Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ALG226+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 06:46:23 AM UTC 2026

% Result   : Theorem 155.44s 42.08s
% Output   : Refutation 157.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :  610
% Syntax   : Number of formulae    : 1938 ( 573 unt;   0 typ;  33 def)
%            Number of atoms       : 6529 (1580 equ;   0 cnn)
%            Maximal formula atoms :   30 (   3 avg)
%            Number of connectives : 24514 (1704   ~; 797   |;1187   &;18648   @)
%                                         ( 101 <=>;2077  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  142 ( 139 usr;  27 con; 0-6 aty)
%            Number of variables   : 4891 (  29   ^;4668   !; 161   ?;4891   :)
%                                         (   0  !>;   0  ?*;   0  @-;  33  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
    v1_xboole_0: $i > $o ).

thf(v2_relat_1_decl,type,
    v2_relat_1: $i > $o ).

thf(m1_pboole_decl,type,
    m1_pboole: $i > $i > $o ).

thf(k1_closure3_decl,type,
    k1_closure3: $i > $i > $i ).

thf(k7_relat_1_decl,type,
    k7_relat_1: $i > $i > $i ).

thf(r6_pboole_decl,type,
    r6_pboole: $i > $i > $i > $o ).

thf(m3_pboole_decl,type,
    m3_pboole: $i > $i > $i > $i > $o ).

thf(k2_pre_circ_decl,type,
    k2_pre_circ: $i > $i > $i ).

thf(m1_subset_1_decl,type,
    m1_subset_1: $i > $i > $o ).

thf(k1_waybel_5_decl,type,
    k1_waybel_5: $i > $i > $i > $i > $i > $i ).

thf(k1_funct_1_decl,type,
    k1_funct_1: $i > $i > $i ).

thf(r2_hidden_decl,type,
    r2_hidden: $i > $i > $o ).

thf(k4_tarski_decl,type,
    k4_tarski: $i > $i > $i ).

thf(k2_zfmisc_1_decl,type,
    k2_zfmisc_1: $i > $i > $i ).

thf(r1_tarski_decl,type,
    r1_tarski: $i > $i > $o ).

thf(k2_xboole_0_decl,type,
    k2_xboole_0: $i > $i > $i ).

thf(k1_tarski_decl,type,
    k1_tarski: $i > $i ).

thf(k1_funct_2_decl,type,
    k1_funct_2: $i > $i > $i ).

thf(k3_xboole_0_decl,type,
    k3_xboole_0: $i > $i > $i ).

thf(k1_zfmisc_1_decl,type,
    k1_zfmisc_1: $i > $i ).

thf(k1_xboole_0_decl,type,
    k1_xboole_0: $i ).

thf(k3_zfmisc_1_decl,type,
    k3_zfmisc_1: $i > $i > $i > $i ).

thf(k5_xboole_0_decl,type,
    k5_xboole_0: $i > $i > $i ).

thf(k4_xboole_0_decl,type,
    k4_xboole_0: $i > $i > $i ).

thf(m1_card_fil_decl,type,
    m1_card_fil: $i > $i > $o ).

thf(r5_pboole_decl,type,
    r5_pboole: $i > $i > $i > $o ).

thf(k4_pboole_decl,type,
    k4_pboole: $i > $i > $i > $i ).

thf(v1_pre_circ_decl,type,
    v1_pre_circ: $i > $i > $o ).

thf(r1_pboole_decl,type,
    r1_pboole: $i > $i > $i > $o ).

thf(r2_pboole_decl,type,
    r2_pboole: $i > $i > $i > $o ).

thf(k2_mboolean_decl,type,
    k2_mboolean: $i > $i > $i ).

thf(k3_mcart_1_decl,type,
    k3_mcart_1: $i > $i > $i > $i ).

thf(k4_card_3_decl,type,
    k4_card_3: $i > $i ).

thf(v2_cat_5_decl,type,
    v2_cat_5: $i > $o ).

thf(m1_cat_5_decl,type,
    m1_cat_5: $i > $i > $o ).

thf(v3_relat_1_decl,type,
    v3_relat_1: $i > $o ).

thf(r4_pboole_decl,type,
    r4_pboole: $i > $i > $i > $o ).

thf(k1_pboole_decl,type,
    k1_pboole: $i > $i ).

thf(k1_mboolean_decl,type,
    k1_mboolean: $i > $i > $i ).

thf(k3_pboole_decl,type,
    k3_pboole: $i > $i > $i > $i ).

thf(k3_tarski_decl,type,
    k3_tarski: $i > $i ).

thf(v5_grcat_1_decl,type,
    v5_grcat_1: $i > $o ).

thf(m3_grcat_1_decl,type,
    m3_grcat_1: $i > $i > $o ).

thf(k2_yellow_7_decl,type,
    k2_yellow_7: $i > $i > $i > $i > $i > $i > $i ).

thf(k5_funct_6_decl,type,
    k5_funct_6: $i > $i > $i > $i ).

thf(m1_finseq_2_decl,type,
    m1_finseq_2: $i > $i > $o ).

thf(k2_pboole_decl,type,
    k2_pboole: $i > $i > $i > $i ).

thf(k10_funct_6_decl,type,
    k10_funct_6: $i > $i ).

thf(m2_card_fil_decl,type,
    m2_card_fil: $i > $i > $o ).

thf(v1_fraenkel_decl,type,
    v1_fraenkel: $i > $o ).

thf(k2_relat_1_decl,type,
    k2_relat_1: $i > $i ).

thf(v1_pralg_2_decl,type,
    v1_pralg_2: $i > $o ).

thf(k1_subset_1_decl,type,
    k1_subset_1: $i > $i ).

thf(a_1_0_card_fil_decl,type,
    a_1_0_card_fil: $i > $i ).

thf(r3_pboole_decl,type,
    r3_pboole: $i > $i > $i > $o ).

thf(r7_pboole_decl,type,
    r7_pboole: $i > $i > $i > $o ).

thf(v1_funcop_1_decl,type,
    v1_funcop_1: $i > $o ).

thf(r3_zfrefle1_decl,type,
    r3_zfrefle1: $i > $i > $o ).

thf(r2_zfrefle1_decl,type,
    r2_zfrefle1: $i > $i > $o ).

thf(k5_pboole_decl,type,
    k5_pboole: $i > $i > $i > $i ).

thf(k11_pboole_decl,type,
    k11_pboole: $i > $i > $i > $i ).

thf(k12_pboole_decl,type,
    k12_pboole: $i > $i > $i > $i ).

thf(a_2_1_closure3_decl,type,
    a_2_1_closure3: $i > $i > $i ).

thf(k4_card_fil_decl,type,
    k4_card_fil: $i > $i ).

thf(v2_setfam_1_decl,type,
    v2_setfam_1: $i > $o ).

thf(k16_domain_1_decl,type,
    k16_domain_1: $i > $i > $i > $i > $i ).

thf(k1_binop_1_decl,type,
    k1_binop_1: $i > $i > $i > $i ).

thf(k1_multop_1_decl,type,
    k1_multop_1: $i > $i > $i > $i > $i ).

thf(r2_altcat_2_decl,type,
    r2_altcat_2: $i > $i > $i > $i > $o ).

thf(m2_pboole_decl,type,
    m2_pboole: $i > $i > $i > $o ).

thf(k21_pralg_1_decl,type,
    k21_pralg_1: $i > $i > $i ).

thf(k15_domain_1_decl,type,
    k15_domain_1: $i > $i > $i > $i > $i ).

thf(a_2_0_closure2_decl,type,
    a_2_0_closure2: $i > $i > $i ).

thf(a_1_0_domain_1_decl,type,
    a_1_0_domain_1: $i > $i ).

thf(k2_cat_5_decl,type,
    k2_cat_5: $i > $i > $i > $i > $i ).

thf(k14_domain_1_decl,type,
    k14_domain_1: $i > $i > $i > $i > $i ).

thf(k17_domain_1_decl,type,
    k17_domain_1: $i > $i > $i > $i > $i ).

thf(m1_pralg_1_decl,type,
    m1_pralg_1: $i > $i > $i > $o ).

thf(k14_pralg_1_decl,type,
    k14_pralg_1: $i > $i > $i > $i > $i ).

thf(a_1_0_pua2mss1_decl,type,
    a_1_0_pua2mss1: $i > $i ).

thf(k1_cat_5_decl,type,
    k1_cat_5: $i > $i > $i > $i > $i ).

thf(k19_pralg_1_decl,type,
    k19_pralg_1: $i > $i > $i > $i ).

thf(k3_funct_5_decl,type,
    k3_funct_5: $i > $i ).

thf(k3_cat_5_decl,type,
    k3_cat_5: $i > $i > $i > $i ).

thf(a_2_0_closure3_decl,type,
    a_2_0_closure3: $i > $i > $i ).

thf(f1_s4_altcat_1_decl,type,
    f1_s4_altcat_1: $i ).

thf(f2_s4_altcat_1_decl,type,
    f2_s4_altcat_1: $i ).

thf(f3_s4_altcat_1_decl,type,
    f3_s4_altcat_1: $i ).

thf(f4_s4_altcat_1_decl,type,
    f4_s4_altcat_1: $i > $i > $i > $i ).

thf(r2_subset_1_decl,type,
    r2_subset_1: $i > $i > $o ).

thf(k7_waybel_5_decl,type,
    k7_waybel_5: $i > $i > $i ).

thf(v2_pboole_decl,type,
    v2_pboole: $i > $i > $o ).

thf(k1_funct_4_decl,type,
    k1_funct_4: $i > $i > $i ).

thf(k1_pralg_3_decl,type,
    k1_pralg_3: $i > $i ).

thf(k3_pua2mss1_decl,type,
    k3_pua2mss1: $i > $i ).

thf(v1_pboole_decl,type,
    v1_pboole: $i > $i > $o ).

thf(f1_s2_pboole_decl,type,
    f1_s2_pboole: $i ).

thf(f2_s2_pboole_decl,type,
    f2_s2_pboole: $i ).

thf(p1_s2_pboole_decl,type,
    p1_s2_pboole: $i > $i > $o ).

thf(k3_qc_lang1_decl,type,
    k3_qc_lang1: $i ).

thf(k4_qc_lang1_decl,type,
    k4_qc_lang1: $i ).

thf(f1_s3_altcat_1_decl,type,
    f1_s3_altcat_1: $i ).

thf(f2_s3_altcat_1_decl,type,
    f2_s3_altcat_1: $i ).

thf(f3_s3_altcat_1_decl,type,
    f3_s3_altcat_1: $i ).

thf(f4_s3_altcat_1_decl,type,
    f4_s3_altcat_1: $i > $i > $i > $i ).

thf(sk1_decl,type,
    sk1: $i ).

thf(sk2_decl,type,
    sk2: $i ).

thf(sk3_decl,type,
    sk3: $i ).

thf(sk4_decl,type,
    sk4: $i > $i ).

thf(sk5_decl,type,
    sk5: $i > $i ).

thf(sk6_decl,type,
    sk6: $i > $i > $i ).

thf(sk7_decl,type,
    sk7: $i > $i > $i ).

thf(sk8_decl,type,
    sk8: $i > $i ).

thf(sk9_decl,type,
    sk9: $i > $i ).

thf(sk10_decl,type,
    sk10: $i > $i ).

thf(sk11_decl,type,
    sk11: $i > $i ).

thf(sk12_decl,type,
    sk12: $i > $i > $i > $o ).

thf(sk13_decl,type,
    sk13: $i > $i > $i > $i ).

thf(sk14_decl,type,
    sk14: $i > $i > $i > $i ).

thf(sk15_decl,type,
    sk15: $i > $i > $i > $i ).

thf(sk19_decl,type,
    sk19: $i > $i ).

thf(sk33_decl,type,
    sk33: $i ).

thf(sk85_decl,type,
    sk85: $i > $i ).

thf(sk95_decl,type,
    sk95: $i > $i > $i ).

thf(sk96_decl,type,
    sk96: $i > $i > $i ).

thf(sk103_decl,type,
    sk103: $i ).

thf(sk105_decl,type,
    sk105: $i > $i ).

thf(sk124_decl,type,
    sk124: $i ).

thf(sk153_decl,type,
    sk153: $i > $i ).

thf(sk181_decl,type,
    sk181: $i ).

thf(sk184_decl,type,
    sk184: $i ).

thf(sk188_decl,type,
    sk188: $i > $i ).

thf(sk190_decl,type,
    sk190: $i ).

thf(sk194_decl,type,
    sk194: $i > $i ).

thf(sk195_decl,type,
    sk195: $i ).

thf(sk197_decl,type,
    sk197: $i ).

thf(sk198_decl,type,
    sk198: $i ).

thf(sk199_decl,type,
    sk199: $i ).

thf(sk200_decl,type,
    sk200: $i ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: $i] :
          ~ ( ~ ( A @ v1_xboole_0 )
           => ! [B: $i] :
                ( ( ( A @ ( B @ m1_pboole ) )
                  & ( B @ v2_relat_1 ) )
               => ! [C: $i] :
                    ( ( ( A @ ( C @ m1_pboole ) )
                      & ( C @ v2_relat_1 ) )
                   => ( ( ( ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) )
                          = ( C @ ( A @ k1_closure3 ) @ ( C @ k7_relat_1 ) ) )
                        & ( ( B @ ( A @ k1_closure3 ) )
                          = ( C @ ( A @ k1_closure3 ) ) ) )
                     => ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: $i] :
          ~ ( ( ( sk1 @ ( A @ m1_pboole ) )
              & ( A @ v2_relat_1 ) )
           => ! [B: $i] :
                ( ( ( sk1 @ ( B @ m1_pboole ) )
                  & ( B @ v2_relat_1 ) )
               => ( ( ( ( A @ ( sk1 @ k1_closure3 ) @ ( A @ k7_relat_1 ) )
                      = ( B @ ( sk1 @ k1_closure3 ) @ ( B @ k7_relat_1 ) ) )
                    & ( ( A @ ( sk1 @ k1_closure3 ) )
                      = ( B @ ( sk1 @ k1_closure3 ) ) ) )
                 => ( B @ ( A @ ( sk1 @ r6_pboole ) ) ) ) ) ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( @+[A: $i] :
          ~ ( ( ( sk1 @ ( A @ m1_pboole ) )
              & ( A @ v2_relat_1 ) )
           => ( ( ( ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) )
                  = ( A @ ( sk1 @ k1_closure3 ) @ ( A @ k7_relat_1 ) ) )
                & ( ( sk2 @ ( sk1 @ k1_closure3 ) )
                  = ( A @ ( sk1 @ k1_closure3 ) ) ) )
             => ( A @ ( sk2 @ ( sk1 @ r6_pboole ) ) ) ) ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( ^ [A: $i] :
        @+[B: $i] :
        ? [C: $i] :
          ( ( C @ ( B @ k4_tarski ) )
          = A ) ) ) ).

thf(sk5_def,definition,
    ( sk5
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ( B @ ( A @ sk4 @ k4_tarski ) )
          = A ) ) ) ).

thf(sk6_def,definition,
    ( sk6
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( B @ ( C @ m1_pboole ) )
           => ! [D: $i] :
                ( ( B @ ( D @ m1_pboole ) )
               => ~ ( ~ ( C @ ( D @ ( B @ r2_pboole ) ) )
                    & ~ ( D @ ( C @ ( B @ r2_pboole ) ) )
                    & ( A @ ( D @ ( B @ r1_pboole ) ) )
                    & ( A @ ( C @ ( B @ r1_pboole ) ) ) ) ) ) ) ) ).

thf(sk7_def,definition,
    ( sk7
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( B @ ( C @ m1_pboole ) )
           => ~ ( ~ ( B @ ( A @ sk6 ) @ ( C @ ( B @ r2_pboole ) ) )
                & ~ ( C @ ( B @ ( A @ sk6 ) @ ( B @ r2_pboole ) ) )
                & ( A @ ( C @ ( B @ r1_pboole ) ) )
                & ( A @ ( B @ ( A @ sk6 ) @ ( B @ r1_pboole ) ) ) ) ) ) ) ).

thf(sk8_def,definition,
    ( sk8
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ~ ? [C: $i,D: $i] :
                ( B
                = ( D @ ( C @ k4_tarski ) ) )
          & ( A @ ( B @ r2_hidden ) ) ) ) ) ).

thf(sk9_def,definition,
    ( sk9
    = ( ^ [A: $i] :
        @+[B: $i] :
        ? [C: $i] : ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ) ) ).

thf(sk10_def,definition,
    ( sk10
    = ( ^ [A: $i] :
        @+[B: $i] : ( B @ ( A @ sk9 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ) ) ).

thf(sk11_def,definition,
    ( sk11
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ m1_cat_5 ) ) ) ) ).

thf(sk13_def,definition,
    ( sk13
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( A @ ( D @ r2_hidden ) )
           => ( ( B @ ( D @ r2_hidden ) )
              | ( C @ ( D @ r2_hidden ) ) ) ) ) ) ).

thf(sk14_def,definition,
    ( sk14
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( ( B @ ( D @ r2_hidden ) )
              | ( C @ ( D @ r2_hidden ) ) )
           => ( A @ ( D @ r2_hidden ) ) ) ) ) ).

thf(sk15_def,definition,
    ( sk15
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( C @ ( D @ m1_subset_1 ) )
           => ( ( ( A @ ( D @ r2_hidden ) )
               => ( B @ ( D @ r2_hidden ) ) )
              & ( ( B @ ( D @ r2_hidden ) )
               => ( A @ ( D @ r2_hidden ) ) ) ) ) ) ) ).

thf(sk19_def,definition,
    ( sk19
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ( B @ v1_xboole_0 )
          & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).

thf(sk33_def,definition,
    ( sk33
    = ( @+[A: $i] :
          ( ! [B: $i] :
              ( ( A @ ( B @ m1_subset_1 ) )
             => ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk85_def,definition,
    ( sk85
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).

thf(sk95_def,definition,
    ( sk95
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( A @ ( C @ r2_hidden ) )
           => ( C = B ) ) ) ) ).

thf(sk96_def,definition,
    ( sk96
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( C = B )
           => ( A @ ( C @ r2_hidden ) ) ) ) ) ).

thf(sk103_def,definition,
    ( sk103
    = ( @+[A: $i] :
          ( ( A @ v1_pralg_2 )
          & ( A @ v1_fraenkel )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk105_def,definition,
    ( sk105
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).

thf(sk124_def,definition,
    ( sk124
    = ( @+[A: $i] :
          ~ ( A @ v2_setfam_1 ) ) ) ).

thf(sk153_def,definition,
    ( sk153
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ m1_finseq_2 ) ) ) ) ).

thf(sk181_def,definition,
    ( sk181
    = ( @+[A: $i] :
          ( ( A @ v1_fraenkel )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk184_def,definition,
    ( sk184
    = ( @+[A: $i] :
          ( ! [B: $i] :
              ( ( f1_s4_altcat_1 @ ( B @ m1_subset_1 ) )
             => ! [C: $i] :
                  ( ( f2_s4_altcat_1 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( f3_s4_altcat_1 @ ( D @ m1_subset_1 ) )
                     => ( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
                        = ( D @ ( C @ ( B @ f4_s4_altcat_1 ) ) ) ) ) ) )
          & ( f3_s4_altcat_1 @ ( f2_s4_altcat_1 @ ( f1_s4_altcat_1 @ k3_zfmisc_1 ) ) @ ( A @ m1_pboole ) ) ) ) ) ).

thf(sk188_def,definition,
    ( sk188
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ ( B @ m1_finseq_2 ) ) ) ) ) ).

thf(sk190_def,definition,
    ( sk190
    = ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).

thf(sk194_def,definition,
    ( sk194
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ m1_pboole ) ) ) ) ).

thf(sk195_def,definition,
    ( sk195
    = ( @+[A: $i] :
          ( ! [B: $i] :
              ( ( f1_s2_pboole @ ( B @ r2_hidden ) )
             => ( ! [C: $i] :
                    ( ( ( C @ ( B @ p1_s2_pboole ) )
                      & ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
                   => ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
                & ! [C: $i] :
                    ( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
                   => ( ( C @ ( B @ p1_s2_pboole ) )
                      & ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
          & ( f1_s2_pboole @ ( A @ m1_pboole ) ) ) ) ) ).

thf(sk197_def,definition,
    ( sk197
    = ( @+[A: $i] :
          ( ( A @ v2_cat_5 )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk198_def,definition,
    ( sk198
    = ( @+[A: $i] :
          ~ ( A @ v1_xboole_0 ) ) ) ).

thf(sk199_def,definition,
    ( sk199
    = ( @+[A: $i] :
          ( ( A @ v5_grcat_1 )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk200_def,definition,
    ( sk200
    = ( @+[A: $i] :
          ( ! [B: $i,C: $i,D: $i] :
              ( ( ( f3_s3_altcat_1 @ ( D @ r2_hidden ) )
                & ( f2_s3_altcat_1 @ ( C @ r2_hidden ) )
                & ( f1_s3_altcat_1 @ ( B @ r2_hidden ) ) )
             => ( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
                = ( D @ ( C @ ( B @ f4_s3_altcat_1 ) ) ) ) )
          & ( f3_s3_altcat_1 @ ( f2_s3_altcat_1 @ ( f1_s3_altcat_1 @ k3_zfmisc_1 ) ) @ ( A @ m1_pboole ) ) ) ) ) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).

thf(643,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(644,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ! [C: $i] : ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
    inference(miniscope,[status(thm)],[643]) ).

thf(645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
      | ~ ( B @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[644]) ).

thf(426,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
      <=> ? [C: $i] :
            ( ( A = C )
            & ( B @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).

thf(2452,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ( ( ? [C: $i] :
              ( ( A = C )
              & ( B @ ( C @ m1_subset_1 ) ) )
         => ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) ) )
        & ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
         => ? [C: $i] :
              ( ( A = C )
              & ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) )
      = ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).

thf(627,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) )
      = ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(628,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) )
      = ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[627]) ).

thf(629,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) ) ),
    inference(lifteq,[status(thm)],[628]) ).

thf(390,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
               => ( ( C @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
                  & ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_pboole) ).

thf(2306,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
               => ( ( C @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
                  & ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(192,axiom,
    ( ( k1_xboole_0 @ k1_tarski @ v1_pralg_2 )
    & ( k1_xboole_0 @ k1_tarski @ v1_fraenkel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_pralg_2) ).

thf(1452,plain,
    ( ( k1_xboole_0 @ k1_tarski @ v1_pralg_2 )
    & ( k1_xboole_0 @ k1_tarski @ v1_fraenkel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(1453,plain,
    ( ( k1_xboole_0 @ k1_tarski @ v1_pralg_2 )
    & ( k1_xboole_0 @ k1_tarski @ v1_fraenkel ) ),
    inference(cnf,[status(esa)],[1452]) ).

thf(1454,plain,
    k1_xboole_0 @ k1_tarski @ v1_fraenkel,
    inference(cnfConj,[status(thm)],[1453]) ).

thf(154,axiom,
    ! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).

thf(1259,plain,
    ! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(1260,plain,
    ! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
    inference(cnf,[status(esa)],[1259]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).

thf(681,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(682,plain,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[681]) ).

thf(683,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
      | ( A = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[682]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(1592,plain,
    ! [A: $i] :
      ( ( ( A = k1_xboole_0 )
       => ( A @ v1_xboole_0 ) )
      & ( ( A @ v1_xboole_0 )
       => ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(1593,plain,
    ( ! [A: $i] :
        ( ( A = k1_xboole_0 )
       => ( A @ v1_xboole_0 ) )
    & ! [A: $i] :
        ( ( A @ v1_xboole_0 )
       => ( A = k1_xboole_0 ) ) ),
    inference(miniscope,[status(thm)],[1592]) ).

thf(1594,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ v1_xboole_0 )
        | ( B != k1_xboole_0 ) )
      & ( ( A = k1_xboole_0 )
        | ~ ( A @ v1_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[1593]) ).

thf(1596,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1594]) ).

thf(1598,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1596]) ).

thf(1599,plain,
    k1_xboole_0 @ v1_xboole_0,
    inference(simp,[status(thm)],[1598]) ).

thf(307,axiom,
    ? [A: $i] :
      ( ( A @ v1_pralg_2 )
      & ( A @ v1_fraenkel )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pralg_2) ).

thf(1972,plain,
    ? [A: $i] :
      ( ( A @ v1_pralg_2 )
      & ( A @ v1_fraenkel )
      & ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(1973,plain,
    ( ( sk103 @ v1_pralg_2 )
    & ( sk103 @ v1_fraenkel )
    & ~ ( sk103 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1972]) ).

thf(1974,plain,
    ~ ( sk103 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1973]) ).

thf(3019,plain,
    ( ( ( sk103 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,1974]) ).

thf(3020,plain,
    ( ( sk103 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3019]) ).

thf(3023,plain,
    sk103 != k1_xboole_0,
    inference(simp,[status(thm)],[3020]) ).

thf(13338,plain,
    ! [A: $i] :
      ( ( A != sk103 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3023]) ).

thf(13339,plain,
    ! [A: $i] :
      ( ( A != sk103 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13338]) ).

thf(13340,plain,
    ~ ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[13339:[bind(A,$thf( sk103 ))]]) ).

thf(15188,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,13340]) ).

thf(15189,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15188]) ).

thf(15280,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) ) )
      | ( A != sk103 ) ),
    inference(simp,[status(thm)],[15189]) ).

thf(15303,plain,
    ( ( sk103 @ ( sk103 @ k2_zfmisc_1 ) )
   != ( sk103 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[15280]) ).

thf(290,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i,C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_qc_lang1) ).

thf(1899,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i,C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(277,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).

thf(1840,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(440,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_pboole) ).

thf(2499,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(447,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( D @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_mboolean) ).

thf(2544,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( D @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(374,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( C @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_mboolean) ).

thf(2250,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( C @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(366,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ k3_tarski ) )
    <=> ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
        <=> ? [D: $i] :
              ( ( A @ ( D @ r2_hidden ) )
              & ( D @ ( C @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).

thf(2199,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( ? [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                  & ( D @ ( C @ r2_hidden ) ) )
             => ( B @ ( C @ r2_hidden ) ) )
            & ( ( B @ ( C @ r2_hidden ) )
             => ? [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                  & ( D @ ( C @ r2_hidden ) ) ) ) )
       => ( B
          = ( A @ k3_tarski ) ) )
      & ( ( B
          = ( A @ k3_tarski ) )
       => ! [C: $i] :
            ( ( ? [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                  & ( D @ ( C @ r2_hidden ) ) )
             => ( B @ ( C @ r2_hidden ) ) )
            & ( ( B @ ( C @ r2_hidden ) )
             => ? [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                  & ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(94,axiom,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( A @ ( B @ m1_subset_1 ) )
         => ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).

thf(973,plain,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( A @ ( B @ m1_subset_1 ) )
         => ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
      & ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(974,plain,
    ! [A: $i] :
      ( ( ~ ( A @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 )
        | ~ ( sk33 @ ( A @ m1_subset_1 ) ) )
      & ~ ( sk33 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[973]) ).

thf(975,plain,
    ~ ( sk33 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[974]) ).

thf(3015,plain,
    ( ( ( sk33 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,975]) ).

thf(3016,plain,
    ( ( sk33 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3015]) ).

thf(3021,plain,
    sk33 != k1_xboole_0,
    inference(simp,[status(thm)],[3016]) ).

thf(284,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k2_pre_circ ) @ m1_pboole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_circ) ).

thf(1878,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k2_pre_circ ) @ m1_pboole ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(1879,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ k2_pre_circ ) @ m1_pboole ) ),
    inference(cnf,[status(esa)],[1878]) ).

thf(172,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).

thf(1337,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(463,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_pboole) ).

thf(2612,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(564,axiom,
    ~ ( k3_qc_lang1 @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_qc_lang1) ).

thf(2962,plain,
    ~ ( k3_qc_lang1 @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(2963,plain,
    ~ ( k3_qc_lang1 @ v1_xboole_0 ),
    inference(polarity_switch,[status(thm)],[2962]) ).

thf(3056,plain,
    ( ( ( k3_qc_lang1 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,2963]) ).

thf(3057,plain,
    ( ( k3_qc_lang1 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3056]) ).

thf(3060,plain,
    k3_qc_lang1 != k1_xboole_0,
    inference(simp,[status(thm)],[3057]) ).

thf(13160,plain,
    ! [A: $i] :
      ( ( A != k3_qc_lang1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3060]) ).

thf(13161,plain,
    ! [A: $i] :
      ( ( A != k3_qc_lang1 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13160]) ).

thf(13162,plain,
    ~ ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[13161:[bind(A,$thf( k3_qc_lang1 ))]]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(670,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(671,plain,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[670]) ).

thf(672,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
      | ( A = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[671]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m1_pboole ) )
            & ( B @ v2_relat_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( C @ m1_pboole ) )
                & ( C @ v2_relat_1 ) )
             => ( ( ( ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) )
                    = ( C @ ( A @ k1_closure3 ) @ ( C @ k7_relat_1 ) ) )
                  & ( ( B @ ( A @ k1_closure3 ) )
                    = ( C @ ( A @ k1_closure3 ) ) ) )
               => ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_closure3) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ~ ( A @ v1_xboole_0 )
       => ! [B: $i] :
            ( ( ( A @ ( B @ m1_pboole ) )
              & ( B @ v2_relat_1 ) )
           => ! [C: $i] :
                ( ( ( A @ ( C @ m1_pboole ) )
                  & ( C @ v2_relat_1 ) )
               => ( ( ( ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) )
                      = ( C @ ( A @ k1_closure3 ) @ ( C @ k7_relat_1 ) ) )
                    & ( ( B @ ( A @ k1_closure3 ) )
                      = ( C @ ( A @ k1_closure3 ) ) ) )
                 => ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(579,plain,
    ~ ! [A: $i] :
        ( ~ ( A @ v1_xboole_0 )
       => ! [B: $i] :
            ( ( ( A @ ( B @ m1_pboole ) )
              & ( B @ v2_relat_1 ) )
           => ! [C: $i] :
                ( ( ( A @ ( C @ m1_pboole ) )
                  & ( C @ v2_relat_1 ) )
               => ( ( ( ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) )
                      = ( C @ ( A @ k1_closure3 ) @ ( C @ k7_relat_1 ) ) )
                    & ( ( B @ ( A @ k1_closure3 ) )
                      = ( C @ ( A @ k1_closure3 ) ) ) )
                 => ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(580,plain,
    ( ~ ( sk3 @ ( sk2 @ ( sk1 @ r6_pboole ) ) )
    & ( ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) )
      = ( sk3 @ ( sk1 @ k1_closure3 ) @ ( sk3 @ k7_relat_1 ) ) )
    & ( ( sk2 @ ( sk1 @ k1_closure3 ) )
      = ( sk3 @ ( sk1 @ k1_closure3 ) ) )
    & ( sk1 @ ( sk3 @ m1_pboole ) )
    & ( sk3 @ v2_relat_1 )
    & ( sk1 @ ( sk2 @ m1_pboole ) )
    & ( sk2 @ v2_relat_1 )
    & ~ ( sk1 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[579]) ).

thf(584,plain,
    ~ ( sk3 @ ( sk2 @ ( sk1 @ r6_pboole ) ) ),
    inference(cnfConj,[status(thm)],[580]) ).

thf(11371,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ~ ( sk3 @ ( k1_xboole_0 @ ( sk1 @ r6_pboole ) ) )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,584]) ).

thf(11372,plain,
    ( ~ ( sk3 @ ( k1_xboole_0 @ ( sk1 @ r6_pboole ) ) )
    | ~ ( sk2 @ v1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11371:[bind(A,$thf( sk2 ))]]) ).

thf(262,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
    <=> ( ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).

thf(1759,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = k1_xboole_0 )
          | ( A = k1_xboole_0 ) )
       => ( ( B @ ( A @ k2_zfmisc_1 ) )
          = k1_xboole_0 ) )
      & ( ( ( B @ ( A @ k2_zfmisc_1 ) )
          = k1_xboole_0 )
       => ( ( B = k1_xboole_0 )
          | ( A = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(1760,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( B = k1_xboole_0 )
          | ( A = k1_xboole_0 ) )
       => ( ( B @ ( A @ k2_zfmisc_1 ) )
          = k1_xboole_0 ) )
    & ! [A: $i,B: $i] :
        ( ( ( B @ ( A @ k2_zfmisc_1 ) )
          = k1_xboole_0 )
       => ( ( B = k1_xboole_0 )
          | ( A = k1_xboole_0 ) ) ) ),
    inference(miniscope,[status(thm)],[1759]) ).

thf(1761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ( D @ ( C @ k2_zfmisc_1 ) )
          = k1_xboole_0 )
        | ( D != k1_xboole_0 ) )
      & ( ( ( D @ ( C @ k2_zfmisc_1 ) )
          = k1_xboole_0 )
        | ( C != k1_xboole_0 ) )
      & ( ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 )
        | ( ( B @ ( A @ k2_zfmisc_1 ) )
         != k1_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[1760]) ).

thf(1763,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1761]) ).

thf(1766,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1763]) ).

thf(1767,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[1766]) ).

thf(566,axiom,
    ~ ( k4_qc_lang1 @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_qc_lang1) ).

thf(2969,plain,
    ~ ( k4_qc_lang1 @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(2970,plain,
    ~ ( k4_qc_lang1 @ v1_xboole_0 ),
    inference(polarity_switch,[status(thm)],[2969]) ).

thf(3062,plain,
    ( ( ( k4_qc_lang1 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,2970]) ).

thf(3063,plain,
    ( ( k4_qc_lang1 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3062]) ).

thf(3066,plain,
    k4_qc_lang1 != k1_xboole_0,
    inference(simp,[status(thm)],[3063]) ).

thf(13396,plain,
    ! [A: $i] :
      ( ( A != k4_qc_lang1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3066]) ).

thf(13397,plain,
    ! [A: $i] :
      ( ( A != k4_qc_lang1 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13396]) ).

thf(13398,plain,
    ~ ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[13397:[bind(A,$thf( k4_qc_lang1 ))]]) ).

thf(15450,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,13398]) ).

thf(15451,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15450]) ).

thf(15535,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( A != k4_qc_lang1 ) ),
    inference(simp,[status(thm)],[15451]) ).

thf(15558,plain,
    ( ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) )
   != ( k4_qc_lang1 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[15535]) ).

thf(76,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( A @ k3_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

thf(909,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k3_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(554,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pboole) ).

thf(2921,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(434,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( ( C @ ( D @ ( A @ k2_pboole ) ) @ ( B @ ( D @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) )
                  & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_pboole) ).

thf(2480,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( ( C @ ( D @ ( A @ k2_pboole ) ) @ ( B @ ( D @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) )
                  & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(310,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v2_relat_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                 => ( B @ ( D @ ( A @ r2_pboole ) ) ) ) )
           => ( B @ ( C @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_mboolean) ).

thf(1982,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v2_relat_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                 => ( B @ ( D @ ( A @ r2_pboole ) ) ) ) )
           => ( B @ ( C @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(142,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ r2_hidden ) )
     => ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).

thf(1179,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ r2_hidden ) )
     => ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k2_xboole_0 ) @ k4_xboole_0 ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(397,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_pboole) ).

thf(2331,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ! [D: $i,E: $i] :
            ( ( E @ ( D @ k4_tarski ) )
           != A )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).

thf(666,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ! [D: $i,E: $i] :
            ( ( E @ ( D @ k4_tarski ) )
           != A )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(273,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
      = ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_mcart_1) ).

thf(1818,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
      = ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(95,axiom,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

thf(977,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(312,axiom,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(1989,plain,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(1990,plain,
    ! [A: $i] : ( A @ ( A @ sk105 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[1989]) ).

thf(976,plain,
    ! [A: $i] :
      ( ~ ( A @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 )
      | ~ ( sk33 @ ( A @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[974]) ).

thf(6468,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ sk105 @ m1_subset_1 ) )
       != ( sk33 @ ( B @ m1_subset_1 ) ) )
      | ~ ( B @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1990,976]) ).

thf(6469,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ sk105 @ m1_subset_1 ) )
       != ( sk33 @ ( B @ m1_subset_1 ) ) )
      | ~ ( B @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6468]) ).

thf(6470,plain,
    ~ ( sk33 @ sk105 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[6469:[bind(A,$thf( sk33 )),bind(B,$thf( sk33 @ sk105 ))]]) ).

thf(6762,plain,
    ( ( ( sk33 @ sk105 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,6470]) ).

thf(6763,plain,
    ( ( sk33 @ sk105 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6762]) ).

thf(6791,plain,
    ( ( sk33 @ sk105 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) )
   != k1_xboole_0 ),
    inference(simp,[status(thm)],[6763]) ).

thf(573,axiom,
    ? [A: $i] :
      ( ( A @ v5_grcat_1 )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_grcat_1) ).

thf(2991,plain,
    ? [A: $i] :
      ( ( A @ v5_grcat_1 )
      & ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(2992,plain,
    ( ( sk199 @ v5_grcat_1 )
    & ~ ( sk199 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[2991]) ).

thf(2993,plain,
    ~ ( sk199 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[2992]) ).

thf(3068,plain,
    ( ( ( sk199 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,2993]) ).

thf(3069,plain,
    ( ( sk199 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3068]) ).

thf(3072,plain,
    sk199 != k1_xboole_0,
    inference(simp,[status(thm)],[3069]) ).

thf(345,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_pboole) ).

thf(2104,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(218,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).

thf(1550,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(1551,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
    inference(cnf,[status(esa)],[1550]) ).

thf(12841,plain,
    ! [A: $i] :
      ( ( A != sk33 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3021]) ).

thf(12842,plain,
    ! [A: $i] :
      ( ( A != sk33 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[12841]) ).

thf(12843,plain,
    ~ ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[12842:[bind(A,$thf( sk33 ))]]) ).

thf(14182,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,12843]) ).

thf(14183,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14182]) ).

thf(14216,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) ) )
      | ( A != sk33 ) ),
    inference(simp,[status(thm)],[14183]) ).

thf(14235,plain,
    ! [A: $i] :
      ( ( A @ ( sk33 @ k2_xboole_0 ) )
     != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[14216]) ).

thf(409,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r1_pboole ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ r2_hidden ) )
               => ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_pboole) ).

thf(2381,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
             => ( C @ ( B @ ( A @ r1_pboole ) ) ) )
            & ( ( C @ ( B @ ( A @ r1_pboole ) ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(334,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( A @ ( B @ ( C @ ( A @ k11_pboole ) ) @ v1_pre_circ ) )
              & ( B @ v2_relat_1 ) )
           => ( A @ ( C @ v1_pre_circ ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_mssubfam) ).

thf(2062,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( A @ ( B @ ( C @ ( A @ k11_pboole ) ) @ v1_pre_circ ) )
              & ( B @ v2_relat_1 ) )
           => ( A @ ( C @ v1_pre_circ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(271,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
    <=> ( ( D @ ( B @ r2_hidden ) )
        & ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).

thf(1808,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( D @ ( B @ r2_hidden ) )
          & ( C @ ( A @ r2_hidden ) ) )
       => ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
      & ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( D @ ( B @ r2_hidden ) )
          & ( C @ ( A @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(118,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
        = ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) )
     => ( ( C = F )
        & ( B = E )
        & ( A = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_mcart_1) ).

thf(1073,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
        = ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) )
     => ( ( C = F )
        & ( B = E )
        & ( A = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(69,axiom,
    ! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_zfmisc_1) ).

thf(873,plain,
    ! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) @ ( k1_xboole_0 @ k1_tarski @ k2_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
        = ( B @ k1_tarski ) )
     => ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).

thf(655,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
        = ( B @ k1_tarski ) )
     => ( A @ ( B @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(214,axiom,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
    <=> ! [B: $i] :
          ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

thf(1527,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( A @ ( B @ r2_hidden ) )
       => ( A = k1_xboole_0 ) )
      & ( ( A = k1_xboole_0 )
       => ! [B: $i] :
            ~ ( A @ ( B @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(1528,plain,
    ( ! [A: $i] :
        ( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
       => ( A = k1_xboole_0 ) )
    & ! [A: $i] :
        ( ( A = k1_xboole_0 )
       => ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
    inference(miniscope,[status(thm)],[1527]) ).

thf(1529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C = k1_xboole_0 )
        | ( C @ ( C @ sk85 @ r2_hidden ) ) )
      & ( ~ ( A @ ( B @ r2_hidden ) )
        | ( A != k1_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[1528]) ).

thf(1530,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ r2_hidden ) )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1529]) ).

thf(1532,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ r2_hidden ) )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1530]) ).

thf(1533,plain,
    ! [A: $i] :
      ~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[1532]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
     => ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).

thf(596,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) )
     => ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(597,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r2_hidden ) )
      | ~ ( B @ ( B @ ( A @ k1_tarski @ k2_xboole_0 ) @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[596]) ).

thf(110,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
        = ( A @ k1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).

thf(1041,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
        = ( A @ k1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(443,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_subset_1) ).

thf(2512,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ m1_pboole ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_pboole) ).

thf(762,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ m1_pboole ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(466,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).

thf(2622,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(100,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
    <=> ( ( A = C )
        | ( B @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_setwiseo) ).

thf(988,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A = C )
          | ( B @ ( A @ r2_hidden ) ) )
       => ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) )
      & ( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
       => ( ( A = C )
          | ( B @ ( A @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(989,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( ( A = C )
          | ( B @ ( A @ r2_hidden ) ) )
       => ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
       => ( ( A = C )
          | ( B @ ( A @ r2_hidden ) ) ) ) ),
    inference(miniscope,[status(thm)],[988]) ).

thf(990,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F @ k1_tarski @ ( E @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
        | ( D != F ) )
      & ( ( F @ k1_tarski @ ( E @ k2_xboole_0 ) @ ( D @ r2_hidden ) )
        | ~ ( E @ ( D @ r2_hidden ) ) )
      & ( ( A = C )
        | ( B @ ( A @ r2_hidden ) )
        | ~ ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ) ),
    inference(cnf,[status(esa)],[989]) ).

thf(993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
      | ( A != C ) ),
    inference(cnfConj,[status(thm)],[990]) ).

thf(996,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r2_hidden ) )
      | ( A != C ) ),
    inference(lifteq,[status(thm)],[993]) ).

thf(997,plain,
    ! [B: $i,A: $i] : ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( B @ r2_hidden ) ),
    inference(simp,[status(thm)],[996]) ).

thf(10244,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
       != ( k1_xboole_0 @ ( C @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[997,1533]) ).

thf(10245,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
     != ( k1_xboole_0 @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[10244]) ).

thf(10285,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k2_xboole_0 ) )
       != k1_xboole_0 )
      | ( B != C ) ),
    inference(simp,[status(thm)],[10245]) ).

thf(10300,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k2_xboole_0 ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[10285]) ).

thf(11580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ k1_tarski @ ( B @ k2_xboole_0 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,10300]) ).

thf(11581,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ k1_tarski @ ( B @ k2_xboole_0 ) ) )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[11580]) ).

thf(11582,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[11581:[bind(A,$thf( F @ k1_tarski @ ( D @ k2_xboole_0 ) )),bind(B,$thf( D )),bind(C,$thf( F ))]]) ).

thf(11880,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ),
    inference(simp,[status(thm)],[11582]) ).

thf(562,axiom,
    ? [A: $i] :
      ~ ( A @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(2956,plain,
    ? [A: $i] :
      ~ ( A @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(2957,plain,
    ~ ! [A: $i] : ( A @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[2956]) ).

thf(2958,plain,
    ~ ( sk198 @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[2957]) ).

thf(3031,plain,
    ( ( ( sk198 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,2958]) ).

thf(3032,plain,
    ( ( sk198 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3031]) ).

thf(3033,plain,
    sk198 != k1_xboole_0,
    inference(simp,[status(thm)],[3032]) ).

thf(13121,plain,
    ! [A: $i] :
      ( ( A != sk198 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3033]) ).

thf(13122,plain,
    ! [A: $i] :
      ( ( A != sk198 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13121]) ).

thf(13123,plain,
    ~ ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[13122:[bind(A,$thf( sk198 ))]]) ).

thf(14669,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,13123]) ).

thf(14670,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14669]) ).

thf(14761,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) ) )
      | ( A != sk198 ) ),
    inference(simp,[status(thm)],[14670]) ).

thf(14786,plain,
    ( ( sk198 @ ( sk198 @ k2_zfmisc_1 ) )
   != ( sk198 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[14761]) ).

thf(559,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                & ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_pboole) ).

thf(2947,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                & ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(297,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
      = ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_xboole_1) ).

thf(1939,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
      = ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(373,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( A @ k1_pboole @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
              & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
           => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_pboole) ).

thf(2248,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( A @ k1_pboole @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
              & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
           => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(216,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_zfmisc_1) ).

thf(1544,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ k2_xboole_0 ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(478,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ ( A @ r2_altcat_2 ) ) ) )
          <=> ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_altcat_2) ).

thf(2676,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
             => ( C @ ( B @ ( A @ ( A @ r2_altcat_2 ) ) ) ) )
            & ( ( C @ ( B @ ( A @ ( A @ r2_altcat_2 ) ) ) )
             => ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(349,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_pboole) ).

thf(2114,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(132,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ! [F: $i,G: $i] :
            ~ ( ( E @ ( C @ k3_xboole_0 ) @ ( G @ r2_hidden ) )
              & ( D @ ( B @ k3_xboole_0 ) @ ( F @ r2_hidden ) )
              & ( A
                = ( G @ ( F @ k4_tarski ) ) ) )
        & ( E @ ( D @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k3_xboole_0 ) @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).

thf(1142,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ! [F: $i,G: $i] :
            ~ ( ( E @ ( C @ k3_xboole_0 ) @ ( G @ r2_hidden ) )
              & ( D @ ( B @ k3_xboole_0 ) @ ( F @ r2_hidden ) )
              & ( A
                = ( G @ ( F @ k4_tarski ) ) ) )
        & ( E @ ( D @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k3_xboole_0 ) @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( A @ k2_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).

thf(614,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(29,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_zfmisc_1) ).

thf(676,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(677,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k5_xboole_0 ) @ k1_zfmisc_1 @ ( A @ ( B @ k4_xboole_0 ) @ k1_zfmisc_1 @ ( B @ ( A @ k4_xboole_0 ) @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
    inference(cnf,[status(esa)],[676]) ).

thf(577,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( C
                = ( B @ ( A @ k1_closure3 ) ) )
            <=> ( C
                = ( B @ ( A @ a_2_0_closure3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).

thf(3004,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( ( C
                  = ( B @ ( A @ a_2_0_closure3 ) ) )
               => ( C
                  = ( B @ ( A @ k1_closure3 ) ) ) )
              & ( ( C
                  = ( B @ ( A @ k1_closure3 ) ) )
               => ( C
                  = ( B @ ( A @ a_2_0_closure3 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(495,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( B @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( B @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_pboole) ).

thf(2740,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( B @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( B @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(255,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_pboole) ).

thf(1735,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(174,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
      = ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_xboole_1) ).

thf(1342,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
      = ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(548,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
                & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pboole) ).

thf(2901,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
                & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ( ( B @ ( A @ r3_zfrefle1 ) )
           => ( B @ ( A @ r2_zfrefle1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfrefle1) ).

thf(2042,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ( ( B @ ( A @ r3_zfrefle1 ) )
           => ( B @ ( A @ r2_zfrefle1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(315,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ k2_pboole ) ) )
        = ( B @ ( C @ ( A @ k2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_pboole) ).

thf(1999,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ k2_pboole ) ) )
        = ( B @ ( C @ ( A @ k2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(53,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( B @ v1_xboole_0 )
      & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(797,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( B @ v1_xboole_0 )
      & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(424,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r5_pboole ) ) )
           => ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_pboole) ).

thf(2448,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r5_pboole ) ) )
           => ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(556,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ v2_relat_1 )
      <=> ! [C: $i] :
            ~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
              & ( A @ ( C @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_pboole) ).

thf(2933,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( ! [C: $i] :
              ~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
                & ( A @ ( C @ r2_hidden ) ) )
         => ( B @ v2_relat_1 ) )
        & ( ( B @ v2_relat_1 )
         => ! [C: $i] :
              ~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
                & ( A @ ( C @ r2_hidden ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(209,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).

thf(1507,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(83,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
      = ( B @ ( A @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).

thf(930,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
      = ( B @ ( A @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(39,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).

thf(744,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(745,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(cnf,[status(esa)],[744]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     => ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_xboole_1) ).

thf(638,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     => ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
      | ~ ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[638]) ).

thf(8052,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( E @ ( D @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) )
      | ( E @ ( D @ k2_xboole_0 ) @ ( C @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,639]) ).

thf(8053,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( E @ ( D @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) )
      | ( E @ ( D @ k2_xboole_0 ) @ ( C @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[8052]) ).

thf(8054,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[8053:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).

thf(496,axiom,
    ? [A: $i] :
      ( ( A @ v1_fraenkel )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_fraenkel) ).

thf(2746,plain,
    ? [A: $i] :
      ( ( A @ v1_fraenkel )
      & ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(2747,plain,
    ( ( sk181 @ v1_fraenkel )
    & ~ ( sk181 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[2746]) ).

thf(2748,plain,
    ~ ( sk181 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[2747]) ).

thf(3025,plain,
    ( ( ( sk181 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,2748]) ).

thf(3026,plain,
    ( ( sk181 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3025]) ).

thf(3027,plain,
    sk181 != k1_xboole_0,
    inference(simp,[status(thm)],[3026]) ).

thf(13401,plain,
    ! [A: $i] :
      ( ( A != sk181 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3027]) ).

thf(13402,plain,
    ! [A: $i] :
      ( ( A != sk181 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13401]) ).

thf(13403,plain,
    ~ ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[13402:[bind(A,$thf( sk181 ))]]) ).

thf(15645,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,13403]) ).

thf(15646,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15645]) ).

thf(15714,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) ) )
      | ( A != sk181 ) ),
    inference(simp,[status(thm)],[15646]) ).

thf(15735,plain,
    ! [A: $i] :
      ( ( sk181 @ ( A @ k2_xboole_0 ) )
     != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[15714]) ).

thf(276,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( A != k1_xboole_0 ) )
    <=> ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
       != k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_mcart_1) ).

thf(1826,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
         != k1_xboole_0 )
       => ( ( C != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( A != k1_xboole_0 ) ) )
      & ( ( ( C != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( A != k1_xboole_0 ) )
       => ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
         != k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(1827,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
         != k1_xboole_0 )
       => ( ( C != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( A != k1_xboole_0 ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( ( C != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( A != k1_xboole_0 ) )
       => ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
         != k1_xboole_0 ) ) ),
    inference(miniscope,[status(thm)],[1826]) ).

thf(1828,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F != k1_xboole_0 )
        | ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) )
          = k1_xboole_0 ) )
      & ( ( E != k1_xboole_0 )
        | ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) )
          = k1_xboole_0 ) )
      & ( ( D != k1_xboole_0 )
        | ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) )
          = k1_xboole_0 ) )
      & ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
         != k1_xboole_0 )
        | ( C = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[1827]) ).

thf(1830,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1828]) ).

thf(1834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1830]) ).

thf(1835,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( k1_xboole_0 @ k3_zfmisc_1 ) ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[1834]) ).

thf(327,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_pboole) ).

thf(2046,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(129,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
    <=> ( ( B = D )
        & ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).

thf(1127,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( B = D )
          & ( C @ ( A @ r2_hidden ) ) )
       => ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
      & ( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( B = D )
          & ( C @ ( A @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(239,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).

thf(1648,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(1649,plain,
    ~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[1648]) ).

thf(1650,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[1649]) ).

thf(177,axiom,
    ( ( k1_xboole_0 @ k3_tarski )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).

thf(1358,plain,
    ( ( k1_xboole_0 @ k3_tarski )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(1359,plain,
    ( ( k1_xboole_0 @ k3_tarski )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1358]) ).

thf(185,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) )
      = ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_xboole_1) ).

thf(1386,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) )
      = ( A @ ( B @ k4_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(251,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
      = ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_xboole_1) ).

thf(1724,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
      = ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(518,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ~ ( B @ v1_xboole_0 )
      & ( A @ ( B @ m1_finseq_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finseq_2) ).

thf(2823,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ~ ( B @ v1_xboole_0 )
      & ( A @ ( B @ m1_finseq_2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(2824,plain,
    ! [A: $i] :
      ( ~ ( A @ sk188 @ v1_xboole_0 )
      & ( A @ ( A @ sk188 @ m1_finseq_2 ) ) ),
    inference(cnf,[status(esa)],[2823]) ).

thf(2825,plain,
    ! [A: $i] : ( A @ ( A @ sk188 @ m1_finseq_2 ) ),
    inference(cnfConj,[status(thm)],[2824]) ).

thf(414,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C
              = ( B @ ( A @ k21_pralg_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ r2_hidden ) )
               => ( ( D @ ( C @ k1_funct_1 ) )
                  = ( D @ ( B @ k1_funct_1 ) @ k1_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_pralg_1) ).

thf(2405,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( ( D @ ( C @ k1_funct_1 ) )
                    = ( D @ ( B @ k1_funct_1 ) @ k1_subset_1 ) ) )
             => ( C
                = ( B @ ( A @ k21_pralg_1 ) ) ) )
            & ( ( C
                = ( B @ ( A @ k21_pralg_1 ) ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( ( D @ ( C @ k1_funct_1 ) )
                    = ( D @ ( B @ k1_funct_1 ) @ k1_subset_1 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(533,axiom,
    ? [A: $i] : ( A @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(2869,plain,
    ? [A: $i] : ( A @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(20,axiom,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

thf(651,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(570,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m1_pboole ) )
            & ( B @ v2_relat_1 ) )
         => ~ ( B @ k2_relat_1 @ k3_tarski @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_pre_circ) ).

thf(2985,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m1_pboole ) )
            & ( B @ v2_relat_1 ) )
         => ~ ( B @ k2_relat_1 @ k3_tarski @ v1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(227,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ~ ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r4_pboole ) ) )
                  & ~ ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_pboole) ).

thf(1576,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ~ ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r4_pboole ) ) )
                  & ~ ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(213,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
    <=> ( ( D @ ( B @ r2_hidden ) )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).

thf(1518,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( D @ ( B @ r2_hidden ) )
          & ( A = C ) )
       => ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
      & ( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( D @ ( B @ r2_hidden ) )
          & ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(245,axiom,
    k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ r1_pboole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_pboole) ).

thf(1703,plain,
    k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ k1_pboole @ ( k1_xboole_0 @ r1_pboole ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(552,axiom,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_pboole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).

thf(2915,plain,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_pboole ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(2916,plain,
    ! [A: $i] : ( A @ ( A @ sk194 @ m1_pboole ) ),
    inference(cnf,[status(esa)],[2915]) ).

thf(37,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k2_xboole_0 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ( ( B @ ( D @ r2_hidden ) )
            | ( A @ ( D @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

thf(705,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( ( B @ ( D @ r2_hidden ) )
                | ( A @ ( D @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
            & ( ( C @ ( D @ r2_hidden ) )
             => ( ( B @ ( D @ r2_hidden ) )
                | ( A @ ( D @ r2_hidden ) ) ) ) )
       => ( C
          = ( B @ ( A @ k2_xboole_0 ) ) ) )
      & ( ( C
          = ( B @ ( A @ k2_xboole_0 ) ) )
       => ! [D: $i] :
            ( ( ( ( B @ ( D @ r2_hidden ) )
                | ( A @ ( D @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
            & ( ( C @ ( D @ r2_hidden ) )
             => ( ( B @ ( D @ r2_hidden ) )
                | ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(706,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( ! [D: $i] :
              ( ( ( B @ ( D @ r2_hidden ) )
                | ( A @ ( D @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
          & ! [D: $i] :
              ( ( C @ ( D @ r2_hidden ) )
             => ( ( B @ ( D @ r2_hidden ) )
                | ( A @ ( D @ r2_hidden ) ) ) ) )
       => ( C
          = ( B @ ( A @ k2_xboole_0 ) ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( C
          = ( B @ ( A @ k2_xboole_0 ) ) )
       => ( ! [D: $i] :
              ( ( ( B @ ( D @ r2_hidden ) )
                | ( A @ ( D @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
          & ! [D: $i] :
              ( ( C @ ( D @ r2_hidden ) )
             => ( ( B @ ( D @ r2_hidden ) )
                | ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[705]) ).

thf(707,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( H
          = ( G @ ( F @ k2_xboole_0 ) ) )
        | ~ ( H @ ( F @ ( G @ ( H @ sk14 ) ) @ r2_hidden ) )
        | ( H @ ( G @ ( F @ sk12 ) ) ) )
      & ( ( H
          = ( G @ ( F @ k2_xboole_0 ) ) )
        | ( G @ ( F @ ( G @ ( H @ sk14 ) ) @ r2_hidden ) )
        | ( F @ ( F @ ( G @ ( H @ sk14 ) ) @ r2_hidden ) )
        | ( H @ ( G @ ( F @ sk12 ) ) ) )
      & ( ( H
          = ( G @ ( F @ k2_xboole_0 ) ) )
        | ~ ( H @ ( G @ ( F @ sk12 ) ) )
        | ~ ( G @ ( F @ ( G @ ( H @ sk13 ) ) @ r2_hidden ) ) )
      & ( ( H
          = ( G @ ( F @ k2_xboole_0 ) ) )
        | ~ ( H @ ( G @ ( F @ sk12 ) ) )
        | ~ ( F @ ( F @ ( G @ ( H @ sk13 ) ) @ r2_hidden ) ) )
      & ( ( H
          = ( G @ ( F @ k2_xboole_0 ) ) )
        | ~ ( H @ ( G @ ( F @ sk12 ) ) )
        | ( H @ ( F @ ( G @ ( H @ sk13 ) ) @ r2_hidden ) ) )
      & ( ( C @ ( E @ r2_hidden ) )
        | ~ ( B @ ( E @ r2_hidden ) )
        | ( C
         != ( B @ ( A @ k2_xboole_0 ) ) ) )
      & ( ( C @ ( E @ r2_hidden ) )
        | ~ ( A @ ( E @ r2_hidden ) )
        | ( C
         != ( B @ ( A @ k2_xboole_0 ) ) ) )
      & ( ( B @ ( D @ r2_hidden ) )
        | ( A @ ( D @ r2_hidden ) )
        | ~ ( C @ ( D @ r2_hidden ) )
        | ( C
         != ( B @ ( A @ k2_xboole_0 ) ) ) ) ),
    inference(cnf,[status(esa)],[706]) ).

thf(709,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ~ ( A @ ( D @ r2_hidden ) )
      | ( C
       != ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(cnfConj,[status(thm)],[707]) ).

thf(718,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ~ ( A @ ( D @ r2_hidden ) )
      | ( C
       != ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[709]) ).

thf(719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
      | ~ ( A @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[718]) ).

thf(798,plain,
    ! [A: $i] :
      ( ( A @ sk19 @ v1_xboole_0 )
      & ( A @ k1_zfmisc_1 @ ( A @ sk19 @ m1_subset_1 ) ) ),
    inference(cnf,[status(esa)],[797]) ).

thf(800,plain,
    ! [A: $i] : ( A @ sk19 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[798]) ).

thf(11694,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk19 @ v1_xboole_0 )
       != ( B @ v1_xboole_0 ) )
      | ~ $true
      | ( B = k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[800,672]) ).

thf(11695,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk19 @ v1_xboole_0 )
       != ( B @ v1_xboole_0 ) )
      | ( B = k1_xboole_0 ) ),
    inference(simp,[status(thm)],[11694]) ).

thf(11696,plain,
    ! [A: $i] :
      ( ( A @ sk19 )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[11695:[bind(A,$thf( C )),bind(B,$thf( C @ sk19 ))]]) ).

thf(11913,plain,
    ! [A: $i] :
      ( ( A @ sk19 )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[11696]) ).

thf(441,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) )
              <=> ( ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ( ( ( D @ ( E @ ( A @ r2_pboole ) ) )
                          & ( C @ ( E @ ( A @ r2_pboole ) ) ) )
                       => ( B @ ( E @ ( A @ r2_pboole ) ) ) ) )
                  & ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_pboole) ).

thf(2501,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( ! [E: $i] :
                        ( ( A @ ( E @ m1_pboole ) )
                       => ( ( ( D @ ( E @ ( A @ r2_pboole ) ) )
                            & ( C @ ( E @ ( A @ r2_pboole ) ) ) )
                         => ( B @ ( E @ ( A @ r2_pboole ) ) ) ) )
                    & ( D @ ( B @ ( A @ r2_pboole ) ) )
                    & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                 => ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) ) )
                & ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) )
                 => ( ! [E: $i] :
                        ( ( A @ ( E @ m1_pboole ) )
                       => ( ( ( D @ ( E @ ( A @ r2_pboole ) ) )
                            & ( C @ ( E @ ( A @ r2_pboole ) ) ) )
                         => ( B @ ( E @ ( A @ r2_pboole ) ) ) ) )
                    & ( D @ ( B @ ( A @ r2_pboole ) ) )
                    & ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(156,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
    <=> ( ( C @ ( A @ r1_tarski ) )
        & ( C @ ( B @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_setwiseo) ).

thf(1264,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( A @ r1_tarski ) )
          & ( C @ ( B @ r2_hidden ) ) )
       => ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) )
      & ( ( C @ ( B @ k1_tarski @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
       => ( ( C @ ( A @ r1_tarski ) )
          & ( C @ ( B @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(1455,plain,
    k1_xboole_0 @ k1_tarski @ v1_pralg_2,
    inference(cnfConj,[status(thm)],[1453]) ).

thf(437,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( A @ ( C @ m2_pboole ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ r2_hidden ) )
               => ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_pboole) ).

thf(2488,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) )
             => ( B @ ( A @ ( C @ m2_pboole ) ) ) )
            & ( ( B @ ( A @ ( C @ m2_pboole ) ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( D @ ( B @ k1_funct_1 ) @ ( D @ ( C @ k1_funct_1 ) @ m1_subset_1 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(114,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ! [E: $i,F: $i,G: $i] :
            ~ ( ( A
                = ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
              & ( D @ ( G @ r2_hidden ) )
              & ( C @ ( F @ r2_hidden ) )
              & ( B @ ( E @ r2_hidden ) ) )
        & ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_mcart_1) ).

thf(1059,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ! [E: $i,F: $i,G: $i] :
            ~ ( ( A
                = ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
              & ( D @ ( G @ r2_hidden ) )
              & ( C @ ( F @ r2_hidden ) )
              & ( B @ ( E @ r2_hidden ) ) )
        & ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(406,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
        <=> ( B @ ( C @ r2_hidden ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

thf(2356,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( ( B @ ( C @ r2_hidden ) )
           => ( A @ ( C @ r2_hidden ) ) )
          & ( ( A @ ( C @ r2_hidden ) )
           => ( B @ ( C @ r2_hidden ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_relat_1) ).

thf(640,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(641,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[640]) ).

thf(642,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[641]) ).

thf(586,plain,
    ( ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) )
    = ( sk3 @ ( sk1 @ k1_closure3 ) @ ( sk3 @ k7_relat_1 ) ) ),
    inference(cnfConj,[status(thm)],[580]) ).

thf(590,plain,
    ( ( sk3 @ ( sk1 @ k1_closure3 ) @ ( sk3 @ k7_relat_1 ) )
    = ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[586]) ).

thf(582,plain,
    ( ( sk2 @ ( sk1 @ k1_closure3 ) )
    = ( sk3 @ ( sk1 @ k1_closure3 ) ) ),
    inference(cnfConj,[status(thm)],[580]) ).

thf(589,plain,
    ( ( sk3 @ ( sk1 @ k1_closure3 ) )
    = ( sk2 @ ( sk1 @ k1_closure3 ) ) ),
    inference(lifteq,[status(thm)],[582]) ).

thf(3034,plain,
    ( ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk3 @ k7_relat_1 ) )
    = ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) ) ),
    inference(rewrite,[status(thm)],[590,589]) ).

thf(3259,plain,
    ! [A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
       != ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk3 @ k7_relat_1 ) ) )
      | ( ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) )
        = k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[642,3034]) ).

thf(3261,plain,
    ! [A: $i] :
      ( ( A
       != ( sk2 @ ( sk1 @ k1_closure3 ) ) )
      | ( sk3 != k1_xboole_0 )
      | ( ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) )
        = k1_xboole_0 ) ),
    inference(simp,[status(thm)],[3259]) ).

thf(3263,plain,
    ( ( sk3 != k1_xboole_0 )
    | ( ( sk2 @ ( sk1 @ k1_closure3 ) @ ( sk2 @ k7_relat_1 ) )
      = k1_xboole_0 ) ),
    inference(simp,[status(thm)],[3261]) ).

thf(15027,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,13162]) ).

thf(15028,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15027]) ).

thf(15103,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( A != k3_qc_lang1 ) ),
    inference(simp,[status(thm)],[15028]) ).

thf(15135,plain,
    ! [A: $i] :
      ( ( k3_qc_lang1 @ ( A @ k2_xboole_0 ) )
     != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[15103]) ).

thf(493,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( C @ ( B @ ( A @ k3_cat_5 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_cat_5) ).

thf(2735,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( C @ ( B @ ( A @ k3_cat_5 ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(515,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( B @ ( A @ r7_pboole ) ) )
              & ( B @ v2_relat_1 ) )
           => ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_pboole) ).

thf(2814,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( B @ ( A @ r7_pboole ) ) )
              & ( B @ v2_relat_1 ) )
           => ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(401,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v2_relat_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                 => ( A @ k1_pboole @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) )
           => ( A @ k1_pboole @ ( B @ ( C @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_mboolean) ).

thf(2339,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v2_relat_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                 => ( A @ k1_pboole @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) )
           => ( A @ k1_pboole @ ( B @ ( C @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(587,plain,
    sk2 @ v2_relat_1,
    inference(cnfConj,[status(thm)],[580]) ).

thf(11024,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( k1_xboole_0 @ v2_relat_1 )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,587]) ).

thf(11025,plain,
    ( ( k1_xboole_0 @ v2_relat_1 )
    | ~ ( sk2 @ v1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11024:[bind(A,$thf( sk2 ))]]) ).

thf(169,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
      = ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_xboole_1) ).

thf(1323,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
      = ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(2826,plain,
    ! [A: $i] :
      ~ ( A @ sk188 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[2824]) ).

thf(3144,plain,
    ! [A: $i] :
      ( ( ( A @ sk188 @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,2826]) ).

thf(3145,plain,
    ! [A: $i] :
      ( ( A @ sk188 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3144]) ).

thf(3148,plain,
    ! [A: $i] :
      ( ( A @ sk188 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[3145]) ).

thf(79,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
      = ( C @ ( B @ k5_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_xboole_1) ).

thf(917,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) )
      = ( C @ ( B @ k5_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(35,axiom,
    ! [A: $i] :
      ~ ( ! [B: $i,C: $i] :
            ~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
        & ! [B: $i] :
            ~ ( ! [C: $i,D: $i] :
                  ( B
                 != ( D @ ( C @ k4_tarski ) ) )
              & ( A @ ( B @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funct_4) ).

thf(697,plain,
    ! [A: $i] :
      ~ ( ! [B: $i,C: $i] :
            ~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
        & ! [B: $i] :
            ~ ( ! [C: $i,D: $i] :
                  ( B
                 != ( D @ ( C @ k4_tarski ) ) )
              & ( A @ ( B @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(698,plain,
    ~ ? [A: $i] :
        ( ~ ? [B: $i,C: $i] : ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
        & ~ ? [B: $i] :
              ( ~ ? [C: $i,D: $i] :
                    ( B
                    = ( D @ ( C @ k4_tarski ) ) )
              & ( A @ ( B @ r2_hidden ) ) ) ),
    inference(miniscope,[status(thm)],[697]) ).

thf(699,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk10 @ ( A @ sk9 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
        | ( ( A @ sk8 )
         != ( C @ ( B @ k4_tarski ) ) ) )
      & ( ( A @ sk10 @ ( A @ sk9 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
        | ( A @ ( A @ sk8 @ r2_hidden ) ) ) ),
    inference(cnf,[status(esa)],[698]) ).

thf(701,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk10 @ ( A @ sk9 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
      | ( ( A @ sk8 )
       != ( C @ ( B @ k4_tarski ) ) ) ),
    inference(cnfConj,[status(thm)],[699]) ).

thf(702,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk10 @ ( A @ sk9 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
      | ( ( A @ sk8 )
       != ( C @ ( B @ k4_tarski ) ) ) ),
    inference(lifteq,[status(thm)],[701]) ).

thf(480,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                      & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                   => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( E @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_pboole) ).

thf(2682,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                      & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                   => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( E @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(9,axiom,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).

thf(604,plain,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(605,plain,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[604]) ).

thf(73,axiom,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(899,plain,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(900,plain,
    ~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[899]) ).

thf(901,plain,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[900]) ).

thf(3119,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ~ ( k1_xboole_0 @ k1_tarski @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[605,901]) ).

thf(3120,plain,
    ~ ( k1_xboole_0 @ k1_tarski @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[3119:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(3121,plain,
    ( ( ( k1_xboole_0 @ k1_tarski @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,3120]) ).

thf(3122,plain,
    ( ( k1_xboole_0 @ k1_tarski @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3121]) ).

thf(3125,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != k1_xboole_0 ),
    inference(simp,[status(thm)],[3122]) ).

thf(418,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
         => ( B @ k2_relat_1 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_pboole) ).

thf(2420,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
         => ( B @ k2_relat_1 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ k3_tarski )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).

thf(902,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ k3_tarski )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(235,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( C @ v1_xboole_0 )
        & ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

thf(1609,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( C @ v1_xboole_0 )
        & ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(258,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) )
    <=> ~ ( ( B @ ( A @ r2_hidden ) )
        <=> ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_0) ).

thf(1741,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( ( ( C @ ( A @ r2_hidden ) )
             => ( B @ ( A @ r2_hidden ) ) )
            & ( ( B @ ( A @ r2_hidden ) )
             => ( C @ ( A @ r2_hidden ) ) ) )
       => ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) ) )
      & ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ r2_hidden ) )
       => ~ ( ( ( C @ ( A @ r2_hidden ) )
             => ( B @ ( A @ r2_hidden ) ) )
            & ( ( B @ ( A @ r2_hidden ) )
             => ( C @ ( A @ r2_hidden ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(469,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( B @ ( C @ ( A @ r2_pboole ) ) )
              & ( B @ v3_relat_1 ) )
           => ( C @ v3_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_pboole) ).

thf(2635,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( B @ ( C @ ( A @ r2_pboole ) ) )
              & ( B @ v3_relat_1 ) )
           => ( C @ v3_relat_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(3306,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,1650]) ).

thf(3307,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3306]) ).

thf(3312,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[3307]) ).

thf(357,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D
                  = ( C @ ( B @ ( A @ k4_pboole ) ) ) )
              <=> ! [E: $i] :
                    ( ( A @ ( E @ r2_hidden ) )
                   => ( ( E @ ( D @ k1_funct_1 ) )
                      = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k4_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_pboole) ).

thf(2158,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k4_xboole_0 ) ) ) )
                 => ( D
                    = ( C @ ( B @ ( A @ k4_pboole ) ) ) ) )
                & ( ( D
                    = ( C @ ( B @ ( A @ k4_pboole ) ) ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k4_xboole_0 ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(272,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_xboole_1) ).

thf(1815,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(264,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ r2_hidden ) )
        & ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
     => ( B @ ( C @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setfam_1) ).

thf(1778,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ r2_hidden ) )
        & ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
     => ( B @ ( C @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(411,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ r2_hidden ) )
             => ( ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ k1_funct_1 ) )
                = ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ k5_xboole_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_pboole) ).

thf(2388,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ r2_hidden ) )
             => ( ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ k1_funct_1 ) )
                = ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ k5_xboole_0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(520,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pboole) ).

thf(2829,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(119,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( C @ ( E @ ( A @ r5_pboole ) ) )
                      & ( B @ ( D @ ( A @ r5_pboole ) ) )
                      & ( E @ ( D @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) )
                   => ( ( B @ ( E @ ( A @ r6_pboole ) ) )
                      & ( C @ ( D @ ( A @ r6_pboole ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_pboole) ).

thf(1087,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( C @ ( E @ ( A @ r5_pboole ) ) )
                      & ( B @ ( D @ ( A @ r5_pboole ) ) )
                      & ( E @ ( D @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) )
                   => ( ( B @ ( E @ ( A @ r6_pboole ) ) )
                      & ( C @ ( D @ ( A @ r6_pboole ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(211,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                  & ( C @ ( B @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_mboolean) ).

thf(1514,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                  & ( C @ ( B @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(167,axiom,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).

thf(1318,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(1319,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1318]) ).

thf(246,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
      = ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_xboole_1) ).

thf(1704,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
      = ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( B @ ( C @ m1_finseq_2 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( A @ ( C @ m1_finseq_2 ) )
                & ~ ( C @ v1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_finseq_2) ).

thf(969,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( B @ ( C @ m1_finseq_2 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( A @ ( C @ m1_finseq_2 ) )
                & ~ ( C @ v1_xboole_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
     => ( ( ( C = F )
          & ( B = E )
          & ( A = D ) )
        | ( C = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_mcart_1) ).

thf(606,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
     => ( ( ( C = F )
          & ( B = E )
          & ( A = D ) )
        | ( C = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(320,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r7_pboole ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                 => ( C @ ( D @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_pboole) ).

thf(2024,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                   => ( C @ ( D @ ( A @ r1_pboole ) ) ) ) )
             => ( C @ ( B @ ( A @ r7_pboole ) ) ) )
            & ( ( C @ ( B @ ( A @ r7_pboole ) ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                   => ( C @ ( D @ ( A @ r1_pboole ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(572,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
           => ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_pboole) ).

thf(2989,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
           => ( C @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(304,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).

thf(1963,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k5_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(81,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_partfun1) ).

thf(924,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( F @ ( C @ k2_xboole_0 ) @ ( E @ ( B @ k2_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(505,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( A @ k1_pboole @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_pboole) ).

thf(2782,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( A @ k1_pboole @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(15668,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,13403]) ).

thf(15669,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15668]) ).

thf(15724,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != sk181 ) ),
    inference(simp,[status(thm)],[15669]) ).

thf(15748,plain,
    ! [A: $i] :
      ( ( A @ ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != sk181 ),
    inference(simp,[status(thm)],[15724]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_card_fil ) )
         => ( B @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_card_fil) ).

thf(646,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_card_fil ) )
         => ( B @ ( A @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(130,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_pre_circ ) @ ( B @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_mboolean) ).

thf(1136,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_pre_circ ) @ ( B @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(555,axiom,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( f1_s2_pboole @ ( B @ r2_hidden ) )
         => ! [C: $i] :
              ( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
            <=> ( ( C @ ( B @ p1_s2_pboole ) )
                & ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) )
      & ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_pboole) ).

thf(2925,plain,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( f1_s2_pboole @ ( B @ r2_hidden ) )
         => ! [C: $i] :
              ( ( ( ( C @ ( B @ p1_s2_pboole ) )
                  & ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
               => ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
              & ( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
               => ( ( C @ ( B @ p1_s2_pboole ) )
                  & ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
      & ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).

thf(1381,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(1382,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
      = A ),
    inference(cnf,[status(esa)],[1381]) ).

thf(1383,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
      = A ),
    inference(lifteq,[status(thm)],[1382]) ).

thf(1816,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1815]) ).

thf(1817,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1816]) ).

thf(10479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
       != ( C @ ( B @ k2_xboole_0 ) ) )
      | ( ( A @ ( B @ k4_xboole_0 ) )
        = k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[1383,1817]) ).

thf(10480,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[10479:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(48,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).

thf(771,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(772,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[771]) ).

thf(3268,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[605,772]) ).

thf(3269,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
    inference(pattern_uni,[status(thm)],[3268:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(6458,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) )
       != ( sk33 @ ( A @ m1_subset_1 ) ) )
      | ~ ( A @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3269,976]) ).

thf(6459,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) )
       != ( sk33 @ ( A @ m1_subset_1 ) ) )
      | ~ ( A @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6458]) ).

thf(6492,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski )
       != sk33 )
      | ( k1_xboole_0 != A )
      | ~ ( A @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6459]) ).

thf(6508,plain,
    ( ( ( k1_xboole_0 @ k1_tarski )
     != sk33 )
    | ~ ( k1_xboole_0 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6492]) ).

thf(7455,plain,
    ( ( ( k1_xboole_0 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( ( k1_xboole_0 @ k1_tarski )
     != sk33 )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,6508]) ).

thf(7456,plain,
    ( ( ( k1_xboole_0 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( ( k1_xboole_0 @ k1_tarski )
     != sk33 ) ),
    inference(simp,[status(thm)],[7455]) ).

thf(7489,plain,
    ( ( ( k1_xboole_0 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) )
     != k1_xboole_0 )
    | ( ( k1_xboole_0 @ k1_tarski )
     != sk33 ) ),
    inference(simp,[status(thm)],[7456]) ).

thf(10785,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k4_xboole_0 ) )
       != ( k1_xboole_0 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk33 ) ),
    inference(paramod_ordered,[status(thm)],[10480,7489]) ).

thf(10786,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k4_xboole_0 ) )
       != ( k1_xboole_0 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk33 ) ),
    inference(simp,[status(thm)],[10785]) ).

thf(10800,plain,
    ! [A: $i] :
      ( ( A
       != ( k1_xboole_0 @ k1_tarski ) )
      | ( A != sk33 )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk33 ) ),
    inference(simp,[status(thm)],[10786]) ).

thf(10816,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk33 ),
    inference(simp,[status(thm)],[10800]) ).

thf(85,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).

thf(937,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(322,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_pboole) ).

thf(2034,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(75,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A
         != ( B @ k1_tarski ) )
        & ( A != k1_xboole_0 )
        & ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
          = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).

thf(905,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A
         != ( B @ k1_tarski ) )
        & ( A != k1_xboole_0 )
        & ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
          = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ( ( A @ v2_cat_5 )
        & ~ ( A @ v1_xboole_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_cat_5 ) )
        <=> ( A @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_cat_5) ).

thf(2616,plain,
    ! [A: $i] :
      ( ( ( A @ v2_cat_5 )
        & ~ ( A @ v1_xboole_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m1_subset_1 ) )
           => ( A @ ( B @ m1_cat_5 ) ) )
          & ( ( A @ ( B @ m1_cat_5 ) )
           => ( A @ ( B @ m1_subset_1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( A @ k1_zfmisc_1 @ ( C @ k3_tarski @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_borsuk_1) ).

thf(1465,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( A @ k1_zfmisc_1 @ ( C @ k3_tarski @ m1_subset_1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(780,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ r1_tarski ) )
          & ( B @ ( A @ r1_tarski ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ r1_tarski ) )
          & ( B @ ( A @ r1_tarski ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(781,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( A @ ( B @ r1_tarski ) )
          & ( B @ ( A @ r1_tarski ) ) )
       => ( A = B ) )
    & ! [A: $i,B: $i] :
        ( ( A = B )
       => ( ( A @ ( B @ r1_tarski ) )
          & ( B @ ( A @ r1_tarski ) ) ) ) ),
    inference(miniscope,[status(thm)],[780]) ).

thf(782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C = D )
        | ~ ( C @ ( D @ r1_tarski ) )
        | ~ ( D @ ( C @ r1_tarski ) ) )
      & ( ( A @ ( B @ r1_tarski ) )
        | ( A != B ) )
      & ( ( B @ ( A @ r1_tarski ) )
        | ( A != B ) ) ),
    inference(cnf,[status(esa)],[781]) ).

thf(783,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ( A != B ) ),
    inference(cnfConj,[status(thm)],[782]) ).

thf(786,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ( A != B ) ),
    inference(lifteq,[status(thm)],[783]) ).

thf(787,plain,
    ! [A: $i] : ( A @ ( A @ r1_tarski ) ),
    inference(simp,[status(thm)],[786]) ).

thf(588,plain,
    ~ ( sk1 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[580]) ).

thf(3017,plain,
    ( ( ( sk1 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,588]) ).

thf(3018,plain,
    ( ( sk1 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3017]) ).

thf(3022,plain,
    sk1 != k1_xboole_0,
    inference(simp,[status(thm)],[3018]) ).

thf(12821,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3022]) ).

thf(12822,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[12821]) ).

thf(12823,plain,
    ~ ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[12822:[bind(A,$thf( sk1 ))]]) ).

thf(13996,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,12823]) ).

thf(13997,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13996]) ).

thf(14037,plain,
    ! [A: $i] :
      ( ( A
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) )
      | ( A != sk1 ) ),
    inference(simp,[status(thm)],[13997]) ).

thf(14056,plain,
    ( ( sk1 @ ( sk1 @ k2_zfmisc_1 ) )
   != sk1 ),
    inference(simp,[status(thm)],[14037]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A @ ( E @ m1_subset_1 ) )
        & ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
        & ( A @ ( C @ m1_pboole ) )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) )
        = ( E @ ( D @ k1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_waybel_5) ).

thf(591,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A @ ( E @ m1_subset_1 ) )
        & ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
        & ( A @ ( C @ m1_pboole ) )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) )
        = ( E @ ( D @ k1_funct_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(123,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ r4_pboole ) ) )
       => ( B @ ( C @ ( A @ r4_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r4_pboole) ).

thf(1109,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ r4_pboole ) ) )
       => ( B @ ( C @ ( A @ r4_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(430,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k5_pboole ) ) )
            = ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_pboole) ).

thf(2469,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k5_pboole ) ) )
            = ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ k5_xboole_0 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_xboole_1) ).

thf(1416,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k5_xboole_0 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(1417,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k5_xboole_0 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1416]) ).

thf(1418,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k5_xboole_0 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1417]) ).

thf(196,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).

thf(1463,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(1464,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
    inference(cnf,[status(esa)],[1463]) ).

thf(13998,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,12823]) ).

thf(13999,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13998]) ).

thf(14040,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != sk1 ) ),
    inference(simp,[status(thm)],[13999]) ).

thf(14061,plain,
    ! [A: $i] :
      ( ( A @ ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != sk1 ),
    inference(simp,[status(thm)],[14040]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
    <=> ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).

thf(617,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( B = D )
          & ( A = C ) )
       => ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
      & ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( B = D )
          & ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(618,plain,
    ( ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( B = D )
          & ( A = C ) )
       => ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
    & ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( B = D )
          & ( A = C ) ) ) ),
    inference(miniscope,[status(thm)],[617]) ).

thf(619,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( H @ k1_tarski @ ( G @ k1_tarski @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
        | ( F != H )
        | ( E != G ) )
      & ( ( B = D )
        | ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
      & ( ( A = C )
        | ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ) ),
    inference(cnf,[status(esa)],[618]) ).

thf(620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[619]) ).

thf(623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
      | ( A = C ) ),
    inference(lifteq,[status(thm)],[620]) ).

thf(376,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ! [D: $i] :
          ( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
         => ( A @ ( D @ m1_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_pboole) ).

thf(2254,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ! [D: $i] :
          ( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
         => ( A @ ( D @ m1_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(56,axiom,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
           => ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
        & ! [C: $i] :
            ~ ( ! [D: $i,E: $i] :
                  ( C
                 != ( E @ ( D @ k4_tarski ) ) )
              & ( A @ ( C @ r2_hidden ) ) ) )
     => ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).

thf(806,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
           => ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
        & ! [C: $i] :
            ~ ( ! [D: $i,E: $i] :
                  ( C
                 != ( E @ ( D @ k4_tarski ) ) )
              & ( A @ ( C @ r2_hidden ) ) ) )
     => ( B @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(451,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_pboole) ).

thf(2555,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(585,plain,
    sk1 @ ( sk3 @ m1_pboole ),
    inference(cnfConj,[status(thm)],[580]) ).

thf(592,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) )
        = ( E @ ( D @ k1_funct_1 ) ) )
      | ~ ( A @ ( E @ m1_subset_1 ) )
      | ~ ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
      | ~ ( A @ ( C @ m1_pboole ) )
      | ( B @ v1_xboole_0 )
      | ( A @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[591]) ).

thf(593,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ m1_subset_1 ) )
      | ~ ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
      | ~ ( A @ ( C @ m1_pboole ) )
      | ( B @ v1_xboole_0 )
      | ( A @ v1_xboole_0 )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) )
        = ( E @ ( D @ k1_funct_1 ) ) ) ),
    inference(lifteq,[status(thm)],[592]) ).

thf(3076,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( sk3 @ m1_pboole ) )
       != ( A @ ( C @ m1_pboole ) ) )
      | ~ ( A @ ( E @ m1_subset_1 ) )
      | ~ ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
      | ~ $true
      | ( B @ v1_xboole_0 )
      | ( A @ v1_xboole_0 )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) )
        = ( E @ ( D @ k1_funct_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[585,593]) ).

thf(3077,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( sk3 @ m1_pboole ) )
       != ( A @ ( C @ m1_pboole ) ) )
      | ~ ( A @ ( E @ m1_subset_1 ) )
      | ~ ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
      | ( B @ v1_xboole_0 )
      | ( A @ v1_xboole_0 )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) )
        = ( E @ ( D @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3076]) ).

thf(3078,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk3 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( sk1 @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk3 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[3077:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).

thf(3082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk3 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( sk1 @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk3 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3078]) ).

thf(3084,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk3 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | $false
      | ( ( C @ ( B @ ( sk3 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(rewrite,[status(thm)],[3082,588]) ).

thf(3085,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk3 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk3 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3084]) ).

thf(3284,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) )
       != ( sk1 @ ( C @ m1_subset_1 ) ) )
      | ~ $true
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk3 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk3 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3269,3085]) ).

thf(3285,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) )
       != ( sk1 @ ( C @ m1_subset_1 ) ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk3 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk3 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3284]) ).

thf(3287,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski )
       != sk1 )
      | ( k1_xboole_0 != C )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk3 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk3 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3285]) ).

thf(3290,plain,
    ! [B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski )
       != sk1 )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk3 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( k1_xboole_0 @ ( B @ ( sk3 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( k1_xboole_0 @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3287]) ).

thf(581,plain,
    sk3 @ v2_relat_1,
    inference(cnfConj,[status(thm)],[580]) ).

thf(13542,plain,
    ! [A: $i] :
      ( ( A != sk3 )
      | ( k1_xboole_0 @ v2_relat_1 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,581]) ).

thf(13543,plain,
    ( ( k1_xboole_0 @ v2_relat_1 )
    | ~ ( sk3 @ ( sk3 @ k2_zfmisc_1 ) @ ( sk3 @ r1_tarski ) ) ),
    inference(pattern_uni,[status(thm)],[13542:[bind(A,$thf( sk3 ))]]) ).

thf(229,axiom,
    ! [A: $i,B: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
         != k1_xboole_0 )
        & ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
         != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).

thf(1581,plain,
    ! [A: $i,B: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
         != k1_xboole_0 )
        & ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
         != k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(399,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_pboole) ).

thf(2335,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k3_tarski )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).

thf(966,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k3_tarski )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(503,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k4_pboole ) ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_pboole) ).

thf(2777,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k4_pboole ) ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).

thf(630,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(631,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
    inference(miniscope,[status(thm)],[630]) ).

thf(632,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ k3_xboole_0 ) @ ( F @ k2_zfmisc_1 ) )
        = ( E @ ( F @ k2_zfmisc_1 ) @ ( D @ ( F @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(634,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
      = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
    inference(cnfConj,[status(thm)],[632]) ).

thf(636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) ) ),
    inference(lifteq,[status(thm)],[634]) ).

thf(637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[636]) ).

thf(14176,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,12843]) ).

thf(14177,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14176]) ).

thf(14220,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != sk33 ) ),
    inference(simp,[status(thm)],[14177]) ).

thf(14240,plain,
    ! [A: $i] :
      ( ( A @ ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != sk33 ),
    inference(simp,[status(thm)],[14220]) ).

thf(19691,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
       != ( D @ ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
       != sk33 ) ),
    inference(paramod_ordered,[status(thm)],[637,14240]) ).

thf(19692,plain,
    ! [A: $i] :
      ( ( A @ ( sk33 @ k3_xboole_0 ) @ ( sk33 @ k2_zfmisc_1 ) )
     != sk33 ),
    inference(pattern_uni,[status(thm)],[19691:[bind(A,$thf( sk33 )),bind(B,$thf( F )),bind(C,$thf( sk33 )),bind(D,$thf( F @ ( sk33 @ k2_zfmisc_1 ) ))]]) ).

thf(19759,plain,
    ! [A: $i] :
      ( ( A @ ( sk33 @ k3_xboole_0 ) @ ( sk33 @ k2_zfmisc_1 ) )
     != sk33 ),
    inference(simp,[status(thm)],[19692]) ).

thf(14124,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,12843]) ).

thf(14125,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14124]) ).

thf(14214,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) ) )
      | ( A != sk33 ) ),
    inference(simp,[status(thm)],[14125]) ).

thf(14232,plain,
    ( ( sk33 @ ( sk33 @ k2_zfmisc_1 ) )
   != ( sk33 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[14214]) ).

thf(667,plain,
    ~ ? [A: $i] :
        ( ~ ? [B: $i,C: $i] :
              ( ( C @ ( B @ k4_tarski ) )
              = A )
        & ? [B: $i,C: $i] : ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
    inference(miniscope,[status(thm)],[666]) ).

thf(668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk5 @ ( A @ sk4 @ k4_tarski ) )
        = A )
      | ~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
    inference(cnf,[status(esa)],[667]) ).

thf(669,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
      | ( ( A @ sk5 @ ( A @ sk4 @ k4_tarski ) )
        = A ) ),
    inference(lifteq,[status(thm)],[668]) ).

thf(978,plain,
    ~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[977]) ).

thf(979,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[978]) ).

thf(3297,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,979]) ).

thf(3298,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3297]) ).

thf(3303,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[3298]) ).

thf(10656,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ sk5 @ ( A @ sk4 @ k4_tarski ) )
       != ( E @ ( D @ k4_tarski ) ) )
      | ( A != k1_xboole_0 )
      | ~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
    inference(paramod_ordered,[status(thm)],[669,3303]) ).

thf(10657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C != k1_xboole_0 )
      | ~ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r2_hidden ) ) ),
    inference(pattern_uni,[status(thm)],[10656:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ sk4 )),bind(E,$thf( G @ sk5 ))]]) ).

thf(10734,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r2_hidden ) ),
    inference(simp,[status(thm)],[10657]) ).

thf(338,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ~ ( ( C @ ( B @ ( A @ r4_pboole ) ) )
                  & ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_pboole) ).

thf(2073,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ~ ( ( C @ ( B @ ( A @ r4_pboole ) ) )
                  & ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( A @ ( B @ v1_pre_circ ) )
        & ( B @ v2_relat_1 ) )
     => ( ! [C: $i] :
            ( ( A @ ( C @ m1_pboole ) )
           => ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
                    & ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
                    & ( B @ ( D @ ( A @ r1_pboole ) ) )
                    & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) )
       => ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_mboolean) ).

thf(684,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( A @ ( B @ v1_pre_circ ) )
        & ( B @ v2_relat_1 ) )
     => ( ! [C: $i] :
            ( ( A @ ( C @ m1_pboole ) )
           => ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
                    & ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
                    & ( B @ ( D @ ( A @ r1_pboole ) ) )
                    & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) )
       => ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(685,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
        | ~ ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk7 ) @ ( A @ r2_pboole ) ) )
        | ~ ( A @ ( B @ m1_pboole ) )
        | ~ ( A @ ( B @ v1_pre_circ ) )
        | ~ ( B @ v2_relat_1 ) )
      & ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
        | ~ ( A @ ( B @ sk7 ) @ ( A @ ( B @ sk6 ) @ ( A @ r2_pboole ) ) )
        | ~ ( A @ ( B @ m1_pboole ) )
        | ~ ( A @ ( B @ v1_pre_circ ) )
        | ~ ( B @ v2_relat_1 ) )
      & ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
        | ( B @ ( A @ ( B @ sk7 ) @ ( A @ r1_pboole ) ) )
        | ~ ( A @ ( B @ m1_pboole ) )
        | ~ ( A @ ( B @ v1_pre_circ ) )
        | ~ ( B @ v2_relat_1 ) )
      & ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
        | ( B @ ( A @ ( B @ sk6 ) @ ( A @ r1_pboole ) ) )
        | ~ ( A @ ( B @ m1_pboole ) )
        | ~ ( A @ ( B @ v1_pre_circ ) )
        | ~ ( B @ v2_relat_1 ) )
      & ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
        | ( A @ ( A @ ( B @ sk7 ) @ m1_pboole ) )
        | ~ ( A @ ( B @ m1_pboole ) )
        | ~ ( A @ ( B @ v1_pre_circ ) )
        | ~ ( B @ v2_relat_1 ) )
      & ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
        | ( A @ ( A @ ( B @ sk6 ) @ m1_pboole ) )
        | ~ ( A @ ( B @ m1_pboole ) )
        | ~ ( A @ ( B @ v1_pre_circ ) )
        | ~ ( B @ v2_relat_1 ) ) ),
    inference(cnf,[status(esa)],[684]) ).

thf(687,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
      | ( B @ ( A @ ( B @ sk6 ) @ ( A @ r1_pboole ) ) )
      | ~ ( A @ ( B @ m1_pboole ) )
      | ~ ( A @ ( B @ v1_pre_circ ) )
      | ~ ( B @ v2_relat_1 ) ),
    inference(cnfConj,[status(thm)],[685]) ).

thf(12970,plain,
    ! [A: $i] :
      ( ( A
       != ( k1_xboole_0 @ k1_tarski ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3125]) ).

thf(12971,plain,
    ! [A: $i] :
      ( ( A
       != ( k1_xboole_0 @ k1_tarski ) )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[12970]) ).

thf(12972,plain,
    ~ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[12971:[bind(A,$thf( k1_xboole_0 @ k1_tarski ))]]) ).

thf(17970,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,12972]) ).

thf(17971,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[17970]) ).

thf(18029,plain,
    ! [A: $i] :
      ( ( A
       != ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) ) )
      | ( A
       != ( k1_xboole_0 @ k1_tarski ) ) ),
    inference(simp,[status(thm)],[17971]) ).

thf(18065,plain,
    ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) )
   != ( k1_xboole_0 @ k1_tarski ) ),
    inference(simp,[status(thm)],[18029]) ).

thf(117,axiom,
    ( ( k1_xboole_0 @ k10_funct_6 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_funct_6) ).

thf(1071,plain,
    ( ( k1_xboole_0 @ k10_funct_6 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(1072,plain,
    ( ( k1_xboole_0 @ k10_funct_6 )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1071]) ).

thf(126,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ ( B @ ( A @ k1_mboolean ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_mboolean) ).

thf(1119,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ ( B @ ( A @ k1_mboolean ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
        = ( A @ k1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).

thf(658,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
        = ( A @ k1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(659,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
       != ( A @ k1_tarski ) ) ),
    inference(cnf,[status(esa)],[658]) ).

thf(660,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_xboole_0 ) )
       != ( A @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[659]) ).

thf(497,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ m1_pboole ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( ( D @ ( C @ k1_funct_1 ) )
             != k1_xboole_0 )
            & ( A = D )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).

thf(2750,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ m1_pboole ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( ? [D: $i] :
              ( ( ( D @ ( C @ k1_funct_1 ) )
               != k1_xboole_0 )
              & ( A = D )
              & ( B @ ( D @ m1_subset_1 ) ) )
         => ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) ) )
        & ( ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) )
         => ? [D: $i] :
              ( ( ( D @ ( C @ k1_funct_1 ) )
               != k1_xboole_0 )
              & ( A = D )
              & ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(232,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
      = ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_xboole_1) ).

thf(1600,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
      = ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(1975,plain,
    sk103 @ v1_fraenkel,
    inference(cnfConj,[status(thm)],[1973]) ).

thf(499,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( B @ ( D @ ( A @ k4_pboole ) ) @ ( C @ ( D @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_pboole) ).

thf(2762,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( B @ ( D @ ( A @ k4_pboole ) ) @ ( C @ ( D @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).

thf(602,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(565,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r6_pboole ) ) )
          <=> ( ( B @ ( C @ ( A @ r2_pboole ) ) )
              & ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pboole) ).

thf(2964,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( ( B @ ( C @ ( A @ r2_pboole ) ) )
                & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
             => ( C @ ( B @ ( A @ r6_pboole ) ) ) )
            & ( ( C @ ( B @ ( A @ r6_pboole ) ) )
             => ( ( B @ ( C @ ( A @ r2_pboole ) ) )
                & ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(278,axiom,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(1843,plain,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(332,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(2058,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(407,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ~ ( C @ v1_xboole_0 )
         => ! [D: $i] :
              ( ~ ( D @ v1_xboole_0 )
             => ( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) )
              <=> ? [E: $i] :
                    ( ? [F: $i] :
                        ( ? [G: $i] :
                            ( ( A
                              = ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
                            & ( D @ ( G @ m1_subset_1 ) ) )
                        & ( C @ ( F @ m1_subset_1 ) ) )
                    & ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_domain_1) ).

thf(2367,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ~ ( C @ v1_xboole_0 )
         => ! [D: $i] :
              ( ~ ( D @ v1_xboole_0 )
             => ( ( ? [E: $i] :
                      ( ? [F: $i] :
                          ( ? [G: $i] :
                              ( ( A
                                = ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
                              & ( D @ ( G @ m1_subset_1 ) ) )
                          & ( C @ ( F @ m1_subset_1 ) ) )
                      & ( B @ ( E @ m1_subset_1 ) ) )
                 => ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) )
                & ( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) )
                 => ? [E: $i] :
                      ( ? [F: $i] :
                          ( ? [G: $i] :
                              ( ( A
                                = ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
                              & ( D @ ( G @ m1_subset_1 ) ) )
                          & ( C @ ( F @ m1_subset_1 ) ) )
                      & ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(292,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ~ ( ( D @ ( B @ ( A @ r5_pboole ) ) )
                  & ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ~ ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_pboole) ).

thf(1928,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ~ ( ( D @ ( B @ ( A @ r5_pboole ) ) )
                  & ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ~ ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(289,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( B @ ( A @ r1_tarski ) )
        & ~ ( A @ ( C @ r2_hidden ) )
        & ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_setwiseo) ).

thf(1896,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( B @ ( A @ r1_tarski ) )
        & ~ ( A @ ( C @ r2_hidden ) )
        & ( C @ k1_tarski @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
      = ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_mcart_1) ).

thf(692,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
      = ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(363,axiom,
    ? [A: $i] :
      ~ ( A @ v2_setfam_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_setfam_1) ).

thf(2190,plain,
    ? [A: $i] :
      ~ ( A @ v2_setfam_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
      | ( B != D )
      | ( A != C ) ),
    inference(cnfConj,[status(thm)],[619]) ).

thf(625,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
      | ( B != D )
      | ( A != C ) ),
    inference(lifteq,[status(thm)],[622]) ).

thf(626,plain,
    ! [B: $i,A: $i] : ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ),
    inference(simp,[status(thm)],[625]) ).

thf(6668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       != ( k1_xboole_0 @ ( C @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[626,1533]) ).

thf(6669,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
     != ( k1_xboole_0 @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[6668]) ).

thf(6718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
       != k1_xboole_0 )
      | ( ( B @ ( A @ k4_tarski ) )
       != C ) ),
    inference(simp,[status(thm)],[6669]) ).

thf(6740,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[6718]) ).

thf(316,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( ( A @ ( C @ m1_pboole ) )
                & ( C @ v2_relat_1 ) )
             => ! [D: $i] :
                  ( ( C @ ( B @ ( A @ k2_pre_circ ) @ ( A @ ( D @ m3_pboole ) ) ) )
                 => ! [E: $i] :
                      ( ( B @ ( E @ m1_subset_1 ) )
                     => ? [F: $i] :
                          ( ( C @ ( F @ ( A @ r3_pboole ) ) )
                          & ( F
                            = ( E @ ( D @ k10_funct_6 @ k1_funct_1 ) ) )
                          & ( A @ ( F @ m1_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_pre_circ) ).

thf(2002,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( ( A @ ( C @ m1_pboole ) )
                & ( C @ v2_relat_1 ) )
             => ! [D: $i] :
                  ( ( C @ ( B @ ( A @ k2_pre_circ ) @ ( A @ ( D @ m3_pboole ) ) ) )
                 => ! [E: $i] :
                      ( ( B @ ( E @ m1_subset_1 ) )
                     => ? [F: $i] :
                          ( ( C @ ( F @ ( A @ r3_pboole ) ) )
                          & ( F
                            = ( E @ ( D @ k10_funct_6 @ k1_funct_1 ) ) )
                          & ( A @ ( F @ m1_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_pboole) ).

thf(998,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(372,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
     => ! [D: $i] :
          ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
         => ( ! [E: $i,F: $i] :
                ( ( ( B @ ( F @ r2_hidden ) )
                  & ( A @ ( E @ r2_hidden ) ) )
               => ( ( F @ ( E @ ( C @ k1_binop_1 ) ) )
                  = ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) )
           => ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_altcat_1) ).

thf(2242,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
     => ! [D: $i] :
          ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
         => ( ! [E: $i,F: $i] :
                ( ( ( B @ ( F @ r2_hidden ) )
                  & ( A @ ( E @ r2_hidden ) ) )
               => ( ( F @ ( E @ ( C @ k1_binop_1 ) ) )
                  = ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) )
           => ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ~ ( ! [B: $i] :
              ~ ( ( A @ ( B @ r2_hidden ) )
                & ( B != k1_xboole_0 ) )
          & ( ( A @ k3_tarski )
           != k1_xboole_0 ) )
      & ~ ( ( ( A @ k3_tarski )
            = k1_xboole_0 )
          & ? [B: $i] :
              ( ( A @ ( B @ r2_hidden ) )
              & ( B != k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_orders_1) ).

thf(1345,plain,
    ! [A: $i] :
      ( ~ ( ! [B: $i] :
              ~ ( ( A @ ( B @ r2_hidden ) )
                & ( B != k1_xboole_0 ) )
          & ( ( A @ k3_tarski )
           != k1_xboole_0 ) )
      & ~ ( ( ( A @ k3_tarski )
            = k1_xboole_0 )
          & ? [B: $i] :
              ( ( A @ ( B @ r2_hidden ) )
              & ( B != k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ? [B: $i] : ( A @ ( B @ m2_card_fil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_card_fil) ).

thf(2799,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ? [B: $i] : ( A @ ( B @ m2_card_fil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_card_fil ) )
         => ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_card_fil) ).

thf(920,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_card_fil ) )
         => ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(2191,plain,
    ~ ! [A: $i] : ( A @ v2_setfam_1 ),
    inference(miniscope,[status(thm)],[2190]) ).

thf(2192,plain,
    ~ ( sk124 @ v2_setfam_1 ),
    inference(cnf,[status(esa)],[2191]) ).

thf(11554,plain,
    ! [A: $i] :
      ( ( A != sk124 )
      | ~ ( k1_xboole_0 @ v2_setfam_1 )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,2192]) ).

thf(11555,plain,
    ( ~ ( k1_xboole_0 @ v2_setfam_1 )
    | ~ ( sk124 @ v1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11554:[bind(A,$thf( sk124 ))]]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).

thf(678,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(24,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).

thf(661,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(494,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(2737,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(388,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ m1_pboole ) )
     => ! [D: $i] :
          ( ( B @ ( D @ m1_pboole ) )
         => ( ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
          <=> ( ! [E: $i] :
                  ( ( A @ ( E @ r2_hidden ) )
                 => ( E @ ( D @ k1_funct_1 ) @ ( E @ ( C @ k1_funct_1 ) @ r1_tarski ) ) )
              & ( B @ ( A @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_altcat_2) ).

thf(2296,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ m1_pboole ) )
     => ! [D: $i] :
          ( ( B @ ( D @ m1_pboole ) )
         => ( ( ( ! [E: $i] :
                    ( ( A @ ( E @ r2_hidden ) )
                   => ( E @ ( D @ k1_funct_1 ) @ ( E @ ( C @ k1_funct_1 ) @ r1_tarski ) ) )
                & ( B @ ( A @ r1_tarski ) ) )
             => ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) )
            & ( ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) )
             => ( ! [E: $i] :
                    ( ( A @ ( E @ r2_hidden ) )
                   => ( E @ ( D @ k1_funct_1 ) @ ( E @ ( C @ k1_funct_1 ) @ r1_tarski ) ) )
                & ( B @ ( A @ r1_tarski ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(238,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                <=> ( C @ ( D @ r2_hidden ) ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).

thf(1636,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
               => ( ( ( C @ ( D @ r2_hidden ) )
                   => ( B @ ( D @ r2_hidden ) ) )
                  & ( ( B @ ( D @ r2_hidden ) )
                   => ( C @ ( D @ r2_hidden ) ) ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(561,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m2_pboole ) ) )
         => ( A @ ( C @ m1_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_pboole) ).

thf(2954,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m2_pboole ) ) )
         => ( A @ ( C @ m1_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(240,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
     => ( ( ( D @ ( B @ r1_tarski ) )
          & ( C @ ( A @ r1_tarski ) ) )
        | ( ( B @ ( A @ k2_zfmisc_1 ) )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).

thf(1651,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
     => ( ( ( D @ ( B @ r1_tarski ) )
          & ( C @ ( A @ r1_tarski ) ) )
        | ( ( B @ ( A @ k2_zfmisc_1 ) )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(15678,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,13403]) ).

thf(15679,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15678]) ).

thf(15726,plain,
    ! [A: $i] :
      ( ( A
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) ) )
      | ( A != sk181 ) ),
    inference(simp,[status(thm)],[15679]) ).

thf(15751,plain,
    ( ( sk181 @ ( sk181 @ k2_zfmisc_1 ) )
   != sk181 ),
    inference(simp,[status(thm)],[15726]) ).

thf(351,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(2118,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ~ ( A @ ( B @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(115,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( A @ k2_mboolean ) @ ( A @ k1_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_mboolean) ).

thf(1067,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( A @ k2_mboolean ) @ ( A @ k1_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(507,axiom,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( f1_s4_altcat_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( f2_s4_altcat_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( f3_s4_altcat_1 @ ( D @ m1_subset_1 ) )
                 => ( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
                    = ( D @ ( C @ ( B @ f4_s4_altcat_1 ) ) ) ) ) ) )
      & ( f3_s4_altcat_1 @ ( f2_s4_altcat_1 @ ( f1_s4_altcat_1 @ k3_zfmisc_1 ) ) @ ( A @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s4_altcat_1) ).

thf(2788,plain,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( f1_s4_altcat_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( f2_s4_altcat_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( f3_s4_altcat_1 @ ( D @ m1_subset_1 ) )
                 => ( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
                    = ( D @ ( C @ ( B @ f4_s4_altcat_1 ) ) ) ) ) ) )
      & ( f3_s4_altcat_1 @ ( f2_s4_altcat_1 @ ( f1_s4_altcat_1 @ k3_zfmisc_1 ) ) @ ( A @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(2789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( ( C @ ( B @ ( A @ ( sk184 @ k1_multop_1 ) ) ) )
          = ( C @ ( B @ ( A @ f4_s4_altcat_1 ) ) ) )
        | ~ ( f3_s4_altcat_1 @ ( C @ m1_subset_1 ) )
        | ~ ( f2_s4_altcat_1 @ ( B @ m1_subset_1 ) )
        | ~ ( f1_s4_altcat_1 @ ( A @ m1_subset_1 ) ) )
      & ( f3_s4_altcat_1 @ ( f2_s4_altcat_1 @ ( f1_s4_altcat_1 @ k3_zfmisc_1 ) ) @ ( sk184 @ m1_pboole ) ) ),
    inference(cnf,[status(esa)],[2788]) ).

thf(2790,plain,
    f3_s4_altcat_1 @ ( f2_s4_altcat_1 @ ( f1_s4_altcat_1 @ k3_zfmisc_1 ) ) @ ( sk184 @ m1_pboole ),
    inference(cnfConj,[status(thm)],[2789]) ).

thf(475,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_pboole) ).

thf(2660,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(549,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ? [C: $i] :
          ( ( B @ ( C @ ( A @ r1_pboole ) ) )
          & ( A @ ( C @ m1_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_pboole) ).

thf(2905,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ? [C: $i] :
          ( ( B @ ( C @ ( A @ r1_pboole ) ) )
          & ( A @ ( C @ m1_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(112,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
    <=> ( ( A != C )
        & ( B @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).

thf(1047,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A != C )
          & ( B @ ( A @ r2_hidden ) ) )
       => ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
      & ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
       => ( ( A != C )
          & ( B @ ( A @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(253,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
      = ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_xboole_1) ).

thf(1730,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
      = ( D @ ( C @ ( B @ k2_xboole_0 ) @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(113,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_xboole_1) ).

thf(1057,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( D @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(158,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
        | ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).

thf(1274,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
        | ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(458,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k11_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_mboolean) ).

thf(2589,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k11_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(60,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k5_xboole_0 ) )
      = ( B @ ( C @ ( A @ k5_xboole_0 ) @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_xboole_1) ).

thf(825,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k5_xboole_0 ) )
      = ( B @ ( C @ ( A @ k5_xboole_0 ) @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).

thf(598,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(275,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mboolean) ).

thf(1824,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(57,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ~ ( ( B @ ( B @ ( A @ r5_pboole ) ) )
          & ( B
           != ( A @ k1_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_pboole) ).

thf(815,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ~ ( ( B @ ( B @ ( A @ r5_pboole ) ) )
          & ( B
           != ( A @ k1_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(413,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r6_pboole ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                <=> ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mboolean) ).

thf(2396,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
                     => ( B @ ( D @ ( A @ r1_pboole ) ) ) )
                    & ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                     => ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) )
             => ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r6_pboole ) ) ) )
            & ( ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r6_pboole ) ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
                     => ( B @ ( D @ ( A @ r1_pboole ) ) ) )
                    & ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                     => ( C @ ( D @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(150,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_fraenkel) ).

thf(1238,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(488,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( ( B @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r6_pboole ) ) )
              & ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_pboole) ).

thf(2705,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( ( B @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r6_pboole ) ) )
              & ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(381,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
                  & ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_pboole) ).

thf(2264,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
                  & ( D @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_xboole_1) ).

thf(746,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(120,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( A @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).

thf(1091,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( A @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(12878,plain,
    ! [A: $i] :
      ( ( A != sk199 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3072]) ).

thf(12879,plain,
    ! [A: $i] :
      ( ( A != sk199 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[12878]) ).

thf(12880,plain,
    ~ ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[12879:[bind(A,$thf( sk199 ))]]) ).

thf(14491,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,12880]) ).

thf(14492,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14491]) ).

thf(14581,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) ) )
      | ( A != sk199 ) ),
    inference(simp,[status(thm)],[14492]) ).

thf(14605,plain,
    ( ( sk199 @ ( sk199 @ k2_zfmisc_1 ) )
   != ( sk199 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[14581]) ).

thf(415,axiom,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_finseq_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_finseq_2) ).

thf(2414,plain,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_finseq_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ k2_xboole_0 ) ) )
      | ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[707]) ).

thf(728,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[712]) ).

thf(729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ( C @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(simp,[status(thm)],[728]) ).

thf(355,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ~ ( D @ v1_xboole_0 )
                 => ( ! [E: $i] :
                        ( ( A @ ( E @ r2_hidden ) )
                      <=> ? [F: $i] :
                            ( ? [G: $i] :
                                ( ? [H: $i] :
                                    ( ( E
                                      = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                                    & ( D @ ( H @ m1_subset_1 ) ) )
                                & ( C @ ( G @ m1_subset_1 ) ) )
                            & ( B @ ( F @ m1_subset_1 ) ) ) )
                   => ( A
                      = ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_domain_1) ).

thf(2132,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ~ ( D @ v1_xboole_0 )
                 => ( ! [E: $i] :
                        ( ( ? [F: $i] :
                              ( ? [G: $i] :
                                  ( ? [H: $i] :
                                      ( ( E
                                        = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                                      & ( D @ ( H @ m1_subset_1 ) ) )
                                  & ( C @ ( G @ m1_subset_1 ) ) )
                              & ( B @ ( F @ m1_subset_1 ) ) )
                         => ( A @ ( E @ r2_hidden ) ) )
                        & ( ( A @ ( E @ r2_hidden ) )
                         => ? [F: $i] :
                              ( ? [G: $i] :
                                  ( ? [H: $i] :
                                      ( ( E
                                        = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                                      & ( D @ ( H @ m1_subset_1 ) ) )
                                  & ( C @ ( G @ m1_subset_1 ) ) )
                              & ( B @ ( F @ m1_subset_1 ) ) ) ) )
                   => ( A
                      = ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(543,axiom,
    ! [A: $i] : ( A @ ( A @ k1_pralg_3 @ m1_pboole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pralg_3) ).

thf(2890,plain,
    ! [A: $i] : ( A @ ( A @ k1_pralg_3 @ m1_pboole ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ? [B: $i] : ( A @ ( B @ m1_card_fil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_card_fil) ).

thf(1883,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ? [B: $i] : ( A @ ( B @ m1_card_fil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(15228,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,13340]) ).

thf(15229,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15228]) ).

thf(15276,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != sk103 ) ),
    inference(simp,[status(thm)],[15229]) ).

thf(15298,plain,
    ! [A: $i] :
      ( ( A @ ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != sk103 ),
    inference(simp,[status(thm)],[15276]) ).

thf(535,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( D @ m1_pboole ) )
     => ! [E: $i] :
          ( ( B @ ( E @ m1_pboole ) )
         => ! [F: $i] :
              ( ( C @ ( F @ m1_pboole ) )
             => ( ( ( F @ ( E @ ( C @ ( B @ r2_altcat_2 ) ) ) )
                  & ( E @ ( D @ ( B @ ( A @ r2_altcat_2 ) ) ) ) )
               => ( F @ ( D @ ( C @ ( A @ r2_altcat_2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_altcat_2) ).

thf(2873,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( D @ m1_pboole ) )
     => ! [E: $i] :
          ( ( B @ ( E @ m1_pboole ) )
         => ! [F: $i] :
              ( ( C @ ( F @ m1_pboole ) )
             => ( ( ( F @ ( E @ ( C @ ( B @ r2_altcat_2 ) ) ) )
                  & ( E @ ( D @ ( B @ ( A @ r2_altcat_2 ) ) ) ) )
               => ( F @ ( D @ ( C @ ( A @ r2_altcat_2 ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(15238,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,13340]) ).

thf(15239,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15238]) ).

thf(15275,plain,
    ! [A: $i] :
      ( ( A
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) ) )
      | ( A != sk103 ) ),
    inference(simp,[status(thm)],[15239]) ).

thf(15296,plain,
    ( ( sk103 @ ( sk103 @ k2_zfmisc_1 ) )
   != sk103 ),
    inference(simp,[status(thm)],[15275]) ).

thf(421,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ k1_pboole @ ( B @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_pboole) ).

thf(2433,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ k1_pboole @ ( B @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(305,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_pboole) ).

thf(1966,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(1967,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1966]) ).

thf(1968,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k1_pboole @ k1_funct_1 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1967]) ).

thf(301,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r1_pboole ) ) )
           => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_mboolean) ).

thf(1951,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r1_pboole ) ) )
           => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(25,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ r5_pboole ) ) )
       => ( B @ ( C @ ( A @ r5_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r5_pboole) ).

thf(664,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ r5_pboole ) ) )
       => ( B @ ( C @ ( A @ r5_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ r5_pboole ) ) )
      | ~ ( C @ ( B @ ( A @ r5_pboole ) ) )
      | ~ ( A @ ( C @ m1_pboole ) )
      | ~ ( A @ ( B @ m1_pboole ) ) ),
    inference(cnf,[status(esa)],[664]) ).

thf(337,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ k2_zfmisc_1 ) )
        = ( B @ ( B @ k2_zfmisc_1 ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).

thf(2068,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ k2_zfmisc_1 ) )
        = ( B @ ( B @ k2_zfmisc_1 ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(583,plain,
    sk1 @ ( sk2 @ m1_pboole ),
    inference(cnfConj,[status(thm)],[580]) ).

thf(135,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_xboole_1) ).

thf(1159,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ k2_xboole_0 ) @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(267,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).

thf(1787,plain,
    ! [A: $i,B: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(43,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( B @ ( C @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_xboole_1) ).

thf(757,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( B @ ( C @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(25823,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk3 @ ( sk3 @ k2_zfmisc_1 ) @ ( sk3 @ r1_tarski ) ) )
      | ( k1_xboole_0 @ v2_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,13543]) ).

thf(25824,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk3 @ ( sk3 @ k2_zfmisc_1 ) @ ( sk3 @ r1_tarski ) ) )
      | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[25823]) ).

thf(25866,plain,
    ! [A: $i] :
      ( ( A
       != ( sk3 @ ( sk3 @ k2_zfmisc_1 ) ) )
      | ( A != sk3 )
      | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[25824]) ).

thf(25888,plain,
    ( ( ( sk3 @ ( sk3 @ k2_zfmisc_1 ) )
     != sk3 )
    | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[25866]) ).

thf(402,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ! [D: $i] :
          ( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
         => ( D @ v1_funcop_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_pboole) ).

thf(2344,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ! [D: $i] :
          ( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
         => ( D @ v1_funcop_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(368,axiom,
    ! [A: $i] :
      ( ( ( A @ v5_grcat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m3_grcat_1 ) )
        <=> ( A @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m3_grcat_1) ).

thf(2228,plain,
    ! [A: $i] :
      ( ( ( A @ v5_grcat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m1_subset_1 ) )
           => ( A @ ( B @ m3_grcat_1 ) ) )
          & ( ( A @ ( B @ m3_grcat_1 ) )
           => ( A @ ( B @ m1_subset_1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(162,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( B @ ( A @ r2_hidden ) ) )
     => ( C @ ( A @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

thf(1291,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( B @ ( A @ r2_hidden ) ) )
     => ( C @ ( A @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(225,axiom,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).

thf(1571,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(1572,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1571]) ).

thf(1573,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1572]) ).

thf(107,axiom,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
          <=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
        & ! [C: $i] :
            ~ ( ! [D: $i,E: $i] :
                  ( C
                 != ( E @ ( D @ k4_tarski ) ) )
              & ( B @ ( C @ r2_hidden ) ) )
        & ! [C: $i] :
            ~ ( ! [D: $i,E: $i] :
                  ( C
                 != ( E @ ( D @ k4_tarski ) ) )
              & ( A @ ( C @ r2_hidden ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).

thf(1012,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
             => ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
            & ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
             => ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
        & ! [C: $i] :
            ~ ( ! [D: $i,E: $i] :
                  ( C
                 != ( E @ ( D @ k4_tarski ) ) )
              & ( B @ ( C @ r2_hidden ) ) )
        & ! [C: $i] :
            ~ ( ! [D: $i,E: $i] :
                  ( C
                 != ( E @ ( D @ k4_tarski ) ) )
              & ( A @ ( C @ r2_hidden ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(108,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).

thf(1032,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(1831,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1828]) ).

thf(1836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1831]) ).

thf(1837,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( k1_xboole_0 @ ( A @ k3_zfmisc_1 ) ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[1836]) ).

thf(180,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) )
      = ( A @ ( B @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

thf(1365,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) )
      = ( A @ ( B @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(477,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k4_card_fil @ ( B @ r2_hidden ) )
        <=> ( A @ ( B @ m1_card_fil ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_card_fil) ).

thf(2670,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m1_card_fil ) )
           => ( A @ k4_card_fil @ ( B @ r2_hidden ) ) )
          & ( ( A @ k4_card_fil @ ( B @ r2_hidden ) )
           => ( A @ ( B @ m1_card_fil ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(517,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( A @ ( A @ r2_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_subset_1) ).

thf(2820,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( A @ ( A @ r2_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(64,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ~ ( ! [C: $i] :
              ( ( A @ ( C @ m1_subset_1 ) )
             => ~ ( B @ ( C @ r2_hidden ) ) )
          & ( B != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).

thf(842,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ~ ( ! [C: $i] :
              ( ( A @ ( C @ m1_subset_1 ) )
             => ~ ( B @ ( C @ r2_hidden ) ) )
          & ( B != k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(127,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k5_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_xboole_1) ).

thf(1121,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k5_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ k2_xboole_0 ) ) )
      | ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[707]) ).

thf(724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[711]) ).

thf(725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ~ ( A @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(simp,[status(thm)],[724]) ).

thf(96,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_mboolean) ).

thf(980,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(105,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k4_xboole_0 ) )
      = ( C @ ( A @ k2_xboole_0 ) @ ( B @ k4_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_xboole_1) ).

thf(1006,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k5_xboole_0 ) @ k4_xboole_0 ) )
      = ( C @ ( A @ k2_xboole_0 ) @ ( B @ k4_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(382,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_pboole) ).

thf(2268,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(576,axiom,
    ? [A: $i] :
      ( ! [B: $i,C: $i,D: $i] :
          ( ( ( f3_s3_altcat_1 @ ( D @ r2_hidden ) )
            & ( f2_s3_altcat_1 @ ( C @ r2_hidden ) )
            & ( f1_s3_altcat_1 @ ( B @ r2_hidden ) ) )
         => ( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
            = ( D @ ( C @ ( B @ f4_s3_altcat_1 ) ) ) ) )
      & ( f3_s3_altcat_1 @ ( f2_s3_altcat_1 @ ( f1_s3_altcat_1 @ k3_zfmisc_1 ) ) @ ( A @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_altcat_1) ).

thf(2999,plain,
    ? [A: $i] :
      ( ! [B: $i,C: $i,D: $i] :
          ( ( ( f3_s3_altcat_1 @ ( D @ r2_hidden ) )
            & ( f2_s3_altcat_1 @ ( C @ r2_hidden ) )
            & ( f1_s3_altcat_1 @ ( B @ r2_hidden ) ) )
         => ( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
            = ( D @ ( C @ ( B @ f4_s3_altcat_1 ) ) ) ) )
      & ( f3_s3_altcat_1 @ ( f2_s3_altcat_1 @ ( f1_s3_altcat_1 @ k3_zfmisc_1 ) ) @ ( A @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(3000,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( ( C @ ( B @ ( A @ ( sk200 @ k1_multop_1 ) ) ) )
          = ( C @ ( B @ ( A @ f4_s3_altcat_1 ) ) ) )
        | ~ ( f3_s3_altcat_1 @ ( C @ r2_hidden ) )
        | ~ ( f2_s3_altcat_1 @ ( B @ r2_hidden ) )
        | ~ ( f1_s3_altcat_1 @ ( A @ r2_hidden ) ) )
      & ( f3_s3_altcat_1 @ ( f2_s3_altcat_1 @ ( f1_s3_altcat_1 @ k3_zfmisc_1 ) ) @ ( sk200 @ m1_pboole ) ) ),
    inference(cnf,[status(esa)],[2999]) ).

thf(3001,plain,
    f3_s3_altcat_1 @ ( f2_s3_altcat_1 @ ( f1_s3_altcat_1 @ k3_zfmisc_1 ) ) @ ( sk200 @ m1_pboole ),
    inference(cnfConj,[status(thm)],[3000]) ).

thf(178,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( B @ ( A @ k4_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_xboole_1) ).

thf(1360,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( B @ ( A @ k4_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(295,axiom,
    k1_xboole_0 @ v1_xboole_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(1936,plain,
    k1_xboole_0 @ v1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(281,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_mboolean) ).

thf(1851,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(558,axiom,
    ? [A: $i] :
      ( ( A @ v2_cat_5 )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_cat_5) ).

thf(2943,plain,
    ? [A: $i] :
      ( ( A @ v2_cat_5 )
      & ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(2944,plain,
    ( ( sk197 @ v2_cat_5 )
    & ~ ( sk197 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[2943]) ).

thf(2946,plain,
    sk197 @ v2_cat_5,
    inference(cnfConj,[status(thm)],[2944]) ).

thf(283,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ k1_tarski ) )
    <=> ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

thf(1857,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( ( C = A )
             => ( B @ ( C @ r2_hidden ) ) )
            & ( ( B @ ( C @ r2_hidden ) )
             => ( C = A ) ) )
       => ( B
          = ( A @ k1_tarski ) ) )
      & ( ( B
          = ( A @ k1_tarski ) )
       => ! [C: $i] :
            ( ( ( C = A )
             => ( B @ ( C @ r2_hidden ) ) )
            & ( ( B @ ( C @ r2_hidden ) )
             => ( C = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(1858,plain,
    ( ! [A: $i,B: $i] :
        ( ( ! [C: $i] :
              ( ( C = A )
             => ( B @ ( C @ r2_hidden ) ) )
          & ! [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
             => ( C = A ) ) )
       => ( B
          = ( A @ k1_tarski ) ) )
    & ! [A: $i,B: $i] :
        ( ( B
          = ( A @ k1_tarski ) )
       => ( ! [C: $i] :
              ( ( C = A )
             => ( B @ ( C @ r2_hidden ) ) )
          & ! [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
             => ( C = A ) ) ) ) ),
    inference(miniscope,[status(thm)],[1857]) ).

thf(1859,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F
          = ( E @ k1_tarski ) )
        | ~ ( F @ ( E @ ( F @ sk96 ) @ r2_hidden ) )
        | ( ( E @ ( F @ sk95 ) )
         != E ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ( ( E @ ( F @ sk96 ) )
          = E )
        | ( ( E @ ( F @ sk95 ) )
         != E ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ~ ( F @ ( E @ ( F @ sk96 ) @ r2_hidden ) )
        | ( F @ ( E @ ( F @ sk95 ) @ r2_hidden ) ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ( ( E @ ( F @ sk96 ) )
          = E )
        | ( F @ ( E @ ( F @ sk95 ) @ r2_hidden ) ) )
      & ( ( B @ ( D @ r2_hidden ) )
        | ( D != A )
        | ( B
         != ( A @ k1_tarski ) ) )
      & ( ( C = A )
        | ~ ( B @ ( C @ r2_hidden ) )
        | ( B
         != ( A @ k1_tarski ) ) ) ),
    inference(cnf,[status(esa)],[1858]) ).

thf(1865,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( C != A )
      | ( B
       != ( A @ k1_tarski ) ) ),
    inference(cnfConj,[status(thm)],[1859]) ).

thf(1872,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( C != A )
      | ( B
       != ( A @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[1865]) ).

thf(1873,plain,
    ! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[1872]) ).

thf(10860,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
       != ( C @ ( B @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1873,10734]) ).

thf(10861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
     != ( C @ ( B @ k2_zfmisc_1 ) @ ( k1_xboole_0 @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[10860]) ).

thf(10875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski )
       != ( C @ ( B @ k2_zfmisc_1 ) ) )
      | ( A != k1_xboole_0 ) ),
    inference(simp,[status(thm)],[10861]) ).

thf(10887,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_zfmisc_1 ) )
     != ( k1_xboole_0 @ k1_tarski ) ),
    inference(simp,[status(thm)],[10875]) ).

thf(408,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_pboole) ).

thf(2377,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).

thf(648,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(649,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ! [C: $i] : ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(miniscope,[status(thm)],[648]) ).

thf(650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ ( B @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[649]) ).

thf(512,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( B @ ( A @ r2_zfrefle1 ) )
       => ( A @ ( B @ r2_zfrefle1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_zfrefle1) ).

thf(2801,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( B @ ( A @ r2_zfrefle1 ) )
       => ( A @ ( B @ r2_zfrefle1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(269,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).

thf(1794,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ r2_hidden ) )
       => ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
          = k1_xboole_0 ) )
      & ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
          = k1_xboole_0 )
       => ( B @ ( A @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(302,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( C @ ( D @ r1_tarski ) )
              & ( B @ ( D @ r1_tarski ) ) )
           => ( A @ ( D @ r1_tarski ) ) )
        & ( C @ ( A @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( A
        = ( C @ ( B @ k3_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).

thf(1953,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( C @ ( D @ r1_tarski ) )
              & ( B @ ( D @ r1_tarski ) ) )
           => ( A @ ( D @ r1_tarski ) ) )
        & ( C @ ( A @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( A
        = ( C @ ( B @ k3_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(124,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
     => ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).

thf(1111,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
     => ( B @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(489,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( A @ ( B @ v1_pre_circ ) )
        & ( B @ v2_relat_1 ) )
     => ~ ( ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ~ ( ! [D: $i] :
                      ( ( A @ ( D @ m1_pboole ) )
                     => ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                       => ( D @ ( C @ ( A @ r2_pboole ) ) ) ) )
                  & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) )
          & ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
                      & ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
                      & ( B @ ( D @ ( A @ r1_pboole ) ) )
                      & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_mssubfam) ).

thf(2709,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( A @ ( B @ v1_pre_circ ) )
        & ( B @ v2_relat_1 ) )
     => ~ ( ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ~ ( ! [D: $i] :
                      ( ( A @ ( D @ m1_pboole ) )
                     => ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                       => ( D @ ( C @ ( A @ r2_pboole ) ) ) ) )
                  & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) )
          & ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
                      & ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
                      & ( B @ ( D @ ( A @ r1_pboole ) ) )
                      & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(14721,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,13123]) ).

thf(14722,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14721]) ).

thf(14759,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != sk198 ) ),
    inference(simp,[status(thm)],[14722]) ).

thf(14783,plain,
    ! [A: $i] :
      ( ( A @ ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != sk198 ),
    inference(simp,[status(thm)],[14759]) ).

thf(492,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) )
              <=> ( ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                          & ( E @ ( C @ ( A @ r2_pboole ) ) ) )
                       => ( E @ ( B @ ( A @ r2_pboole ) ) ) ) )
                  & ( B @ ( D @ ( A @ r2_pboole ) ) )
                  & ( B @ ( C @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_pboole) ).

thf(2726,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( ! [E: $i] :
                        ( ( A @ ( E @ m1_pboole ) )
                       => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                            & ( E @ ( C @ ( A @ r2_pboole ) ) ) )
                         => ( E @ ( B @ ( A @ r2_pboole ) ) ) ) )
                    & ( B @ ( D @ ( A @ r2_pboole ) ) )
                    & ( B @ ( C @ ( A @ r2_pboole ) ) ) )
                 => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) ) )
                & ( ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r6_pboole ) ) )
                 => ( ! [E: $i] :
                        ( ( A @ ( E @ m1_pboole ) )
                       => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                            & ( E @ ( C @ ( A @ r2_pboole ) ) ) )
                         => ( E @ ( B @ ( A @ r2_pboole ) ) ) ) )
                    & ( B @ ( D @ ( A @ r2_pboole ) ) )
                    & ( B @ ( C @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(131,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_card_fil ) )
         => ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_card_fil) ).

thf(1138,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_card_fil ) )
         => ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(491,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( A @ k1_pboole @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                  & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_pboole) ).

thf(2724,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( A @ k1_pboole @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                  & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(529,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k7_waybel_5 ) @ m1_pboole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_waybel_5) ).

thf(2858,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k7_waybel_5 ) @ m1_pboole ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( B @ k2_relat_1 @ ( C @ m1_subset_1 ) )
             => ? [D: $i] :
                  ( ( C
                    = ( D @ ( B @ k1_funct_1 ) ) )
                  & ( A @ ( D @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_pboole) ).

thf(2537,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( B @ k2_relat_1 @ ( C @ m1_subset_1 ) )
             => ? [D: $i] :
                  ( ( C
                    = ( D @ ( B @ k1_funct_1 ) ) )
                  & ( A @ ( D @ r2_hidden ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(224,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
        = k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_xboole_1) ).

thf(1567,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
        = k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(427,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
              <=> ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) )
                  & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_mboolean) ).

thf(2460,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) )
                    & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
                 => ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
                & ( ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                 => ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) )
                    & ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(11624,plain,
    ! [A: $i] :
      ( ( A != sk3 )
      | ( k1_xboole_0 @ v2_relat_1 )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,581]) ).

thf(11625,plain,
    ( ( k1_xboole_0 @ v2_relat_1 )
    | ~ ( sk3 @ v1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11624:[bind(A,$thf( sk3 ))]]) ).

thf(12135,plain,
    ( ( ( sk3 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( k1_xboole_0 @ v2_relat_1 )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,11625]) ).

thf(12136,plain,
    ( ( ( sk3 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[12135]) ).

thf(12151,plain,
    ( ( sk3 != k1_xboole_0 )
    | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[12136]) ).

thf(14543,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,12880]) ).

thf(14544,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14543]) ).

thf(14587,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != sk199 ) ),
    inference(simp,[status(thm)],[14544]) ).

thf(14613,plain,
    ! [A: $i] :
      ( ( A @ ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != sk199 ),
    inference(simp,[status(thm)],[14587]) ).

thf(298,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
      = ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_1) ).

thf(1942,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
      = ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(394,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( B @ ( B @ ( A @ r2_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_pboole) ).

thf(2323,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( B @ ( B @ ( A @ r2_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
               => ( ( D @ ( B @ ( A @ r4_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_pboole) ).

thf(933,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
               => ( ( D @ ( B @ ( A @ r4_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(453,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( A @ ( B @ v1_pre_circ ) )
        & ( B @ v2_relat_1 ) )
     => ~ ( ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ~ ( ! [D: $i] :
                      ( ( A @ ( D @ m1_pboole ) )
                     => ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                       => ( C @ ( D @ ( A @ r2_pboole ) ) ) ) )
                  & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) )
          & ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
                      & ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
                      & ( B @ ( D @ ( A @ r1_pboole ) ) )
                      & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_mssubfam) ).

thf(2561,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( A @ ( B @ v1_pre_circ ) )
        & ( B @ v2_relat_1 ) )
     => ~ ( ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ~ ( ! [D: $i] :
                      ( ( A @ ( D @ m1_pboole ) )
                     => ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                       => ( C @ ( D @ ( A @ r2_pboole ) ) ) ) )
                  & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) )
          & ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ~ ( ~ ( C @ ( D @ ( A @ r2_pboole ) ) )
                      & ~ ( D @ ( C @ ( A @ r2_pboole ) ) )
                      & ( B @ ( D @ ( A @ r1_pboole ) ) )
                      & ( B @ ( C @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(13963,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,12823]) ).

thf(13964,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13963]) ).

thf(14033,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) )
      | ( A != sk1 ) ),
    inference(simp,[status(thm)],[13964]) ).

thf(14052,plain,
    ! [A: $i] :
      ( ( sk1 @ ( A @ k2_xboole_0 ) )
     != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[14033]) ).

thf(392,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_pboole) ).

thf(2312,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(296,axiom,
    ! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k2_pre_circ ) @ ( B @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_mboolean) ).

thf(1937,plain,
    ! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k2_pre_circ ) @ ( B @ ( A @ k2_pre_circ ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(347,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_pboole) ).

thf(2108,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(15062,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,13162]) ).

thf(15063,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15062]) ).

thf(15096,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != k3_qc_lang1 ) ),
    inference(simp,[status(thm)],[15063]) ).

thf(15126,plain,
    ! [A: $i] :
      ( ( A @ ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != k3_qc_lang1 ),
    inference(simp,[status(thm)],[15096]) ).

thf(134,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
        = ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_xboole_1) ).

thf(1155,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( B @ ( C @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
        = ( B @ ( C @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(191,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k2_zfmisc_1 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ? [E: $i,F: $i] :
              ( ( D
                = ( F @ ( E @ k4_tarski ) ) )
              & ( B @ ( F @ r2_hidden ) )
              & ( A @ ( E @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).

thf(1419,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ? [E: $i,F: $i] :
                  ( ( D
                    = ( F @ ( E @ k4_tarski ) ) )
                  & ( B @ ( F @ r2_hidden ) )
                  & ( A @ ( E @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
            & ( ( C @ ( D @ r2_hidden ) )
             => ? [E: $i,F: $i] :
                  ( ( D
                    = ( F @ ( E @ k4_tarski ) ) )
                  & ( B @ ( F @ r2_hidden ) )
                  & ( A @ ( E @ r2_hidden ) ) ) ) )
       => ( C
          = ( B @ ( A @ k2_zfmisc_1 ) ) ) )
      & ( ( C
          = ( B @ ( A @ k2_zfmisc_1 ) ) )
       => ! [D: $i] :
            ( ( ? [E: $i,F: $i] :
                  ( ( D
                    = ( F @ ( E @ k4_tarski ) ) )
                  & ( B @ ( F @ r2_hidden ) )
                  & ( A @ ( E @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
            & ( ( C @ ( D @ r2_hidden ) )
             => ? [E: $i,F: $i] :
                  ( ( D
                    = ( F @ ( E @ k4_tarski ) ) )
                  & ( B @ ( F @ r2_hidden ) )
                  & ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(11560,plain,
    ! [A: $i] :
      ( ( A != sk3 )
      | ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,585]) ).

thf(11561,plain,
    ( ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
    | ~ ( sk3 @ v1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11560:[bind(A,$thf( sk3 ))]]) ).

thf(14892,plain,
    ( ( ( sk3 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,11561]) ).

thf(14893,plain,
    ( ( ( sk3 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( sk1 @ ( k1_xboole_0 @ m1_pboole ) ) ),
    inference(simp,[status(thm)],[14892]) ).

thf(14914,plain,
    ( ( sk3 != k1_xboole_0 )
    | ( sk1 @ ( k1_xboole_0 @ m1_pboole ) ) ),
    inference(simp,[status(thm)],[14893]) ).

thf(537,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( B @ ( A @ r2_subset_1 ) )
       => ( A @ ( B @ r2_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_subset_1) ).

thf(2877,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( B @ ( A @ r2_subset_1 ) )
       => ( A @ ( B @ r2_subset_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(143,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( ( C = k1_xboole_0 )
            & ( B
              = ( A @ k1_tarski ) ) )
        & ~ ( ( C
              = ( A @ k1_tarski ) )
            & ( B = k1_xboole_0 ) )
        & ~ ( ( C
              = ( A @ k1_tarski ) )
            & ( B
              = ( A @ k1_tarski ) ) )
        & ( ( A @ k1_tarski )
          = ( C @ ( B @ k2_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).

thf(1182,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( ( C = k1_xboole_0 )
            & ( B
              = ( A @ k1_tarski ) ) )
        & ~ ( ( C
              = ( A @ k1_tarski ) )
            & ( B = k1_xboole_0 ) )
        & ~ ( ( C
              = ( A @ k1_tarski ) )
            & ( B
              = ( A @ k1_tarski ) ) )
        & ( ( A @ k1_tarski )
          = ( C @ ( B @ k2_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(257,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).

thf(1739,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(195,axiom,
    ! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(1461,plain,
    ! [A: $i] : ( A @ ( A @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(686,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
      | ( A @ ( A @ ( B @ sk7 ) @ m1_pboole ) )
      | ~ ( A @ ( B @ m1_pboole ) )
      | ~ ( A @ ( B @ v1_pre_circ ) )
      | ~ ( B @ v2_relat_1 ) ),
    inference(cnfConj,[status(thm)],[685]) ).

thf(330,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).

thf(2053,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(371,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ k1_pboole @ ( B @ ( A @ k1_pboole @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_pboole) ).

thf(2240,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ k1_pboole @ ( B @ ( A @ k1_pboole @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
      = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
    inference(cnfConj,[status(thm)],[632]) ).

thf(635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
      = ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) ) ),
    inference(lifteq,[status(thm)],[633]) ).

thf(19713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
       != ( D @ ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
      | ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
       != sk33 ) ),
    inference(paramod_ordered,[status(thm)],[635,14240]) ).

thf(19714,plain,
    ! [A: $i] :
      ( ( sk33 @ ( A @ ( sk33 @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
     != sk33 ),
    inference(pattern_uni,[status(thm)],[19713:[bind(A,$thf( sk33 )),bind(B,$thf( E )),bind(C,$thf( sk33 )),bind(D,$thf( sk33 @ ( E @ k2_zfmisc_1 ) ))]]) ).

thf(19735,plain,
    ! [A: $i] :
      ( ( sk33 @ ( A @ ( sk33 @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
     != sk33 ),
    inference(simp,[status(thm)],[19714]) ).

thf(236,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).

thf(1612,plain,
    ! [A: $i,B: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(473,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ~ ( ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ~ ( ( C @ ( E @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                          & ( D @ ( E @ ( A @ r2_pboole ) ) )
                          & ( A @ ( E @ v1_pre_circ ) ) ) )
                  & ( C @ ( D @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                  & ( A @ ( C @ v1_pre_circ ) )
                  & ( A @ ( B @ v1_pre_circ ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_mssubfam) ).

thf(2649,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ~ ( ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ~ ( ( C @ ( E @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                          & ( D @ ( E @ ( A @ r2_pboole ) ) )
                          & ( A @ ( E @ v1_pre_circ ) ) ) )
                  & ( C @ ( D @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                  & ( A @ ( C @ v1_pre_circ ) )
                  & ( A @ ( B @ v1_pre_circ ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(569,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ r6_pboole ) ) )
      <=> ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r6_pboole) ).

thf(2978,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( ( B = C )
         => ( C @ ( B @ ( A @ r6_pboole ) ) ) )
        & ( ( C @ ( B @ ( A @ r6_pboole ) ) )
         => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(431,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k3_pboole ) ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pboole) ).

thf(2472,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k3_pboole ) ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(200,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
           => ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_pboole) ).

thf(1478,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
           => ( C @ ( B @ ( A @ r5_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(10476,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
       != ( sk33 @ sk105 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[1817,6791]) ).

thf(10477,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
     != ( sk33 @ sk105 @ k1_tarski @ ( sk33 @ k4_xboole_0 ) ) ),
    inference(simp,[status(thm)],[10476]) ).

thf(10539,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( sk33 @ sk105 @ k1_tarski ) )
      | ( A != sk33 ) ),
    inference(simp,[status(thm)],[10477]) ).

thf(10560,plain,
    ! [A: $i] :
      ( ( A @ ( sk33 @ k2_xboole_0 ) )
     != ( sk33 @ sk105 @ k1_tarski ) ),
    inference(simp,[status(thm)],[10539]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_pboole) ).

thf(653,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r5_pboole ) ) )
      | ~ ( A @ ( C @ m1_pboole ) )
      | ~ ( A @ ( B @ m1_pboole ) ) ),
    inference(cnf,[status(esa)],[653]) ).

thf(219,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( B @ ( D @ m1_subset_1 ) )
               => ( C @ ( D @ r2_hidden ) ) )
           => ( C @ ( B @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).

thf(1552,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( B @ ( D @ m1_subset_1 ) )
               => ( C @ ( D @ r2_hidden ) ) )
           => ( C @ ( B @ r1_tarski ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).

thf(1930,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(1931,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1930]) ).

thf(1932,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1931]) ).

thf(428,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ k1_pboole @ ( B @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_pboole) ).

thf(2465,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ k1_pboole @ ( B @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(300,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(1947,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(103,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( A @ ( C @ v1_pre_circ ) )
              & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
           => ( A @ ( B @ v1_pre_circ ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_mssubfam) ).

thf(1002,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( A @ ( C @ v1_pre_circ ) )
              & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
           => ( A @ ( B @ v1_pre_circ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(2945,plain,
    ~ ( sk197 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[2944]) ).

thf(3028,plain,
    ( ( ( sk197 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,2945]) ).

thf(3029,plain,
    ( ( sk197 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3028]) ).

thf(3030,plain,
    sk197 != k1_xboole_0,
    inference(simp,[status(thm)],[3029]) ).

thf(13623,plain,
    ! [A: $i] :
      ( ( A != sk197 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,3030]) ).

thf(13624,plain,
    ! [A: $i] :
      ( ( A != sk197 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13623]) ).

thf(13625,plain,
    ~ ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[13624:[bind(A,$thf( sk197 ))]]) ).

thf(15962,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,13625]) ).

thf(15963,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15962]) ).

thf(16035,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) ) )
      | ( A != sk197 ) ),
    inference(simp,[status(thm)],[15963]) ).

thf(16058,plain,
    ! [A: $i] :
      ( ( sk197 @ ( A @ k2_xboole_0 ) )
     != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[16035]) ).

thf(2870,plain,
    sk190 @ v1_xboole_0,
    inference(cnf,[status(esa)],[2869]) ).

thf(11608,plain,
    ! [A: $i] :
      ( ( ( sk190 @ v1_xboole_0 )
       != ( A @ v1_xboole_0 ) )
      | ~ $true
      | ( A = k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[2870,672]) ).

thf(11609,plain,
    ! [A: $i] :
      ( ( ( sk190 @ v1_xboole_0 )
       != ( A @ v1_xboole_0 ) )
      | ( A = k1_xboole_0 ) ),
    inference(simp,[status(thm)],[11608]) ).

thf(11610,plain,
    sk190 = k1_xboole_0,
    inference(pattern_uni,[status(thm)],[11609:[bind(A,$thf( sk190 ))]]) ).

thf(3105,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,901]) ).

thf(3106,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3105]) ).

thf(3109,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[3106]) ).

thf(386,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) )
              <=> ( ( D @ ( B @ ( A @ r1_pboole ) ) )
                  & ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_pboole) ).

thf(2285,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
                    & ( C @ ( B @ ( A @ r1_pboole ) ) ) )
                 => ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) ) )
                & ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) )
                 => ( ( D @ ( B @ ( A @ r1_pboole ) ) )
                    & ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(125,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                 => ( C @ ( D @ r2_hidden ) ) ) )
           => ( C @ ( B @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).

thf(1114,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                 => ( C @ ( D @ r2_hidden ) ) ) )
           => ( C @ ( B @ r1_tarski ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(647,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r2_hidden ) )
      | ~ ( A @ ( B @ m1_card_fil ) )
      | ( A @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[646]) ).

thf(155,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).

thf(1261,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(1262,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
        = k1_xboole_0 )
      | ( A = k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1261]) ).

thf(1263,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
        = k1_xboole_0 )
      | ( A = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1262]) ).

thf(425,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ ( A @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(2450,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ ( A @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(353,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ( ( B @ k4_card_3 @ v1_pralg_2 )
        & ( B @ k4_card_3 @ v1_fraenkel )
        & ~ ( B @ k4_card_3 @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_pralg_2) ).

thf(2125,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ( ( B @ k4_card_3 @ v1_pralg_2 )
        & ( B @ k4_card_3 @ v1_fraenkel )
        & ~ ( B @ k4_card_3 @ v1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(523,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ m1_pboole ) )
     => ! [D: $i] :
          ( ( B @ ( D @ m1_pboole ) )
         => ( ( ( C @ ( D @ ( A @ ( B @ r2_altcat_2 ) ) ) )
              & ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_altcat_2) ).

thf(2836,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ m1_pboole ) )
     => ! [D: $i] :
          ( ( B @ ( D @ m1_pboole ) )
         => ( ( ( C @ ( D @ ( A @ ( B @ r2_altcat_2 ) ) ) )
              & ( D @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(193,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
      = ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).

thf(1456,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
      = ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(98,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ k1_funct_2 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_fraenkel) ).

thf(984,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ k1_funct_2 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(910,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k3_xboole_0 ) )
      = A ),
    inference(cnf,[status(esa)],[909]) ).

thf(911,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k3_xboole_0 ) )
      = A ),
    inference(lifteq,[status(thm)],[910]) ).

thf(15508,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,13398]) ).

thf(15509,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15508]) ).

thf(15536,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( A != k4_qc_lang1 ) ),
    inference(simp,[status(thm)],[15509]) ).

thf(15560,plain,
    ! [A: $i] :
      ( ( A @ ( k4_qc_lang1 @ k2_xboole_0 ) )
     != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[15536]) ).

thf(439,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_pboole) ).

thf(2497,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ k2_xboole_0 ) ) )
      | ~ ( C @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( C @ ( B @ ( A @ sk12 ) ) ) ),
    inference(cnfConj,[status(thm)],[707]) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( C @ ( B @ ( A @ sk12 ) ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[714]) ).

thf(721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( C @ ( B @ ( A @ sk12 ) ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(simp,[status(thm)],[720]) ).

thf(501,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D
                  = ( C @ ( B @ ( A @ k3_pboole ) ) ) )
              <=> ! [E: $i] :
                    ( ( A @ ( E @ r2_hidden ) )
                   => ( ( E @ ( D @ k1_funct_1 ) )
                      = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pboole) ).

thf(2766,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) )
                 => ( D
                    = ( C @ ( B @ ( A @ k3_pboole ) ) ) ) )
                & ( ( D
                    = ( C @ ( B @ ( A @ k3_pboole ) ) ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k3_xboole_0 ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i,F: $i] :
          ( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
        <=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
     => ( ( B @ ( A @ k2_zfmisc_1 ) )
        = ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).

thf(1246,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i,F: $i] :
          ( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
           => ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
          & ( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
           => ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) )
     => ( ( B @ ( A @ k2_zfmisc_1 ) )
        = ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(448,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( A @ ( F @ r2_hidden ) )
        & ( F @ ( E @ r2_hidden ) )
        & ( E @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).

thf(2546,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( A @ ( F @ r2_hidden ) )
        & ( F @ ( E @ r2_hidden ) )
        & ( E @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(540,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k19_pralg_1 ) ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_pralg_1) ).

thf(2883,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k19_pralg_1 ) ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(508,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( B @ ( A @ r7_pboole ) ) )
              & ( B @ v2_relat_1 ) )
           => ( C @ v2_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_pboole) ).

thf(2793,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( B @ ( A @ r7_pboole ) ) )
              & ( B @ v2_relat_1 ) )
           => ( C @ v2_relat_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(138,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
      | ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).

thf(1167,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
      | ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(2749,plain,
    sk181 @ v1_fraenkel,
    inference(cnfConj,[status(thm)],[2747]) ).

thf(313,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ k3_pboole ) ) )
        = ( B @ ( C @ ( A @ k3_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_pboole) ).

thf(1991,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ k3_pboole ) ) )
        = ( B @ ( C @ ( A @ k3_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(145,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
    <=> ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

thf(1202,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ r1_tarski ) )
       => ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
      & ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
       => ( B @ ( A @ r1_tarski ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(51,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
                  & ( C @ ( B @ ( A @ r1_pboole ) ) ) )
               => ( D @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_pboole) ).

thf(792,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
                  & ( C @ ( B @ ( A @ r1_pboole ) ) ) )
               => ( D @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(223,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
            | ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
         => ( D @ ( B @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).

thf(1563,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
            | ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
         => ( D @ ( B @ r1_tarski ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(656,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ r2_hidden ) )
      | ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
       != ( B @ k1_tarski ) ) ),
    inference(cnf,[status(esa)],[655]) ).

thf(657,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ r2_hidden ) )
      | ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
       != ( B @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[656]) ).

thf(46,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ v3_relat_1 )
       => ( A @ ( B @ v1_pre_circ ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_mssubfam) ).

thf(765,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ v3_relat_1 )
       => ( A @ ( B @ v1_pre_circ ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(279,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
     => ( C @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_xboole_1) ).

thf(1846,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ r1_tarski ) )
     => ( C @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(1048,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( ( A != C )
          & ( B @ ( A @ r2_hidden ) ) )
       => ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
       => ( ( A != C )
          & ( B @ ( A @ r2_hidden ) ) ) ) ),
    inference(miniscope,[status(thm)],[1047]) ).

thf(1049,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F @ k1_tarski @ ( E @ k4_xboole_0 ) @ ( D @ r2_hidden ) )
        | ( D = F )
        | ~ ( E @ ( D @ r2_hidden ) ) )
      & ( ( A != C )
        | ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
      & ( ( B @ ( A @ r2_hidden ) )
        | ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ) ),
    inference(cnf,[status(esa)],[1048]) ).

thf(1051,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != C )
      | ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[1049]) ).

thf(1053,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
      | ( A != C ) ),
    inference(lifteq,[status(thm)],[1051]) ).

thf(1054,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ r2_hidden ) ),
    inference(simp,[status(thm)],[1053]) ).

thf(15246,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,13340]) ).

thf(15247,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15246]) ).

thf(15283,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) ) )
      | ( A != sk103 ) ),
    inference(simp,[status(thm)],[15247]) ).

thf(15307,plain,
    ! [A: $i] :
      ( ( A @ ( sk103 @ k2_xboole_0 ) )
     != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[15283]) ).

thf(139,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_mboolean) ).

thf(1170,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ r2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(160,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_card_fil ) )
         => ( B @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_card_fil) ).

thf(1286,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_card_fil ) )
         => ( B @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(11373,plain,
    ! [A: $i] :
      ( ( A != sk3 )
      | ~ ( k1_xboole_0 @ ( sk2 @ ( sk1 @ r6_pboole ) ) )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,584]) ).

thf(11374,plain,
    ( ~ ( k1_xboole_0 @ ( sk2 @ ( sk1 @ r6_pboole ) ) )
    | ~ ( sk3 @ v1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11373:[bind(A,$thf( sk3 ))]]) ).

thf(17222,plain,
    ( ( ( sk3 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ ( k1_xboole_0 @ ( sk2 @ ( sk1 @ r6_pboole ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,11374]) ).

thf(17223,plain,
    ( ( ( sk3 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ ( k1_xboole_0 @ ( sk2 @ ( sk1 @ r6_pboole ) ) ) ),
    inference(simp,[status(thm)],[17222]) ).

thf(17250,plain,
    ( ( sk3 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk2 @ ( sk1 @ r6_pboole ) ) ) ),
    inference(simp,[status(thm)],[17223]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ~ ( A @ k1_pboole @ ( B @ ( A @ r3_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_pboole) ).

thf(2995,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ~ ( A @ k1_pboole @ ( B @ ( A @ r3_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(89,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ( B @ ( C @ r2_hidden ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).

thf(953,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ( B @ ( C @ r2_hidden ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(476,axiom,
    ! [A: $i] :
      ( ( A @ v2_setfam_1 )
    <=> ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ~ ( A @ ( B @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_setfam_1) ).

thf(2662,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ~ ( B @ v1_xboole_0 )
           => ~ ( A @ ( B @ r2_hidden ) ) )
       => ( A @ v2_setfam_1 ) )
      & ( ( A @ v2_setfam_1 )
       => ! [B: $i] :
            ( ~ ( B @ v1_xboole_0 )
           => ~ ( A @ ( B @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ! [E: $i,F: $i] :
            ~ ( ( D
                = ( F @ ( E @ k4_tarski ) ) )
              & ( C @ ( F @ r2_hidden ) )
              & ( B @ ( E @ r2_hidden ) ) )
        & ( A @ ( D @ r2_hidden ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).

thf(773,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ! [E: $i,F: $i] :
            ~ ( ( D
                = ( F @ ( E @ k4_tarski ) ) )
              & ( C @ ( F @ r2_hidden ) )
              & ( B @ ( E @ r2_hidden ) ) )
        & ( A @ ( D @ r2_hidden ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(52,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
      = ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).

thf(794,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
      = ( D @ ( B @ k4_xboole_0 ) @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ( ~ ( B @ ( A @ k1_pboole @ ( A @ r4_pboole ) ) )
            & ~ ( A @ k1_pboole @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_pboole) ).

thf(926,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ( ~ ( B @ ( A @ k1_pboole @ ( A @ r4_pboole ) ) )
            & ~ ( A @ k1_pboole @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(550,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m1_pboole ) )
            & ( B @ v2_relat_1 ) )
         => ( B
            = ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) @ ( A @ k1_pboole @ k1_funct_4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_closure3) ).

thf(2909,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m1_pboole ) )
            & ( B @ v2_relat_1 ) )
         => ( B
            = ( B @ ( A @ k1_closure3 ) @ ( B @ k7_relat_1 ) @ ( A @ k1_pboole @ k1_funct_4 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(10570,plain,
    ! [B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
       != ( B @ ( sk33 @ k2_xboole_0 ) ) )
      | ( A
       != ( sk33 @ sk105 @ k1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[1383,10560]) ).

thf(10571,plain,
    ( ( sk33 @ sk105 @ k1_tarski )
   != sk33 ),
    inference(pattern_uni,[status(thm)],[10570:[bind(A,$thf( sk33 )),bind(B,$thf( k1_xboole_0 ))]]) ).

thf(260,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
      = ( B @ ( A @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_xboole_1) ).

thf(1754,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) )
      = ( B @ ( A @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(412,axiom,
    ! [A: $i,B: $i] :
      ~ ( ! [C: $i] :
            ~ ( ! [D: $i] :
                  ~ ( ( C @ ( D @ r2_hidden ) )
                    & ( B @ ( D @ r2_hidden ) ) )
              & ( B @ ( C @ r2_hidden ) ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).

thf(2391,plain,
    ! [A: $i,B: $i] :
      ~ ( ! [C: $i] :
            ~ ( ! [D: $i] :
                  ~ ( ( C @ ( D @ r2_hidden ) )
                    & ( B @ ( D @ r2_hidden ) ) )
              & ( B @ ( C @ r2_hidden ) ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(356,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ( ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( E @ ( A @ r1_pboole ) ) )
                          & ( C @ ( B @ ( A @ k2_pboole ) ) @ ( D @ ( A @ r1_pboole ) ) ) )
                       => ( ( A @ k1_pboole @ ( E @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                          | ( D = E ) ) ) ) )
              & ( C @ ( B @ ( A @ k2_pboole ) ) @ v2_relat_1 ) )
           => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_mboolean) ).

thf(2149,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ( ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( E @ ( A @ r1_pboole ) ) )
                          & ( C @ ( B @ ( A @ k2_pboole ) ) @ ( D @ ( A @ r1_pboole ) ) ) )
                       => ( ( A @ k1_pboole @ ( E @ ( D @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                          | ( D = E ) ) ) ) )
              & ( C @ ( B @ ( A @ k2_pboole ) ) @ v2_relat_1 ) )
           => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(456,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( C @ ( D @ ( C @ ( B @ ( A @ k17_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_domain_1) ).

thf(2585,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( C @ ( D @ ( C @ ( B @ ( A @ k17_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(202,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mboolean) ).

thf(1483,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(67,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C
              = ( B @ ( A @ k1_mboolean ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ r2_hidden ) )
               => ( ( D @ ( C @ k1_funct_1 ) )
                  = ( D @ ( B @ k1_funct_1 ) @ k1_zfmisc_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mboolean) ).

thf(856,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( ( D @ ( C @ k1_funct_1 ) )
                    = ( D @ ( B @ k1_funct_1 ) @ k1_zfmisc_1 ) ) )
             => ( C
                = ( B @ ( A @ k1_mboolean ) ) ) )
            & ( ( C
                = ( B @ ( A @ k1_mboolean ) ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( ( D @ ( C @ k1_funct_1 ) )
                    = ( D @ ( B @ k1_funct_1 ) @ k1_zfmisc_1 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(165,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).

thf(1301,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(689,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
      | ( B @ ( A @ ( B @ sk7 ) @ ( A @ r1_pboole ) ) )
      | ~ ( A @ ( B @ m1_pboole ) )
      | ~ ( A @ ( B @ v1_pre_circ ) )
      | ~ ( B @ v2_relat_1 ) ),
    inference(cnfConj,[status(thm)],[685]) ).

thf(252,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
      = ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_xboole_1) ).

thf(1727,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k4_xboole_0 ) )
      = ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(210,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ! [E: $i,F: $i] :
            ( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
           => ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( D @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).

thf(1510,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ! [E: $i,F: $i] :
            ( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
           => ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( D @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(3079,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( sk2 @ m1_pboole ) )
       != ( A @ ( C @ m1_pboole ) ) )
      | ~ ( A @ ( E @ m1_subset_1 ) )
      | ~ ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
      | ~ $true
      | ( B @ v1_xboole_0 )
      | ( A @ v1_xboole_0 )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) )
        = ( E @ ( D @ k1_funct_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[583,593]) ).

thf(3080,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk1 @ ( sk2 @ m1_pboole ) )
       != ( A @ ( C @ m1_pboole ) ) )
      | ~ ( A @ ( E @ m1_subset_1 ) )
      | ~ ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
      | ( B @ v1_xboole_0 )
      | ( A @ v1_xboole_0 )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) )
        = ( E @ ( D @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3079]) ).

thf(3081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( sk1 @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk2 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[3080:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).

thf(3083,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( sk1 @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk2 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3081]) ).

thf(3090,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | $false
      | ( ( C @ ( B @ ( sk2 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(rewrite,[status(thm)],[3083,588]) ).

thf(3091,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk2 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3090]) ).

thf(3282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) )
       != ( sk1 @ ( C @ m1_subset_1 ) ) )
      | ~ $true
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk2 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3269,3091]) ).

thf(3283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ) )
       != ( sk1 @ ( C @ m1_subset_1 ) ) )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk2 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3282]) ).

thf(3286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski )
       != sk1 )
      | ( k1_xboole_0 != C )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( C @ ( B @ ( sk2 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3283]) ).

thf(3289,plain,
    ! [B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_tarski )
       != sk1 )
      | ~ ( A @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( B @ m3_pboole ) ) ) )
      | ( A @ v1_xboole_0 )
      | ( ( k1_xboole_0 @ ( B @ ( sk2 @ ( A @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( k1_xboole_0 @ ( B @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3286]) ).

thf(545,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ r3_pboole ) ) )
       => ~ ( B @ ( C @ ( A @ r3_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r3_pboole) ).

thf(2894,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ r3_pboole ) ) )
       => ~ ( B @ ( C @ ( A @ r3_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(379,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
           => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_pboole) ).

thf(2260,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
           => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

thf(600,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(601,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ r1_tarski ) )
      | ~ ( C @ ( B @ r1_tarski ) )
      | ~ ( B @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[600]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                <=> ( C @ ( D @ r2_hidden ) ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).

thf(732,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( ( C @ ( D @ r2_hidden ) )
                   => ( B @ ( D @ r2_hidden ) ) )
                  & ( ( B @ ( D @ r2_hidden ) )
                   => ( C @ ( D @ r2_hidden ) ) ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(527,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v2_relat_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                <=> ( B @ ( D @ ( A @ r1_pboole ) ) ) ) )
           => ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_pboole) ).

thf(2849,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v2_relat_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_pboole ) )
               => ( ( ( B @ ( D @ ( A @ r1_pboole ) ) )
                   => ( C @ ( D @ ( A @ r1_pboole ) ) ) )
                  & ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                   => ( B @ ( D @ ( A @ r1_pboole ) ) ) ) ) )
           => ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(444,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ~ ( D @ v1_xboole_0 )
                 => ( ( A
                      = ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) )
                  <=> ! [E: $i] :
                        ( ( A @ ( E @ r2_hidden ) )
                      <=> ? [F: $i] :
                            ( ? [G: $i] :
                                ( ? [H: $i] :
                                    ( ( E
                                      = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                                    & ( D @ ( H @ m1_subset_1 ) ) )
                                & ( C @ ( G @ m1_subset_1 ) ) )
                            & ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_domain_1) ).

thf(2514,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ~ ( D @ v1_xboole_0 )
                 => ( ( ! [E: $i] :
                          ( ( ? [F: $i] :
                                ( ? [G: $i] :
                                    ( ? [H: $i] :
                                        ( ( E
                                          = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                                        & ( D @ ( H @ m1_subset_1 ) ) )
                                    & ( C @ ( G @ m1_subset_1 ) ) )
                                & ( B @ ( F @ m1_subset_1 ) ) )
                           => ( A @ ( E @ r2_hidden ) ) )
                          & ( ( A @ ( E @ r2_hidden ) )
                           => ? [F: $i] :
                                ( ? [G: $i] :
                                    ( ? [H: $i] :
                                        ( ( E
                                          = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                                        & ( D @ ( H @ m1_subset_1 ) ) )
                                    & ( C @ ( G @ m1_subset_1 ) ) )
                                & ( B @ ( F @ m1_subset_1 ) ) ) ) )
                     => ( A
                        = ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) )
                    & ( ( A
                        = ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) )
                     => ! [E: $i] :
                          ( ( ? [F: $i] :
                                ( ? [G: $i] :
                                    ( ? [H: $i] :
                                        ( ( E
                                          = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                                        & ( D @ ( H @ m1_subset_1 ) ) )
                                    & ( C @ ( G @ m1_subset_1 ) ) )
                                & ( B @ ( F @ m1_subset_1 ) ) )
                           => ( A @ ( E @ r2_hidden ) ) )
                          & ( ( A @ ( E @ r2_hidden ) )
                           => ? [F: $i] :
                                ( ? [G: $i] :
                                    ( ? [H: $i] :
                                        ( ( E
                                          = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                                        & ( D @ ( H @ m1_subset_1 ) ) )
                                    & ( C @ ( G @ m1_subset_1 ) ) )
                                & ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(70,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( ~ ( B @ ( A @ ( C @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
          & ~ ( A @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
          & ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_mcart_1) ).

thf(875,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( ~ ( B @ ( A @ ( C @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
          & ~ ( A @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
          & ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(244,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k4_pboole ) ) @ ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ r2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_mboolean) ).

thf(1701,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ k1_mboolean ) @ ( A @ k4_pboole ) ) @ ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ r2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(128,axiom,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
      = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_5) ).

thf(1124,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
      = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(519,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_pboole) ).

thf(2827,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(563,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( B @ ( B @ ( A @ r6_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r6_pboole) ).

thf(2959,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( B @ ( B @ ( A @ r6_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(903,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ k3_tarski )
      = A ),
    inference(cnf,[status(esa)],[902]) ).

thf(904,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ k3_tarski )
      = A ),
    inference(lifteq,[status(thm)],[903]) ).

thf(693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
      = ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k1_tarski ) ),
    inference(cnf,[status(esa)],[692]) ).

thf(694,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
      = ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[693]) ).

thf(328,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
      = ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_1) ).

thf(2048,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
      = ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(2859,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ k7_waybel_5 ) @ m1_pboole ) ),
    inference(cnf,[status(esa)],[2858]) ).

thf(237,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ k1_zfmisc_1 ) )
    <=> ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
        <=> ( A @ ( C @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

thf(1615,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( ( A @ ( C @ r1_tarski ) )
             => ( B @ ( C @ r2_hidden ) ) )
            & ( ( B @ ( C @ r2_hidden ) )
             => ( A @ ( C @ r1_tarski ) ) ) )
       => ( B
          = ( A @ k1_zfmisc_1 ) ) )
      & ( ( B
          = ( A @ k1_zfmisc_1 ) )
       => ! [C: $i] :
            ( ( ( A @ ( C @ r1_tarski ) )
             => ( B @ ( C @ r2_hidden ) ) )
            & ( ( B @ ( C @ r2_hidden ) )
             => ( A @ ( C @ r1_tarski ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(266,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_xboole_1) ).

thf(1784,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k5_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(3474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A != sk1 )
      | ( C != k1_xboole_0 )
      | ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ),
    inference(paramod_ordered,[status(thm)],[623,3022]) ).

thf(3475,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ~ ( C @ k1_tarski @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( sk1 @ k4_tarski ) @ r2_hidden ) ) ),
    inference(pattern_uni,[status(thm)],[3474:[bind(A,$thf( sk1 ))]]) ).

thf(4494,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( sk1 @ k4_tarski ) @ r2_hidden ) ),
    inference(simp,[status(thm)],[3475]) ).

thf(186,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ~ ( A @ ( D @ r2_hidden ) )
        <=> ( ( B @ ( D @ r2_hidden ) )
          <=> ( C @ ( D @ r2_hidden ) ) ) )
     => ( A
        = ( C @ ( B @ k5_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_0) ).

thf(1389,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( ( ( ( C @ ( D @ r2_hidden ) )
               => ( B @ ( D @ r2_hidden ) ) )
              & ( ( B @ ( D @ r2_hidden ) )
               => ( C @ ( D @ r2_hidden ) ) ) )
           => ~ ( A @ ( D @ r2_hidden ) ) )
          & ( ~ ( A @ ( D @ r2_hidden ) )
           => ( ( ( C @ ( D @ r2_hidden ) )
               => ( B @ ( D @ r2_hidden ) ) )
              & ( ( B @ ( D @ r2_hidden ) )
               => ( C @ ( D @ r2_hidden ) ) ) ) ) )
     => ( A
        = ( C @ ( B @ k5_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(259,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     => ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_xboole_1) ).

thf(1752,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     => ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(86,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
     != k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).

thf(940,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
     != k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(941,plain,
    ~ ? [A: $i,B: $i] :
        ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
        = k1_xboole_0 ),
    inference(miniscope,[status(thm)],[940]) ).

thf(942,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
     != k1_xboole_0 ),
    inference(cnf,[status(esa)],[941]) ).

thf(943,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
     != k1_xboole_0 ),
    inference(lifteq,[status(thm)],[942]) ).

thf(11498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k1_tarski @ k2_xboole_0 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,943]) ).

thf(11499,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k1_tarski @ k2_xboole_0 ) ) )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[11498]) ).

thf(11500,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[11499:[bind(A,$thf( E @ ( F @ k1_tarski @ k2_xboole_0 ) )),bind(B,$thf( F )),bind(C,$thf( E ))]]) ).

thf(11851,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ v1_xboole_0 ),
    inference(simp,[status(thm)],[11500]) ).

thf(514,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( ( A @ ( D @ m1_pboole ) )
                & ( D @ v2_relat_1 ) )
             => ( ! [E: $i] :
                    ( ( A @ ( E @ m1_pboole ) )
                   => ( ( D @ ( E @ ( A @ r1_pboole ) ) )
                    <=> ( ( C @ ( E @ ( A @ r1_pboole ) ) )
                        & ( B @ ( E @ ( A @ r1_pboole ) ) ) ) ) )
               => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( D @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_pboole) ).

thf(2806,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( ( A @ ( D @ m1_pboole ) )
                & ( D @ v2_relat_1 ) )
             => ( ! [E: $i] :
                    ( ( A @ ( E @ m1_pboole ) )
                   => ( ( ( ( C @ ( E @ ( A @ r1_pboole ) ) )
                          & ( B @ ( E @ ( A @ r1_pboole ) ) ) )
                       => ( D @ ( E @ ( A @ r1_pboole ) ) ) )
                      & ( ( D @ ( E @ ( A @ r1_pboole ) ) )
                       => ( ( C @ ( E @ ( A @ r1_pboole ) ) )
                          & ( B @ ( E @ ( A @ r1_pboole ) ) ) ) ) ) )
               => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( D @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(485,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) )
               => ( ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_pboole) ).

thf(2695,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) )
               => ( ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(204,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r5_pboole ) ) )
           => ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_pboole) ).

thf(1488,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r5_pboole ) ) )
           => ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(395,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ k5_pboole ) ) )
        = ( B @ ( C @ ( A @ k5_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_pboole) ).

thf(2326,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ k5_pboole ) ) )
        = ( B @ ( C @ ( A @ k5_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(247,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ( ( A != k1_xboole_0 )
       => ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).

thf(1707,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ( ( A != k1_xboole_0 )
       => ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(254,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) )
               => ( D @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_pboole) ).

thf(1733,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) )
               => ( D @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(1239,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel ),
    inference(cnf,[status(esa)],[1238]) ).

thf(13946,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,12823]) ).

thf(13947,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13946]) ).

thf(14039,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) )
      | ( A != sk1 ) ),
    inference(simp,[status(thm)],[13947]) ).

thf(14059,plain,
    ( ( sk1 @ ( sk1 @ k2_zfmisc_1 ) )
   != ( sk1 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[14039]) ).

thf(452,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ k1_pboole @ ( B @ ( A @ k1_pboole @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
        & ( A @ k1_pboole @ ( A @ k1_pboole @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_pboole) ).

thf(2557,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ k1_pboole @ ( B @ ( A @ k1_pboole @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
        & ( A @ k1_pboole @ ( A @ k1_pboole @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( ( A @ v2_cat_5 )
        & ~ ( A @ v1_xboole_0 ) )
     => ? [B: $i] : ( A @ ( B @ m1_cat_5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_cat_5) ).

thf(703,plain,
    ! [A: $i] :
      ( ( ( A @ v2_cat_5 )
        & ~ ( A @ v1_xboole_0 ) )
     => ? [B: $i] : ( A @ ( B @ m1_cat_5 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(704,plain,
    ! [A: $i] :
      ( ( A @ ( A @ sk11 @ m1_cat_5 ) )
      | ~ ( A @ v2_cat_5 )
      | ( A @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[703]) ).

thf(15686,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,13403]) ).

thf(15687,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15686]) ).

thf(15712,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) ) )
      | ( A != sk181 ) ),
    inference(simp,[status(thm)],[15687]) ).

thf(15733,plain,
    ! [A: $i] :
      ( ( A @ ( sk181 @ k2_xboole_0 ) )
     != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[15712]) ).

thf(176,axiom,
    ! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k1_pboole @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mboolean) ).

thf(1356,plain,
    ! [A: $i] : ( k1_xboole_0 @ k1_tarski @ ( A @ k2_pre_circ ) @ ( A @ k1_pboole @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(364,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_pboole) ).

thf(2193,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(2891,plain,
    ! [A: $i] : ( A @ ( A @ k1_pralg_3 @ m1_pboole ) ),
    inference(cnf,[status(esa)],[2890]) ).

thf(157,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_xboole_1) ).

thf(1271,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
      = ( C @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(607,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C = F )
        | ( C = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 )
        | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
         != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) )
      & ( ( B = E )
        | ( C = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 )
        | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
         != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) )
      & ( ( A = D )
        | ( C = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 )
        | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
         != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[606]) ).

thf(608,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C = k1_xboole_0 )
      | ( B = k1_xboole_0 )
      | ( A = k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
       != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
    inference(cnfConj,[status(thm)],[607]) ).

thf(611,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C = k1_xboole_0 )
      | ( B = k1_xboole_0 )
      | ( A = k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
       != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
    inference(lifteq,[status(thm)],[608]) ).

thf(432,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r2_pboole ) ) )
            & ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_pboole) ).

thf(2474,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( A @ r2_pboole ) ) )
            & ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(403,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
                  | ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_mboolean) ).

thf(2346,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
                  | ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(62,axiom,
    ! [A: $i] : ( A @ k1_pboole @ ( A @ k1_pboole @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_mboolean) ).

thf(831,plain,
    ! [A: $i] : ( A @ k1_pboole @ ( A @ k1_pboole @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(340,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
                  & ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) )
               => ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_pboole) ).

thf(2084,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
                  & ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) ) )
               => ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(528,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_pboole) ).

thf(2856,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(615,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_xboole_0 ) )
      = A ),
    inference(cnf,[status(esa)],[614]) ).

thf(616,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_xboole_0 ) )
      = A ),
    inference(lifteq,[status(thm)],[615]) ).

thf(141,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
         => ( B @ ( C @ r1_tarski ) ) )
     => ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).

thf(1175,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
         => ( B @ ( C @ r1_tarski ) ) )
     => ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(442,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
               => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_pboole) ).

thf(2510,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r2_pboole ) ) )
               => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(14164,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,12843]) ).

thf(14165,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14164]) ).

thf(14222,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != sk33 ) ),
    inference(simp,[status(thm)],[14165]) ).

thf(14243,plain,
    ! [A: $i] :
      ( ( A @ ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != sk33 ),
    inference(simp,[status(thm)],[14222]) ).

thf(282,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ ( B @ ( A @ k2_mboolean ) @ v1_pre_circ ) )
       => ( ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ( ( B @ ( C @ ( A @ r1_pboole ) ) )
               => ( A @ ( C @ v1_pre_circ ) ) ) )
          & ( A @ ( B @ v1_pre_circ ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_mssubfam) ).

thf(1853,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ ( B @ ( A @ k2_mboolean ) @ v1_pre_circ ) )
       => ( ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ( ( B @ ( C @ ( A @ r1_pboole ) ) )
               => ( A @ ( C @ v1_pre_circ ) ) ) )
          & ( A @ ( B @ v1_pre_circ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(187,axiom,
    ! [A: $i] :
      ( ( A @ v1_fraenkel )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( B @ v1_fraenkel ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_altcat_1) ).

thf(1408,plain,
    ! [A: $i] :
      ( ( A @ v1_fraenkel )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( B @ v1_fraenkel ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(159,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
          <=> ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r1_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_mboolean) ).

thf(1282,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r1_pboole ) ) )
             => ( C @ ( B @ ( A @ r2_pboole ) ) ) )
            & ( ( C @ ( B @ ( A @ r2_pboole ) ) )
             => ( C @ ( A @ k1_mboolean ) @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(433,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( D @ ( C @ ( B @ ( A @ k2_cat_5 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_cat_5) ).

thf(2478,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( D @ ( C @ ( B @ ( A @ k2_cat_5 ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(2415,plain,
    ! [A: $i] : ( A @ ( A @ sk153 @ m1_finseq_2 ) ),
    inference(cnf,[status(esa)],[2414]) ).

thf(438,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ ( B @ ( A @ k1_pboole @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
        & ( B @ ( A @ k1_pboole @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_pboole) ).

thf(2493,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ ( B @ ( A @ k1_pboole @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
        & ( B @ ( A @ k1_pboole @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(571,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ ( B @ ( A @ k21_pralg_1 ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k21_pralg_1) ).

thf(2987,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ ( B @ ( A @ k21_pralg_1 ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(470,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_pboole) ).

thf(2637,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(419,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ v1_fraenkel )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_0_closure2 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( A
              = ( C @ ( D @ k1_funct_1 ) ) )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure2) ).

thf(2422,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ v1_fraenkel )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( ? [D: $i] :
              ( ( A
                = ( C @ ( D @ k1_funct_1 ) ) )
              & ( B @ ( D @ m1_subset_1 ) ) )
         => ( C @ ( B @ a_2_0_closure2 ) @ ( A @ r2_hidden ) ) )
        & ( ( C @ ( B @ a_2_0_closure2 ) @ ( A @ r2_hidden ) )
         => ? [D: $i] :
              ( ( A
                = ( C @ ( D @ k1_funct_1 ) ) )
              & ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(226,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).

thf(1574,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).

thf(1009,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(1010,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1009]) ).

thf(1011,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1010]) ).

thf(343,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ v3_relat_1 )
      <=> ! [C: $i] :
            ( ( A @ ( C @ r2_hidden ) )
           => ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_pboole) ).

thf(2097,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( ! [C: $i] :
              ( ( A @ ( C @ r2_hidden ) )
             => ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) )
         => ( B @ v3_relat_1 ) )
        & ( ( B @ v3_relat_1 )
         => ! [C: $i] :
              ( ( A @ ( C @ r2_hidden ) )
             => ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(14719,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,13123]) ).

thf(14720,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14719]) ).

thf(14763,plain,
    ! [A: $i] :
      ( ( A
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) ) )
      | ( A != sk198 ) ),
    inference(simp,[status(thm)],[14720]) ).

thf(14788,plain,
    ( ( sk198 @ ( sk198 @ k2_zfmisc_1 ) )
   != sk198 ),
    inference(simp,[status(thm)],[14763]) ).

thf(230,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
      = ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_xboole_1) ).

thf(1589,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
      = ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(294,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( B @ ( A @ k3_xboole_0 ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).

thf(1933,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( B @ ( A @ k3_xboole_0 ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(206,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( D @ ( C @ r1_tarski ) )
              & ( D @ ( A @ r1_tarski ) ) )
           => ( D @ ( B @ r1_tarski ) ) )
        & ( B @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( B
        = ( C @ ( A @ k2_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_xboole_1) ).

thf(1492,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( D @ ( C @ r1_tarski ) )
              & ( D @ ( A @ r1_tarski ) ) )
           => ( D @ ( B @ r1_tarski ) ) )
        & ( B @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( B
        = ( C @ ( A @ k2_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(233,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_xboole_1) ).

thf(1603,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k5_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(350,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r1_pboole ) ) ) )
               => ( D @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_pboole) ).

thf(2116,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r1_pboole ) ) ) )
               => ( D @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(524,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_pralg_1 ) ) )
         => ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v1_funcop_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pralg_1) ).

thf(2839,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_pralg_1 ) ) )
         => ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v1_funcop_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(546,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( ( A @ k3_pua2mss1 )
        = ( A @ a_1_0_pua2mss1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_pua2mss1) ).

thf(2896,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( ( A @ k3_pua2mss1 )
        = ( A @ a_1_0_pua2mss1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(599,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
      | ( B @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[598]) ).

thf(534,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r7_pboole ) ) )
                  & ( C @ ( B @ ( A @ r7_pboole ) ) ) )
               => ( D @ ( B @ ( A @ r7_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_pboole) ).

thf(2871,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r7_pboole ) ) )
                  & ( C @ ( B @ ( A @ r7_pboole ) ) ) )
               => ( D @ ( B @ ( A @ r7_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(365,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( D @ ( C @ ( B @ ( A @ k16_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_domain_1) ).

thf(2197,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( D @ ( C @ ( B @ ( A @ k16_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(306,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).

thf(1969,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(18351,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
       != ( D @ ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
       != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[637,14061]) ).

thf(18352,plain,
    ! [A: $i] :
      ( ( A @ ( sk1 @ k3_xboole_0 ) @ ( sk1 @ k2_zfmisc_1 ) )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[18351:[bind(A,$thf( sk1 )),bind(B,$thf( F )),bind(C,$thf( sk1 )),bind(D,$thf( F @ ( sk1 @ k2_zfmisc_1 ) ))]]) ).

thf(18414,plain,
    ! [A: $i] :
      ( ( A @ ( sk1 @ k3_xboole_0 ) @ ( sk1 @ k2_zfmisc_1 ) )
     != sk1 ),
    inference(simp,[status(thm)],[18352]) ).

thf(360,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_pboole) ).

thf(2180,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k4_card_fil @ m1_subset_1 ) )
        & ~ ( A @ k4_card_fil @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_card_fil) ).

thf(2182,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k4_card_fil @ m1_subset_1 ) )
        & ~ ( A @ k4_card_fil @ v1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(199,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ! [E: $i] :
            ( ( A @ ( E @ m1_subset_1 ) )
           => ! [F: $i] :
                ( ( B @ ( F @ m1_subset_1 ) )
               => ( D
                 != ( F @ ( E @ k4_tarski ) ) ) ) )
        & ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
        & ( C @ ( D @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_grcat_1) ).

thf(1471,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ! [E: $i] :
            ( ( A @ ( E @ m1_subset_1 ) )
           => ! [F: $i] :
                ( ( B @ ( F @ m1_subset_1 ) )
               => ( D
                 != ( F @ ( E @ k4_tarski ) ) ) ) )
        & ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
        & ( C @ ( D @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(136,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
      = ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).

thf(1162,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_xboole_0 ) @ k2_xboole_0 ) )
      = ( C @ ( B @ k2_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(15500,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,13398]) ).

thf(15501,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15500]) ).

thf(15549,plain,
    ! [A: $i] :
      ( ( A
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( A != k4_qc_lang1 ) ),
    inference(simp,[status(thm)],[15501]) ).

thf(15575,plain,
    ( ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) )
   != k4_qc_lang1 ),
    inference(simp,[status(thm)],[15549]) ).

thf(568,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( B @ k4_card_3 @ v1_fraenkel )
        & ~ ( B @ k4_card_3 @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_pralg_1) ).

thf(2974,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( B @ k4_card_3 @ v1_fraenkel )
        & ~ ( B @ k4_card_3 @ v1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(393,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C
              = ( B @ ( A @ k2_mboolean ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ r2_hidden ) )
               => ( ( D @ ( C @ k1_funct_1 ) )
                  = ( D @ ( B @ k1_funct_1 ) @ k3_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mboolean) ).

thf(2314,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( ( D @ ( C @ k1_funct_1 ) )
                    = ( D @ ( B @ k1_funct_1 ) @ k3_tarski ) ) )
             => ( C
                = ( B @ ( A @ k2_mboolean ) ) ) )
            & ( ( C
                = ( B @ ( A @ k2_mboolean ) ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( ( D @ ( C @ k1_funct_1 ) )
                    = ( D @ ( B @ k1_funct_1 ) @ k3_tarski ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(467,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( B @ ( B @ ( A @ k3_pboole ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_pboole) ).

thf(2625,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( B @ ( B @ ( A @ k3_pboole ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(274,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ k1_funct_2 ) @ ( A @ ( C @ k1_funct_2 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_5) ).

thf(1821,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ ( C @ k1_funct_2 ) @ ( A @ ( C @ k1_funct_2 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
     => ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).

thf(594,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
     => ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(65,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = ( D @ ( C @ k2_zfmisc_1 ) ) )
     => ( ( ( B = D )
          & ( A = C ) )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).

thf(848,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = ( D @ ( C @ k2_zfmisc_1 ) ) )
     => ( ( ( B = D )
          & ( A = C ) )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(700,plain,
    ! [A: $i] :
      ( ( A @ sk10 @ ( A @ sk9 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
      | ( A @ ( A @ sk8 @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[699]) ).

thf(11160,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,583]) ).

thf(11161,plain,
    ( ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
    | ~ ( sk2 @ v1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11160:[bind(A,$thf( sk2 ))]]) ).

thf(14380,plain,
    ( ( ( sk2 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( sk1 @ ( k1_xboole_0 @ m1_pboole ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,11161]) ).

thf(14381,plain,
    ( ( ( sk2 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( sk1 @ ( k1_xboole_0 @ m1_pboole ) ) ),
    inference(simp,[status(thm)],[14380]) ).

thf(14402,plain,
    ( ( sk2 != k1_xboole_0 )
    | ( sk1 @ ( k1_xboole_0 @ m1_pboole ) ) ),
    inference(simp,[status(thm)],[14381]) ).

thf(133,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
    <=> ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).

thf(1149,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ r2_hidden ) )
       => ( B @ ( A @ k1_tarski @ r1_tarski ) ) )
      & ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
       => ( B @ ( A @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A @ ( A @ k1_tarski @ m1_card_fil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_card_fil) ).

thf(964,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A @ ( A @ k1_tarski @ m1_card_fil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(220,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ~ ( ( C @ ( B @ ( A @ r5_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_pboole) ).

thf(1556,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ~ ( ( C @ ( B @ ( A @ r5_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(446,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( B @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
               => ( B @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_pboole) ).

thf(2542,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( B @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
               => ( B @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(472,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_pboole) ).

thf(2647,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(375,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_pboole) ).

thf(2252,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(163,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).

thf(1293,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(450,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r5_pboole ) ) )
           => ( B @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_pboole) ).

thf(2553,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r5_pboole ) ) )
           => ( B @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(2926,plain,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( f1_s2_pboole @ ( B @ r2_hidden ) )
         => ( ! [C: $i] :
                ( ( ( C @ ( B @ p1_s2_pboole ) )
                  & ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
               => ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) ) )
            & ! [C: $i] :
                ( ( B @ ( A @ k1_funct_1 ) @ ( C @ r2_hidden ) )
               => ( ( C @ ( B @ p1_s2_pboole ) )
                  & ( B @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) ) ) ) ) )
      & ( f1_s2_pboole @ ( A @ m1_pboole ) ) ),
    inference(miniscope,[status(thm)],[2925]) ).

thf(2927,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( sk195 @ k1_funct_1 ) @ ( C @ r2_hidden ) )
        | ~ ( C @ ( A @ p1_s2_pboole ) )
        | ~ ( A @ ( f2_s2_pboole @ k1_funct_1 ) @ ( C @ r2_hidden ) )
        | ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
      & ( ( B @ ( A @ p1_s2_pboole ) )
        | ~ ( A @ ( sk195 @ k1_funct_1 ) @ ( B @ r2_hidden ) )
        | ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
      & ( ( A @ ( f2_s2_pboole @ k1_funct_1 ) @ ( B @ r2_hidden ) )
        | ~ ( A @ ( sk195 @ k1_funct_1 ) @ ( B @ r2_hidden ) )
        | ~ ( f1_s2_pboole @ ( A @ r2_hidden ) ) )
      & ( f1_s2_pboole @ ( sk195 @ m1_pboole ) ) ),
    inference(cnf,[status(esa)],[2926]) ).

thf(2928,plain,
    f1_s2_pboole @ ( sk195 @ m1_pboole ),
    inference(cnfConj,[status(thm)],[2927]) ).

thf(7917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
       != ( C @ ( B @ k1_funct_2 ) ) )
      | ( k1_xboole_0 @ v1_fraenkel )
      | ( A = k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[1263,1239]) ).

thf(7918,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ v1_fraenkel )
      | ( A = k1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[7917:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(8187,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( k1_xboole_0 @ v1_fraenkel ) ),
    inference(paramod_ordered,[status(thm)],[7918,3022]) ).

thf(8188,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ v1_fraenkel ) ),
    inference(simp,[status(thm)],[8187]) ).

thf(8189,plain,
    k1_xboole_0 @ v1_fraenkel,
    inference(pattern_uni,[status(thm)],[8188:[bind(A,$thf( sk1 ))]]) ).

thf(11760,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ v1_fraenkel )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,8189]) ).

thf(11761,plain,
    ! [A: $i] :
      ( ( A @ v1_fraenkel )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11760:[]]) ).

thf(396,axiom,
    ! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pboole) ).

thf(2329,plain,
    ! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( ( A @ v5_grcat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ? [B: $i] : ( A @ ( B @ m3_grcat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_grcat_1) ).

thf(912,plain,
    ! [A: $i] :
      ( ( ( A @ v5_grcat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ? [B: $i] : ( A @ ( B @ m3_grcat_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(423,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ~ ( ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ! [F: $i] :
                          ( ( A @ ( F @ m1_pboole ) )
                         => ~ ( ( F @ ( E @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                              & ( D @ ( F @ ( A @ r2_pboole ) ) )
                              & ( A @ ( F @ v1_pre_circ ) )
                              & ( C @ ( E @ ( A @ r2_pboole ) ) )
                              & ( A @ ( E @ v1_pre_circ ) ) ) ) )
                  & ( D @ ( C @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                  & ( A @ ( B @ v1_pre_circ ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_mssubfam) ).

thf(2439,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ~ ( ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ! [F: $i] :
                          ( ( A @ ( F @ m1_pboole ) )
                         => ~ ( ( F @ ( E @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                              & ( D @ ( F @ ( A @ r2_pboole ) ) )
                              & ( A @ ( F @ v1_pre_circ ) )
                              & ( C @ ( E @ ( A @ r2_pboole ) ) )
                              & ( A @ ( E @ v1_pre_circ ) ) ) ) )
                  & ( D @ ( C @ ( A @ k11_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                  & ( A @ ( B @ v1_pre_circ ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(404,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
                  | ( C @ ( B @ ( A @ r1_pboole ) ) ) )
               => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_pboole) ).

thf(2350,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r1_pboole ) ) )
                  | ( C @ ( B @ ( A @ r1_pboole ) ) ) )
               => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(90,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) )
        = ( A @ ( B @ k4_xboole_0 ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).

thf(959,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) )
        = ( A @ ( B @ k4_xboole_0 ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(335,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_pboole) ).

thf(2064,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(99,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_mboolean) ).

thf(986,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ k2_mboolean ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(510,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ( ( B @ v2_relat_1 )
           => ~ ( B @ v3_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_pboole) ).

thf(2797,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ( ( B @ v2_relat_1 )
           => ~ ( B @ v3_relat_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(102,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_mboolean) ).

thf(1000,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( B @ ( A @ k1_mboolean ) @ ( A @ k2_mboolean ) @ ( A @ r6_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(319,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_pboole) ).

thf(2022,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(1844,plain,
    ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[1843]) ).

thf(1845,plain,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[1844]) ).

thf(3138,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,1845]) ).

thf(3139,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3138]) ).

thf(3142,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[3139]) ).

thf(14549,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,12880]) ).

thf(14550,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14549]) ).

thf(14588,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) ) )
      | ( A != sk199 ) ),
    inference(simp,[status(thm)],[14550]) ).

thf(14614,plain,
    ! [A: $i] :
      ( ( A @ ( sk199 @ k2_xboole_0 ) )
     != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[14588]) ).

thf(484,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_pboole) ).

thf(2693,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(13986,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,12823]) ).

thf(13987,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[13986]) ).

thf(14030,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != sk1 ) ),
    inference(simp,[status(thm)],[13987]) ).

thf(14049,plain,
    ! [A: $i] :
      ( ( A @ ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != sk1 ),
    inference(simp,[status(thm)],[14030]) ).

thf(97,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).

thf(982,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(983,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(cnf,[status(esa)],[982]) ).

thf(339,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D
                  = ( C @ ( B @ ( A @ k2_pboole ) ) ) )
              <=> ! [E: $i] :
                    ( ( A @ ( E @ r2_hidden ) )
                   => ( ( E @ ( D @ k1_funct_1 ) )
                      = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_pboole) ).

thf(2075,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_xboole_0 ) ) ) )
                 => ( D
                    = ( C @ ( B @ ( A @ k2_pboole ) ) ) ) )
                & ( ( D
                    = ( C @ ( B @ ( A @ k2_pboole ) ) ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_xboole_0 ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(417,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( D @ ( C @ ( B @ ( A @ k15_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_domain_1) ).

thf(2418,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( D @ ( C @ ( B @ ( A @ k15_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(329,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_pboole) ).

thf(2051,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(111,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
      = ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).

thf(1044,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
      = ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(34,axiom,
    ( ( k1_xboole_0 @ k4_card_3 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_card_3) ).

thf(695,plain,
    ( ( k1_xboole_0 @ k4_card_3 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(341,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D
                  = ( C @ ( B @ ( A @ k12_pboole ) ) ) )
              <=> ! [E: $i] :
                    ( ( A @ ( E @ r2_hidden ) )
                   => ( ( E @ ( D @ k1_funct_1 ) )
                      = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k1_funct_2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d22_pboole) ).

thf(2086,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k1_funct_2 ) ) ) )
                 => ( D
                    = ( C @ ( B @ ( A @ k12_pboole ) ) ) ) )
                & ( ( D
                    = ( C @ ( B @ ( A @ k12_pboole ) ) ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k1_funct_2 ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(15997,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,13625]) ).

thf(15998,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15997]) ).

thf(16038,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != sk197 ) ),
    inference(simp,[status(thm)],[15998]) ).

thf(16062,plain,
    ! [A: $i] :
      ( ( A @ ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != sk197 ),
    inference(simp,[status(thm)],[16038]) ).

thf(189,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).

thf(1413,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(12104,plain,
    ( ( ( sk2 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( k1_xboole_0 @ v2_relat_1 )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,11025]) ).

thf(12105,plain,
    ( ( ( sk2 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[12104]) ).

thf(12120,plain,
    ( ( sk2 != k1_xboole_0 )
    | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[12105]) ).

thf(109,axiom,
    ! [A: $i,B: $i] :
      ~ ( ! [C: $i] :
            ~ ( ( C != B )
              & ( A @ ( C @ r2_hidden ) ) )
        & ( A != k1_xboole_0 )
        & ( A
         != ( B @ k1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).

thf(1034,plain,
    ! [A: $i,B: $i] :
      ~ ( ! [C: $i] :
            ~ ( ( C != B )
              & ( A @ ( C @ r2_hidden ) ) )
        & ( A != k1_xboole_0 )
        & ( A
         != ( B @ k1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(662,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(miniscope,[status(thm)],[661]) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ ( B @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[662]) ).

thf(242,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ( ( B @ a_1_0_card_fil @ ( A @ r2_hidden ) )
      <=> ? [C: $i] :
            ( ( B @ ( C @ m1_card_fil ) )
            & ( A = C )
            & ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_card_fil) ).

thf(1684,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ( ( ? [C: $i] :
              ( ( B @ ( C @ m1_card_fil ) )
              & ( A = C )
              & ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
         => ( B @ a_1_0_card_fil @ ( A @ r2_hidden ) ) )
        & ( ( B @ a_1_0_card_fil @ ( A @ r2_hidden ) )
         => ? [C: $i] :
              ( ( B @ ( C @ m1_card_fil ) )
              & ( A = C )
              & ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(369,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( A @ k1_pboole @ ( C @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_pboole) ).

thf(2234,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( A @ k1_pboole @ ( C @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(173,axiom,
    ! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k2_pre_circ ) @ ( B @ ( A @ k2_pre_circ ) @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_mboolean) ).

thf(1340,plain,
    ! [A: $i,B: $i] : ( B @ k1_zfmisc_1 @ ( A @ k2_pre_circ ) @ ( B @ ( A @ k2_pre_circ ) @ ( A @ k1_mboolean ) @ ( A @ r6_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(967,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k3_tarski )
      = A ),
    inference(cnf,[status(esa)],[966]) ).

thf(968,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k3_tarski )
      = A ),
    inference(lifteq,[status(thm)],[967]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
        = ( A @ k1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).

thf(673,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
        = ( A @ k1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(674,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
        = ( A @ k1_tarski ) )
      | ~ ( B @ ( A @ r2_hidden ) ) ),
    inference(cnf,[status(esa)],[673]) ).

thf(675,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ r2_hidden ) )
      | ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
        = ( A @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[674]) ).

thf(516,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( A != B )
        & ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(2816,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( A != B )
        & ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(15945,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,13625]) ).

thf(15946,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15945]) ).

thf(16030,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) ) )
      | ( A != sk197 ) ),
    inference(simp,[status(thm)],[15946]) ).

thf(16052,plain,
    ( ( sk197 @ ( sk197 @ k2_zfmisc_1 ) )
   != ( sk197 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[16030]) ).

thf(464,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ ( D @ ( C @ ( B @ ( A @ k1_cat_5 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_cat_5) ).

thf(2614,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ ( D @ ( C @ ( B @ ( A @ k1_cat_5 ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(146,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).

thf(1208,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(12272,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,11851]) ).

thf(12273,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k1_tarski @ k2_xboole_0 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12272]) ).

thf(12288,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k1_tarski @ k2_xboole_0 ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[12273]) ).

thf(87,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( C @ ( B @ r1_tarski ) )
        & ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
          | ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
        & ( A != k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).

thf(944,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( C @ ( B @ r1_tarski ) )
        & ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
          | ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
        & ( A != k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(198,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
                  | ( C @ ( B @ ( A @ r4_pboole ) ) ) )
               => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_pboole) ).

thf(1467,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
                  | ( C @ ( B @ ( A @ r4_pboole ) ) ) )
               => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(2994,plain,
    sk199 @ v5_grcat_1,
    inference(cnfConj,[status(thm)],[2992]) ).

thf(506,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( B @ ( D @ ( A @ k2_pboole ) ) @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
                & ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_pboole) ).

thf(2784,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( B @ ( D @ ( A @ k2_pboole ) ) @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
                & ( D @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(679,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(cnf,[status(esa)],[678]) ).

thf(680,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(lifteq,[status(thm)],[679]) ).

thf(1508,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
      = A ),
    inference(cnf,[status(esa)],[1507]) ).

thf(1509,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k5_xboole_0 ) )
      = A ),
    inference(lifteq,[status(thm)],[1508]) ).

thf(14141,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,12843]) ).

thf(14142,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14141]) ).

thf(14213,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) ) )
      | ( A != sk33 ) ),
    inference(simp,[status(thm)],[14142]) ).

thf(14230,plain,
    ! [A: $i] :
      ( ( sk33 @ ( A @ k2_xboole_0 ) )
     != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[14213]) ).

thf(41,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ( ( ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ( ( B @ ( C @ ( A @ r1_pboole ) ) )
               => ( A @ ( C @ v1_pre_circ ) ) ) )
          & ( A @ ( B @ v1_pre_circ ) ) )
       => ( A @ ( B @ ( A @ k2_mboolean ) @ v1_pre_circ ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_mssubfam) ).

thf(749,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ( ( ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ( ( B @ ( C @ ( A @ r1_pboole ) ) )
               => ( A @ ( C @ v1_pre_circ ) ) ) )
          & ( A @ ( B @ v1_pre_circ ) ) )
       => ( A @ ( B @ ( A @ k2_mboolean ) @ v1_pre_circ ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(468,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ! [C: $i] :
            ( ( A @ ( C @ r2_hidden ) )
           => ( ( C @ ( B @ k1_funct_1 ) )
              = k1_xboole_0 ) )
       => ( B
          = ( A @ k1_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_pboole) ).

thf(2629,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ! [C: $i] :
            ( ( A @ ( C @ r2_hidden ) )
           => ( ( C @ ( B @ k1_funct_1 ) )
              = k1_xboole_0 ) )
       => ( B
          = ( A @ k1_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(481,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( A @ k1_pboole @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_pboole) ).

thf(2684,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( A @ k1_pboole @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(398,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_pboole) ).

thf(2333,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(377,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_pboole) ).

thf(2256,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( D @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(42,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).

thf(754,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(16810,plain,
    ( ( ( sk2 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ ( sk3 @ ( k1_xboole_0 @ ( sk1 @ r6_pboole ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,11372]) ).

thf(16811,plain,
    ( ( ( sk2 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ ( sk3 @ ( k1_xboole_0 @ ( sk1 @ r6_pboole ) ) ) ),
    inference(simp,[status(thm)],[16810]) ).

thf(16838,plain,
    ( ( sk2 != k1_xboole_0 )
    | ~ ( sk3 @ ( k1_xboole_0 @ ( sk1 @ r6_pboole ) ) ) ),
    inference(simp,[status(thm)],[16811]) ).

thf(547,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m1_pralg_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pralg_1) ).

thf(2899,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m1_pralg_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(10444,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1873,1054]) ).

thf(10445,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ k1_tarski @ ( A @ r2_hidden ) )
     != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[10444]) ).

thf(10458,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski )
       != ( C @ k1_tarski @ ( B @ k4_xboole_0 ) ) )
      | ( A != C ) ),
    inference(simp,[status(thm)],[10445]) ).

thf(10471,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
     != ( B @ k1_tarski ) ),
    inference(simp,[status(thm)],[10458]) ).

thf(20131,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
       != ( D @ ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
       != sk199 ) ),
    inference(paramod_ordered,[status(thm)],[637,14613]) ).

thf(20132,plain,
    ! [A: $i] :
      ( ( A @ ( sk199 @ k3_xboole_0 ) @ ( sk199 @ k2_zfmisc_1 ) )
     != sk199 ),
    inference(pattern_uni,[status(thm)],[20131:[bind(A,$thf( sk199 )),bind(B,$thf( F )),bind(C,$thf( sk199 )),bind(D,$thf( F @ ( sk199 @ k2_zfmisc_1 ) ))]]) ).

thf(20196,plain,
    ! [A: $i] :
      ( ( A @ ( sk199 @ k3_xboole_0 ) @ ( sk199 @ k2_zfmisc_1 ) )
     != sk199 ),
    inference(simp,[status(thm)],[20132]) ).

thf(217,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( B @ ( A @ k2_xboole_0 ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).

thf(1547,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( B @ ( A @ k2_xboole_0 ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(263,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) )
    <=> ( ( F @ ( C @ r2_hidden ) )
        & ( E @ ( B @ r2_hidden ) )
        & ( D @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_mcart_1) ).

thf(1770,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( ( F @ ( C @ r2_hidden ) )
          & ( E @ ( B @ r2_hidden ) )
          & ( D @ ( A @ r2_hidden ) ) )
       => ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) ) )
      & ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) )
       => ( ( F @ ( C @ r2_hidden ) )
          & ( E @ ( B @ r2_hidden ) )
          & ( D @ ( A @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(14686,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,13123]) ).

thf(14687,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14686]) ).

thf(14753,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) ) )
      | ( A != sk198 ) ),
    inference(simp,[status(thm)],[14687]) ).

thf(14775,plain,
    ! [A: $i] :
      ( ( sk198 @ ( A @ k2_xboole_0 ) )
     != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[14753]) ).

thf(333,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_pboole) ).

thf(2060,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(18368,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
       != ( D @ ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
      | ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
       != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[635,14061]) ).

thf(18369,plain,
    ! [A: $i] :
      ( ( sk1 @ ( A @ ( sk1 @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[18368:[bind(A,$thf( sk1 )),bind(B,$thf( E )),bind(C,$thf( sk1 )),bind(D,$thf( sk1 @ ( E @ k2_zfmisc_1 ) ))]]) ).

thf(18390,plain,
    ! [A: $i] :
      ( ( sk1 @ ( A @ ( sk1 @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
     != sk1 ),
    inference(simp,[status(thm)],[18369]) ).

thf(733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B = C )
        | ~ ( B @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
        | ~ ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
        | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
      & ( ( B = C )
        | ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
        | ~ ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
        | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
      & ( ( B = C )
        | ~ ( B @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
        | ( B @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
        | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
      & ( ( B = C )
        | ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
        | ( B @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
        | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
      & ( ( B = C )
        | ( A @ ( A @ ( B @ ( C @ sk15 ) ) @ m1_subset_1 ) )
        | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[732]) ).

thf(734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
      | ( B @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
      | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[733]) ).

thf(739,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
      | ( B @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
      | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
      | ( B = C ) ),
    inference(lifteq,[status(thm)],[734]) ).

thf(181,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k4_tarski ) )
        = ( D @ ( C @ k4_tarski ) ) )
     => ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).

thf(1368,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k4_tarski ) )
        = ( D @ ( C @ k4_tarski ) ) )
     => ( ( B = D )
        & ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(265,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).

thf(1780,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(490,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
              & ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_pboole) ).

thf(2720,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( ( B @ ( B @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
              & ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(122,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
    <=> ( ( A
          = ( B @ k1_tarski ) )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).

thf(1098,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( B @ k1_tarski ) )
          | ( A = k1_xboole_0 ) )
       => ( B @ k1_tarski @ ( A @ r1_tarski ) ) )
      & ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
       => ( ( A
            = ( B @ k1_tarski ) )
          | ( A = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(521,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ ( A @ r3_zfrefle1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_zfrefle1) ).

thf(2831,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ ( A @ r3_zfrefle1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(690,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
      | ~ ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk7 ) @ ( A @ r2_pboole ) ) )
      | ~ ( A @ ( B @ m1_pboole ) )
      | ~ ( A @ ( B @ v1_pre_circ ) )
      | ~ ( B @ v2_relat_1 ) ),
    inference(cnfConj,[status(thm)],[685]) ).

thf(212,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( A @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
        & ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
     => ( C @ ( B @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_xboole_1) ).

thf(1516,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( A @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
        & ( C @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) )
     => ( C @ ( B @ ( A @ k5_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(531,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ r6_pboole ) ) )
       => ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r6_pboole) ).

thf(2863,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( C @ ( B @ ( A @ r6_pboole ) ) )
       => ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(303,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
               => ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_pboole) ).

thf(1961,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
               => ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(652,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    inference(cnf,[status(esa)],[651]) ).

thf(9258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k3_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[652,645]) ).

thf(9259,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k3_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[9258]) ).

thf(9260,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( k1_xboole_0 @ k3_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[9259:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).

thf(9293,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( k1_xboole_0 @ k3_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[9260]) ).

thf(13644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( k1_xboole_0 @ k3_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) )
      | ~ $true
      | ( C = k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[9293,683]) ).

thf(13645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( k1_xboole_0 @ k3_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) )
      | ( C = k1_xboole_0 ) ),
    inference(simp,[status(thm)],[13644]) ).

thf(13646,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k3_xboole_0 ) )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[13645:[bind(A,$thf( K @ ( k1_xboole_0 @ k3_xboole_0 ) @ ( K @ ( k1_xboole_0 @ k3_xboole_0 ) @ k2_zfmisc_1 ) )),bind(B,$thf( K )),bind(C,$thf( K @ ( k1_xboole_0 @ k3_xboole_0 ) ))]]) ).

thf(13813,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k3_xboole_0 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[13646]) ).

thf(410,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r1_pboole ) ) )
           => ( C @ ( A @ ( B @ m2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_mssubfam) ).

thf(2386,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r1_pboole ) ) )
           => ( C @ ( A @ ( B @ m2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(14727,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,13123]) ).

thf(14728,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14727]) ).

thf(14755,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) ) )
      | ( A != sk198 ) ),
    inference(simp,[status(thm)],[14728]) ).

thf(14778,plain,
    ! [A: $i] :
      ( ( A @ ( sk198 @ k2_xboole_0 ) )
     != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[14755]) ).

thf(715,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ k2_xboole_0 ) ) )
      | ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( C @ ( B @ ( A @ sk12 ) ) ) ),
    inference(cnfConj,[status(thm)],[707]) ).

thf(716,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( C @ ( B @ ( A @ sk12 ) ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[715]) ).

thf(717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ r2_hidden ) )
      | ( C @ ( B @ ( A @ sk12 ) ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(simp,[status(thm)],[716]) ).

thf(149,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_xboole_1) ).

thf(1235,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k3_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(400,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_pboole) ).

thf(2337,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(291,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k4_xboole_0 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ( ~ ( B @ ( D @ r2_hidden ) )
            & ( A @ ( D @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

thf(1901,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( ~ ( B @ ( D @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
            & ( ( C @ ( D @ r2_hidden ) )
             => ( ~ ( B @ ( D @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) ) ) )
       => ( C
          = ( B @ ( A @ k4_xboole_0 ) ) ) )
      & ( ( C
          = ( B @ ( A @ k4_xboole_0 ) ) )
       => ! [D: $i] :
            ( ( ( ~ ( B @ ( D @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
            & ( ( C @ ( D @ r2_hidden ) )
             => ( ~ ( B @ ( D @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(148,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( A @ ( E @ r2_hidden ) )
        <=> ? [F: $i,G: $i,H: $i] :
              ( ( E
                = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
              & ( D @ ( H @ r2_hidden ) )
              & ( C @ ( G @ r2_hidden ) )
              & ( B @ ( F @ r2_hidden ) ) ) )
     => ( A
        = ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_mcart_1) ).

thf(1218,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( ? [F: $i,G: $i,H: $i] :
                ( ( E
                  = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                & ( D @ ( H @ r2_hidden ) )
                & ( C @ ( G @ r2_hidden ) )
                & ( B @ ( F @ r2_hidden ) ) )
           => ( A @ ( E @ r2_hidden ) ) )
          & ( ( A @ ( E @ r2_hidden ) )
           => ? [F: $i,G: $i,H: $i] :
                ( ( E
                  = ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
                & ( D @ ( H @ r2_hidden ) )
                & ( C @ ( G @ r2_hidden ) )
                & ( B @ ( F @ r2_hidden ) ) ) ) )
     => ( A
        = ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(405,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( E @ ( C @ k1_funct_1 ) @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
        & ( A @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_yellow_7 ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_7) ).

thf(2354,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( E @ ( C @ k1_funct_1 ) @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
        & ( A @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_yellow_7 ) ) ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(268,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( C @ ( A @ k1_funct_2 ) )
          = k1_xboole_0 )
        & ( ( C @ ( B @ k1_funct_2 ) )
         != k1_xboole_0 )
        & ( ( B @ ( A @ k1_funct_2 ) )
         != k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_altcat_1) ).

thf(1790,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( C @ ( A @ k1_funct_2 ) )
          = k1_xboole_0 )
        & ( ( C @ ( B @ k1_funct_2 ) )
         != k1_xboole_0 )
        & ( ( B @ ( A @ k1_funct_2 ) )
         != k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(311,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pboole) ).

thf(1987,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( D @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(250,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
    <=> ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
         => ( B @ ( C @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

thf(1716,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( A @ ( C @ r2_hidden ) )
           => ( B @ ( C @ r2_hidden ) ) )
       => ( B @ ( A @ r1_tarski ) ) )
      & ( ( B @ ( A @ r1_tarski ) )
       => ! [C: $i] :
            ( ( A @ ( C @ r2_hidden ) )
           => ( B @ ( C @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(482,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k11_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k12_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_mboolean) ).

thf(2688,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k11_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k12_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(15050,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,13162]) ).

thf(15051,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15050]) ).

thf(15101,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != k3_qc_lang1 ) ),
    inference(simp,[status(thm)],[15051]) ).

thf(15132,plain,
    ! [A: $i] :
      ( ( A @ ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != k3_qc_lang1 ),
    inference(simp,[status(thm)],[15101]) ).

thf(384,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m1_pboole ) )
         => ( ! [D: $i,E: $i,F: $i] :
                ( ( ( A @ ( F @ r2_hidden ) )
                  & ( A @ ( E @ r2_hidden ) )
                  & ( A @ ( D @ r2_hidden ) ) )
               => ( ( F @ ( E @ ( D @ ( B @ k1_multop_1 ) ) ) )
                  = ( F @ ( E @ ( D @ ( C @ k1_multop_1 ) ) ) ) ) )
           => ( B @ ( C @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_altcat_1) ).

thf(2276,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m1_pboole ) )
         => ( ! [D: $i,E: $i,F: $i] :
                ( ( ( A @ ( F @ r2_hidden ) )
                  & ( A @ ( E @ r2_hidden ) )
                  & ( A @ ( D @ r2_hidden ) ) )
               => ( ( F @ ( E @ ( D @ ( B @ k1_multop_1 ) ) ) )
                  = ( F @ ( E @ ( D @ ( C @ k1_multop_1 ) ) ) ) ) )
           => ( B @ ( C @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(309,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_pboole) ).

thf(1980,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(487,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
          <=> ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_pboole) ).

thf(2701,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
             => ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) )
            & ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
             => ( B @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(436,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ ( D @ ( C @ ( B @ ( A @ k14_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_domain_1) ).

thf(2486,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ ( D @ ( C @ ( B @ ( A @ k14_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(88,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
               => ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_pboole) ).

thf(951,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) )
               => ( D @ ( B @ ( A @ k4_pboole ) ) @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(326,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k2_pboole ) ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pboole) ).

thf(2044,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k2_pboole ) ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(15502,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,13398]) ).

thf(15503,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15502]) ).

thf(15534,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != k4_qc_lang1 ) ),
    inference(simp,[status(thm)],[15503]) ).

thf(15557,plain,
    ! [A: $i] :
      ( ( A @ ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != k4_qc_lang1 ),
    inference(simp,[status(thm)],[15534]) ).

thf(153,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).

thf(1257,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(215,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
        = A )
    <=> ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).

thf(1536,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( A @ ( B @ r2_hidden ) )
       => ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
          = A ) )
      & ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
          = A )
       => ~ ( A @ ( B @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(270,axiom,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
      & ( A @ k1_subset_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).

thf(1802,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
      & ( A @ k1_subset_1 @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(610,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( C = k1_xboole_0 )
      | ( B = k1_xboole_0 )
      | ( A = k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
       != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
    inference(cnfConj,[status(thm)],[607]) ).

thf(613,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( C = k1_xboole_0 )
      | ( B = k1_xboole_0 )
      | ( A = k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
       != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
    inference(lifteq,[status(thm)],[610]) ).

thf(15680,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,13403]) ).

thf(15681,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15680]) ).

thf(15715,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != sk181 ) ),
    inference(simp,[status(thm)],[15681]) ).

thf(15736,plain,
    ! [A: $i] :
      ( ( A @ ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != sk181 ),
    inference(simp,[status(thm)],[15715]) ).

thf(557,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ r3_pboole ) ) )
      <=> ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_pboole) ).

thf(2939,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( ( C @ ( B @ ( A @ r1_pboole ) ) )
         => ( C @ ( B @ ( A @ r3_pboole ) ) ) )
        & ( ( C @ ( B @ ( A @ r3_pboole ) ) )
         => ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(609,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( C = k1_xboole_0 )
      | ( B = k1_xboole_0 )
      | ( A = k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
       != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
    inference(cnfConj,[status(thm)],[607]) ).

thf(612,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( C = k1_xboole_0 )
      | ( B = k1_xboole_0 )
      | ( A = k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
       != ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
    inference(lifteq,[status(thm)],[609]) ).

thf(151,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r1_pboole ) ) )
          <=> ? [D: $i] :
                ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                & ( D @ ( B @ ( A @ r1_pboole ) ) )
                & ( A @ ( D @ m1_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_mboolean) ).

thf(1240,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ? [D: $i] :
                  ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                  & ( D @ ( B @ ( A @ r1_pboole ) ) )
                  & ( A @ ( D @ m1_pboole ) ) )
             => ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r1_pboole ) ) ) )
            & ( ( C @ ( A @ k2_mboolean ) @ ( B @ ( A @ r1_pboole ) ) )
             => ? [D: $i] :
                  ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                  & ( D @ ( B @ ( A @ r1_pboole ) ) )
                  & ( A @ ( D @ m1_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(331,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_pboole) ).

thf(2056,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r5_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(525,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_pboole) ).

thf(2843,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( C @ ( B @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

thf(1485,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(208,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).

thf(1504,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ~ ( B @ ( D @ r2_hidden ) )
      | ( C
       != ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(cnfConj,[status(thm)],[707]) ).

thf(726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ~ ( B @ ( D @ r2_hidden ) )
      | ( C
       != ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[713]) ).

thf(727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) )
      | ~ ( B @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[726]) ).

thf(530,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ ( A @ r2_zfrefle1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_zfrefle1) ).

thf(2860,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ ( A @ r2_zfrefle1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(15010,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,13162]) ).

thf(15011,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15010]) ).

thf(15108,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( A != k3_qc_lang1 ) ),
    inference(simp,[status(thm)],[15011]) ).

thf(15116,plain,
    ( ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) )
   != ( k3_qc_lang1 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[15108]) ).

thf(15985,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,13625]) ).

thf(15986,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15985]) ).

thf(16028,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != sk197 ) ),
    inference(simp,[status(thm)],[15986]) ).

thf(16049,plain,
    ! [A: $i] :
      ( ( A @ ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != sk197 ),
    inference(simp,[status(thm)],[16028]) ).

thf(321,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
           => ( ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) )
              & ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_pboole) ).

thf(2030,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
           => ( ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) )
              & ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(595,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) )
      | ~ ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ),
    inference(cnf,[status(esa)],[594]) ).

thf(544,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v2_relat_1 ) )
         => ( ( C @ ( A @ ( B @ m2_pboole ) ) )
           => ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_mssubfam) ).

thf(2892,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( ( A @ ( C @ m1_pboole ) )
            & ( C @ v2_relat_1 ) )
         => ( ( C @ ( A @ ( B @ m2_pboole ) ) )
           => ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(1832,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C != k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1828]) ).

thf(1838,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C != k1_xboole_0 )
      | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1832]) ).

thf(1839,plain,
    ! [B: $i,A: $i] :
      ( ( k1_xboole_0 @ ( B @ ( A @ k3_zfmisc_1 ) ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[1838]) ).

thf(194,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ ( E @ r1_tarski ) )
        & ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( F @ ( D @ ( B @ k3_zfmisc_1 ) ) @ ( E @ ( C @ ( A @ k3_zfmisc_1 ) ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_mcart_1) ).

thf(1459,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ ( E @ r1_tarski ) )
        & ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( F @ ( D @ ( B @ k3_zfmisc_1 ) ) @ ( E @ ( C @ ( A @ k3_zfmisc_1 ) ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(541,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_pboole) ).

thf(2885,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m2_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(44,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).

thf(759,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(147,axiom,
    ! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).

thf(1216,plain,
    ! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(1125,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
      = ( k1_xboole_0 @ k1_tarski ) ),
    inference(cnf,[status(esa)],[1124]) ).

thf(1126,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
      = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[1125]) ).

thf(575,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_pboole) ).

thf(2997,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(348,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
          <=> ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_pboole) ).

thf(2110,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
             => ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) )
            & ( ( A @ k1_pboole @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) )
             => ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(502,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) )
               => ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pboole) ).

thf(2775,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r1_pboole ) ) )
               => ( C @ ( B @ ( A @ r1_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(14709,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,13123]) ).

thf(14710,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ ( sk198 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14709]) ).

thf(14765,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk198 @ ( sk198 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != sk198 ) ),
    inference(simp,[status(thm)],[14710]) ).

thf(14791,plain,
    ! [A: $i] :
      ( ( A @ ( sk198 @ ( sk198 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != sk198 ),
    inference(simp,[status(thm)],[14765]) ).

thf(532,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ ( B @ v2_pboole ) )
      <=> ( B @ v2_relat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_v2_pboole) ).

thf(2865,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( ( B @ v2_relat_1 )
         => ( A @ ( B @ v2_pboole ) ) )
        & ( ( A @ ( B @ v2_pboole ) )
         => ( B @ v2_relat_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(536,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k12_pboole ) ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_pboole) ).

thf(2875,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k12_pboole ) ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(422,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ v3_relat_1 )
      <=> ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_pboole) ).

thf(2435,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) )
         => ( B @ v3_relat_1 ) )
        & ( ( B @ v3_relat_1 )
         => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(498,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_pboole) ).

thf(2760,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(391,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( B @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
               => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_pboole) ).

thf(2310,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( B @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
               => ( D @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(688,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
      | ( A @ ( A @ ( B @ sk6 ) @ m1_pboole ) )
      | ~ ( A @ ( B @ m1_pboole ) )
      | ~ ( A @ ( B @ v1_pre_circ ) )
      | ~ ( B @ v2_relat_1 ) ),
    inference(cnfConj,[status(thm)],[685]) ).

thf(367,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( C @ ( B @ ( A @ r7_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_pboole) ).

thf(2226,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( C @ ( B @ ( A @ r7_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(471,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( ( C @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
              & ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_pboole) ).

thf(2643,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
           => ( ( C @ ( B @ ( C @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
              & ( C @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(459,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( B @ ( A @ ( C @ m1_pralg_1 ) ) )
        & ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k14_pralg_1 ) ) ) )
        = ( D @ ( C @ k1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k14_pralg_1) ).

thf(2591,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( B @ ( A @ ( C @ m1_pralg_1 ) ) )
        & ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k14_pralg_1 ) ) ) )
        = ( D @ ( C @ k1_funct_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(170,axiom,
    ! [A: $i] :
      ~ ( ! [B: $i] :
            ~ ( ! [C: $i,D: $i,E: $i] :
                  ~ ( ( B
                      = ( E @ ( D @ ( C @ k3_mcart_1 ) ) ) )
                    & ( ( A @ ( D @ r2_hidden ) )
                      | ( A @ ( C @ r2_hidden ) ) ) )
              & ( A @ ( B @ r2_hidden ) ) )
        & ( A != k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_mcart_1) ).

thf(1326,plain,
    ! [A: $i] :
      ~ ( ! [B: $i] :
            ~ ( ! [C: $i,D: $i,E: $i] :
                  ~ ( ( B
                      = ( E @ ( D @ ( C @ k3_mcart_1 ) ) ) )
                    & ( ( A @ ( D @ r2_hidden ) )
                      | ( A @ ( C @ r2_hidden ) ) ) )
              & ( A @ ( B @ r2_hidden ) ) )
        & ( A != k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(460,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ r2_hidden ) )
               => ( ( D @ ( B @ k1_funct_1 ) )
                  = ( D @ ( C @ k1_funct_1 ) ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_pboole) ).

thf(2594,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ r2_hidden ) )
               => ( ( D @ ( B @ k1_funct_1 ) )
                  = ( D @ ( C @ k1_funct_1 ) ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(358,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_1_closure3 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( ( D @ ( C @ k1_funct_1 ) )
             != k1_xboole_0 )
            & ( A = D )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_closure3) ).

thf(2167,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( ? [D: $i] :
              ( ( ( D @ ( C @ k1_funct_1 ) )
               != k1_xboole_0 )
              & ( A = D )
              & ( B @ ( D @ m1_subset_1 ) ) )
         => ( C @ ( B @ a_2_1_closure3 ) @ ( A @ r2_hidden ) ) )
        & ( ( C @ ( B @ a_2_1_closure3 ) @ ( A @ r2_hidden ) )
         => ? [D: $i] :
              ( ( ( D @ ( C @ k1_funct_1 ) )
               != k1_xboole_0 )
              & ( A = D )
              & ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(385,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k2_pboole ) ) @ ( C @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_pboole) ).

thf(2283,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( B @ ( C @ ( A @ k2_pboole ) ) @ ( C @ ( A @ k5_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(387,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
             => ! [D: $i] :
                  ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
                 => ( ! [E: $i] :
                        ( ( A @ ( E @ m1_subset_1 ) )
                       => ! [F: $i] :
                            ( ( B @ ( F @ m1_subset_1 ) )
                           => ( ( F @ ( E @ ( C @ k1_binop_1 ) ) )
                              = ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ) )
                   => ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_altcat_1) ).

thf(2290,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
             => ! [D: $i] :
                  ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
                 => ( ! [E: $i] :
                        ( ( A @ ( E @ m1_subset_1 ) )
                       => ! [F: $i] :
                            ( ( B @ ( F @ m1_subset_1 ) )
                           => ( ( F @ ( E @ ( C @ k1_binop_1 ) ) )
                              = ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ) )
                   => ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(3070,plain,
    ( ( ( sk199 @ v1_xboole_0 )
     != ( sk190 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2870,2993]) ).

thf(3071,plain,
    ( ( sk199 @ v1_xboole_0 )
   != ( sk190 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[3070]) ).

thf(3073,plain,
    sk199 != sk190,
    inference(simp,[status(thm)],[3071]) ).

thf(4095,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A != sk199 )
      | ( C != sk190 )
      | ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ),
    inference(paramod_ordered,[status(thm)],[623,3073]) ).

thf(4096,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != sk190 )
      | ~ ( C @ k1_tarski @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( sk199 @ k4_tarski ) @ r2_hidden ) ) ),
    inference(pattern_uni,[status(thm)],[4095:[bind(A,$thf( sk199 ))]]) ).

thf(4361,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( sk190 @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( sk199 @ k4_tarski ) @ r2_hidden ) ),
    inference(simp,[status(thm)],[4096]) ).

thf(12662,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( sk199 @ k4_tarski ) @ r2_hidden ) ),
    inference(rewrite,[status(thm)],[4361,11610]) ).

thf(567,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A
        = ( A @ a_1_0_domain_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).

thf(2971,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A
        = ( A @ a_1_0_domain_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(500,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                      & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                   => ( E @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_pboole) ).

thf(2764,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                      & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                   => ( E @ ( C @ ( A @ k3_pboole ) ) @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(416,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                      & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                   => ( E @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pboole) ).

thf(2416,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( E @ ( D @ ( A @ r2_pboole ) ) )
                      & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                   => ( E @ ( C @ ( A @ k2_pboole ) ) @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(16241,plain,
    ( ( ( sk124 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ ( k1_xboole_0 @ v2_setfam_1 )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1599,11555]) ).

thf(16242,plain,
    ( ( ( sk124 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
    inference(simp,[status(thm)],[16241]) ).

thf(16257,plain,
    ( ( sk124 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v2_setfam_1 ) ),
    inference(simp,[status(thm)],[16242]) ).

thf(12983,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( k1_xboole_0 @ v2_relat_1 )
      | ~ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[683,587]) ).

thf(12984,plain,
    ( ( k1_xboole_0 @ v2_relat_1 )
    | ~ ( sk2 @ ( sk2 @ k2_zfmisc_1 ) @ ( sk2 @ r1_tarski ) ) ),
    inference(pattern_uni,[status(thm)],[12983:[bind(A,$thf( sk2 ))]]) ).

thf(25151,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk2 @ ( sk2 @ k2_zfmisc_1 ) @ ( sk2 @ r1_tarski ) ) )
      | ( k1_xboole_0 @ v2_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,12984]) ).

thf(25152,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk2 @ ( sk2 @ k2_zfmisc_1 ) @ ( sk2 @ r1_tarski ) ) )
      | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[25151]) ).

thf(25197,plain,
    ! [A: $i] :
      ( ( A
       != ( sk2 @ ( sk2 @ k2_zfmisc_1 ) ) )
      | ( A != sk2 )
      | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[25152]) ).

thf(25227,plain,
    ( ( ( sk2 @ ( sk2 @ k2_zfmisc_1 ) )
     != sk2 )
    | ( k1_xboole_0 @ v2_relat_1 ) ),
    inference(simp,[status(thm)],[25197]) ).

thf(462,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_pboole) ).

thf(2608,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( B @ ( C @ ( A @ k2_pboole ) ) @ ( B @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) )
            & ( C @ ( B @ ( A @ k2_pboole ) ) @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(420,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k1_mboolean ) @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_mboolean) ).

thf(2431,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k1_mboolean ) @ ( B @ ( C @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( A @ k1_mboolean ) @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(3476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C != sk1 )
      | ( A != k1_xboole_0 )
      | ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ),
    inference(paramod_ordered,[status(thm)],[623,3022]) ).

thf(3477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ~ ( C @ k1_tarski @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ),
    inference(pattern_uni,[status(thm)],[3476:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).

thf(4495,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( sk1 @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ ( k1_xboole_0 @ k4_tarski ) @ r2_hidden ) ),
    inference(simp,[status(thm)],[3477]) ).

thf(354,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( C @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_pboole) ).

thf(2130,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
               => ( C @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( C @ ( D @ ( A @ k3_pboole ) ) @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ r2_hidden ) )
      | ( A @ ( D @ r2_hidden ) )
      | ~ ( C @ ( D @ r2_hidden ) )
      | ( C
       != ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(cnfConj,[status(thm)],[707]) ).

thf(730,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ r2_hidden ) )
      | ( A @ ( D @ r2_hidden ) )
      | ~ ( C @ ( D @ r2_hidden ) )
      | ( C
       != ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[708]) ).

thf(731,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( A @ ( C @ r2_hidden ) )
      | ~ ( B @ ( A @ k2_xboole_0 ) @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[730]) ).

thf(15467,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,13398]) ).

thf(15468,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15467]) ).

thf(15537,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( A != k4_qc_lang1 ) ),
    inference(simp,[status(thm)],[15468]) ).

thf(15561,plain,
    ! [A: $i] :
      ( ( k4_qc_lang1 @ ( A @ k2_xboole_0 ) )
     != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[15537]) ).

thf(221,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_xboole_1) ).

thf(1558,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(380,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( B @ ( D @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_pboole) ).

thf(2262,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( B @ ( D @ ( A @ k2_pboole ) ) @ ( D @ ( C @ ( A @ k2_pboole ) ) @ ( C @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k3_pboole ) ) @ ( A @ k3_pboole ) ) @ ( B @ ( D @ ( A @ k3_pboole ) ) @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ k2_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(78,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( E @ ( C @ k1_funct_1 ) @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
        & ( A @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_yellow_7 ) ) ) ) ) )
        = ( F @ ( E @ ( D @ k5_funct_6 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_yellow_7) ).

thf(914,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( E @ ( C @ k1_funct_1 ) @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
        & ( A @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_yellow_7 ) ) ) ) ) )
        = ( F @ ( E @ ( D @ k5_funct_6 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(551,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( B @ ( B @ ( A @ r7_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r7_pboole) ).

thf(2912,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( B @ ( B @ ( A @ r7_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(2330,plain,
    ! [A: $i] : ( A @ ( A @ k1_pboole @ m1_pboole ) ),
    inference(cnf,[status(esa)],[2329]) ).

thf(479,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k5_pboole ) ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_pboole) ).

thf(2680,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k5_pboole ) ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(553,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ ( B @ v1_pboole ) )
      <=> ( B @ v3_relat_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_v1_pboole) ).

thf(2917,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( ( B @ v3_relat_1 )
         => ( A @ ( B @ v1_pboole ) ) )
        & ( ( A @ ( B @ v1_pboole ) )
         => ( B @ v3_relat_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(314,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( B @ ( A @ r2_pboole ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ r2_hidden ) )
               => ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_pboole) ).

thf(1994,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) )
             => ( C @ ( B @ ( A @ r2_pboole ) ) ) )
            & ( ( C @ ( B @ ( A @ r2_pboole ) ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ r2_hidden ) )
                 => ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r1_tarski ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(504,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ~ ( ( ( D @ ( C @ ( A @ k3_pboole ) ) )
                        = ( A @ k1_pboole ) )
                      & ( D @ ( B @ ( A @ r3_pboole ) ) )
                      & ( C @ ( B @ ( A @ r3_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_pboole) ).

thf(2779,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ~ ( ( ( D @ ( C @ ( A @ k3_pboole ) ) )
                        = ( A @ k1_pboole ) )
                      & ( D @ ( B @ ( A @ r3_pboole ) ) )
                      & ( C @ ( B @ ( A @ r3_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(14531,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,12880]) ).

thf(14532,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14531]) ).

thf(14574,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != sk199 ) ),
    inference(simp,[status(thm)],[14532]) ).

thf(14596,plain,
    ! [A: $i] :
      ( ( A @ ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != sk199 ),
    inference(simp,[status(thm)],[14574]) ).

thf(455,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D
                  = ( C @ ( B @ ( A @ k11_pboole ) ) ) )
              <=> ! [E: $i] :
                    ( ( A @ ( E @ r2_hidden ) )
                   => ( ( E @ ( D @ k1_funct_1 ) )
                      = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_pboole) ).

thf(2576,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) )
                 => ( D
                    = ( C @ ( B @ ( A @ k11_pboole ) ) ) ) )
                & ( ( D
                    = ( C @ ( B @ ( A @ k11_pboole ) ) ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ r2_hidden ) )
                     => ( ( E @ ( D @ k1_funct_1 ) )
                        = ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ k2_zfmisc_1 ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(336,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ v1_pre_circ ) )
              & ( B @ v2_relat_1 ) )
           => ( A @ ( C @ v1_pre_circ ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_mssubfam) ).

thf(2066,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ v1_pre_circ ) )
              & ( B @ v2_relat_1 ) )
           => ( A @ ( C @ v1_pre_circ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(352,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( ( A @ ( D @ m1_pboole ) )
                & ( D @ v2_relat_1 ) )
             => ( ( ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ( ( D @ ( E @ ( A @ r1_pboole ) ) )
                       => ( A @ k1_pboole @ ( C @ ( E @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) )
                  & ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_mboolean ) @ ( C @ ( A @ r2_pboole ) ) ) )
               => ( B @ ( A @ k2_mboolean ) @ ( C @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_mboolean) ).

thf(2120,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( ( A @ ( D @ m1_pboole ) )
                & ( D @ v2_relat_1 ) )
             => ( ( ! [E: $i] :
                      ( ( A @ ( E @ m1_pboole ) )
                     => ( ( D @ ( E @ ( A @ r1_pboole ) ) )
                       => ( A @ k1_pboole @ ( C @ ( E @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) )
                  & ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ k2_mboolean ) @ ( C @ ( A @ r2_pboole ) ) ) )
               => ( B @ ( A @ k2_mboolean ) @ ( C @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(15068,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,13162]) ).

thf(15069,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15068]) ).

thf(15095,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( A != k3_qc_lang1 ) ),
    inference(simp,[status(thm)],[15069]) ).

thf(15124,plain,
    ! [A: $i] :
      ( ( A @ ( k3_qc_lang1 @ k2_xboole_0 ) )
     != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[15095]) ).

thf(342,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ~ ( B @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_pboole) ).

thf(2095,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ~ ( B @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(288,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = ( A @ ( B @ k2_zfmisc_1 ) ) )
     => ( ( A = B )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).

thf(1893,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = ( A @ ( B @ k2_zfmisc_1 ) ) )
     => ( ( A = B )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(323,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 ) )
     => ! [D: $i] :
          ( ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
         => ( ( D @ v1_funcop_1 )
            & ( D @ v2_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel_5) ).

thf(2036,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 ) )
     => ! [D: $i] :
          ( ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
         => ( ( D @ v1_funcop_1 )
            & ( D @ v2_relat_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(166,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
    <=> ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).

thf(1309,plain,
    ! [A: $i,B: $i] :
      ( ( ( A != B )
       => ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
          = ( A @ k1_tarski ) ) )
      & ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
          = ( A @ k1_tarski ) )
       => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(378,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( A @ k1_pboole @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                  & ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_pboole) ).

thf(2258,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( A @ k1_pboole @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                  & ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(344,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ k1_pboole @ ( B @ ( A @ r2_pboole ) ) )
       => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_pboole) ).

thf(2102,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ k1_pboole @ ( B @ ( A @ r2_pboole ) ) )
       => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ~ ( A @ v2_setfam_1 )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_setfam_1) ).

thf(2302,plain,
    ! [A: $i] :
      ( ~ ( A @ v2_setfam_1 )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ ( B @ m1_subset_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(15490,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[745,13398]) ).

thf(15491,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
     != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ ( k4_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15490]) ).

thf(15541,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != k4_qc_lang1 ) ),
    inference(simp,[status(thm)],[15491]) ).

thf(15565,plain,
    ! [A: $i] :
      ( ( A @ ( k4_qc_lang1 @ ( k4_qc_lang1 @ k2_zfmisc_1 ) @ k4_xboole_0 ) )
     != k4_qc_lang1 ),
    inference(simp,[status(thm)],[15541]) ).

thf(228,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).

thf(1578,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( ( B @ ( A @ k1_tarski @ k2_xboole_0 ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(14004,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,12823]) ).

thf(14005,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) @ ( sk1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14004]) ).

thf(14043,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) )
      | ( A != sk1 ) ),
    inference(simp,[status(thm)],[14005]) ).

thf(14065,plain,
    ! [A: $i] :
      ( ( A @ ( sk1 @ k2_xboole_0 ) )
     != ( sk1 @ ( sk1 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[14043]) ).

thf(63,axiom,
    ! [A: $i] :
      ~ ( ! [B: $i] :
            ~ ( ! [C: $i,D: $i] :
                  ~ ( ( B
                      = ( D @ ( C @ k4_tarski ) ) )
                    & ( ( A @ ( D @ r2_hidden ) )
                      | ( A @ ( C @ r2_hidden ) ) ) )
              & ( A @ ( B @ r2_hidden ) ) )
        & ( A != k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).

thf(833,plain,
    ! [A: $i] :
      ~ ( ! [B: $i] :
            ~ ( ! [C: $i,D: $i] :
                  ~ ( ( B
                      = ( D @ ( C @ k4_tarski ) ) )
                    & ( ( A @ ( D @ r2_hidden ) )
                      | ( A @ ( C @ r2_hidden ) ) ) )
              & ( A @ ( B @ r2_hidden ) ) )
        & ( A != k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(457,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r5_pboole ) ) )
                  & ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_pboole) ).

thf(2587,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( C @ ( A @ r5_pboole ) ) )
                  & ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( A @ k1_pboole @ ( B @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(58,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( A @ ( B @ v1_pre_circ ) )
      <=> ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_mssubfam) ).

thf(818,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) )
         => ( A @ ( B @ v1_pre_circ ) ) )
        & ( ( A @ ( B @ v1_pre_circ ) )
         => ( A @ ( B @ ( A @ k1_mboolean ) @ v1_pre_circ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(560,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( ( A @ k4_card_fil )
        = ( A @ a_1_0_card_fil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_card_fil) ).

thf(2951,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( ( A @ k4_card_fil )
        = ( A @ a_1_0_card_fil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(261,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A @ ( E @ m1_subset_1 ) )
        & ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
        & ( A @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) @ k2_relat_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel_5) ).

thf(1757,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A @ ( E @ m1_subset_1 ) )
        & ( B @ ( A @ k2_pre_circ ) @ ( C @ ( A @ ( D @ m3_pboole ) ) ) )
        & ( A @ ( C @ m1_pboole ) )
        & ( C @ v2_relat_1 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( E @ ( D @ ( C @ ( B @ ( A @ k1_waybel_5 ) ) ) ) @ k2_relat_1 @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
      | ~ ( D @ ( C @ r1_tarski ) )
      | ~ ( B @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[602]) ).

thf(66,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) )
               => ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_pboole) ).

thf(854,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) )
               => ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(317,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ v1_xboole_0 )
       => ( ( A @ ( B @ m1_subset_1 ) )
        <=> ( B @ v1_xboole_0 ) ) )
      & ( ~ ( A @ v1_xboole_0 )
       => ( ( A @ ( B @ m1_subset_1 ) )
        <=> ( A @ ( B @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).

thf(2008,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ v1_xboole_0 )
       => ( ( ( B @ v1_xboole_0 )
           => ( A @ ( B @ m1_subset_1 ) ) )
          & ( ( A @ ( B @ m1_subset_1 ) )
           => ( B @ v1_xboole_0 ) ) ) )
      & ( ~ ( A @ v1_xboole_0 )
       => ( ( ( A @ ( B @ r2_hidden ) )
           => ( A @ ( B @ m1_subset_1 ) ) )
          & ( ( A @ ( B @ m1_subset_1 ) )
           => ( A @ ( B @ r2_hidden ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(68,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
     => ( ( ( C = F )
          & ( B = E )
          & ( A = D ) )
        | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_mcart_1) ).

thf(865,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
        = ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
     => ( ( ( C = F )
          & ( B = E )
          & ( A = D ) )
        | ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(201,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
      = ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).

thf(1480,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ k3_tarski )
      = ( B @ k3_tarski @ ( A @ k3_tarski @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(15060,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,13162]) ).

thf(15061,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) @ ( k3_qc_lang1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15060]) ).

thf(15094,plain,
    ! [A: $i] :
      ( ( A
       != ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) ) )
      | ( A != k3_qc_lang1 ) ),
    inference(simp,[status(thm)],[15061]) ).

thf(15123,plain,
    ( ( k3_qc_lang1 @ ( k3_qc_lang1 @ k2_zfmisc_1 ) )
   != k3_qc_lang1 ),
    inference(simp,[status(thm)],[15094]) ).

thf(241,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k3_xboole_0 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ( ( B @ ( D @ r2_hidden ) )
            & ( A @ ( D @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

thf(1657,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ! [D: $i] :
            ( ( ( ( B @ ( D @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
            & ( ( C @ ( D @ r2_hidden ) )
             => ( ( B @ ( D @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) ) ) )
       => ( C
          = ( B @ ( A @ k3_xboole_0 ) ) ) )
      & ( ( C
          = ( B @ ( A @ k3_xboole_0 ) ) )
       => ! [D: $i] :
            ( ( ( ( B @ ( D @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) )
             => ( C @ ( D @ r2_hidden ) ) )
            & ( ( C @ ( D @ r2_hidden ) )
             => ( ( B @ ( D @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(54,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_mboolean) ).

thf(801,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( A @ ( B @ ( A @ k2_mboolean ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(15205,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,13340]) ).

thf(15206,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15205]) ).

thf(15271,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) ) )
      | ( A != sk103 ) ),
    inference(simp,[status(thm)],[15206]) ).

thf(15292,plain,
    ! [A: $i] :
      ( ( sk103 @ ( A @ k2_xboole_0 ) )
     != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[15271]) ).

thf(179,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).

thf(1363,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(362,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( B @ ( B @ ( A @ k2_pboole ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_pboole) ).

thf(2186,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( ( B @ ( B @ ( A @ k2_pboole ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(3270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) )
       != ( sk1 @ ( D @ m1_subset_1 ) ) )
      | ~ $true
      | ~ ( B @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( C @ m3_pboole ) ) ) )
      | ( B @ v1_xboole_0 )
      | ( ( D @ ( C @ ( sk2 @ ( B @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( D @ ( C @ k1_funct_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[772,3091]) ).

thf(3271,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) )
       != ( sk1 @ ( D @ m1_subset_1 ) ) )
      | ~ ( B @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( C @ m3_pboole ) ) ) )
      | ( B @ v1_xboole_0 )
      | ( ( D @ ( C @ ( sk2 @ ( B @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( D @ ( C @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3270]) ).

thf(3274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_zfmisc_1 )
       != sk1 )
      | ( k1_xboole_0 != D )
      | ~ ( B @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( C @ m3_pboole ) ) ) )
      | ( B @ v1_xboole_0 )
      | ( ( D @ ( C @ ( sk2 @ ( B @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( D @ ( C @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3271]) ).

thf(3277,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_zfmisc_1 )
       != sk1 )
      | ~ ( B @ ( sk1 @ k2_pre_circ ) @ ( sk2 @ ( sk1 @ ( C @ m3_pboole ) ) ) )
      | ( B @ v1_xboole_0 )
      | ( ( k1_xboole_0 @ ( C @ ( sk2 @ ( B @ ( sk1 @ k1_waybel_5 ) ) ) ) )
        = ( k1_xboole_0 @ ( C @ k1_funct_1 ) ) ) ),
    inference(simp,[status(thm)],[3274]) ).

thf(171,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) )
               => ( C @ ( D @ ( A @ r4_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_pboole) ).

thf(1335,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r4_pboole ) ) ) )
               => ( C @ ( D @ ( A @ r4_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(243,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
    <=> ~ ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).

thf(1693,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ r2_hidden ) )
       => ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
          = ( A @ k1_tarski ) ) )
      & ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
          = ( A @ k1_tarski ) )
       => ~ ( B @ ( A @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(454,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
            & ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pboole) ).

thf(2572,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( C @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) )
            & ( B @ ( C @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(14541,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,12880]) ).

thf(14542,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14541]) ).

thf(14578,plain,
    ! [A: $i] :
      ( ( A
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) ) )
      | ( A != sk199 ) ),
    inference(simp,[status(thm)],[14542]) ).

thf(14600,plain,
    ( ( sk199 @ ( sk199 @ k2_zfmisc_1 ) )
   != sk199 ),
    inference(simp,[status(thm)],[14578]) ).

thf(222,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_xboole_1) ).

thf(1561,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k5_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(140,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
      = ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_xboole_1) ).

thf(1172,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) )
      = ( A @ ( C @ k2_xboole_0 ) @ ( C @ ( B @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k3_xboole_0 ) @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(72,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
     => ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).

thf(897,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
     => ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(188,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k5_xboole_0 ) )
      = ( A @ ( B @ k5_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).

thf(1410,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k5_xboole_0 ) )
      = ( A @ ( B @ k5_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( C != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( B != C )
        & ( ( A @ k1_tarski )
          = ( C @ ( B @ k2_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).

thf(767,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( C != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( B != C )
        & ( ( A @ k1_tarski )
          = ( C @ ( B @ k2_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(161,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
      = ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).

thf(1288,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_xboole_0 ) @ ( B @ ( A @ k2_xboole_0 ) @ k2_zfmisc_1 ) )
      = ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_xboole_0 ) @ k2_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(248,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) )
      = ( A @ ( B @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

thf(1710,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) )
      = ( A @ ( B @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(144,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ~ ( ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ~ ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                      & ( B @ ( D @ ( A @ r1_pboole ) ) ) ) )
              & ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_pboole) ).

thf(1197,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ~ ( ! [D: $i] :
                  ( ( A @ ( D @ m1_pboole ) )
                 => ~ ( ( C @ ( D @ ( A @ r1_pboole ) ) )
                      & ( B @ ( D @ ( A @ r1_pboole ) ) ) ) )
              & ( C @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(61,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
      = ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).

thf(828,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
      = ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(509,axiom,
    ! [A: $i] :
      ( ~ ( A @ v2_setfam_1 )
     => ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_setfam_1) ).

thf(2795,plain,
    ! [A: $i] :
      ( ~ ( A @ v2_setfam_1 )
     => ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(324,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_fraenkel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_closure2) ).

thf(2040,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_fraenkel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(696,plain,
    ( ( k1_xboole_0 @ k4_card_3 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[695]) ).

thf(137,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_zfmisc_1) ).

thf(1165,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_xboole_0 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(15628,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1260,13403]) ).

thf(15629,plain,
    ! [A: $i] :
      ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
     != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) @ ( sk181 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15628]) ).

thf(15719,plain,
    ! [A: $i] :
      ( ( ( A @ k3_tarski @ k1_zfmisc_1 )
       != ( sk181 @ ( sk181 @ k2_zfmisc_1 ) ) )
      | ( A != sk181 ) ),
    inference(simp,[status(thm)],[15629]) ).

thf(15741,plain,
    ( ( sk181 @ ( sk181 @ k2_zfmisc_1 ) )
   != ( sk181 @ k3_tarski @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[15719]) ).

thf(71,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ! [G: $i,H: $i] :
            ( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
          <=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
        & ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).

thf(886,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ! [G: $i,H: $i] :
            ( ( ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
             => ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
            & ( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
             => ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) ) )
        & ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(449,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ ( B @ ( A @ k1_pboole @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) )
        & ( B @ ( A @ k1_pboole @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_pboole) ).

thf(2549,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( ( B @ ( B @ ( A @ k1_pboole @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) )
        & ( B @ ( A @ k1_pboole @ ( B @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( B @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
      | ~ ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
      | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[733]) ).

thf(740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
      | ~ ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ r2_hidden ) )
      | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
      | ~ ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
      | ( B = C ) ),
    inference(lifteq,[status(thm)],[738]) ).

thf(308,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_xboole_1) ).

thf(1977,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k2_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(429,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_pboole) ).

thf(2467,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( C @ ( D @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( C @ ( D @ ( B @ ( A @ k2_pboole ) ) @ ( A @ r2_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(59,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
        = ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).

thf(822,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
        = ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(14508,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[8054,12880]) ).

thf(14509,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) @ ( sk199 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14508]) ).

thf(14580,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ k2_xboole_0 ) )
       != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) ) )
      | ( A != sk199 ) ),
    inference(simp,[status(thm)],[14509]) ).

thf(14603,plain,
    ! [A: $i] :
      ( ( sk199 @ ( A @ k2_xboole_0 ) )
     != ( sk199 @ ( sk199 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[14580]) ).

thf(691,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ k2_mboolean ) @ ( A @ r1_pboole ) ) )
      | ~ ( A @ ( B @ sk7 ) @ ( A @ ( B @ sk6 ) @ ( A @ r2_pboole ) ) )
      | ~ ( A @ ( B @ m1_pboole ) )
      | ~ ( A @ ( B @ v1_pre_circ ) )
      | ~ ( B @ v2_relat_1 ) ),
    inference(cnfConj,[status(thm)],[685]) ).

thf(383,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ~ ( C @ v1_xboole_0 )
         => ~ ( ! [D: $i] :
                  ( ( B @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ ( E @ m1_subset_1 ) )
                     => ( A
                       != ( E @ ( D @ k4_tarski ) ) ) ) )
              & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_domain_1) ).

thf(2270,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ~ ( C @ v1_xboole_0 )
         => ~ ( ! [D: $i] :
                  ( ( B @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ ( E @ m1_subset_1 ) )
                     => ( A
                       != ( E @ ( D @ k4_tarski ) ) ) ) )
              & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(121,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
              <=> ( ( D @ ( B @ ( A @ r5_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_mboolean) ).

thf(1093,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( ( D @ ( B @ ( A @ r5_pboole ) ) )
                    & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                 => ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) ) )
                & ( ( D @ ( C @ ( A @ k4_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
                 => ( ( D @ ( B @ ( A @ r5_pboole ) ) )
                    & ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(621,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[619]) ).

thf(624,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
      | ( B = D ) ),
    inference(lifteq,[status(thm)],[621]) ).

thf(513,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ m1_pboole ) )
        & ( A @ ( C @ m1_pboole ) ) )
     => ( C @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_altcat_2) ).

thf(2803,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ m1_pboole ) )
        & ( A @ ( C @ m1_pboole ) ) )
     => ( C @ ( C @ ( B @ ( A @ r2_altcat_2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(526,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ( ( B @ v3_relat_1 )
           => ~ ( B @ v2_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_pboole) ).

thf(2847,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ( ( B @ v3_relat_1 )
           => ~ ( B @ v2_relat_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(461,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ( ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) )
      <=> ? [C: $i] :
            ( ( A
              = ( C @ k1_tarski ) )
            & ( B @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_pua2mss1) ).

thf(2600,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ( ( ? [C: $i] :
              ( ( A
                = ( C @ k1_tarski ) )
              & ( B @ ( C @ m1_subset_1 ) ) )
         => ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) ) )
        & ( ( B @ a_1_0_pua2mss1 @ ( A @ r2_hidden ) )
         => ? [C: $i] :
              ( ( A
                = ( C @ k1_tarski ) )
              & ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(184,axiom,
    ! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_xboole_1) ).

thf(1384,plain,
    ! [A: $i,B: $i,C: $i] : ( C @ ( B @ k2_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(182,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_xboole_1) ).

thf(1378,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(1976,plain,
    sk103 @ v1_pralg_2,
    inference(cnfConj,[status(thm)],[1973]) ).

thf(207,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ~ ( ( B
                = ( A @ k1_pboole ) )
              & ( B @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_pboole) ).

thf(1500,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ~ ( ( B
                = ( A @ k1_pboole ) )
              & ( B @ ( B @ ( A @ r4_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ k2_xboole_0 ) ) )
      | ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[707]) ).

thf(722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[710]) ).

thf(723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ sk12 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk13 ) ) @ r2_hidden ) )
      | ( C
        = ( B @ ( A @ k2_xboole_0 ) ) ) ),
    inference(simp,[status(thm)],[722]) ).

thf(249,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
      = ( B @ ( A @ k4_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).

thf(1713,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( A @ k2_xboole_0 ) @ k4_xboole_0 ) )
      = ( B @ ( A @ k4_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(285,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B
        = ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).

thf(1880,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B
        = ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(104,axiom,
    ! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_xboole_1) ).

thf(1004,plain,
    ! [A: $i,B: $i,C: $i] : ( C @ ( A @ k2_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(16003,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1551,13625]) ).

thf(16004,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_xboole_0 ) @ ( A @ r1_tarski ) )
     != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[16003]) ).

thf(16037,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_xboole_0 ) )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) ) )
      | ( A != sk197 ) ),
    inference(simp,[status(thm)],[16004]) ).

thf(16061,plain,
    ! [A: $i] :
      ( ( A @ ( sk197 @ k2_xboole_0 ) )
     != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) ) ),
    inference(simp,[status(thm)],[16037]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( A @ v1_fraenkel )
     => ! [B: $i] :
          ( ( A @ ( B @ r1_tarski ) )
         => ( B @ v1_fraenkel ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_fraenkel) ).

thf(1299,plain,
    ! [A: $i] :
      ( ( A @ v1_fraenkel )
     => ! [B: $i] :
          ( ( A @ ( B @ r1_tarski ) )
         => ( B @ v1_fraenkel ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(435,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( A @ k1_pboole @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( A @ k1_pboole @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pboole) ).

thf(2484,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( ( A @ k1_pboole @ ( D @ ( C @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
               => ( A @ k1_pboole @ ( D @ ( B @ ( A @ k3_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(287,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

thf(1885,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ r1_tarski ) )
       => ( ( B @ ( A @ k4_xboole_0 ) )
          = k1_xboole_0 ) )
      & ( ( ( B @ ( A @ k4_xboole_0 ) )
          = k1_xboole_0 )
       => ( B @ ( A @ r1_tarski ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(486,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mboolean) ).

thf(2699,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ( B @ ( A @ k1_pboole @ ( A @ r2_pboole ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(234,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
        | ( A @ ( C @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).

thf(1606,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
        | ( A @ ( C @ r2_hidden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(538,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_pboole @ ( B @ ( A @ ( C @ m3_pboole ) ) ) )
         => ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_mssubfam) ).

thf(2879,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_pboole ) )
        & ( B @ v2_relat_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_pboole @ ( B @ ( A @ ( C @ m3_pboole ) ) ) )
         => ( A @ k1_pboole @ ( C @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(55,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k5_xboole_0 ) )
      = ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).

thf(803,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k5_xboole_0 ) )
      = ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ k2_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(539,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_pboole) ).

thf(2881,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( D @ ( C @ ( A @ k5_pboole ) ) @ ( B @ ( A @ k5_pboole ) ) @ ( D @ ( C @ ( B @ ( A @ k5_pboole ) ) @ ( A @ k5_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(256,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).

thf(1737,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(542,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ( ( C @ ( B @ k1_funct_4 ) )
                = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_closure3) ).

thf(2887,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_pboole ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_pboole ) )
             => ( ( C @ ( B @ k1_funct_4 ) )
                = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(318,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
               => ( ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_pboole) ).

thf(2018,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ( ( D @ ( C @ ( A @ k3_pboole ) ) @ ( B @ ( A @ r2_pboole ) ) )
               => ( ( D @ ( B @ ( A @ r2_pboole ) ) )
                  & ( C @ ( B @ ( A @ r2_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(280,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
      = ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).

thf(1848,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
      = ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(522,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ m1_pboole ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_pboole) ).

thf(2834,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_pboole ) )
        & ( A @ ( B @ m1_pboole ) ) )
     => ( A @ ( C @ ( B @ ( A @ k11_pboole ) ) @ m1_pboole ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(346,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ m1_subset_1 ) )
     => ( ( B @ ( A @ r2_hidden ) )
        | ( B @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

thf(2106,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ m1_subset_1 ) )
     => ( ( B @ ( A @ r2_hidden ) )
        | ( B @ v1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(116,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).

thf(1069,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( B @ ( C @ ( A @ k2_xboole_0 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(14174,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,12843]) ).

thf(14175,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) @ ( sk33 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14174]) ).

thf(14217,plain,
    ! [A: $i] :
      ( ( A
       != ( sk33 @ ( sk33 @ k2_zfmisc_1 ) ) )
      | ( A != sk33 ) ),
    inference(simp,[status(thm)],[14175]) ).

thf(14236,plain,
    ( ( sk33 @ ( sk33 @ k2_zfmisc_1 ) )
   != sk33 ),
    inference(simp,[status(thm)],[14217]) ).

thf(578,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
              & ( B @ v2_relat_1 ) )
           => ( C @ v2_relat_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_pboole) ).

thf(3013,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( ( ( C @ ( B @ ( A @ r2_pboole ) ) )
              & ( B @ v2_relat_1 ) )
           => ( C @ v2_relat_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(15995,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ r1_tarski ) )
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[787,13625]) ).

thf(15996,plain,
    ! [A: $i] :
      ( ( A @ ( A @ r1_tarski ) )
     != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) @ ( sk197 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15995]) ).

thf(16042,plain,
    ! [A: $i] :
      ( ( A
       != ( sk197 @ ( sk197 @ k2_zfmisc_1 ) ) )
      | ( A != sk197 ) ),
    inference(simp,[status(thm)],[15996]) ).

thf(16066,plain,
    ( ( sk197 @ ( sk197 @ k2_zfmisc_1 ) )
   != sk197 ),
    inference(simp,[status(thm)],[16042]) ).

thf(15240,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1464,13340]) ).

thf(15241,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) )
     != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ ( sk103 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15240]) ).

thf(15285,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk103 @ ( sk103 @ k2_zfmisc_1 ) ) )
      | ( ( B @ ( A @ k3_xboole_0 ) )
       != sk103 ) ),
    inference(simp,[status(thm)],[15241]) ).

thf(15310,plain,
    ! [A: $i] :
      ( ( A @ ( sk103 @ ( sk103 @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
     != sk103 ),
    inference(simp,[status(thm)],[15285]) ).

thf(168,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).

thf(1320,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) )
      = ( B @ ( A @ k3_xboole_0 ) @ ( A @ k5_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(299,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
                      & ( E @ ( D @ ( A @ r2_pboole ) ) )
                      & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                   => ( E @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_pboole) ).

thf(1945,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_pboole ) )
             => ! [E: $i] :
                  ( ( A @ ( E @ m1_pboole ) )
                 => ( ( ( D @ ( B @ ( A @ r4_pboole ) ) )
                      & ( E @ ( D @ ( A @ r2_pboole ) ) )
                      & ( C @ ( B @ ( A @ r2_pboole ) ) ) )
                   => ( E @ ( C @ ( A @ r4_pboole ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(483,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ k19_pralg_1 ) ) )
        = ( C @ k3_funct_5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k19_pralg_1) ).

thf(2690,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ k19_pralg_1 ) ) )
        = ( C @ k3_funct_5 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(11114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ k1_tarski @ ( B @ k1_tarski @ k2_zfmisc_1 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[672,6740]) ).

thf(11115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ k1_tarski @ ( B @ k1_tarski @ k2_zfmisc_1 ) ) )
      | ~ ( A @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[11114]) ).

thf(11116,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[11115:[bind(A,$thf( G @ k1_tarski @ ( F @ k1_tarski @ k2_zfmisc_1 ) )),bind(B,$thf( F )),bind(C,$thf( G ))]]) ).

thf(11985,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ v1_xboole_0 ),
    inference(simp,[status(thm)],[11116]) ).

thf(370,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_pboole) ).

thf(2238,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_pboole ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_pboole ) )
         => ( C @ ( B @ ( A @ k3_pboole ) ) @ ( C @ ( B @ ( A @ k4_pboole ) ) @ ( B @ ( A @ k4_pboole ) ) @ ( A @ r6_pboole ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(205,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).

thf(1490,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(1764,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1761]) ).

thf(1768,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1764]) ).

thf(1769,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[1768]) ).

thf(359,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( A @ ( E @ r2_hidden ) )
        & ( E @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).

thf(2177,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( A @ ( E @ r2_hidden ) )
        & ( E @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(474,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) )
        = ( B @ ( B @ ( B @ k3_zfmisc_1 ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_mcart_1) ).

thf(2655,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) )
        = ( B @ ( B @ ( B @ k3_zfmisc_1 ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(84800,plain,
    $false,
    inference(e,[status(thm)],[645,2452,629,2306,1454,15303,1899,1840,2499,2544,2250,2199,3021,1879,1337,2612,13162,11372,1767,15558,909,2921,2480,1982,1179,2331,666,1818,977,6791,3072,2104,683,14235,2381,2062,1808,1073,873,655,1533,597,1041,2512,762,2622,11880,14786,2947,1939,2248,1544,2676,2114,1142,614,677,3004,2740,1735,1260,1342,2901,2042,1999,797,2448,2933,1507,930,670,15735,1835,2046,1127,973,1650,1359,1386,1724,2825,2405,2869,651,2985,1576,1518,1703,12843,2916,719,11913,2501,1264,1455,2488,1059,2356,3263,15135,2735,2814,2339,11025,587,1323,3148,917,702,2682,3125,1826,2420,902,8054,638,6470,1609,1741,2635,3312,2158,1815,1778,2388,2829,1087,1514,1319,1704,969,606,2024,13123,2989,1963,924,2782,15748,646,1136,2925,10816,937,2034,905,2616,1465,14056,591,1109,2469,1418,14061,623,1383,2254,806,2555,3290,13543,1581,2335,966,2777,19759,14232,10734,2073,687,18065,1072,1119,660,2750,1600,1975,2762,602,2964,1843,2058,2367,1928,1896,692,2190,6740,2002,998,2242,1345,988,2799,920,11555,3303,678,661,2737,2296,1636,2954,1651,15751,2118,1067,2790,2660,2905,1047,1730,1057,1274,2589,825,598,3022,630,1824,815,2396,1238,2705,2264,746,1091,2969,14605,2414,729,2132,2890,1883,15298,2958,2873,15296,2433,1968,1951,665,2068,583,1159,1787,757,25888,2344,2228,1291,1573,1012,1032,1837,3269,1365,2670,2826,2820,3033,842,1592,697,1121,725,980,1006,593,2268,3001,3060,1360,1936,1851,1259,2946,10887,2377,650,2801,1794,1953,1111,2709,1878,14783,2726,1138,2724,2858,2537,1567,2460,12151,14613,1942,2323,933,2561,669,14052,2312,642,637,1937,2108,15126,1155,1419,14914,2877,11625,1182,1739,1461,901,686,2053,2240,19735,1612,2649,2978,2472,1478,10560,654,1974,1552,1932,2465,1947,1002,16058,11610,3109,13340,2285,1114,647,1263,997,2450,2125,2836,1456,984,911,15560,2497,721,2766,1599,1246,605,1759,13398,2546,2883,1071,2915,2793,1167,2749,1857,1991,2788,1318,1202,792,1563,657,765,1846,1054,15307,2748,1170,2963,1286,17250,12823,2995,953,2662,773,794,926,2909,1648,10571,1754,2391,2149,2585,1483,856,1301,689,1727,1510,745,3289,11561,2894,2260,601,584,732,2849,772,2514,875,1701,1124,2827,2959,904,975,2970,694,2048,2859,1615,1784,4494,1389,10480,1752,11851,579,2806,2991,2695,1488,2326,1707,1733,1239,14059,2557,704,15733,1356,672,2193,3023,2891,1271,611,787,3091,1464,2474,2346,831,2084,2856,616,1175,2510,979,604,681,14243,1853,1408,1282,2478,2415,2493,2987,2637,2422,1574,1011,2097,14788,1589,1933,1492,1603,2116,2839,2943,2945,3066,2896,1571,599,2871,2197,1969,18414,2180,2182,1471,3027,1162,3034,15575,626,2974,2314,2625,1821,594,848,700,14402,1149,964,1556,2542,2647,943,2252,1293,2553,2928,1381,11761,2329,912,2439,2962,2350,959,780,2064,986,2797,1000,2022,3142,14614,2999,653,2693,14049,658,983,2075,2418,2051,1044,695,2086,16062,1413,11161,12120,1034,1873,663,1684,2234,648,1340,968,675,2816,16052,2614,1208,589,12288,944,1467,2994,2784,680,1509,14230,749,2629,1990,617,2684,2333,2256,754,16838,14240,2899,1551,10471,20196,1845,1547,1770,14775,705,2060,2192,18390,739,1368,1780,2720,1098,2831,690,1516,2863,640,1961,13813,2386,14778,673,585,717,1235,2337,1901,1218,643,2354,1790,1987,1716,1452,2688,15132,11374,2276,1980,2701,2486,951,13403,2044,15557,744,1257,703,1536,1802,613,15736,2939,612,1240,2056,1358,600,2843,1485,1972,1504,727,10300,2860,15116,16049,2030,595,2892,1839,627,1459,1966,2885,1817,581,759,1216,1126,2997,2110,2775,771,14791,2865,2875,2435,2760,2310,976,688,2226,2643,2591,1326,2594,2167,2283,2290,12662,2971,13625,2764,2416,3085,16257,588,652,12880,25227,2823,2608,2431,4495,2130,731,15561,1558,2262,914,2912,2330,2680,899,2917,1994,2779,14596,2956,2576,2066,2120,15124,2095,684,1893,2036,1309,2258,2102,2302,15565,1578,14065,833,2587,12972,818,2951,1527,1757,603,854,2008,865,1480,15123,1657,2746,664,801,1989,15292,1363,2186,3277,1335,1693,2572,14600,1561,1172,897,1410,767,1288,1710,1197,3030,828,635,2795,2040,696,1165,15741,886,2549,740,1977,1261,2467,12984,822,14603,691,2270,1093,1930,624,2803,2847,2600,1384,596,1378,1976,1550,1500,723,8189,1713,982,1880,1004,16061,1299,2484,1885,2699,1606,2879,803,940,2881,1737,2887,2018,1848,1416,639,2834,2993,2106,1069,14236,3013,16066,15310,1320,1945,1009,2690,1463,11985,2238,1490,1769,676,2177,2655]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ALG226+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40  % Computer : n017.cluster.edu
% 0.14/0.40  % Model    : x86_64 x86_64
% 0.14/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40  % Memory   : 8046.5625MB
% 0.14/0.40  % OS       : Linux 6.8.0-71-generic
% 0.14/0.40  % CPULimit : 300
% 0.14/0.40  % WCLimit  : 300
% 0.14/0.40  % DateTime : Sat Sep 26 21:31:23 UTC 2026
% 0.14/0.41  % CPUTime  : 
% 0.14/0.41  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 7.49/2.95  % [INFO] 	 Parsing done (1961ms). 
% 7.49/2.97  % [INFO] 	 Running in sequential loop mode. 
% 7.88/3.16  % [INFO] 	 eprover registered as external prover. 
% 7.88/3.17  % [INFO] 	 Scanning for conjecture ... 
% 11.54/4.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 16950 axioms. Running axiom selection ... 
% 14.33/6.15  % [INFO] 	 Axiom selection finished. Selected 576 axioms (removed 16374 axioms). 
% 15.26/6.57  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 15.58/6.61  % [INFO] 	 Type checking passed. 
% 15.58/6.61  % [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 ... 
% 155.44/42.07  % External prover 'e' found a proof!
% 155.44/42.07  % [INFO] 	 Killing All external provers ... 
% 155.44/42.07  % Time passed: 41521ms (effective reasoning time: 39097ms)
% 155.44/42.07  % 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)>
% 155.44/42.08  % Axioms used in derivation (576): rc2_setfam_1, existence_m2_pboole, t24_mboolean, t34_mboolean, fraenkel_a_1_0_domain_1, t1_mboolean, t92_pboole, t44_xboole_1, t13_zfmisc_1, t143_pboole, t102_pboole, t42_xboole_1, dt_k15_domain_1, t5_fraenkel, t21_zfmisc_1, t5_boole, t6_mboolean, dt_k11_pboole, antisymmetry_r3_pboole, t19_xboole_1, t62_pboole, t109_pboole, t20_zfmisc_1, fc1_zfmisc_1, d1_tarski, t135_zfmisc_1, dt_k1_pralg_3, t27_mboolean, t17_xboole_1, t112_xboole_1, d3_mcart_1, t8_altcat_1, t105_zfmisc_1, t1_funct_4, t92_xboole_1, t23_xboole_1, dt_k2_pre_circ, redefinition_k19_pralg_1, t58_pboole, d3_subset_1, reflexivity_r2_pboole, rc6_grcat_1, t140_zfmisc_1, t24_pboole, t1_closure3, t109_xboole_1, cc1_mssubfam, idempotence_k3_xboole_0, t110_xboole_1, t136_pboole, t1_boole, t7_subset_1, t38_mcart_1, d12_pboole, t29_mcart_1, d3_closure3, t3_xboole_1, t97_xboole_1, fc1_xboole_0, t113_zfmisc_1, t48_domain_1, t34_xboole_1, t113_xboole_1, t111_zfmisc_1, t44_pboole, t19_mboolean, t101_xboole_1, t4_ordinal1, t1_subset, t10_partfun1, t25_pboole, t64_funct_5, t8_subset_1, t28_mboolean, t85_pboole, t20_mboolean, d5_xboole_0, t52_zfmisc_1, fc4_subset_1, t17_pboole, t36_pboole, t43_xboole_1, t81_zfmisc_1, t18_xboole_1, t33_mboolean, t6_xboole_1, t22_mboolean, t73_pboole, t39_pboole, t96_zfmisc_1, t1_pralg_2, d5_pboole, t17_mboolean, dt_k1_subset_1, t25_xboole_1, t107_finseq_2, t2_boole, t35_zfmisc_1, t117_zfmisc_1, t59_pboole, t1_qc_lang1, t122_zfmisc_1, t37_pboole, t66_pboole, t110_zfmisc_1, dt_k19_pralg_1, t43_zfmisc_1, t108_pboole, t27_xboole_1, t95_zfmisc_1, t140_pboole, t99_zfmisc_1, t28_pboole, t12_mssubfam, t5_card_fil, dt_k17_domain_1, rc1_fraenkel, t141_pboole, dt_m3_pboole, t45_zfmisc_1, t69_zfmisc_1, t43_pboole, t19_pboole, t103_zfmisc_1, dt_k4_pboole, t9_altcat_2, s2_pboole, d8_pboole, d1_mboolean, t21_pboole, t37_xboole_1, t9_xboole_1, rc1_pralg_2, t41_zfmisc_1, existence_m3_grcat_1, t95_xboole_1, t112_pboole, t16_mboolean, fc2_pboole, dt_k14_domain_1, t84_pboole, t103_pboole, d9_pboole, t128_pboole, t9_pboole, d7_pboole, t16_pboole, t142_pboole, t49_zfmisc_1, commutativity_k3_pboole, commutativity_k3_xboole_0, t23_mboolean, fraenkel_a_2_0_closure3, t86_pboole, t135_pboole, t129_zfmisc_1, t27_mssubfam, t150_pboole, t18_pboole, t52_pboole, t63_pboole, symmetry_r5_pboole, t115_zfmisc_1, existence_m2_card_fil, t123_pboole, t35_pboole, t137_zfmisc_1, fc2_xboole_0, dt_k2_pboole, t49_mcart_1, d1_xboole_0, d15_pboole, t108_xboole_1, t130_pboole, t129_pboole, t138_zfmisc_1, t130_zfmisc_1, t51_xboole_1, t36_mcart_1, t108_zfmisc_1, t118_zfmisc_1, t122_pboole, t132_pboole, dt_m2_card_fil, dt_k2_cat_5, t119_pboole, cc1_pboole, t46_zfmisc_1, t94_pboole, fc2_funct_2, t6_boole, rc2_subset_1, t50_xboole_1, redefinition_m3_grcat_1, t1_xboole_1, t7_mboolean, t20_pboole, t97_pboole, fc1_fraenkel, t17_domain_1, t52_xboole_1, t19_mssubfam, fraenkel_a_1_0_card_fil, t22_pboole, t37_mboolean, commutativity_k2_xboole_0, t15_domain_1, t13_mboolean, dt_k4_card_fil, t29_mboolean, t68_pboole, t48_pboole, t128_zfmisc_1, t5_altcat_1, t98_pboole, t5_subset, existence_m1_cat_5, t94_zfmisc_1, idempotence_k2_pboole, d2_mboolean, t63_funct_5, d22_pboole, t6_pboole, t32_mboolean, t113_pboole, t79_zfmisc_1, t1_zfmisc_1, t77_mcart_1, t28_mcart_1, t40_pboole, t4_pboole, rc3_setfam_1, t127_pboole, t123_zfmisc_1, fc2_subset_1, fraenkel_a_2_1_closure3, d3_zfmisc_1, t102_xboole_1, t72_mcart_1, t2_tarski, t67_zfmisc_1, t9_altcat_1, t15_mboolean, t23_pboole, t97_zfmisc_1, cc1_altcat_1, t102_zfmisc_1, t106_pboole, t144_pboole, t33_xboole_1, t27_pboole, t19_card_3, t5_pboole, redefinition_v1_pboole, t25_borsuk_1, t2_zfmisc_1, t148_pboole, t87_pboole, t4_subset, fc3_xboole_0, d2_xboole_0, t30_xboole_1, cc1_closure2, d17_pboole, t124_pboole, t32_xboole_1, t5_ordinal1, t4_boole, t53_xboole_1, t21_xboole_1, dt_k2_mboolean, t34_pboole, dt_k1_cat_5, d4_tarski, dt_k1_mboolean, reflexivity_r2_zfrefle1, reflexivity_r3_zfrefle1, commutativity_k2_pboole, t29_xboole_1, t96_xboole_1, t74_mcart_1, commutativity_k5_xboole_0, t88_pboole, t141_zfmisc_1, t99_pboole, t1_xboole_0, t7_boole, t11_card_fil, fc4_qc_lang1, t104_zfmisc_1, t3_ordinal1, t9_domain_1, dt_k16_domain_1, redefinition_k2_yellow_7, t139_zfmisc_1, d2_subset_1, t54_pboole, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, t48_xboole_1, redefinition_m1_cat_5, t137_pboole, t5_setwiseo, t101_pboole, dt_m1_card_fil, t3_mboolean, t7_ordinal1, t67_pboole, dt_k3_pboole, d16_pboole, t31_xboole_1, t4_subset_1, t91_orders_1, t50_pboole, t60_pboole, t89_pboole, t21_mboolean, cc2_setfam_1, reflexivity_r6_pboole, rc1_subset_1, t12_pboole, cc3_pboole, t61_pboole, t24_xboole_1, t17_fraenkel, t6_closure3, existence_m3_pboole, t116_zfmisc_1, t64_zfmisc_1, t47_pboole, t20_xboole_1, t20_mssubfam, dt_m2_pboole, t16_mssubfam, t14_funct_2, t134_pboole, t124_zfmisc_1, existence_m1_pboole, t6_setwiseo, t54_xboole_1, t8_altcat_2, t120_zfmisc_1, redefinition_k14_pralg_1, d14_pboole, t55_xboole_1, t5_realset1, t3_subset, t55_subset_1, d2_zfmisc_1, fc5_subset_1, t10_altcat_1, existence_m1_subset_1, t35_xboole_1, d6_xboole_0, t44_zfmisc_1, t110_pboole, t47_xboole_1, idempotence_k3_pboole, t23_mssubfam, d4_pboole, t107_zfmisc_1, t106_zfmisc_1, t121_pboole, t114_pboole, t125_zfmisc_1, t8_setwiseo, t69_pboole, fc3_qc_lang1, t115_pboole, t14_xboole_1, t44_setfam_1, t31_mboolean, redefinition_r6_pboole, t92_zfmisc_1, t9_zfrefle1, s4_altcat_1, t42_pboole, t100_zfmisc_1, t26_xboole_1, t15_xboole_1, t86_zfmisc_1, t98_xboole_1, t138_pboole, t37_mcart_1, t114_zfmisc_1, t31_zfmisc_1, d1_zfmisc_1, t16_xboole_1, t64_pboole, t12_mboolean, t111_xboole_1, t26_mssubfam, t79_pboole, t71_pboole, commutativity_k5_pboole, t15_card_fil, t22_xboole_1, t84_zfmisc_1, t81_pboole, cc2_pboole, fraenkel_a_1_0_pua2mss1, t139_pboole, t70_pboole, t100_xboole_1, t8_xboole_1, t8_pboole, rc2_cat_5, t28_xboole_1, d3_tarski, t151_pboole, t39_zfmisc_1, t119_zfmisc_1, t104_pboole, t13_xboole_1, t83_zfmisc_1, reflexivity_r1_tarski, symmetry_r2_subset_1, fraenkel_a_2_0_closure2, t10_pre_circ, t6_zfmisc_1, t10_altcat_2, t77_pboole, t56_setfam_1, t75_pboole, t2_xboole_1, t38_pboole, t9_mcart_1, t18_mssubfam, t56_pboole, t121_zfmisc_1, t10_subset_1, t53_pboole, t4_xboole_1, t10_pboole, t76_pboole, t1_partfun1, t41_xboole_1, t39_mcart_1, t96_pboole, d2_altcat_2, t26_mboolean, dt_k1_pboole, t133_pboole, d4_xboole_0, t11_mboolean, dt_m1_pralg_1, t18_zfmisc_1, t126_pboole, t41_pboole, t36_xboole_1, t51_zfmisc_1, t4_card_fil, t94_xboole_1, t18_mboolean, t15_pboole, t49_xboole_1, existence_m1_pralg_1, t93_xboole_1, t57_pboole, t11_xboole_1, t100_pboole, d9_card_fil, s3_altcat_1, t68_zfmisc_1, t11_pboole, t78_pboole, t21_mssubfam, t29_mssubfam, t73_mcart_1, t8_boole, rc1_xboole_0, t105_pboole, t35_mcart_1, t34_zfmisc_1, t80_zfmisc_1, t111_pboole, reflexivity_r2_altcat_2, t24_zfmisc_1, t49_pboole, t12_xboole_1, t111_relat_1, t5_mboolean, t37_zfmisc_1, t72_pboole, t149_pboole, t109_zfmisc_1, t134_zfmisc_1, t126_zfmisc_1, t2_subset, existence_m1_finseq_2, t26_pboole, dt_k3_cat_5, reflexivity_r7_pboole, t3_pboole, fc1_pralg_2, t51_pboole, t116_pboole, t65_pboole, idempotence_k2_xboole_0, t48_subset_1, fc3_pralg_1, dt_k2_yellow_7, dt_k21_pralg_1, d13_pboole, t36_mboolean, t46_xboole_1, d10_xboole_0, d11_setfam_1, t120_pboole, t7_xboole_1, d21_pboole, t80_pboole, redefinition_k1_waybel_5, t22_mssubfam, t147_pboole, t5_xboole_1, t35_mboolean, dt_k5_pboole, t83_pboole, t88_funct_6, cc1_waybel_5, t91_xboole_1, t3_boole, t6_ordinal1, t28_mssubfam, t82_pboole, t30_mboolean, t16_domain_1, fc1_waybel_5, t2_grcat_1, t49_subset_1, t7_tarski, t99_xboole_1, dt_k7_waybel_5, redefinition_r3_pboole, t29_pboole, t9_mboolean, symmetry_r4_pboole, t145_pboole, t40_zfmisc_1, rc2_xboole_0, t45_xboole_1, existence_m1_card_fil, t2_xboole_0, symmetry_r6_pboole, d20_pralg_1, t74_pboole, t118_pboole, t10_mboolean, symmetry_r2_zfrefle1, t112_zfmisc_1, dt_k12_pboole, t40_xboole_1, t46_pboole, t10_xboole_1, t2_mboolean, t11_mssubfam, t65_zfmisc_1, t63_subset_1, d3_xboole_0, t39_xboole_1, t55_pboole, antisymmetry_r2_hidden, fc1_funct_2, t6_pre_circ, redefinition_v2_pboole, rc1_finseq_2, t91_pboole, t95_pboole, t38_xboole_1, t13_pua2mss1, irreflexivity_r2_subset_1, t7_pboole, t45_pboole, t146_pboole
% 155.44/42.08  % No. of inferences in proof: 1905
% 155.44/42.08  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 41521 ms resp. 39097 ms w/o parsing
% 157.36/42.62  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 157.36/42.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------