TSTP Solution File: SEV179^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV179^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 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 : n028.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 : Sun May  5 09:41:38 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   38 (  23 unt;   7 typ;   0 def)
%            Number of atoms       :  141 (  60 equ;   0 cnn)
%            Maximal formula atoms :    2 (   4 avg)
%            Number of connectives :  277 (  39   ~;   4   |;  25   &; 189   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   83 (  83   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   7 usr;   3 con; 0-2 aty)
%                                         (   0  !!;  19  ??;   0 @@+;   0 @@-)
%            Number of variables   :   62 (  46   ^  10   !;   4   ?;  62   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_0,type,
    cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).

thf(func_def_2,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_13,type,
    sK0: ( $i > $o ) > $i ).

thf(func_def_15,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(func_def_16,type,
    sK3: $i > $o ).

thf(func_def_17,type,
    sK4: $i > $o ).

thf(func_def_18,type,
    sK5: $i > $o ).

thf(f53,plain,
    $false,
    inference(trivial_inequality_removal,[],[f52]) ).

thf(f52,plain,
    $true = $false,
    inference(forward_demodulation,[],[f42,f27]) ).

thf(f27,plain,
    ( $false
    = ( sK3 @ ( sK0 @ sK3 ) ) ),
    inference(not_proxy_clausification,[],[f26]) ).

thf(f26,plain,
    ( $true
    = ( ~ ( sK3 @ ( sK0 @ sK3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f24]) ).

thf(f24,plain,
    ( $true
    = ( ~ ( sK3 @ ( sK0 @ sK3 ) )
      & ( ( sK0 @ sK3 )
        = ( sK0
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( sK0 @ Y1 ) )
                  & ( ( sK0 @ Y1 )
                    = Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f23]) ).

thf(f23,plain,
    ( $true
    = ( ^ [Y0: $i > $o] :
          ( ~ ( Y0 @ ( sK0 @ Y0 ) )
          & ( ( sK0 @ Y0 )
            = ( sK0
              @ ^ [Y1: $i] :
                  ( ?? @ ( $i > $o )
                  @ ^ [Y2: $i > $o] :
                      ( ~ ( Y2 @ ( sK0 @ Y2 ) )
                      & ( ( sK0 @ Y2 )
                        = Y1 ) ) ) ) ) )
      @ sK3 ) ),
    inference(sigma_clausification,[],[f22]) ).

thf(f22,plain,
    ( $true
    = ( ?? @ ( $i > $o )
      @ ^ [Y0: $i > $o] :
          ( ~ ( Y0 @ ( sK0 @ Y0 ) )
          & ( ( sK0 @ Y0 )
            = ( sK0
              @ ^ [Y1: $i] :
                  ( ?? @ ( $i > $o )
                  @ ^ [Y2: $i > $o] :
                      ( ~ ( Y2 @ ( sK0 @ Y2 ) )
                      & ( ( sK0 @ Y2 )
                        = Y1 ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f21]) ).

thf(f21,plain,
    ( $true
    = ( ^ [Y0: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y1: $i > $o] :
              ( ~ ( Y1 @ ( sK0 @ Y1 ) )
              & ( ( sK0 @ Y1 )
                = Y0 ) ) )
      @ ( sK0
        @ ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK0 @ Y1 ) )
                & ( ( sK0 @ Y1 )
                  = Y0 ) ) ) ) ) ),
    inference(equality_resolution,[],[f20]) ).

thf(f20,plain,
    ! [X1: $i > $o] :
      ( ( ( sK0 @ X1 )
       != ( sK0
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( sK0 @ Y1 ) )
                  & ( ( sK0 @ Y1 )
                    = Y0 ) ) ) ) )
      | ( $true
        = ( X1 @ ( sK0 @ X1 ) ) ) ),
    inference(equality_proxy_clausification,[],[f19]) ).

thf(f19,plain,
    ! [X1: $i > $o] :
      ( ( $true
        = ( X1 @ ( sK0 @ X1 ) ) )
      | ( ( ( sK0 @ X1 )
          = ( sK0
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK0 @ Y1 ) )
                    & ( ( sK0 @ Y1 )
                      = Y0 ) ) ) ) )
        = $false ) ),
    inference(not_proxy_clausification,[],[f18]) ).

thf(f18,plain,
    ! [X1: $i > $o] :
      ( ( $false
        = ( ~ ( X1 @ ( sK0 @ X1 ) ) ) )
      | ( ( ( sK0 @ X1 )
          = ( sK0
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK0 @ Y1 ) )
                    & ( ( sK0 @ Y1 )
                      = Y0 ) ) ) ) )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ! [X1: $i > $o] :
      ( $false
      = ( ~ ( X1 @ ( sK0 @ X1 ) )
        & ( ( sK0 @ X1 )
          = ( sK0
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK0 @ Y1 ) )
                    & ( ( sK0 @ Y1 )
                      = Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f16]) ).

thf(f16,plain,
    ! [X1: $i > $o] :
      ( ( ^ [Y0: $i > $o] :
            ( ~ ( Y0 @ ( sK0 @ Y0 ) )
            & ( ( sK0 @ Y0 )
              = ( sK0
                @ ^ [Y1: $i] :
                    ( ?? @ ( $i > $o )
                    @ ^ [Y2: $i > $o] :
                        ( ~ ( Y2 @ ( sK0 @ Y2 ) )
                        & ( ( sK0 @ Y2 )
                          = Y1 ) ) ) ) ) )
        @ X1 )
      = $false ),
    inference(pi_clausification,[],[f15]) ).

thf(f15,plain,
    ( $true
   != ( ?? @ ( $i > $o )
      @ ^ [Y0: $i > $o] :
          ( ~ ( Y0 @ ( sK0 @ Y0 ) )
          & ( ( sK0 @ Y0 )
            = ( sK0
              @ ^ [Y1: $i] :
                  ( ?? @ ( $i > $o )
                  @ ^ [Y2: $i > $o] :
                      ( ~ ( Y2 @ ( sK0 @ Y2 ) )
                      & ( ( sK0 @ Y2 )
                        = Y1 ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f14]) ).

thf(f14,plain,
    ( $true
   != ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y2: $i > $o] :
              ( ~ ( Y2 @ ( Y0 @ Y2 ) )
              & ( ( Y0 @ Y2 )
                = Y1 ) ) )
      @ sK0
      @ ( sK0
        @ ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y2: $i > $o] :
                  ( ~ ( Y2 @ ( Y0 @ Y2 ) )
                  & ( ( Y0 @ Y2 )
                    = Y1 ) ) )
          @ sK0 ) ) ) ),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

thf(f12,plain,
    ( cD_FOR_X5309
    = ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y2: $i > $o] :
              ( ~ ( Y2 @ ( Y0 @ Y2 ) )
              & ( ( Y0 @ Y2 )
                = Y1 ) ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( cD_FOR_X5309
    = ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y2: $i > $o] :
              ( ~ ( Y2 @ ( Y0 @ Y2 ) )
              & ( ( Y0 @ Y2 )
                = Y1 ) ) ) ) ),
    inference(fool_elimination,[],[f7]) ).

thf(f7,plain,
    ( cD_FOR_X5309
    = ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
        ? [X2: $i > $o] :
          ( ( ( X0 @ X2 )
            = X1 )
          & ~ ( X2 @ ( X0 @ X2 ) ) ) ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( cD_FOR_X5309
    = ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
        ? [X2: $i > $o] :
          ( ( ( X0 @ X2 )
            = X1 )
          & ~ ( X2 @ ( X0 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.VuOFkLULov/Vampire---4.8_14595',cD_FOR_X5309_def) ).

thf(f13,plain,
    ( $true
   != ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ( $true
   != ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).

thf(f10,plain,
    ( ? [X0: ( $i > $o ) > $i] :
        ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
       != $true )
   => ( $true
     != ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ? [X0: ( $i > $o ) > $i] :
      ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
     != $true ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ! [X0: ( $i > $o ) > $i] :
        ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
        = $true ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,negated_conjecture,
    ~ ! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
    inference(negated_conjecture,[],[f2]) ).

thf(f2,conjecture,
    ! [X0: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.VuOFkLULov/Vampire---4.8_14595',cTHM144C_pme) ).

thf(f42,plain,
    ( $true
    = ( sK3 @ ( sK0 @ sK3 ) ) ),
    inference(equality_resolution,[],[f30]) ).

thf(f30,plain,
    ! [X0: $i > $o] :
      ( ( ( sK0 @ X0 )
       != ( sK0 @ sK3 ) )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(superposition,[],[f20,f28]) ).

thf(f28,plain,
    ( ( sK0 @ sK3 )
    = ( sK0
      @ ^ [Y0: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y1: $i > $o] :
              ( ~ ( Y1 @ ( sK0 @ Y1 ) )
              & ( ( sK0 @ Y1 )
                = Y0 ) ) ) ) ),
    inference(equality_proxy_clausification,[],[f25]) ).

thf(f25,plain,
    ( $true
    = ( ( sK0 @ sK3 )
      = ( sK0
        @ ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK0 @ Y1 ) )
                & ( ( sK0 @ Y1 )
                  = Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SEV179^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.12/0.15  % 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
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 12:18:33 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TH0_THM_EQU_NAR problem
% 0.15/0.36  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/tmp/tmp.VuOFkLULov/Vampire---4.8_14595
% 0.15/0.38  % (14789)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 Vampire---4 for (3000ds/4Mi)
% 0.15/0.38  % (14790)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 Vampire---4 for (3000ds/27Mi)
% 0.15/0.38  % (14791)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.15/0.38  % (14791)Instruction limit reached!
% 0.15/0.38  % (14791)------------------------------
% 0.15/0.38  % (14791)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (14791)Termination reason: Unknown
% 0.15/0.38  % (14791)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (14791)Memory used [KB]: 5500
% 0.15/0.38  % (14791)Time elapsed: 0.004 s
% 0.15/0.38  % (14791)Instructions burned: 2 (million)
% 0.15/0.38  % (14791)------------------------------
% 0.15/0.38  % (14791)------------------------------
% 0.15/0.38  % (14793)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (3000ds/275Mi)
% 0.15/0.38  % (14795)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (3000ds/3Mi)
% 0.15/0.38  % (14788)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (3000ds/183Mi)
% 0.15/0.38  % (14793)Refutation not found, incomplete strategy
% 0.15/0.38  % (14793)------------------------------
% 0.15/0.38  % (14793)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (14793)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38  
% 0.15/0.38  
% 0.15/0.38  % (14793)Memory used [KB]: 5373
% 0.15/0.38  % (14793)Time elapsed: 0.002 s
% 0.15/0.38  % (14793)Instructions burned: 1 (million)
% 0.15/0.38  % (14793)------------------------------
% 0.15/0.38  % (14793)------------------------------
% 0.15/0.38  % (14789)Instruction limit reached!
% 0.15/0.38  % (14789)------------------------------
% 0.15/0.38  % (14789)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (14789)Termination reason: Unknown
% 0.15/0.38  % (14789)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (14789)Memory used [KB]: 5500
% 0.15/0.38  % (14789)Time elapsed: 0.006 s
% 0.15/0.38  % (14789)Instructions burned: 5 (million)
% 0.15/0.38  % (14789)------------------------------
% 0.15/0.38  % (14789)------------------------------
% 0.15/0.38  % (14795)Refutation not found, incomplete strategy
% 0.15/0.38  % (14795)------------------------------
% 0.15/0.38  % (14795)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (14795)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38  
% 0.15/0.38  
% 0.15/0.38  % (14795)Memory used [KB]: 5500
% 0.15/0.38  % (14795)Time elapsed: 0.003 s
% 0.15/0.38  % (14795)Instructions burned: 2 (million)
% 0.15/0.38  % (14795)------------------------------
% 0.15/0.38  % (14795)------------------------------
% 0.15/0.38  % (14790)First to succeed.
% 0.15/0.38  % (14792)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.15/0.38  % (14792)Instruction limit reached!
% 0.15/0.38  % (14792)------------------------------
% 0.15/0.38  % (14792)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (14792)Termination reason: Unknown
% 0.15/0.38  % (14792)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (14792)Memory used [KB]: 895
% 0.15/0.38  % (14792)Time elapsed: 0.003 s
% 0.15/0.38  % (14792)Instructions burned: 2 (million)
% 0.15/0.38  % (14792)------------------------------
% 0.15/0.38  % (14792)------------------------------
% 0.15/0.38  % (14788)Also succeeded, but the first one will report.
% 0.15/0.38  % (14790)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for Vampire---4
% 0.15/0.38  % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.38  % (14790)------------------------------
% 0.15/0.38  % (14790)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (14790)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (14790)Memory used [KB]: 5500
% 0.15/0.38  % (14790)Time elapsed: 0.007 s
% 0.15/0.38  % (14790)Instructions burned: 5 (million)
% 0.15/0.38  % (14790)------------------------------
% 0.15/0.38  % (14790)------------------------------
% 0.15/0.38  % (14787)Success in time 0.018 s
% 0.15/0.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------