TSTP Solution File: ITP072^1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : ITP072^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 22:27:51 EDT 2024

% Result   : Theorem 217.01s 39.53s
% Output   : Refutation 217.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  134 (  66 unt;  21 typ;   0 def)
%            Number of atoms       :  263 ( 133 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  533 (  98   ~;  56   |;   0   &; 363   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   9 con; 0-2 aty)
%            Number of variables   :  127 (   6   ^ 120   !;   1   ?; 127   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_se933006839lle_hf_type,type,
    set_se933006839lle_hf: $tType ).

thf(set_HF_Mirabelle_hf_type,type,
    set_HF_Mirabelle_hf: $tType ).

thf(hF_Mirabelle_hf_type,type,
    hF_Mirabelle_hf: $tType ).

thf(set_nat_type,type,
    set_nat: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(finite1213132899lle_hf_type,type,
    finite1213132899lle_hf: set_HF_Mirabelle_hf > nat ).

thf(finite586181922lle_hf_type,type,
    finite586181922lle_hf: set_HF_Mirabelle_hf > $o ).

thf(zero_z189798548lle_hf_type,type,
    zero_z189798548lle_hf: hF_Mirabelle_hf ).

thf(zero_zero_nat_type,type,
    zero_zero_nat: nat ).

thf(hF_Mirabelle_HF_type,type,
    hF_Mirabelle_HF: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).

thf(hF_Mirabelle_hfset_type,type,
    hF_Mirabelle_hfset: hF_Mirabelle_hf > set_HF_Mirabelle_hf ).

thf(hF_Mirabelle_hmem_type,type,
    hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).

thf(bot_bot_nat_type,type,
    bot_bot_nat: nat ).

thf(bot_bo53200981lle_hf_type,type,
    bot_bo53200981lle_hf: set_HF_Mirabelle_hf ).

thf(ord_less_eq_nat_type,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(ord_le432112161lle_hf_type,type,
    ord_le432112161lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).

thf(insert9649339lle_hf_type,type,
    insert9649339lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).

thf(member1367349282lle_hf_type,type,
    member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).

thf(z_type,type,
    z: hF_Mirabelle_hf ).

thf(sk60_type,type,
    sk60: hF_Mirabelle_hf ).

thf(sk561_type,type,
    sk561: hF_Mirabelle_hf ).

thf(98,axiom,
    ! [A: set_HF_Mirabelle_hf] :
      ( ~ ( finite586181922lle_hf @ A )
     => ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_card_Oinfinite) ).

thf(583,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ~ ( finite586181922lle_hf @ A )
     => ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(584,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ A )
      | ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat ) ),
    inference(cnf,[status(esa)],[583]) ).

thf(585,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat )
      | ( finite586181922lle_hf @ A ) ),
    inference(lifteq,[status(thm)],[584]) ).

thf(131,axiom,
    ! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_finite__hfset) ).

thf(706,plain,
    ! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(707,plain,
    ! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) ),
    inference(cnf,[status(esa)],[706]) ).

thf(24,axiom,
    ! [A: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ A )
     => ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_card__insert__le) ).

thf(220,plain,
    ! [A: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ A )
     => ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(221,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ A )
     => ! [B: hF_Mirabelle_hf] : ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ A ) ) ) ),
    inference(miniscope,[status(thm)],[220]) ).

thf(222,plain,
    ! [B: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
      ( ~ ( finite586181922lle_hf @ A )
      | ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[221]) ).

thf(8350,plain,
    ! [C: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ B ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ C @ B ) ) )
      | ( ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) )
       != ( finite586181922lle_hf @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[707,222]) ).

thf(8351,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ B ) ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[8350:[bind(A,$thf( D )),bind(B,$thf( hF_Mirabelle_hfset @ D ))]]) ).

thf(8427,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ B ) ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
    inference(simp,[status(thm)],[8351]) ).

thf(21,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
     => ( A = bot_bot_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_bot_Oextremum__uniqueI) ).

thf(213,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
     => ( A = bot_bot_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(214,plain,
    ! [A: nat] :
      ( ~ ( ord_less_eq_nat @ A @ bot_bot_nat )
      | ( A = bot_bot_nat ) ),
    inference(cnf,[status(esa)],[213]) ).

thf(215,plain,
    ! [A: nat] :
      ( ( A = bot_bot_nat )
      | ~ ( ord_less_eq_nat @ A @ bot_bot_nat ) ),
    inference(lifteq,[status(thm)],[214]) ).

thf(129,axiom,
    bot_bot_nat = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_bot__nat__def) ).

thf(700,plain,
    bot_bot_nat = zero_zero_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(701,plain,
    bot_bot_nat = zero_zero_nat,
    inference(lifteq,[status(thm)],[700]) ).

thf(1764,plain,
    ! [A: nat] :
      ( ( A = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
    inference(rewrite,[status(thm)],[215,701]) ).

thf(6,axiom,
    ! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ A )
     => ( ( ord_le432112161lle_hf @ B @ A )
       => ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_card__seteq) ).

thf(160,plain,
    ! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ A )
     => ( ( ord_le432112161lle_hf @ B @ A )
       => ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(161,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ A )
     => ! [B: set_HF_Mirabelle_hf] :
          ( ( ord_le432112161lle_hf @ B @ A )
         => ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
           => ( B = A ) ) ) ),
    inference(miniscope,[status(thm)],[160]) ).

thf(162,plain,
    ! [B: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
      ( ~ ( finite586181922lle_hf @ A )
      | ~ ( ord_le432112161lle_hf @ B @ A )
      | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
      | ( B = A ) ),
    inference(cnf,[status(esa)],[161]) ).

thf(163,plain,
    ! [B: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
      ( ( B = A )
      | ~ ( finite586181922lle_hf @ A )
      | ~ ( ord_le432112161lle_hf @ B @ A )
      | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) ) ),
    inference(lifteq,[status(thm)],[162]) ).

thf(122,axiom,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_HF__hfset) ).

thf(680,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(681,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
      = A ),
    inference(cnf,[status(esa)],[680]) ).

thf(682,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[681]) ).

thf(140,axiom,
    ( zero_z189798548lle_hf
    = ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Zero__hf__def) ).

thf(728,plain,
    ( zero_z189798548lle_hf
    = ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(729,plain,
    ( ( hF_Mirabelle_HF @ bot_bo53200981lle_hf )
    = zero_z189798548lle_hf ),
    inference(lifteq,[status(thm)],[728]) ).

thf(1520,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( A = zero_z189798548lle_hf )
      | ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
       != ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ) ),
    inference(paramod_ordered,[status(thm)],[682,729]) ).

thf(1526,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( A = zero_z189798548lle_hf )
      | ( ( hF_Mirabelle_hfset @ A )
       != bot_bo53200981lle_hf ) ),
    inference(simp,[status(thm)],[1520]) ).

thf(1,conjecture,
    ( ( z = zero_z189798548lle_hf )
    = ( ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( z = zero_z189798548lle_hf )
   != ( ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(149,plain,
    ( ( z = zero_z189798548lle_hf )
   != ( ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(150,plain,
    ( ( z = zero_z189798548lle_hf )
   != ( ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
    inference(lifteq,[status(thm)],[149]) ).

thf(754,plain,
    ( ( z != zero_z189798548lle_hf )
    | ~ ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z ) ),
    inference(bool_ext,[status(thm)],[150]) ).

thf(756,plain,
    ( ( z != zero_z189798548lle_hf )
    | ~ ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z ) ),
    inference(lifteq,[status(thm)],[754]) ).

thf(758,plain,
    ( ( hF_Mirabelle_hmem @ sk60 @ z )
    | ( z != zero_z189798548lle_hf ) ),
    inference(cnf,[status(esa)],[756]) ).

thf(143,axiom,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hmem__hempty) ).

thf(735,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(736,plain,
    ~ ? [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
    inference(miniscope,[status(thm)],[735]) ).

thf(737,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
    inference(cnf,[status(esa)],[736]) ).

thf(834,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( z != zero_z189798548lle_hf )
      | ( ( hF_Mirabelle_hmem @ sk60 @ z )
       != ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ) ),
    inference(paramod_ordered,[status(thm)],[758,737]) ).

thf(836,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( z != zero_z189798548lle_hf )
      | ( sk60 != A )
      | ( z != zero_z189798548lle_hf ) ),
    inference(simp,[status(thm)],[834]) ).

thf(838,plain,
    z != zero_z189798548lle_hf,
    inference(simp,[status(thm)],[836]) ).

thf(2298,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( hF_Mirabelle_hfset @ A )
       != bot_bo53200981lle_hf )
      | ( A != z ) ),
    inference(paramod_ordered,[status(thm)],[1526,838]) ).

thf(2299,plain,
    ( ( hF_Mirabelle_hfset @ z )
   != bot_bo53200981lle_hf ),
    inference(pattern_uni,[status(thm)],[2298:[bind(A,$thf( z ))]]) ).

thf(2403,plain,
    ! [B: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
      ( ~ ( finite586181922lle_hf @ A )
      | ~ ( ord_le432112161lle_hf @ B @ A )
      | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
      | ( B != bot_bo53200981lle_hf )
      | ( A
       != ( hF_Mirabelle_hfset @ z ) ) ),
    inference(paramod_ordered,[status(thm)],[163,2299]) ).

thf(2404,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ~ ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ z ) )
      | ~ ( ord_le432112161lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) )
      | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ ( finite1213132899lle_hf @ A ) )
      | ( A != bot_bo53200981lle_hf ) ),
    inference(pattern_uni,[status(thm)],[2403:[bind(A,$thf( hF_Mirabelle_hfset @ z )),bind(B,$thf( B ))]]) ).

thf(2406,plain,
    ( ~ ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ z ) )
    | ~ ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ ( hF_Mirabelle_hfset @ z ) )
    | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ ( finite1213132899lle_hf @ bot_bo53200981lle_hf ) ) ),
    inference(simp,[status(thm)],[2404]) ).

thf(71,axiom,
    ! [A: set_HF_Mirabelle_hf] : ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_empty__subsetI) ).

thf(438,plain,
    ! [A: set_HF_Mirabelle_hf] : ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(439,plain,
    ! [A: set_HF_Mirabelle_hf] : ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A ),
    inference(cnf,[status(esa)],[438]) ).

thf(115,axiom,
    ( ( finite1213132899lle_hf @ bot_bo53200981lle_hf )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_card_Oempty) ).

thf(654,plain,
    ( ( finite1213132899lle_hf @ bot_bo53200981lle_hf )
    = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(655,plain,
    ( ( finite1213132899lle_hf @ bot_bo53200981lle_hf )
    = zero_zero_nat ),
    inference(lifteq,[status(thm)],[654]) ).

thf(2464,plain,
    ( ~ $true
    | ~ $true
    | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ zero_zero_nat ) ),
    inference(rewrite,[status(thm)],[2406,707,439,655]) ).

thf(2465,plain,
    ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ zero_zero_nat ),
    inference(simp,[status(thm)],[2464]) ).

thf(2476,plain,
    ! [A: nat] :
      ( ~ ( ord_less_eq_nat @ A @ zero_zero_nat )
      | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ A )
      | ( zero_zero_nat != zero_zero_nat ) ),
    inference(paramod_ordered,[status(thm)],[1764,2465]) ).

thf(2477,plain,
    ! [A: nat] :
      ( ~ ( ord_less_eq_nat @ A @ zero_zero_nat )
      | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ A ) ),
    inference(pattern_uni,[status(thm)],[2476:[]]) ).

thf(3,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_bot_Oextremum__unique) ).

thf(151,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(152,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ),
    inference(cnf,[status(esa)],[151]) ).

thf(153,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ),
    inference(lifteq,[status(thm)],[152]) ).

thf(773,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
      = ( A = zero_zero_nat ) ),
    inference(rewrite,[status(thm)],[153,701]) ).

thf(2949,plain,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
      | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ A ) ),
    inference(rewrite,[status(thm)],[2477,773]) ).

thf(2950,plain,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
      | ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ A ) ),
    inference(lifteq,[status(thm)],[2949]) ).

thf(12415,plain,
    ! [C: nat,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( C != zero_zero_nat )
      | ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ B ) ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) )
       != ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[8427,2950]) ).

thf(12416,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) )
     != zero_zero_nat ),
    inference(pattern_uni,[status(thm)],[12415:[bind(A,$thf( E )),bind(B,$thf( z )),bind(C,$thf( finite1213132899lle_hf @ ( insert9649339lle_hf @ E @ ( hF_Mirabelle_hfset @ z ) ) ))]]) ).

thf(12524,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) )
     != zero_zero_nat ),
    inference(simp,[status(thm)],[12416]) ).

thf(12575,plain,
    ! [B: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ A )
      | ( ( finite1213132899lle_hf @ A )
       != ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ ( hF_Mirabelle_hfset @ z ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[585,12524]) ).

thf(12576,plain,
    ! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) ),
    inference(pattern_uni,[status(thm)],[12575:[bind(A,$thf( insert9649339lle_hf @ C @ ( hF_Mirabelle_hfset @ z ) )),bind(B,$thf( C ))]]) ).

thf(12591,plain,
    ! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) ),
    inference(simp,[status(thm)],[12576]) ).

thf(99,axiom,
    ! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ B ) )
      = ( finite586181922lle_hf @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_finite__insert) ).

thf(586,plain,
    ! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ B ) )
      = ( finite586181922lle_hf @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(587,plain,
    ! [B: set_HF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ B ) )
      = ( finite586181922lle_hf @ B ) ),
    inference(cnf,[status(esa)],[586]) ).

thf(588,plain,
    ! [B: set_HF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ B ) )
      = ( finite586181922lle_hf @ B ) ),
    inference(lifteq,[status(thm)],[587]) ).

thf(12618,plain,
    finite586181922lle_hf @ ( hF_Mirabelle_hfset @ z ),
    inference(rewrite,[status(thm)],[12591,588]) ).

thf(116,axiom,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ! [B: hF_Mirabelle_hf] :
            ~ ( member1367349282lle_hf @ B @ A ) )
      = ( A = bot_bo53200981lle_hf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_all__not__in__conv) ).

thf(656,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ! [B: hF_Mirabelle_hf] :
            ~ ( member1367349282lle_hf @ B @ A ) )
      = ( A = bot_bo53200981lle_hf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(657,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ! [B: hF_Mirabelle_hf] :
            ~ ( member1367349282lle_hf @ B @ A ) )
      = ( A = bot_bo53200981lle_hf ) ),
    inference(cnf,[status(esa)],[656]) ).

thf(658,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ! [B: hF_Mirabelle_hf] :
            ~ ( member1367349282lle_hf @ B @ A ) )
      = ( A = bot_bo53200981lle_hf ) ),
    inference(lifteq,[status(thm)],[657]) ).

thf(63,axiom,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat )
      = ( ( A = bot_bo53200981lle_hf )
        | ~ ( finite586181922lle_hf @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_card__eq__0__iff) ).

thf(412,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat )
      = ( ( A = bot_bo53200981lle_hf )
        | ~ ( finite586181922lle_hf @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(413,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat )
      = ( ( A = bot_bo53200981lle_hf )
        | ~ ( finite586181922lle_hf @ A ) ) ),
    inference(cnf,[status(esa)],[412]) ).

thf(414,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ( A = bot_bo53200981lle_hf )
        | ~ ( finite586181922lle_hf @ A ) )
      = ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat ) ),
    inference(lifteq,[status(thm)],[413]) ).

thf(17471,plain,
    ! [B: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
      ( ( ( ! [C: hF_Mirabelle_hf] :
              ~ ( member1367349282lle_hf @ C @ A )
          | ~ ( finite586181922lle_hf @ B ) )
        = ( ( finite1213132899lle_hf @ B )
          = zero_zero_nat ) )
      | ( ( A = bot_bo53200981lle_hf )
       != ( B = bot_bo53200981lle_hf ) ) ),
    inference(paramod_ordered,[status(thm)],[658,414]) ).

thf(17472,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ! [B: hF_Mirabelle_hf] :
            ~ ( member1367349282lle_hf @ B @ A )
        | ~ ( finite586181922lle_hf @ A ) )
      = ( ( finite1213132899lle_hf @ A )
        = zero_zero_nat ) ),
    inference(pattern_uni,[status(thm)],[17471:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(35334,plain,
    ! [A: set_HF_Mirabelle_hf] :
      ( ( ( ! [B: hF_Mirabelle_hf] :
              ~ ( member1367349282lle_hf @ B @ A ) )
        = ( ( finite1213132899lle_hf @ A )
          = zero_zero_nat ) )
      | ( ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ z ) )
       != ( finite586181922lle_hf @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12618,17472]) ).

thf(35335,plain,
    ( ( ! [A: hF_Mirabelle_hf] :
          ~ ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) )
    = ( ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) )
      = zero_zero_nat ) ),
    inference(pattern_uni,[status(thm)],[35334:[bind(A,$thf( hF_Mirabelle_hfset @ z ))]]) ).

thf(141,axiom,
    ( hF_Mirabelle_hmem
    = ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_hmem__def) ).

thf(730,plain,
    ( hF_Mirabelle_hmem
    = ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(731,plain,
    ( ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) )
    = hF_Mirabelle_hmem ),
    inference(lifteq,[status(thm)],[730]) ).

thf(785,plain,
    ! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) )
      = ( hF_Mirabelle_hmem @ A @ B ) ),
    inference(func_ext,[status(esa)],[731]) ).

thf(17479,plain,
    ! [B: set_HF_Mirabelle_hf,A: hF_Mirabelle_hf] :
      ( ( ( B = bot_bo53200981lle_hf )
        = ( ( finite1213132899lle_hf @ B )
          = zero_zero_nat ) )
      | ( ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) )
       != ( finite586181922lle_hf @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[707,414]) ).

thf(17480,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ A ) )
        = zero_zero_nat )
      = ( ( hF_Mirabelle_hfset @ A )
        = bot_bo53200981lle_hf ) ),
    inference(pattern_uni,[status(thm)],[17479:[bind(A,$thf( C )),bind(B,$thf( hF_Mirabelle_hfset @ C ))]]) ).

thf(17721,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ( ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ A ) )
        = zero_zero_nat )
      = ( ( hF_Mirabelle_hfset @ A )
        = bot_bo53200981lle_hf ) ),
    inference(simp,[status(thm)],[17480]) ).

thf(35753,plain,
    ( ( ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z ) )
    = ( ( hF_Mirabelle_hfset @ z )
      = bot_bo53200981lle_hf ) ),
    inference(rewrite,[status(thm)],[35335,785,17721]) ).

thf(35754,plain,
    ( ~ ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z )
    | ( ( hF_Mirabelle_hfset @ z )
      = bot_bo53200981lle_hf ) ),
    inference(bool_ext,[status(thm)],[35753]) ).

thf(35941,plain,
    ( ( ( hF_Mirabelle_hfset @ z )
      = bot_bo53200981lle_hf )
    | ~ ! [A: hF_Mirabelle_hf] :
          ~ ( hF_Mirabelle_hmem @ A @ z ) ),
    inference(lifteq,[status(thm)],[35754]) ).

thf(36026,plain,
    ( ( hF_Mirabelle_hmem @ sk561 @ z )
    | ( ( hF_Mirabelle_hfset @ z )
      = bot_bo53200981lle_hf ) ),
    inference(cnf,[status(esa)],[35941]) ).

thf(755,plain,
    ( ( z = zero_z189798548lle_hf )
    | ! [A: hF_Mirabelle_hf] :
        ~ ( hF_Mirabelle_hmem @ A @ z ) ),
    inference(bool_ext,[status(thm)],[150]) ).

thf(757,plain,
    ( ( z = zero_z189798548lle_hf )
    | ! [A: hF_Mirabelle_hf] :
        ~ ( hF_Mirabelle_hmem @ A @ z ) ),
    inference(lifteq,[status(thm)],[755]) ).

thf(759,plain,
    ! [A: hF_Mirabelle_hf] :
      ( ~ ( hF_Mirabelle_hmem @ A @ z )
      | ( z = zero_z189798548lle_hf ) ),
    inference(cnf,[status(esa)],[757]) ).

thf(842,plain,
    ! [A: hF_Mirabelle_hf] :
      ~ ( hF_Mirabelle_hmem @ A @ z ),
    inference(simplifyReflect,[status(thm)],[759,838]) ).

thf(38993,plain,
    ( $false
    | ( ( hF_Mirabelle_hfset @ z )
      = bot_bo53200981lle_hf ) ),
    inference(rewrite,[status(thm)],[36026,842]) ).

thf(38994,plain,
    ( ( hF_Mirabelle_hfset @ z )
    = bot_bo53200981lle_hf ),
    inference(simp,[status(thm)],[38993]) ).

thf(38995,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[38994,2299]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ITP072^1 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat May 18 18:19:54 EDT 2024
% 0.20/0.35  % CPUTime  : 
% 0.99/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.89/1.30  % [INFO] 	 Parsing done (357ms). 
% 2.21/1.31  % [INFO] 	 Running in sequential loop mode. 
% 3.05/1.66  % [INFO] 	 nitpick registered as external prover. 
% 3.05/1.66  % [INFO] 	 Scanning for conjecture ... 
% 3.42/1.79  % [INFO] 	 Found a conjecture (or negated_conjecture) and 351 axioms. Running axiom selection ... 
% 3.69/1.92  % [INFO] 	 Axiom selection finished. Selected 146 axioms (removed 205 axioms). 
% 3.95/2.05  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.18/2.07  % [INFO] 	 Type checking passed. 
% 4.18/2.08  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 216.76/39.36  % [INFO] 	 Killing All external provers ... 
% 217.01/39.53  % Time passed: 38883ms (effective reasoning time: 38051ms)
% 217.01/39.53  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 217.01/39.53  % Axioms used in derivation (16): fact_9_Zero__hf__def, fact_14_HF__hfset, fact_106_bot__nat__def, fact_2_hmem__hempty, fact_117_finite__insert, fact_168_card_Oempty, fact_5_hmem__def, fact_169_card_Oinfinite, fact_20_all__not__in__conv, fact_164_empty__subsetI, fact_248_card__insert__le, fact_244_card__seteq, fact_107_finite__hfset, fact_208_bot_Oextremum__unique, fact_210_bot_Oextremum__uniqueI, fact_228_card__eq__0__iff
% 217.01/39.53  % No. of inferences in proof: 113
% 217.01/39.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 38883 ms resp. 38051 ms w/o parsing
% 217.40/39.62  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 217.40/39.62  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------