TSTP Solution File: SEV239^5 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV239^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% 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 : Mon Jun 24 16:02:25 EDT 2024

% Result   : Theorem 0.14s 0.31s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   61 (  10 unt;   0 typ;   0 def)
%            Number of atoms       :  365 ( 140 equ;  23 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :  351 (  50   ~;  75   |;  36   &; 162   @)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  12 usr;  13 con; 0-2 aty)
%                                         (   0  !!;  22  ??;   0 @@+;   0 @@-)
%            Number of variables   :   72 (  46   ^  20   !;   6   ?;  72   :)

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

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

thf(func_def_1,type,
    y: a > $o ).

thf(func_def_13,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_14,type,
    sK2: a ).

thf(func_def_15,type,
    sK3: a > $o ).

thf(func_def_16,type,
    sK4: a ).

thf(func_def_17,type,
    sK5: a ).

thf(f123,plain,
    $false,
    inference(avatar_sat_refutation,[],[f37,f42,f47,f55,f63,f69,f122]) ).

thf(f122,plain,
    ( ~ spl0_1
    | spl0_2
    | ~ spl0_3
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f121]) ).

thf(f121,plain,
    ( $false
    | ~ spl0_1
    | spl0_2
    | ~ spl0_3
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f120,f35]) ).

thf(f35,plain,
    ( ( ( y @ sK2 )
     != $true )
    | spl0_2 ),
    inference(avatar_component_clause,[],[f34]) ).

thf(f34,plain,
    ( spl0_2
  <=> ( ( y @ sK2 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f120,plain,
    ( ( ( y @ sK2 )
      = $true )
    | ~ spl0_1
    | ~ spl0_3
    | ~ spl0_4 ),
    inference(superposition,[],[f41,f118]) ).

thf(f118,plain,
    ( ( sK2 = sK4 )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f113]) ).

thf(f113,plain,
    ( ( sK2 = sK4 )
    | ( $true = $false )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(superposition,[],[f76,f32]) ).

thf(f32,plain,
    ( ( $true
      = ( sK3 @ sK2 ) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f30]) ).

thf(f30,plain,
    ( spl0_1
  <=> ( $true
      = ( sK3 @ sK2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f76,plain,
    ( ! [X1: a] :
        ( ( $false
          = ( sK3 @ X1 ) )
        | ( sK4 = X1 ) )
    | ~ spl0_4 ),
    inference(equality_proxy_clausification,[],[f73]) ).

thf(f73,plain,
    ( ! [X1: a] :
        ( ( $true
          = ( sK4 = X1 ) )
        | ( $false
          = ( sK3 @ X1 ) ) )
    | ~ spl0_4 ),
    inference(binary_proxy_clausification,[],[f71]) ).

thf(f71,plain,
    ( ! [X1: a] :
        ( ( sK4 = X1 )
        = ( sK3 @ X1 ) )
    | ~ spl0_4 ),
    inference(argument_congruence,[],[f46]) ).

thf(f46,plain,
    ( ( sK3
      = ( (=) @ sK4 ) )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f44]) ).

thf(f44,plain,
    ( spl0_4
  <=> ( sK3
      = ( (=) @ sK4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f41,plain,
    ( ( $true
      = ( y @ sK4 ) )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f39]) ).

thf(f39,plain,
    ( spl0_3
  <=> ( $true
      = ( y @ sK4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f69,plain,
    ( ~ spl0_2
    | ~ spl0_6 ),
    inference(avatar_contradiction_clause,[],[f68]) ).

thf(f68,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f64]) ).

thf(f64,plain,
    ( ( $true = $false )
    | ~ spl0_2
    | ~ spl0_6 ),
    inference(superposition,[],[f54,f36]) ).

thf(f36,plain,
    ( ( ( y @ sK2 )
      = $true )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f34]) ).

thf(f54,plain,
    ( ( ( y @ sK2 )
      = $false )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f52]) ).

thf(f52,plain,
    ( spl0_6
  <=> ( ( y @ sK2 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

thf(f63,plain,
    ( ~ spl0_2
    | ~ spl0_5 ),
    inference(avatar_contradiction_clause,[],[f62]) ).

thf(f62,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_5 ),
    inference(trivial_inequality_removal,[],[f58]) ).

thf(f58,plain,
    ( ( $true = $false )
    | ( sK2 != sK2 )
    | ~ spl0_2
    | ~ spl0_5 ),
    inference(superposition,[],[f57,f36]) ).

thf(f57,plain,
    ( ! [X0: a] :
        ( ( $false
          = ( y @ X0 ) )
        | ( sK2 != X0 ) )
    | ~ spl0_5 ),
    inference(equality_proxy_clausification,[],[f56]) ).

thf(f56,plain,
    ( ! [X0: a] :
        ( ( $false
          = ( X0 = sK2 ) )
        | ( $false
          = ( y @ X0 ) ) )
    | ~ spl0_5 ),
    inference(equality_resolution,[],[f50]) ).

thf(f50,plain,
    ( ! [X2: a,X1: a > $o] :
        ( ( ( (=) @ X2 )
         != X1 )
        | ( $false
          = ( X1 @ sK2 ) )
        | ( ( y @ X2 )
          = $false ) )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f49]) ).

thf(f49,plain,
    ( spl0_5
  <=> ! [X2: a,X1: a > $o] :
        ( ( ( y @ X2 )
          = $false )
        | ( $false
          = ( X1 @ sK2 ) )
        | ( ( (=) @ X2 )
         != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f55,plain,
    ( spl0_5
    | spl0_6 ),
    inference(avatar_split_clause,[],[f19,f52,f49]) ).

thf(f19,plain,
    ! [X2: a,X1: a > $o] :
      ( ( ( y @ X2 )
        = $false )
      | ( ( y @ sK2 )
        = $false )
      | ( ( (=) @ X2 )
       != X1 )
      | ( $false
        = ( X1 @ sK2 ) ) ),
    inference(equality_proxy_clausification,[],[f18]) ).

thf(f18,plain,
    ! [X2: a,X1: a > $o] :
      ( ( $false
        = ( X1 @ sK2 ) )
      | ( ( y @ X2 )
        = $false )
      | ( ( y @ sK2 )
        = $false )
      | ( $false
        = ( X1
          = ( (=) @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ! [X2: a,X1: a > $o] :
      ( ( ( y @ sK2 )
        = $false )
      | ( $false
        = ( ( X1
            = ( (=) @ X2 ) )
          & ( y @ X2 ) ) )
      | ( $false
        = ( X1 @ sK2 ) ) ),
    inference(beta_eta_normalization,[],[f16]) ).

thf(f16,plain,
    ! [X2: a,X1: a > $o] :
      ( ( ( y @ sK2 )
        = $false )
      | ( $false
        = ( X1 @ sK2 ) )
      | ( $false
        = ( ^ [Y0: a] :
              ( ( X1
                = ( (=) @ Y0 ) )
              & ( y @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f15]) ).

thf(f15,plain,
    ! [X1: a > $o] :
      ( ( ( y @ sK2 )
        = $false )
      | ( $false
        = ( X1 @ sK2 ) )
      | ( $false
        = ( ?? @ a
          @ ^ [Y0: a] :
              ( ( X1
                = ( (=) @ Y0 ) )
              & ( y @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f14,plain,
    ! [X1: a > $o] :
      ( ( ( y @ sK2 )
        = $false )
      | ( $false
        = ( ( ?? @ a
            @ ^ [Y0: a] :
                ( ( X1
                  = ( (=) @ Y0 ) )
                & ( y @ Y0 ) ) )
          & ( X1 @ sK2 ) ) ) ),
    inference(beta_eta_normalization,[],[f13]) ).

thf(f13,plain,
    ! [X1: a > $o] :
      ( ( $false
        = ( ^ [Y0: a > $o] :
              ( ( ?? @ a
                @ ^ [Y1: a] :
                    ( ( Y0
                      = ( (=) @ Y1 ) )
                    & ( y @ Y1 ) ) )
              & ( Y0 @ sK2 ) )
          @ X1 ) )
      | ( ( y @ sK2 )
        = $false ) ),
    inference(pi_clausification,[],[f12]) ).

thf(f12,plain,
    ( ( ( y @ sK2 )
      = $false )
    | ( ( ?? @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( ?? @ a
              @ ^ [Y1: a] :
                  ( ( Y0
                    = ( (=) @ Y1 ) )
                  & ( y @ Y1 ) ) )
            & ( Y0 @ sK2 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f10]) ).

thf(f10,plain,
    ( ( ?? @ ( a > $o )
      @ ^ [Y0: a > $o] :
          ( ( ?? @ a
            @ ^ [Y1: a] :
                ( ( Y0
                  = ( (=) @ Y1 ) )
                & ( y @ Y1 ) ) )
          & ( Y0 @ sK2 ) ) )
   != ( y @ sK2 ) ),
    inference(beta_eta_normalization,[],[f9]) ).

thf(f9,plain,
    ( ( ^ [Y0: a] :
          ( ?? @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( ?? @ a
                @ ^ [Y2: a] :
                    ( ( Y1
                      = ( (=) @ Y2 ) )
                    & ( y @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ sK2 )
   != ( y @ sK2 ) ),
    inference(negative_extensionality,[],[f8]) ).

thf(f8,plain,
    ( y
   != ( ^ [Y0: a] :
          ( ?? @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( ?? @ a
                @ ^ [Y2: a] :
                    ( ( Y1
                      = ( (=) @ Y2 ) )
                    & ( y @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f7]) ).

thf(f7,plain,
    ( y
   != ( ^ [Y0: a] :
          ( ?? @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( ?? @ a
                @ ^ [Y2: a] :
                    ( ( Y1
                      = ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
                        @ Y2 ) )
                    & ( y @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f6]) ).

thf(f6,plain,
    ( y
   != ( ^ [Y0: a] :
          ( ?? @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( ?? @ a
                @ ^ [Y2: a] :
                    ( ( Y1
                      = ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
                        @ Y2 ) )
                    & ( y @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) ) ) ),
    inference(flattening,[],[f5]) ).

thf(f5,plain,
    ( y
   != ( ^ [Y0: a] :
          ( ?? @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( ?? @ a
                @ ^ [Y2: a] :
                    ( ( Y1
                      = ( ^ [Y3: a,Y4: a] : ( Y3 = Y4 )
                        @ Y2 ) )
                    & ( y @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ( ( ^ [X0: a] :
        ? [X1: a > $o] :
          ( ( X1 @ X0 )
          & ? [X2: a] :
              ( ( y @ X2 )
              & ( X1
                = ( ^ [X0: a,X3: a] : ( X0 = X3 )
                  @ X2 ) ) ) ) )
    = y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5211_pme) ).

thf(f47,plain,
    ( spl0_2
    | spl0_4 ),
    inference(avatar_split_clause,[],[f28,f44,f34]) ).

thf(f28,plain,
    ( ( sK3
      = ( (=) @ sK4 ) )
    | ( ( y @ sK2 )
      = $true ) ),
    inference(equality_proxy_clausification,[],[f27]) ).

thf(f27,plain,
    ( ( ( y @ sK2 )
      = $true )
    | ( $true
      = ( sK3
        = ( (=) @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f25]) ).

thf(f25,plain,
    ( ( ( y @ sK2 )
      = $true )
    | ( $true
      = ( ( sK3
          = ( (=) @ sK4 ) )
        & ( y @ sK4 ) ) ) ),
    inference(beta_eta_normalization,[],[f24]) ).

thf(f24,plain,
    ( ( ( y @ sK2 )
      = $true )
    | ( $true
      = ( ^ [Y0: a] :
            ( ( sK3
              = ( (=) @ Y0 ) )
            & ( y @ Y0 ) )
        @ sK4 ) ) ),
    inference(sigma_clausification,[],[f23]) ).

thf(f23,plain,
    ( ( ( y @ sK2 )
      = $true )
    | ( $true
      = ( ?? @ a
        @ ^ [Y0: a] :
            ( ( sK3
              = ( (=) @ Y0 ) )
            & ( y @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f21]) ).

thf(f21,plain,
    ( ( ( y @ sK2 )
      = $true )
    | ( $true
      = ( ( ?? @ a
          @ ^ [Y0: a] :
              ( ( sK3
                = ( (=) @ Y0 ) )
              & ( y @ Y0 ) ) )
        & ( sK3 @ sK2 ) ) ) ),
    inference(beta_eta_normalization,[],[f20]) ).

thf(f20,plain,
    ( ( $true
      = ( ^ [Y0: a > $o] :
            ( ( ?? @ a
              @ ^ [Y1: a] :
                  ( ( Y0
                    = ( (=) @ Y1 ) )
                  & ( y @ Y1 ) ) )
            & ( Y0 @ sK2 ) )
        @ sK3 ) )
    | ( ( y @ sK2 )
      = $true ) ),
    inference(sigma_clausification,[],[f11]) ).

thf(f11,plain,
    ( ( ( ?? @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( ?? @ a
              @ ^ [Y1: a] :
                  ( ( Y0
                    = ( (=) @ Y1 ) )
                  & ( y @ Y1 ) ) )
            & ( Y0 @ sK2 ) ) )
      = $true )
    | ( ( y @ sK2 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f10]) ).

thf(f42,plain,
    ( spl0_2
    | spl0_3 ),
    inference(avatar_split_clause,[],[f26,f39,f34]) ).

thf(f26,plain,
    ( ( $true
      = ( y @ sK4 ) )
    | ( ( y @ sK2 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f25]) ).

thf(f37,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f22,f34,f30]) ).

thf(f22,plain,
    ( ( $true
      = ( sK3 @ sK2 ) )
    | ( ( y @ sK2 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : SEV239^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.08  % Command    : run_vampire %s %d THM
% 0.08/0.28  % Computer : n028.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit   : 300
% 0.08/0.28  % WCLimit    : 300
% 0.08/0.28  % DateTime   : Fri Jun 21 19:12:53 EDT 2024
% 0.08/0.28  % CPUTime    : 
% 0.13/0.29  This is a TH0_THM_EQU_NAR problem
% 0.13/0.29  Running higher-order theorem proving
% 0.13/0.29  Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.14/0.30  % (15158)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.30  % (15159)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)
% 0.14/0.31  % (15158)First to succeed.
% 0.14/0.31  % (15159)Instruction limit reached!
% 0.14/0.31  % (15159)------------------------------
% 0.14/0.31  % (15159)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.31  % (15159)Termination reason: Unknown
% 0.14/0.31  % (15159)Termination phase: Saturation
% 0.14/0.31  
% 0.14/0.31  % (15159)Memory used [KB]: 5500
% 0.14/0.31  % (15159)Time elapsed: 0.005 s
% 0.14/0.31  % (15159)Instructions burned: 5 (million)
% 0.14/0.31  % (15159)------------------------------
% 0.14/0.31  % (15159)------------------------------
% 0.14/0.31  % (15162)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)
% 0.14/0.31  % (15161)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.31  % (15158)Refutation found. Thanks to Tanya!
% 0.14/0.31  % SZS status Theorem for theBenchmark
% 0.14/0.31  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.31  % (15158)------------------------------
% 0.14/0.31  % (15158)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.31  % (15158)Termination reason: Refutation
% 0.14/0.31  
% 0.14/0.31  % (15158)Memory used [KB]: 5500
% 0.14/0.31  % (15158)Time elapsed: 0.005 s
% 0.14/0.31  % (15158)Instructions burned: 5 (million)
% 0.14/0.31  % (15158)------------------------------
% 0.14/0.31  % (15158)------------------------------
% 0.14/0.31  % (15157)Success in time 0.004 s
%------------------------------------------------------------------------------