TSTP Solution File: SEV177^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV177^5 : 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 : n004.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 04:12:16 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   34 (  20 unt;   6 typ;   0 def)
%            Number of atoms       :  142 (  70 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  302 (  44   ~;   4   |;  34   &; 192   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   81 (  81   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   6 usr;   3 con; 0-2 aty)
%                                         (   0  !!;  23  ??;   0 @@+;   0 @@-)
%            Number of variables   :   71 (  49   ^  14   !;   7   ?;  71   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_10,type,
    sK0: $i > $o ).

thf(func_def_11,type,
    sK1: ( $i > $o ) > $i ).

thf(func_def_13,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_14,type,
    sK4: $i > $o ).

thf(func_def_15,type,
    sK5: $i > $o ).

thf(func_def_16,type,
    sK6: $i > $o ).

thf(f49,plain,
    $false,
    inference(trivial_inequality_removal,[],[f48]) ).

thf(f48,plain,
    $true = $false,
    inference(forward_demodulation,[],[f38,f24]) ).

thf(f24,plain,
    ( ( sK4 @ ( sK1 @ sK4 ) )
    = $false ),
    inference(not_proxy_clausification,[],[f23]) ).

thf(f23,plain,
    ( $true
    = ( ~ ( sK4 @ ( sK1 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f21]) ).

thf(f21,plain,
    ( ( ~ ( sK4 @ ( sK1 @ sK4 ) )
      & ( ( sK1 @ sK4 )
        = ( sK1
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                  & ( ( sK1 @ Y1 )
                    = Y0 ) ) ) ) ) )
    = $true ),
    inference(beta_eta_normalization,[],[f20]) ).

thf(f20,plain,
    ( $true
    = ( ^ [Y0: $i > $o] :
          ( ~ ( Y0 @ ( sK1 @ Y0 ) )
          & ( ( sK1 @ Y0 )
            = ( sK1
              @ ^ [Y1: $i] :
                  ( ?? @ ( $i > $o )
                  @ ^ [Y2: $i > $o] :
                      ( ~ ( Y2 @ ( sK1 @ Y2 ) )
                      & ( ( sK1 @ Y2 )
                        = Y1 ) ) ) ) ) )
      @ sK4 ) ),
    inference(sigma_clausification,[],[f19]) ).

thf(f19,plain,
    ( ( ?? @ ( $i > $o )
      @ ^ [Y0: $i > $o] :
          ( ~ ( Y0 @ ( sK1 @ Y0 ) )
          & ( ( sK1 @ Y0 )
            = ( sK1
              @ ^ [Y1: $i] :
                  ( ?? @ ( $i > $o )
                  @ ^ [Y2: $i > $o] :
                      ( ~ ( Y2 @ ( sK1 @ Y2 ) )
                      & ( ( sK1 @ Y2 )
                        = Y1 ) ) ) ) ) ) )
    = $true ),
    inference(beta_eta_normalization,[],[f18]) ).

thf(f18,plain,
    ( $true
    = ( ^ [Y0: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y1: $i > $o] :
              ( ~ ( Y1 @ ( sK1 @ Y1 ) )
              & ( ( sK1 @ Y1 )
                = Y0 ) ) )
      @ ( sK1
        @ ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                & ( ( sK1 @ Y1 )
                  = Y0 ) ) ) ) ) ),
    inference(equality_resolution,[],[f17]) ).

thf(f17,plain,
    ! [X1: $i > $o] :
      ( ( ( sK1 @ X1 )
       != ( sK1
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                  & ( ( sK1 @ Y1 )
                    = Y0 ) ) ) ) )
      | ( $true
        = ( X1 @ ( sK1 @ X1 ) ) ) ),
    inference(equality_proxy_clausification,[],[f16]) ).

thf(f16,plain,
    ! [X1: $i > $o] :
      ( ( $true
        = ( X1 @ ( sK1 @ X1 ) ) )
      | ( ( ( sK1 @ X1 )
          = ( sK1
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                    & ( ( sK1 @ Y1 )
                      = Y0 ) ) ) ) )
        = $false ) ),
    inference(not_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ! [X1: $i > $o] :
      ( ( $false
        = ( ~ ( X1 @ ( sK1 @ X1 ) ) ) )
      | ( ( ( sK1 @ X1 )
          = ( sK1
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                    & ( ( sK1 @ Y1 )
                      = Y0 ) ) ) ) )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f14,plain,
    ! [X1: $i > $o] :
      ( ( ~ ( X1 @ ( sK1 @ X1 ) )
        & ( ( sK1 @ X1 )
          = ( sK1
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                    & ( ( sK1 @ Y1 )
                      = Y0 ) ) ) ) ) )
      = $false ),
    inference(beta_eta_normalization,[],[f13]) ).

thf(f13,plain,
    ! [X1: $i > $o] :
      ( $false
      = ( ^ [Y0: $i > $o] :
            ( ~ ( Y0 @ ( sK1 @ Y0 ) )
            & ( ( sK1 @ Y0 )
              = ( sK1
                @ ^ [Y1: $i] :
                    ( ?? @ ( $i > $o )
                    @ ^ [Y2: $i > $o] :
                        ( ~ ( Y2 @ ( sK1 @ Y2 ) )
                        & ( ( sK1 @ Y2 )
                          = Y1 ) ) ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f12]) ).

thf(f12,plain,
    ( ( ?? @ ( $i > $o )
      @ ^ [Y0: $i > $o] :
          ( ~ ( Y0 @ ( sK1 @ Y0 ) )
          & ( ( sK1 @ Y0 )
            = ( sK1
              @ ^ [Y1: $i] :
                  ( ?? @ ( $i > $o )
                  @ ^ [Y2: $i > $o] :
                      ( ~ ( Y2 @ ( sK1 @ Y2 ) )
                      & ( ( sK1 @ Y2 )
                        = Y1 ) ) ) ) ) ) )
   != $true ),
    inference(beta_eta_normalization,[],[f11]) ).

thf(f11,plain,
    ( $true
   != ( ^ [Y0: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y1: $i > $o] :
              ( ~ ( Y1 @ ( sK1 @ Y1 ) )
              & ( ( sK1 @ Y1 )
                = Y0 ) ) )
      @ ( sK1
        @ ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                & ( ( sK1 @ Y1 )
                  = Y0 ) ) ) ) ) ),
    inference(definition_unfolding,[],[f10,f9,f9]) ).

thf(f9,plain,
    ( sK0
    = ( ^ [Y0: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y1: $i > $o] :
              ( ~ ( Y1 @ ( sK1 @ Y1 ) )
              & ( ( sK1 @ Y1 )
                = Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( $true
     != ( sK0 @ ( sK1 @ sK0 ) ) )
    & ( sK0
      = ( ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                & ( ( sK1 @ Y1 )
                  = Y0 ) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: $i > $o,X1: ( $i > $o ) > $i] :
        ( ( ( X0 @ ( X1 @ X0 ) )
         != $true )
        & ( ( ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( X1 @ Y1 ) )
                    & ( ( X1 @ Y1 )
                      = Y0 ) ) ) )
          = X0 ) )
   => ( ( $true
       != ( sK0 @ ( sK1 @ sK0 ) ) )
      & ( sK0
        = ( ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                  & ( ( sK1 @ Y1 )
                    = Y0 ) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f6,plain,
    ? [X0: $i > $o,X1: ( $i > $o ) > $i] :
      ( ( ( X0 @ ( X1 @ X0 ) )
       != $true )
      & ( ( ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( X1 @ Y1 ) )
                  & ( ( X1 @ Y1 )
                    = Y0 ) ) ) )
        = X0 ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: $i > $o,X1: ( $i > $o ) > $i] :
        ( ( ( ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( X1 @ Y1 ) )
                    & ( ( X1 @ Y1 )
                      = Y0 ) ) ) )
          = X0 )
       => ( ( X0 @ ( X1 @ X0 ) )
          = $true ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ! [X1: $i > $o,X0: ( $i > $o ) > $i] :
      ( ( X1
        = ( ^ [X2: $i] :
            ? [X3: $i > $o] :
              ( ( ( X0 @ X3 )
                = X2 )
              & ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
     => ( X1 @ ( X0 @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM144_pme) ).

thf(f10,plain,
    ( $true
   != ( sK0 @ ( sK1 @ sK0 ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f38,plain,
    ( ( sK4 @ ( sK1 @ sK4 ) )
    = $true ),
    inference(equality_resolution,[],[f27]) ).

thf(f27,plain,
    ! [X0: $i > $o] :
      ( ( ( sK1 @ sK4 )
       != ( sK1 @ X0 ) )
      | ( $true
        = ( X0 @ ( sK1 @ X0 ) ) ) ),
    inference(superposition,[],[f17,f25]) ).

thf(f25,plain,
    ( ( sK1 @ sK4 )
    = ( sK1
      @ ^ [Y0: $i] :
          ( ?? @ ( $i > $o )
          @ ^ [Y1: $i > $o] :
              ( ~ ( Y1 @ ( sK1 @ Y1 ) )
              & ( ( sK1 @ Y1 )
                = Y0 ) ) ) ) ),
    inference(equality_proxy_clausification,[],[f22]) ).

thf(f22,plain,
    ( ( ( sK1 @ sK4 )
      = ( sK1
        @ ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                & ( ( sK1 @ Y1 )
                  = Y0 ) ) ) ) )
    = $true ),
    inference(binary_proxy_clausification,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : SEV177^5 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.16  % 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
% 0.15/0.36  % Computer : n004.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % 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   : Sun May 19 19:10:38 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/benchmark/theBenchmark.p
% 0.15/0.38  % (18892)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.15/0.38  % (18894)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)
% 0.15/0.38  % (18895)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.15/0.38  % (18892)Instruction limit reached!
% 0.15/0.38  % (18892)------------------------------
% 0.15/0.38  % (18892)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (18892)Termination reason: Unknown
% 0.15/0.38  % (18892)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (18892)Memory used [KB]: 5500
% 0.15/0.38  % (18892)Time elapsed: 0.003 s
% 0.15/0.38  % (18892)Instructions burned: 2 (million)
% 0.15/0.38  % (18892)------------------------------
% 0.15/0.38  % (18892)------------------------------
% 0.15/0.38  % (18893)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)
% 0.15/0.38  % (18896)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)
% 0.15/0.38  % (18889)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.15/0.38  % (18893)Instruction limit reached!
% 0.15/0.38  % (18893)------------------------------
% 0.15/0.38  % (18893)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (18893)Termination reason: Unknown
% 0.15/0.38  % (18893)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (18893)Memory used [KB]: 5500
% 0.15/0.38  % (18893)Time elapsed: 0.003 s
% 0.15/0.38  % (18893)Instructions burned: 2 (million)
% 0.15/0.38  % (18893)------------------------------
% 0.15/0.38  % (18893)------------------------------
% 0.15/0.38  % (18894)First to succeed.
% 0.15/0.38  % (18896)Refutation not found, incomplete strategy
% 0.15/0.38  % (18896)------------------------------
% 0.15/0.38  % (18896)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (18896)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38  
% 0.15/0.38  
% 0.15/0.38  % (18896)Memory used [KB]: 5500
% 0.15/0.38  % (18896)Time elapsed: 0.003 s
% 0.15/0.38  % (18896)Instructions burned: 2 (million)
% 0.15/0.38  % (18896)------------------------------
% 0.15/0.38  % (18896)------------------------------
% 0.15/0.38  % (18891)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)
% 0.15/0.38  % (18895)Also succeeded, but the first one will report.
% 0.15/0.38  % (18894)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (18894)------------------------------
% 0.15/0.38  % (18894)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (18894)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (18894)Memory used [KB]: 5500
% 0.15/0.38  % (18894)Time elapsed: 0.005 s
% 0.15/0.38  % (18894)Instructions burned: 4 (million)
% 0.15/0.38  % (18894)------------------------------
% 0.15/0.38  % (18894)------------------------------
% 0.15/0.38  % (18888)Success in time 0.014 s
% 0.15/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------