TSTP Solution File: SEV055^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV055^5 : 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 : n016.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 04:11:51 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   25 (   4 unt;   7 typ;   0 def)
%            Number of atoms       :  231 (  96 equ;   0 cnn)
%            Maximal formula atoms :   22 (  12 avg)
%            Number of connectives :  462 (  47   ~;  35   |;  46   &; 303   @)
%                                         (   0 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   62 (  62   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  146 (   5   ^ 116   !;  24   ?; 146   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

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

thf(func_def_7,type,
    sK3: a > ( a > $o ) > a ).

thf(func_def_10,type,
    ph5: 
      !>[X0: $tType] : X0 ).

thf(f38,plain,
    $false,
    inference(trivial_inequality_removal,[],[f35]) ).

thf(f35,plain,
    $true != $true,
    inference(superposition,[],[f18,f34]) ).

thf(f34,plain,
    ! [X7: a] :
      ( ( sK0
        @ ( sK1
          @ ^ [Y0: a] : $false )
        @ X7 )
      = $true ),
    inference(trivial_inequality_removal,[],[f33]) ).

thf(f33,plain,
    ! [X7: a] :
      ( ( ( sK0
          @ ( sK1
            @ ^ [Y0: a] : $false )
          @ X7 )
        = $true )
      | ( $false = $true ) ),
    inference(beta_eta_normalization,[],[f28]) ).

thf(f28,plain,
    ! [X7: a] :
      ( ( ( ^ [Y0: a] : $false
          @ ( sK3 @ X7
            @ ^ [Y0: a] : $false ) )
        = $true )
      | ( ( sK0
          @ ( sK1
            @ ^ [Y0: a] : $false )
          @ X7 )
        = $true ) ),
    inference(primitive_instantiation,[],[f16]) ).

thf(f16,plain,
    ! [X6: a > $o,X7: a] :
      ( ( ( X6 @ ( sK3 @ X7 @ X6 ) )
        = $true )
      | ( ( sK0 @ ( sK1 @ X6 ) @ X7 )
        = $true ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ! [X3: a] :
        ( ( sK0 @ X3 @ ( sK2 @ X3 ) )
       != $true )
    & ! [X4: a,X5: a] :
        ( ( ( sK0 @ ( sK2 @ X5 ) @ ( sK2 @ X4 ) )
          = $true )
        | ( ( sK0 @ X5 @ X4 )
         != $true ) )
    & ! [X6: a > $o] :
        ( ! [X7: a] :
            ( ( ( ( X6 @ ( sK3 @ X7 @ X6 ) )
                = $true )
              & ( ( sK0 @ ( sK3 @ X7 @ X6 ) @ X7 )
               != $true ) )
            | ( ( sK0 @ ( sK1 @ X6 ) @ X7 )
              = $true ) )
        & ! [X9: a] :
            ( ( ( sK0 @ X9 @ ( sK1 @ X6 ) )
              = $true )
            | ( ( X6 @ X9 )
             != $true ) ) )
    & ! [X10: a,X11: a,X12: a] :
        ( ( ( sK0 @ X10 @ X11 )
          = $true )
        | ( ( sK0 @ X10 @ X12 )
         != $true )
        | ( ( sK0 @ X12 @ X11 )
         != $true ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9]) ).

thf(f9,plain,
    ( ? [X0: a > a > $o,X1: ( a > $o ) > a] :
        ( ? [X2: a > a] :
            ( ! [X3: a] :
                ( $true
               != ( X0 @ X3 @ ( X2 @ X3 ) ) )
            & ! [X4: a,X5: a] :
                ( ( ( X0 @ ( X2 @ X5 ) @ ( X2 @ X4 ) )
                  = $true )
                | ( ( X0 @ X5 @ X4 )
                 != $true ) ) )
        & ! [X6: a > $o] :
            ( ! [X7: a] :
                ( ? [X8: a] :
                    ( ( ( X6 @ X8 )
                      = $true )
                    & ( ( X0 @ X8 @ X7 )
                     != $true ) )
                | ( ( X0 @ ( X1 @ X6 ) @ X7 )
                  = $true ) )
            & ! [X9: a] :
                ( ( ( X0 @ X9 @ ( X1 @ X6 ) )
                  = $true )
                | ( ( X6 @ X9 )
                 != $true ) ) )
        & ! [X10: a,X11: a,X12: a] :
            ( ( ( X0 @ X10 @ X11 )
              = $true )
            | ( ( X0 @ X10 @ X12 )
             != $true )
            | ( ( X0 @ X12 @ X11 )
             != $true ) ) )
   => ( ? [X2: a > a] :
          ( ! [X3: a] :
              ( ( sK0 @ X3 @ ( X2 @ X3 ) )
             != $true )
          & ! [X5: a,X4: a] :
              ( ( ( sK0 @ ( X2 @ X5 ) @ ( X2 @ X4 ) )
                = $true )
              | ( ( sK0 @ X5 @ X4 )
               != $true ) ) )
      & ! [X6: a > $o] :
          ( ! [X7: a] :
              ( ? [X8: a] :
                  ( ( ( X6 @ X8 )
                    = $true )
                  & ( ( sK0 @ X8 @ X7 )
                   != $true ) )
              | ( ( sK0 @ ( sK1 @ X6 ) @ X7 )
                = $true ) )
          & ! [X9: a] :
              ( ( ( sK0 @ X9 @ ( sK1 @ X6 ) )
                = $true )
              | ( ( X6 @ X9 )
               != $true ) ) )
      & ! [X12: a,X11: a,X10: a] :
          ( ( ( sK0 @ X10 @ X11 )
            = $true )
          | ( ( sK0 @ X10 @ X12 )
           != $true )
          | ( ( sK0 @ X12 @ X11 )
           != $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ( ? [X2: a > a] :
        ( ! [X3: a] :
            ( ( sK0 @ X3 @ ( X2 @ X3 ) )
           != $true )
        & ! [X5: a,X4: a] :
            ( ( ( sK0 @ ( X2 @ X5 ) @ ( X2 @ X4 ) )
              = $true )
            | ( ( sK0 @ X5 @ X4 )
             != $true ) ) )
   => ( ! [X3: a] :
          ( ( sK0 @ X3 @ ( sK2 @ X3 ) )
         != $true )
      & ! [X5: a,X4: a] :
          ( ( ( sK0 @ ( sK2 @ X5 ) @ ( sK2 @ X4 ) )
            = $true )
          | ( ( sK0 @ X5 @ X4 )
           != $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X6: a > $o,X7: a] :
      ( ? [X8: a] :
          ( ( ( X6 @ X8 )
            = $true )
          & ( ( sK0 @ X8 @ X7 )
           != $true ) )
     => ( ( ( X6 @ ( sK3 @ X7 @ X6 ) )
          = $true )
        & ( ( sK0 @ ( sK3 @ X7 @ X6 ) @ X7 )
         != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ? [X0: a > a > $o,X1: ( a > $o ) > a] :
      ( ? [X2: a > a] :
          ( ! [X3: a] :
              ( $true
             != ( X0 @ X3 @ ( X2 @ X3 ) ) )
          & ! [X4: a,X5: a] :
              ( ( ( X0 @ ( X2 @ X5 ) @ ( X2 @ X4 ) )
                = $true )
              | ( ( X0 @ X5 @ X4 )
               != $true ) ) )
      & ! [X6: a > $o] :
          ( ! [X7: a] :
              ( ? [X8: a] :
                  ( ( ( X6 @ X8 )
                    = $true )
                  & ( ( X0 @ X8 @ X7 )
                   != $true ) )
              | ( ( X0 @ ( X1 @ X6 ) @ X7 )
                = $true ) )
          & ! [X9: a] :
              ( ( ( X0 @ X9 @ ( X1 @ X6 ) )
                = $true )
              | ( ( X6 @ X9 )
               != $true ) ) )
      & ! [X10: a,X11: a,X12: a] :
          ( ( ( X0 @ X10 @ X11 )
            = $true )
          | ( ( X0 @ X10 @ X12 )
           != $true )
          | ( ( X0 @ X12 @ X11 )
           != $true ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ? [X0: a > a > $o,X1: ( a > $o ) > a] :
      ( ? [X9: a > a] :
          ( ! [X12: a] :
              ( ( X0 @ X12 @ ( X9 @ X12 ) )
             != $true )
          & ! [X11: a,X10: a] :
              ( ( ( X0 @ ( X9 @ X10 ) @ ( X9 @ X11 ) )
                = $true )
              | ( ( X0 @ X10 @ X11 )
               != $true ) ) )
      & ! [X2: a > $o] :
          ( ! [X3: a] :
              ( ? [X4: a] :
                  ( ( ( X2 @ X4 )
                    = $true )
                  & ( ( X0 @ X4 @ X3 )
                   != $true ) )
              | ( ( X0 @ ( X1 @ X2 ) @ X3 )
                = $true ) )
          & ! [X5: a] :
              ( ( ( X0 @ X5 @ ( X1 @ X2 ) )
                = $true )
              | ( ( X2 @ X5 )
               != $true ) ) )
      & ! [X7: a,X6: a,X8: a] :
          ( ( ( X0 @ X7 @ X6 )
            = $true )
          | ( ( X0 @ X7 @ X8 )
           != $true )
          | ( ( X0 @ X8 @ X6 )
           != $true ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ? [X1: ( a > $o ) > a,X0: a > a > $o] :
      ( ? [X9: a > a] :
          ( ! [X12: a] :
              ( ( X0 @ X12 @ ( X9 @ X12 ) )
             != $true )
          & ! [X11: a,X10: a] :
              ( ( ( X0 @ ( X9 @ X10 ) @ ( X9 @ X11 ) )
                = $true )
              | ( ( X0 @ X10 @ X11 )
               != $true ) ) )
      & ! [X8: a,X7: a,X6: a] :
          ( ( ( X0 @ X7 @ X6 )
            = $true )
          | ( ( X0 @ X8 @ X6 )
           != $true )
          | ( ( X0 @ X7 @ X8 )
           != $true ) )
      & ! [X2: a > $o] :
          ( ! [X3: a] :
              ( ? [X4: a] :
                  ( ( ( X2 @ X4 )
                    = $true )
                  & ( ( X0 @ X4 @ X3 )
                   != $true ) )
              | ( ( X0 @ ( X1 @ X2 ) @ X3 )
                = $true ) )
          & ! [X5: a] :
              ( ( ( X0 @ X5 @ ( X1 @ X2 ) )
                = $true )
              | ( ( X2 @ X5 )
               != $true ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

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

thf(f4,plain,
    ~ ! [X0: a > a > $o,X1: ( a > $o ) > a] :
        ( ( ! [X2: a > $o] :
              ( ! [X3: a] :
                  ( ! [X4: a] :
                      ( ( X2 @ X4 )
                     => ( X0 @ X4 @ X3 ) )
                 => ( X0 @ ( X1 @ X2 ) @ X3 ) )
              & ! [X5: a] :
                  ( ( X2 @ X5 )
                 => ( X0 @ X5 @ ( X1 @ X2 ) ) ) )
          & ! [X6: a,X7: a,X8: a] :
              ( ( ( X0 @ X8 @ X6 )
                & ( X0 @ X7 @ X8 ) )
             => ( X0 @ X7 @ X6 ) ) )
       => ! [X9: a > a] :
            ( ! [X10: a,X11: a] :
                ( ( X0 @ X10 @ X11 )
               => ( X0 @ ( X9 @ X10 ) @ ( X9 @ X11 ) ) )
           => ? [X12: a] : ( X0 @ X12 @ ( X9 @ X12 ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a > a > $o,X1: ( a > $o ) > a] :
        ( ( ! [X5: a > $o] :
              ( ! [X6: a] :
                  ( ! [X7: a] :
                      ( ( X5 @ X7 )
                     => ( X0 @ X7 @ X6 ) )
                 => ( X0 @ ( X1 @ X5 ) @ X6 ) )
              & ! [X4: a] :
                  ( ( X5 @ X4 )
                 => ( X0 @ X4 @ ( X1 @ X5 ) ) ) )
          & ! [X4: a,X2: a,X3: a] :
              ( ( ( X0 @ X3 @ X4 )
                & ( X0 @ X2 @ X3 ) )
             => ( X0 @ X2 @ X4 ) ) )
       => ! [X8: a > a] :
            ( ! [X2: a,X3: a] :
                ( ( X0 @ X2 @ X3 )
               => ( X0 @ ( X8 @ X2 ) @ ( X8 @ X3 ) ) )
           => ? [X9: a] : ( X0 @ X9 @ ( X8 @ X9 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > a > $o,X1: ( a > $o ) > a] :
      ( ( ! [X5: a > $o] :
            ( ! [X6: a] :
                ( ! [X7: a] :
                    ( ( X5 @ X7 )
                   => ( X0 @ X7 @ X6 ) )
               => ( X0 @ ( X1 @ X5 ) @ X6 ) )
            & ! [X4: a] :
                ( ( X5 @ X4 )
               => ( X0 @ X4 @ ( X1 @ X5 ) ) ) )
        & ! [X4: a,X2: a,X3: a] :
            ( ( ( X0 @ X3 @ X4 )
              & ( X0 @ X2 @ X3 ) )
           => ( X0 @ X2 @ X4 ) ) )
     => ! [X8: a > a] :
          ( ! [X2: a,X3: a] :
              ( ( X0 @ X2 @ X3 )
             => ( X0 @ ( X8 @ X2 ) @ ( X8 @ X3 ) ) )
         => ? [X9: a] : ( X0 @ X9 @ ( X8 @ X9 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM402_pme) ).

thf(f18,plain,
    ! [X3: a] :
      ( ( sK0 @ X3 @ ( sK2 @ X3 ) )
     != $true ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEV055^5 : 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
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 19:23:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a TH0_THM_NEQ_NAR problem
% 0.13/0.35  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
% 0.13/0.37  % (23173)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37  % (23171)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)
% 0.13/0.37  % (23170)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37  % (23172)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)
% 0.13/0.37  % (23175)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 (2999ds/275Mi)
% 0.13/0.37  % (23176)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37  % (23173)Instruction limit reached!
% 0.13/0.37  % (23173)------------------------------
% 0.13/0.37  % (23173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (23173)Termination reason: Unknown
% 0.13/0.37  % (23173)Termination phase: Preprocessing 3
% 0.13/0.37  
% 0.13/0.37  % (23173)Memory used [KB]: 895
% 0.13/0.37  % (23173)Time elapsed: 0.003 s
% 0.13/0.37  % (23173)Instructions burned: 2 (million)
% 0.13/0.37  % (23173)------------------------------
% 0.13/0.37  % (23173)------------------------------
% 0.13/0.37  % (23171)Instruction limit reached!
% 0.13/0.37  % (23171)------------------------------
% 0.13/0.37  % (23171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (23171)Termination reason: Unknown
% 0.13/0.37  % (23174)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)
% 0.13/0.37  % (23171)Termination phase: Saturation
% 0.13/0.37  
% 0.13/0.37  % (23171)Memory used [KB]: 5500
% 0.13/0.37  % (23171)Time elapsed: 0.005 s
% 0.13/0.37  % (23171)Instructions burned: 4 (million)
% 0.13/0.37  % (23171)------------------------------
% 0.13/0.37  % (23171)------------------------------
% 0.13/0.37  % (23174)Instruction limit reached!
% 0.13/0.37  % (23174)------------------------------
% 0.13/0.37  % (23174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (23174)Termination reason: Unknown
% 0.13/0.37  % (23174)Termination phase: Saturation
% 0.13/0.37  
% 0.13/0.37  % (23174)Memory used [KB]: 1023
% 0.13/0.37  % (23174)Time elapsed: 0.003 s
% 0.13/0.37  % (23174)Instructions burned: 3 (million)
% 0.13/0.37  % (23174)------------------------------
% 0.13/0.37  % (23174)------------------------------
% 0.13/0.37  % (23175)First to succeed.
% 0.13/0.38  % (23175)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Theorem for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38  % (23175)------------------------------
% 0.22/0.38  % (23175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38  % (23175)Termination reason: Refutation
% 0.22/0.38  
% 0.22/0.38  % (23175)Memory used [KB]: 5500
% 0.22/0.38  % (23175)Time elapsed: 0.008 s
% 0.22/0.38  % (23175)Instructions burned: 6 (million)
% 0.22/0.38  % (23175)------------------------------
% 0.22/0.38  % (23175)------------------------------
% 0.22/0.38  % (23169)Success in time 0.008 s
% 0.22/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------