TSTP Solution File: SEV195^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV195^5 : 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 : n008.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 04:12:20 EDT 2024

% Result   : Theorem 0.12s 0.32s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   28 (   3 unt;   8 typ;   0 def)
%            Number of atoms       :  149 ( 111 equ;   0 cnn)
%            Maximal formula atoms :   11 (   7 avg)
%            Number of connectives :  320 (  56   ~;  24   |;  54   &; 168   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  128 (   9   ^  98   !;  20   ?; 128   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_1,type,
    cP: a > a > a ).

thf(func_def_2,type,
    cZ: a ).

thf(func_def_6,type,
    sK0: ( a > $o ) > a ).

thf(func_def_7,type,
    sK1: ( a > $o ) > a ).

thf(func_def_8,type,
    sK2: a ).

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

thf(f271,plain,
    $false,
    inference(trivial_inequality_removal,[],[f243]) ).

thf(f243,plain,
    ( ( sK2 != sK2 )
    | ( cZ != cZ ) ),
    inference(superposition,[],[f15,f205]) ).

thf(f205,plain,
    ! [X0: a] :
      ( ( cZ = X0 )
      | ( sK2 != X0 ) ),
    inference(superposition,[],[f14,f88]) ).

thf(f88,plain,
    ! [X0: a] :
      ( ( ( cP
          @ ( sK1
            @ ^ [Y0: a] : ( X0 != Y0 ) )
          @ ( sK0
            @ ^ [Y0: a] : ( X0 != Y0 ) ) )
        = X0 )
      | ( cZ = X0 ) ),
    inference(equality_proxy_clausification,[],[f87]) ).

thf(f87,plain,
    ! [X0: a] :
      ( ( ( cP
          @ ( sK1
            @ ^ [Y0: a] : ( X0 != Y0 ) )
          @ ( sK0
            @ ^ [Y0: a] : ( X0 != Y0 ) ) )
        = X0 )
      | ( $true
        = ( X0 = cZ ) ) ),
    inference(not_proxy_clausification,[],[f86]) ).

thf(f86,plain,
    ! [X0: a] :
      ( ( ( X0 != cZ )
       != $true )
      | ( ( cP
          @ ( sK1
            @ ^ [Y0: a] : ( X0 != Y0 ) )
          @ ( sK0
            @ ^ [Y0: a] : ( X0 != Y0 ) ) )
        = X0 ) ),
    inference(beta_eta_normalization,[],[f81]) ).

thf(f81,plain,
    ! [X0: a] :
      ( ( ( cP
          @ ( sK1
            @ ^ [Y0: a] : ( X0 != Y0 ) )
          @ ( sK0
            @ ^ [Y0: a] : ( X0 != Y0 ) ) )
        = X0 )
      | ( ( ^ [Y0: a] : ( X0 != Y0 )
          @ cZ )
       != $true ) ),
    inference(leibniz_equality_elimination,[],[f17]) ).

thf(f17,plain,
    ! [X2: a > $o,X5: a] :
      ( ( ( X2 @ ( cP @ ( sK1 @ X2 ) @ ( sK0 @ X2 ) ) )
       != $true )
      | ( ( X2 @ X5 )
        = $true )
      | ( ( X2 @ cZ )
       != $true ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ( ! [X0: a,X1: a] :
        ( cZ
       != ( cP @ X1 @ X0 ) )
    & ! [X2: a > $o] :
        ( ( ( ( X2 @ ( sK1 @ X2 ) )
            = $true )
          & ( ( X2 @ ( cP @ ( sK1 @ X2 ) @ ( sK0 @ X2 ) ) )
           != $true )
          & ( ( X2 @ ( sK0 @ X2 ) )
            = $true ) )
        | ! [X5: a] :
            ( ( X2 @ X5 )
            = $true )
        | ( ( X2 @ cZ )
         != $true ) )
    & ( cZ != sK2 )
    & ! [X7: a,X8: a] :
        ( sK2
       != ( cP @ X8 @ X7 ) )
    & ! [X9: a,X10: a,X11: a,X12: a] :
        ( ( ( X9 = X10 )
          & ( X11 = X12 ) )
        | ( ( cP @ X11 @ X9 )
         != ( cP @ X12 @ X10 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).

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

thf(f10,plain,
    ( ? [X6: a] :
        ( ( cZ != X6 )
        & ! [X7: a,X8: a] :
            ( ( cP @ X8 @ X7 )
           != X6 ) )
   => ( ( cZ != sK2 )
      & ! [X8: a,X7: a] :
          ( sK2
         != ( cP @ X8 @ X7 ) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

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

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

thf(f1,conjecture,
    ( ( ! [X4: a > $o] :
          ( ( ! [X1: a,X0: a] :
                ( ( ( X4 @ X0 )
                  & ( X4 @ X1 ) )
               => ( X4 @ ( cP @ X0 @ X1 ) ) )
            & ( X4 @ cZ ) )
         => ! [X0: a] : ( X4 @ X0 ) )
      & ! [X1: a,X0: a] :
          ( ( cP @ X0 @ X1 )
         != cZ )
      & ! [X0: a,X1: a,X2: a,X3: a] :
          ( ( ( cP @ X0 @ X2 )
            = ( cP @ X1 @ X3 ) )
         => ( ( X2 = X3 )
            & ( X0 = X1 ) ) ) )
   => ! [X0: a] :
        ( ( cZ = X0 )
        | ? [X5: a,X1: a] :
            ( ( cP @ X1 @ X5 )
            = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_LEM1D_pme) ).

thf(f14,plain,
    ! [X8: a,X7: a] :
      ( sK2
     != ( cP @ X8 @ X7 ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f15,plain,
    cZ != sK2,
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : SEV195^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.09  % 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
% 0.08/0.29  % Computer : n008.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit   : 300
% 0.08/0.29  % WCLimit    : 300
% 0.08/0.29  % DateTime   : Sun May 19 18:32:07 EDT 2024
% 0.08/0.29  % CPUTime    : 
% 0.08/0.29  This is a TH0_THM_EQU_NAR problem
% 0.08/0.29  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
% 0.08/0.30  % (686)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.08/0.31  % (687)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)
% 0.08/0.31  % (690)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)
% 0.08/0.31  % (691)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)
% 0.08/0.31  % (692)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.08/0.31  % (689)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.08/0.31  % (688)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)
% 0.08/0.31  % (693)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)
% 0.08/0.31  % (689)Instruction limit reached!
% 0.08/0.31  % (689)------------------------------
% 0.08/0.31  % (689)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.31  % (689)Termination reason: Unknown
% 0.08/0.31  % (689)Termination phase: Preprocessing 3
% 0.08/0.31  % (690)Instruction limit reached!
% 0.08/0.31  % (690)------------------------------
% 0.08/0.31  % (690)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.31  % (690)Termination reason: Unknown
% 0.08/0.31  % (690)Termination phase: Property scanning
% 0.08/0.31  
% 0.08/0.31  % (690)Memory used [KB]: 895
% 0.08/0.31  % (690)Time elapsed: 0.002 s
% 0.08/0.31  % (690)Instructions burned: 2 (million)
% 0.08/0.31  % (690)------------------------------
% 0.08/0.31  % (690)------------------------------
% 0.08/0.31  
% 0.08/0.31  % (689)Memory used [KB]: 895
% 0.08/0.31  % (689)Time elapsed: 0.002 s
% 0.08/0.31  % (689)Instructions burned: 2 (million)
% 0.08/0.31  % (689)------------------------------
% 0.08/0.31  % (689)------------------------------
% 0.08/0.31  % (693)Instruction limit reached!
% 0.08/0.31  % (693)------------------------------
% 0.08/0.31  % (693)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.31  % (693)Termination reason: Unknown
% 0.08/0.31  % (693)Termination phase: Saturation
% 0.08/0.31  
% 0.08/0.31  % (693)Memory used [KB]: 5500
% 0.08/0.31  % (693)Time elapsed: 0.004 s
% 0.08/0.31  % (693)Instructions burned: 3 (million)
% 0.08/0.31  % (693)------------------------------
% 0.08/0.31  % (693)------------------------------
% 0.08/0.31  % (688)Refutation not found, incomplete strategy
% 0.08/0.31  % (688)------------------------------
% 0.08/0.31  % (688)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.31  % (688)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.31  
% 0.08/0.31  
% 0.08/0.31  % (688)Memory used [KB]: 5500
% 0.08/0.31  % (688)Time elapsed: 0.003 s
% 0.08/0.31  % (688)Instructions burned: 2 (million)
% 0.08/0.31  % (688)------------------------------
% 0.08/0.31  % (688)------------------------------
% 0.08/0.31  % (687)Instruction limit reached!
% 0.08/0.31  % (687)------------------------------
% 0.08/0.31  % (687)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.31  % (687)Termination reason: Unknown
% 0.08/0.31  % (687)Termination phase: Saturation
% 0.08/0.31  
% 0.08/0.31  % (687)Memory used [KB]: 5500
% 0.08/0.31  % (687)Time elapsed: 0.004 s
% 0.08/0.31  % (687)Instructions burned: 4 (million)
% 0.08/0.31  % (687)------------------------------
% 0.08/0.31  % (687)------------------------------
% 0.12/0.32  % (692)Instruction limit reached!
% 0.12/0.32  % (692)------------------------------
% 0.12/0.32  % (692)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.32  % (692)Termination reason: Unknown
% 0.12/0.32  % (692)Termination phase: Saturation
% 0.12/0.32  
% 0.12/0.32  % (692)Memory used [KB]: 5628
% 0.12/0.32  % (692)Time elapsed: 0.014 s
% 0.12/0.32  % (692)Instructions burned: 19 (million)
% 0.12/0.32  % (692)------------------------------
% 0.12/0.32  % (692)------------------------------
% 0.12/0.32  % (691)First to succeed.
% 0.12/0.32  % (691)Refutation found. Thanks to Tanya!
% 0.12/0.32  % SZS status Theorem for theBenchmark
% 0.12/0.32  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.32  % (691)------------------------------
% 0.12/0.32  % (691)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.32  % (691)Termination reason: Refutation
% 0.12/0.32  
% 0.12/0.32  % (691)Memory used [KB]: 5628
% 0.12/0.32  % (691)Time elapsed: 0.015 s
% 0.12/0.32  % (691)Instructions burned: 18 (million)
% 0.12/0.32  % (691)------------------------------
% 0.12/0.32  % (691)------------------------------
% 0.12/0.32  % (685)Success in time 0.026 s
% 0.12/0.32  % Vampire---4.8 exiting
%------------------------------------------------------------------------------