6: b,X5: b] :
            ( ( ( f @ X3 @ X5 )
              & ( f @ X3 @ X6 ) )
           => ( cS @ X5 @ X6 ) )
        & ! [X3: a] :
          ? [X4: b] : ( f @ X3 @ X4 )
        & ! [X8: a,X7: a,X4: b] :
            ( ( ( f @ X7 @ X4 )
              & ( f @ X8 @ X4 ) )
           => ( cR @ X7 @ X8 ) ) )
     => ! [X3: a] :
        ? [X4: b] :
        ! [X2: a] :
          ( ( f @ X3 @ X4 )
          | ( ( cR @ X3 @ z )
            & ~ ( f @ X2 @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM552C_pme) ).

thf(f15,plain,
    ! [X13: b] :
      ( ( f @ sK1 @ X13 )
     != $true ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEV097^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14  % 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
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 18:31:53 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  % (20479)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37  % (20473)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37  % (20475)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)
% 0.14/0.37  % (20474)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)
% 0.14/0.37  % (20476)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37  % (20477)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)
% 0.14/0.37  % (20480)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)
% 0.14/0.37  % (20476)Instruction limit reached!
% 0.14/0.37  % (20476)------------------------------
% 0.14/0.37  % (20476)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (20476)Termination reason: Unknown
% 0.14/0.37  % (20477)Instruction limit reached!
% 0.14/0.37  % (20477)------------------------------
% 0.14/0.37  % (20477)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (20476)Termination phase: Preprocessing 3
% 0.14/0.37  
% 0.14/0.37  % (20476)Memory used [KB]: 895
% 0.14/0.37  % (20476)Time elapsed: 0.003 s
% 0.14/0.37  % (20476)Instructions burned: 2 (million)
% 0.14/0.37  % (20476)------------------------------
% 0.14/0.37  % (20476)------------------------------
% 0.14/0.37  % (20477)Termination reason: Unknown
% 0.14/0.37  % (20477)Termination phase: Property scanning
% 0.14/0.37  
% 0.14/0.37  % (20477)Memory used [KB]: 895
% 0.14/0.37  % (20477)Time elapsed: 0.003 s
% 0.14/0.37  % (20477)Instructions burned: 2 (million)
% 0.14/0.37  % (20477)------------------------------
% 0.14/0.37  % (20477)------------------------------
% 0.14/0.37  % (20479)First to succeed.
% 0.14/0.37  % (20480)Instruction limit reached!
% 0.14/0.37  % (20480)------------------------------
% 0.14/0.37  % (20480)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (20480)Termination reason: Unknown
% 0.14/0.37  % (20480)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (20480)Memory used [KB]: 5500
% 0.14/0.37  % (20480)Time elapsed: 0.004 s
% 0.14/0.37  % (20480)Instructions burned: 3 (million)
% 0.14/0.37  % (20480)------------------------------
% 0.14/0.37  % (20480)------------------------------
% 0.14/0.37  % (20474)Instruction limit reached!
% 0.14/0.37  % (20474)------------------------------
% 0.14/0.37  % (20474)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (20474)Termination reason: Unknown
% 0.14/0.37  % (20474)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (20474)Memory used [KB]: 5500
% 0.14/0.37  % (20474)Time elapsed: 0.005 s
% 0.14/0.37  % (20474)Instructions burned: 4 (million)
% 0.14/0.37  % (20474)------------------------------
% 0.14/0.37  % (20474)------------------------------
% 0.14/0.37  % (20473)Also succeeded, but the first one will report.
% 0.14/0.37  % (20475)Also succeeded, but the first one will report.
% 0.14/0.37  % (20479)Refutation found. Thanks to Tanya!
% 0.14/0.37  % SZS status Theorem for theBenchmark
% 0.14/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37  % (20479)------------------------------
% 0.14/0.37  % (20479)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (20479)Termination reason: Refutation
% 0.14/0.37  
% 0.14/0.37  % (20479)Memory used [KB]: 5500
% 0.14/0.37  % (20479)Time elapsed: 0.006 s
% 0.14/0.37  % (20479)Instructions burned: 3 (million)
% 0.14/0.37  % (20479)------------------------------
% 0.14/0.37  % (20479)------------------------------
% 0.14/0.37  % (20472)Success in time 0.007 s
% 0.14/0.37  % Vampire---4.8 exiting
%------------------------------------------------------------------------------