TSTP Solution File: ALG259^2 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ALG259^2 : TPTP v8.2.0. 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 : n020.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 May 20 18:20:26 EDT 2024

% Result   : Theorem 0.29s 0.51s
% Output   : Refutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   72 (  49 unt;  21 typ;   0 def)
%            Number of atoms       :  221 (  90 equ;   0 cnn)
%            Maximal formula atoms :    2 (   4 avg)
%            Number of connectives :  647 (  39   ~;   0   |;   0   &; 510   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   83 (  83   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  20 usr;  11 con; 0-4 aty)
%                                         (  80  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  179 ( 142   ^  37   !;   0   ?; 179   :)

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

thf(type_def_7,type,
    subst: $tType ).

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

thf(func_def_1,type,
    subst: $tType ).

thf(func_def_2,type,
    one: term ).

thf(func_def_3,type,
    ap: term > term > term ).

thf(func_def_4,type,
    lam: term > term ).

thf(func_def_5,type,
    sub: term > subst > term ).

thf(func_def_6,type,
    id: subst ).

thf(func_def_7,type,
    sh: subst ).

thf(func_def_8,type,
    push: term > subst > subst ).

thf(func_def_9,type,
    comp: subst > subst > subst ).

thf(func_def_10,type,
    var: term > $o ).

thf(func_def_18,type,
    hoasap: subst > term > subst > term > term ).

thf(func_def_73,type,
    hoaslam: subst > ( subst > term > term ) > term ).

thf(func_def_86,type,
    hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).

thf(func_def_107,type,
    hoasvar: subst > term > subst > $o ).

thf(func_def_121,type,
    pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).

thf(func_def_142,type,
    sK1: subst > term > term ).

thf(func_def_143,type,
    sK2: term ).

thf(func_def_144,type,
    sK3: term ).

thf(f551,plain,
    $false,
    inference(equality_resolution,[],[f550]) ).

thf(f550,plain,
    ! [X0: term] :
      ( ( lam @ X0 )
     != ( lam @ ( sK1 @ sh @ one ) ) ),
    inference(superposition,[],[f532,f549]) ).

thf(f549,plain,
    ( ( lam @ ( sK1 @ sh @ one ) )
    = ( ap @ ( sub @ sK3 @ id ) @ sK2 ) ),
    inference(equality_proxy_clausification,[],[f548]) ).

thf(f548,plain,
    ( $true
    = ( ( ap @ ( sub @ sK3 @ id ) @ sK2 )
      = ( lam @ ( sK1 @ sh @ one ) ) ) ),
    inference(not_proxy_clausification,[],[f547]) ).

thf(f547,plain,
    ( $false
    = ( ( ap @ ( sub @ sK3 @ id ) @ sK2 )
     != ( lam @ ( sK1 @ sh @ one ) ) ) ),
    inference(beta_eta_normalization,[],[f546]) ).

thf(f546,plain,
    ( $false
    = ( ^ [Y0: term] :
          ( ( ap @ ( sub @ Y0 @ id ) @ sK2 )
         != ( lam @ ( sK1 @ sh @ one ) ) )
      @ sK3 ) ),
    inference(sigma_clausification,[],[f545]) ).

thf(f545,plain,
    ( $false
    = ( !! @ term
      @ ^ [Y0: term] :
          ( ( ap @ ( sub @ Y0 @ id ) @ sK2 )
         != ( lam @ ( sK1 @ sh @ one ) ) ) ) ),
    inference(beta_eta_normalization,[],[f544]) ).

thf(f544,plain,
    ( $false
    = ( ^ [Y0: term] :
          ( !! @ term
          @ ^ [Y1: term] :
              ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
             != ( lam @ ( sK1 @ sh @ one ) ) ) )
      @ sK2 ) ),
    inference(sigma_clausification,[],[f535]) ).

thf(f535,plain,
    ( $false
    = ( !! @ term
      @ ^ [Y0: term] :
          ( !! @ term
          @ ^ [Y1: term] :
              ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
             != ( lam @ ( sK1 @ sh @ one ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f534]) ).

thf(f534,plain,
    ( ( ( !! @ subst
        @ ^ [Y0: subst] :
            ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( sK1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
                    = ( sub @ ( sK1 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
     => ( !! @ term
        @ ^ [Y0: term] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
               != ( lam @ ( sK1 @ sh @ one ) ) ) ) ) )
    = $false ),
    inference(beta_eta_normalization,[],[f533]) ).

thf(f533,plain,
    ( ( ^ [Y0: subst > term > term] :
          ( ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ subst
                @ ^ [Y2: subst] :
                    ( !! @ term
                    @ ^ [Y3: term] :
                        ( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
                        = ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
         => ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
                   != ( lam @ ( Y0 @ sh @ one ) ) ) ) ) )
      @ sK1 )
    = $false ),
    inference(sigma_clausification,[],[f523]) ).

thf(f523,plain,
    ( ( !! @ ( subst > term > term )
      @ ^ [Y0: subst > term > term] :
          ( ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ subst
                @ ^ [Y2: subst] :
                    ( !! @ term
                    @ ^ [Y3: term] :
                        ( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
                        = ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
         => ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
                   != ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f522]) ).

thf(f522,plain,
    ( $true
   != ( ( !! @ term
        @ ^ [Y0: term] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( lam @ Y1 )
                   != ( ap @ Y2 @ Y0 ) ) ) ) )
     => ( !! @ ( subst > term > term )
        @ ^ [Y0: subst > term > term] :
            ( ( !! @ subst
              @ ^ [Y1: subst] :
                  ( !! @ subst
                  @ ^ [Y2: subst] :
                      ( !! @ term
                      @ ^ [Y3: term] :
                          ( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
                          = ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
           => ( !! @ term
              @ ^ [Y1: term] :
                  ( !! @ term
                  @ ^ [Y2: term] :
                      ( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
                     != ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f521]) ).

thf(f521,plain,
    ( $true
   != ( ( !! @ term
        @ ^ [Y0: term] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( lam @ Y1 )
                   != ( ap @ Y2 @ Y0 ) ) ) ) )
     => ( !! @ ( subst > term > term )
        @ ^ [Y0: subst > term > term] :
            ( ( !! @ subst
              @ ^ [Y1: subst] :
                  ( !! @ subst
                  @ ^ [Y2: subst] :
                      ( !! @ term
                      @ ^ [Y3: term] :
                          ( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
                          = ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
           => ( !! @ term
              @ ^ [Y1: term] :
                  ( !! @ term
                  @ ^ [Y2: term] :
                      ( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
                        @ id
                        @ Y2
                        @ id
                        @ Y1 )
                     != ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
                        @ id
                        @ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ),
    inference(definition_unfolding,[],[f347,f476]) ).

thf(f476,plain,
    ( hoaslamnotap_lthm
    = ( ( !! @ term
        @ ^ [Y0: term] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( lam @ Y1 )
                   != ( ap @ Y2 @ Y0 ) ) ) ) )
     => ( !! @ ( subst > term > term )
        @ ^ [Y0: subst > term > term] :
            ( ( !! @ subst
              @ ^ [Y1: subst] :
                  ( !! @ subst
                  @ ^ [Y2: subst] :
                      ( !! @ term
                      @ ^ [Y3: term] :
                          ( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
                          = ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
           => ( !! @ term
              @ ^ [Y1: term] :
                  ( !! @ term
                  @ ^ [Y2: term] :
                      ( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
                        @ id
                        @ Y2
                        @ id
                        @ Y1 )
                     != ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
                        @ id
                        @ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ),
    inference(definition_unfolding,[],[f443,f371,f452]) ).

thf(f452,plain,
    ( hoaslamnotap
    = ( !! @ ( subst > term > term )
      @ ^ [Y0: subst > term > term] :
          ( ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ subst
                @ ^ [Y2: subst] :
                    ( !! @ term
                    @ ^ [Y3: term] :
                        ( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
                        = ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
         => ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
                      @ id
                      @ Y2
                      @ id
                      @ Y1 )
                   != ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
                      @ id
                      @ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
    inference(definition_unfolding,[],[f379,f419,f363]) ).

thf(f363,plain,
    ( hoaslam
    = ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
    inference(cnf_transformation,[],[f260]) ).

thf(f260,plain,
    ( hoaslam
    = ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
    inference(fool_elimination,[],[f259]) ).

thf(f259,plain,
    ( ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) )
    = hoaslam ),
    inference(rectify,[],[f56]) ).

thf(f56,axiom,
    ( ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) )
    = hoaslam ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslam) ).

thf(f419,plain,
    ( hoasap
    = ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
    inference(cnf_transformation,[],[f295]) ).

thf(f295,plain,
    ( hoasap
    = ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
    inference(fool_elimination,[],[f294]) ).

thf(f294,plain,
    ( ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) )
    = hoasap ),
    inference(rectify,[],[f55]) ).

thf(f55,axiom,
    ( ( ^ [X2: subst,X0: term,X3: subst,X1: term] : ( ap @ ( sub @ X0 @ X3 ) @ X1 ) )
    = hoasap ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasap) ).

thf(f379,plain,
    ( hoaslamnotap
    = ( !! @ ( subst > term > term )
      @ ^ [Y0: subst > term > term] :
          ( ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ subst
                @ ^ [Y2: subst] :
                    ( !! @ term
                    @ ^ [Y3: term] :
                        ( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
                        = ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
         => ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( hoasap @ id @ Y2 @ id @ Y1 )
                   != ( hoaslam @ id
                      @ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
    inference(cnf_transformation,[],[f132]) ).

thf(f132,plain,
    ( hoaslamnotap
    = ( !! @ ( subst > term > term )
      @ ^ [Y0: subst > term > term] :
          ( ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ subst
                @ ^ [Y2: subst] :
                    ( !! @ term
                    @ ^ [Y3: term] :
                        ( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
                        = ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
         => ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( hoasap @ id @ Y2 @ id @ Y1 )
                   != ( hoaslam @ id
                      @ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f131]) ).

thf(f131,plain,
    ( hoaslamnotap
    = ( ! [X0: subst > term > term] :
          ( ! [X1: term,X2: subst,X3: subst] :
              ( ( X0 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) )
              = ( sub @ ( X0 @ X2 @ X1 ) @ X3 ) )
         => ! [X4: term,X5: term] :
              ( ( hoasap @ id @ X4 @ id @ X5 )
             != ( hoaslam @ id
                @ ^ [X6: subst,X7: term] : ( X0 @ X6 @ X7 ) ) ) ) ) ),
    inference(rectify,[],[f67]) ).

thf(f67,axiom,
    ( hoaslamnotap
    = ( ! [X10: subst > term > term] :
          ( ! [X0: term,X2: subst,X3: subst] :
              ( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
              = ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
         => ! [X0: term,X1: term] :
              ( ( hoasap @ id @ X0 @ id @ X1 )
             != ( hoaslam @ id
                @ ^ [X2: subst,X6: term] : ( X10 @ X2 @ X6 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap) ).

thf(f371,plain,
    ( lamnotap
    = ( !! @ term
      @ ^ [Y0: term] :
          ( !! @ term
          @ ^ [Y1: term] :
              ( !! @ term
              @ ^ [Y2: term] :
                  ( ( lam @ Y1 )
                 != ( ap @ Y2 @ Y0 ) ) ) ) ) ),
    inference(cnf_transformation,[],[f230]) ).

thf(f230,plain,
    ( lamnotap
    = ( !! @ term
      @ ^ [Y0: term] :
          ( !! @ term
          @ ^ [Y1: term] :
              ( !! @ term
              @ ^ [Y2: term] :
                  ( ( lam @ Y1 )
                 != ( ap @ Y2 @ Y0 ) ) ) ) ) ),
    inference(fool_elimination,[],[f229]) ).

thf(f229,plain,
    ( lamnotap
    = ( ! [X0: term,X1: term,X2: term] :
          ( ( lam @ X1 )
         != ( ap @ X0 @ X2 ) ) ) ),
    inference(rectify,[],[f20]) ).

thf(f20,axiom,
    ( lamnotap
    = ( ! [X1: term,X0: term,X6: term] :
          ( ( lam @ X0 )
         != ( ap @ X1 @ X6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotap) ).

thf(f443,plain,
    ( hoaslamnotap_lthm
    = ( lamnotap
     => hoaslamnotap ) ),
    inference(cnf_transformation,[],[f236]) ).

thf(f236,plain,
    ( hoaslamnotap_lthm
    = ( lamnotap
     => hoaslamnotap ) ),
    inference(fool_elimination,[],[f235]) ).

thf(f235,plain,
    ( ( hoaslamnotap_lthm = lamnotap )
   => hoaslamnotap ),
    inference(rectify,[],[f69]) ).

thf(f69,axiom,
    ( ( hoaslamnotap_lthm = lamnotap )
   => hoaslamnotap ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap_lthm) ).

thf(f347,plain,
    hoaslamnotap_lthm != $true,
    inference(cnf_transformation,[],[f329]) ).

thf(f329,plain,
    hoaslamnotap_lthm != $true,
    inference(flattening,[],[f299]) ).

thf(f299,plain,
    hoaslamnotap_lthm != $true,
    inference(fool_elimination,[],[f298]) ).

thf(f298,plain,
    ~ hoaslamnotap_lthm,
    inference(rectify,[],[f115]) ).

thf(f115,negated_conjecture,
    ~ hoaslamnotap_lthm,
    inference(negated_conjecture,[],[f114]) ).

thf(f114,conjecture,
    hoaslamnotap_lthm,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(f532,plain,
    ! [X2: term,X3: term,X1: term] :
      ( ( ap @ X3 @ X1 )
     != ( lam @ X2 ) ),
    inference(equality_proxy_clausification,[],[f531]) ).

thf(f531,plain,
    ! [X2: term,X3: term,X1: term] :
      ( ( ( lam @ X2 )
        = ( ap @ X3 @ X1 ) )
      = $false ),
    inference(not_proxy_clausification,[],[f530]) ).

thf(f530,plain,
    ! [X2: term,X3: term,X1: term] :
      ( $true
      = ( ( lam @ X2 )
       != ( ap @ X3 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f529]) ).

thf(f529,plain,
    ! [X2: term,X3: term,X1: term] :
      ( $true
      = ( ^ [Y0: term] :
            ( ( lam @ X2 )
           != ( ap @ Y0 @ X1 ) )
        @ X3 ) ),
    inference(pi_clausification,[],[f528]) ).

thf(f528,plain,
    ! [X2: term,X1: term] :
      ( $true
      = ( !! @ term
        @ ^ [Y0: term] :
            ( ( lam @ X2 )
           != ( ap @ Y0 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f527]) ).

thf(f527,plain,
    ! [X2: term,X1: term] :
      ( $true
      = ( ^ [Y0: term] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( ( lam @ Y0 )
               != ( ap @ Y1 @ X1 ) ) )
        @ X2 ) ),
    inference(pi_clausification,[],[f526]) ).

thf(f526,plain,
    ! [X1: term] :
      ( $true
      = ( !! @ term
        @ ^ [Y0: term] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( ( lam @ Y0 )
               != ( ap @ Y1 @ X1 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f525]) ).

thf(f525,plain,
    ! [X1: term] :
      ( $true
      = ( ^ [Y0: term] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( !! @ term
                @ ^ [Y2: term] :
                    ( ( lam @ Y1 )
                   != ( ap @ Y2 @ Y0 ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f524]) ).

thf(f524,plain,
    ( $true
    = ( !! @ term
      @ ^ [Y0: term] :
          ( !! @ term
          @ ^ [Y1: term] :
              ( !! @ term
              @ ^ [Y2: term] :
                  ( ( lam @ Y1 )
                 != ( ap @ Y2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f522]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15  % Problem    : ALG259^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.18/0.18  % 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
% 0.19/0.42  % Computer : n020.cluster.edu
% 0.19/0.42  % Model    : x86_64 x86_64
% 0.19/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42  % Memory   : 8042.1875MB
% 0.19/0.42  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.42  % CPULimit   : 300
% 0.19/0.42  % WCLimit    : 300
% 0.19/0.42  % DateTime   : Sat May 18 22:57:38 EDT 2024
% 0.19/0.42  % CPUTime    : 
% 0.19/0.42  This is a TH0_THM_EQU_NAR problem
% 0.19/0.42  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
% 0.19/0.46  % (18220)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.46  % (18224)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.46  % (18219)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)
% 0.19/0.46  % (18218)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)
% 0.19/0.46  % (18222)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)
% 0.19/0.46  % (18221)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)
% 0.19/0.46  % (18223)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.46  % (18217)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.29/0.46  % (18220)Instruction limit reached!
% 0.29/0.46  % (18220)------------------------------
% 0.29/0.46  % (18220)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.46  % (18220)Termination reason: Unknown
% 0.29/0.46  % (18220)Termination phase: shuffling
% 0.29/0.46  
% 0.29/0.46  % (18220)Memory used [KB]: 1279
% 0.29/0.46  % (18220)Time elapsed: 0.004 s
% 0.29/0.46  % (18220)Instructions burned: 3 (million)
% 0.29/0.46  % (18220)------------------------------
% 0.29/0.46  % (18220)------------------------------
% 0.29/0.46  % (18221)Instruction limit reached!
% 0.29/0.46  % (18221)------------------------------
% 0.29/0.46  % (18221)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.46  % (18221)Termination reason: Unknown
% 0.29/0.46  % (18221)Termination phase: shuffling
% 0.29/0.46  
% 0.29/0.46  % (18221)Memory used [KB]: 1279
% 0.29/0.46  % (18221)Time elapsed: 0.004 s
% 0.29/0.46  % (18221)Instructions burned: 3 (million)
% 0.29/0.46  % (18221)------------------------------
% 0.29/0.46  % (18221)------------------------------
% 0.29/0.46  % (18224)Instruction limit reached!
% 0.29/0.46  % (18224)------------------------------
% 0.29/0.46  % (18224)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.46  % (18224)Termination reason: Unknown
% 0.29/0.46  % (18224)Termination phase: shuffling
% 0.29/0.46  
% 0.29/0.46  % (18224)Memory used [KB]: 1279
% 0.29/0.46  % (18224)Time elapsed: 0.004 s
% 0.29/0.46  % (18224)Instructions burned: 4 (million)
% 0.29/0.46  % (18224)------------------------------
% 0.29/0.46  % (18224)------------------------------
% 0.29/0.46  % (18218)Instruction limit reached!
% 0.29/0.46  % (18218)------------------------------
% 0.29/0.46  % (18218)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.46  % (18218)Termination reason: Unknown
% 0.29/0.46  % (18218)Termination phase: shuffling
% 0.29/0.46  
% 0.29/0.46  % (18218)Memory used [KB]: 1279
% 0.29/0.46  % (18218)Time elapsed: 0.005 s
% 0.29/0.46  % (18218)Instructions burned: 5 (million)
% 0.29/0.46  % (18218)------------------------------
% 0.29/0.46  % (18218)------------------------------
% 0.29/0.47  % (18223)Instruction limit reached!
% 0.29/0.47  % (18223)------------------------------
% 0.29/0.47  % (18223)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.47  % (18223)Termination reason: Unknown
% 0.29/0.47  % (18223)Termination phase: Property scanning
% 0.29/0.47  
% 0.29/0.47  % (18223)Memory used [KB]: 1663
% 0.29/0.47  % (18223)Time elapsed: 0.013 s
% 0.29/0.47  % (18223)Instructions burned: 18 (million)
% 0.29/0.47  % (18223)------------------------------
% 0.29/0.47  % (18223)------------------------------
% 0.29/0.47  % (18219)Instruction limit reached!
% 0.29/0.47  % (18219)------------------------------
% 0.29/0.47  % (18219)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.47  % (18219)Termination reason: Unknown
% 0.29/0.47  % (18219)Termination phase: Property scanning
% 0.29/0.47  
% 0.29/0.47  % (18219)Memory used [KB]: 1791
% 0.29/0.47  % (18219)Time elapsed: 0.017 s
% 0.29/0.47  % (18219)Instructions burned: 28 (million)
% 0.29/0.47  % (18219)------------------------------
% 0.29/0.47  % (18219)------------------------------
% 0.29/0.47  % (18222)Refutation not found, incomplete strategy
% 0.29/0.47  % (18222)------------------------------
% 0.29/0.47  % (18222)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.47  % (18222)Termination reason: Refutation not found, incomplete strategy
% 0.29/0.47  
% 0.29/0.47  
% 0.29/0.47  % (18222)Memory used [KB]: 6140
% 0.29/0.47  % (18222)Time elapsed: 0.018 s
% 0.29/0.47  % (18222)Instructions burned: 25 (million)
% 0.29/0.47  % (18222)------------------------------
% 0.29/0.47  % (18222)------------------------------
% 0.29/0.47  % (18227)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.29/0.47  % (18226)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.29/0.47  % (18225)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.29/0.47  % (18228)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.29/0.48  % (18227)Instruction limit reached!
% 0.29/0.48  % (18227)------------------------------
% 0.29/0.48  % (18227)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.48  % (18227)Termination reason: Unknown
% 0.29/0.48  % (18227)Termination phase: shuffling
% 0.29/0.48  
% 0.29/0.48  % (18227)Memory used [KB]: 1279
% 0.29/0.48  % (18227)Time elapsed: 0.004 s
% 0.29/0.48  % (18227)Instructions burned: 4 (million)
% 0.29/0.48  % (18227)------------------------------
% 0.29/0.48  % (18227)------------------------------
% 0.29/0.48  % (18226)Instruction limit reached!
% 0.29/0.48  % (18226)------------------------------
% 0.29/0.48  % (18226)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.48  % (18226)Termination reason: Unknown
% 0.29/0.48  % (18226)Termination phase: Property scanning
% 0.29/0.48  
% 0.29/0.48  % (18226)Memory used [KB]: 1663
% 0.29/0.48  % (18226)Time elapsed: 0.011 s
% 0.29/0.48  % (18226)Instructions burned: 15 (million)
% 0.29/0.48  % (18226)------------------------------
% 0.29/0.48  % (18226)------------------------------
% 0.29/0.48  % (18229)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.29/0.49  % (18230)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.29/0.49  % (18229)Instruction limit reached!
% 0.29/0.49  % (18229)------------------------------
% 0.29/0.49  % (18229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.49  % (18229)Termination reason: Unknown
% 0.29/0.49  % (18229)Termination phase: shuffling
% 0.29/0.49  
% 0.29/0.49  % (18229)Memory used [KB]: 1407
% 0.29/0.49  % (18229)Time elapsed: 0.007 s
% 0.29/0.49  % (18229)Instructions burned: 8 (million)
% 0.29/0.49  % (18229)------------------------------
% 0.29/0.49  % (18229)------------------------------
% 0.29/0.49  % (18231)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.29/0.49  % (18231)Instruction limit reached!
% 0.29/0.49  % (18231)------------------------------
% 0.29/0.49  % (18231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.49  % (18232)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.29/0.49  % (18231)Termination reason: Unknown
% 0.29/0.49  % (18231)Termination phase: shuffling
% 0.29/0.49  
% 0.29/0.49  % (18231)Memory used [KB]: 1279
% 0.29/0.49  % (18231)Time elapsed: 0.004 s
% 0.29/0.49  % (18231)Instructions burned: 3 (million)
% 0.29/0.49  % (18231)------------------------------
% 0.29/0.49  % (18231)------------------------------
% 0.29/0.49  % (18225)Instruction limit reached!
% 0.29/0.49  % (18225)------------------------------
% 0.29/0.49  % (18225)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.49  % (18225)Termination reason: Unknown
% 0.29/0.49  % (18232)Instruction limit reached!
% 0.29/0.49  % (18232)------------------------------
% 0.29/0.49  % (18232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.49  % (18232)Termination reason: Unknown
% 0.29/0.49  % (18232)Termination phase: shuffling
% 0.29/0.49  
% 0.29/0.49  % (18232)Memory used [KB]: 1279
% 0.29/0.49  % (18232)Time elapsed: 0.004 s
% 0.29/0.49  % (18232)Instructions burned: 3 (million)
% 0.29/0.49  % (18232)------------------------------
% 0.29/0.49  % (18232)------------------------------
% 0.29/0.49  % (18225)Termination phase: Property scanning
% 0.29/0.49  
% 0.29/0.49  % (18225)Memory used [KB]: 1791
% 0.29/0.49  % (18225)Time elapsed: 0.022 s
% 0.29/0.49  % (18225)Instructions burned: 38 (million)
% 0.29/0.49  % (18225)------------------------------
% 0.29/0.49  % (18225)------------------------------
% 0.29/0.50  % (18230)Instruction limit reached!
% 0.29/0.50  % (18230)------------------------------
% 0.29/0.50  % (18230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.50  % (18230)Termination reason: Unknown
% 0.29/0.50  % (18230)Termination phase: shuffling
% 0.29/0.50  
% 0.29/0.50  % (18230)Memory used [KB]: 1535
% 0.29/0.50  % (18230)Time elapsed: 0.011 s
% 0.29/0.50  % (18230)Instructions burned: 16 (million)
% 0.29/0.50  % (18230)------------------------------
% 0.29/0.50  % (18230)------------------------------
% 0.29/0.50  % (18233)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.29/0.50  % (18217)First to succeed.
% 0.29/0.50  % (18233)Instruction limit reached!
% 0.29/0.50  % (18233)------------------------------
% 0.29/0.50  % (18233)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.50  % (18233)Termination reason: Unknown
% 0.29/0.50  % (18233)Termination phase: shuffling
% 0.29/0.50  
% 0.29/0.50  % (18233)Memory used [KB]: 1407
% 0.29/0.50  % (18233)Time elapsed: 0.006 s
% 0.29/0.50  % (18233)Instructions burned: 8 (million)
% 0.29/0.50  % (18233)------------------------------
% 0.29/0.50  % (18233)------------------------------
% 0.29/0.51  % (18234)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.29/0.51  % (18217)Refutation found. Thanks to Tanya!
% 0.29/0.51  % SZS status Theorem for theBenchmark
% 0.29/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.51  % (18217)------------------------------
% 0.29/0.51  % (18217)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.29/0.51  % (18217)Termination reason: Refutation
% 0.29/0.51  
% 0.29/0.51  % (18217)Memory used [KB]: 6652
% 0.29/0.51  % (18217)Time elapsed: 0.050 s
% 0.29/0.51  % (18217)Instructions burned: 88 (million)
% 0.29/0.51  % (18217)------------------------------
% 0.29/0.51  % (18217)------------------------------
% 0.29/0.51  % (18216)Success in time 0.068 s
% 0.29/0.51  % Vampire---4.8 exiting
%------------------------------------------------------------------------------