TSTP Solution File: LAT351+1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT351+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:28:03 EDT 2023

% Result   : Theorem 9.90s 2.98s
% Output   : Refutation 10.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  171
% Syntax   : Number of formulae    :  285 (  33 unt;  59 typ;   0 def)
%            Number of atoms       : 1369 (  38 equ;   0 cnn)
%            Maximal formula atoms :   21 (   6 avg)
%            Number of connectives : 3605 ( 203   ~;   2   |; 918   &;2259   @)
%                                         (   5 <=>; 218  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   74 (  74   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   61 (  59 usr;   2 con; 0-3 aty)
%            Number of variables   :  341 (   0   ^; 284   !;  57   ?; 341   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v2_orders_2_type,type,
    v2_orders_2: $i > $o ).

thf(v3_orders_2_type,type,
    v3_orders_2: $i > $o ).

thf(v4_orders_2_type,type,
    v4_orders_2: $i > $o ).

thf(v1_lattice3_type,type,
    v1_lattice3: $i > $o ).

thf(v2_lattice3_type,type,
    v2_lattice3: $i > $o ).

thf(v3_lattice3_type,type,
    v3_lattice3: $i > $o ).

thf(v3_waybel_3_type,type,
    v3_waybel_3: $i > $o ).

thf(l1_orders_2_type,type,
    l1_orders_2: $i > $o ).

thf(r1_waybel22_type,type,
    r1_waybel22: $i > $i > $o ).

thf(k1_card_1_type,type,
    k1_card_1: $i > $i ).

thf(r5_waybel_1_type,type,
    r5_waybel_1: $i > $i > $o ).

thf(k2_yellow_1_type,type,
    k2_yellow_1: $i > $i ).

thf(k9_waybel_0_type,type,
    k9_waybel_0: $i > $i ).

thf(k3_yellow_1_type,type,
    k3_yellow_1: $i > $i ).

thf(v1_relat_1_type,type,
    v1_relat_1: $i > $o ).

thf(v1_funct_1_type,type,
    v1_funct_1: $i > $o ).

thf(v2_funct_1_type,type,
    v2_funct_1: $i > $o ).

thf(r1_tarski_type,type,
    r1_tarski: $i > $i > $o ).

thf(v1_xboole_0_type,type,
    v1_xboole_0: $i > $o ).

thf(m2_relset_1_type,type,
    m2_relset_1: $i > $i > $i > $o ).

thf(m1_relset_1_type,type,
    m1_relset_1: $i > $i > $i > $o ).

thf(k2_zfmisc_1_type,type,
    k2_zfmisc_1: $i > $i > $i ).

thf(v1_setfam_1_type,type,
    v1_setfam_1: $i > $o ).

thf(m1_subset_1_type,type,
    m1_subset_1: $i > $i > $o ).

thf(k1_zfmisc_1_type,type,
    k1_zfmisc_1: $i > $i ).

thf(r2_hidden_type,type,
    r2_hidden: $i > $i > $o ).

thf(v3_struct_0_type,type,
    v3_struct_0: $i > $o ).

thf(l1_struct_0_type,type,
    l1_struct_0: $i > $o ).

thf(u1_struct_0_type,type,
    u1_struct_0: $i > $i ).

thf(k1_struct_0_type,type,
    k1_struct_0: $i > $i > $i ).

thf(k1_tarski_type,type,
    k1_tarski: $i > $i ).

thf(g1_orders_2_type,type,
    g1_orders_2: $i > $i > $i ).

thf(k1_waybel22_type,type,
    k1_waybel22: $i > $i ).

thf(a_1_0_waybel22_type,type,
    a_1_0_waybel22: $i > $i ).

thf(k1_xboole_0_type,type,
    k1_xboole_0: $i ).

thf(v1_orders_2_type,type,
    v1_orders_2: $i > $o ).

thf(v3_realset2_type,type,
    v3_realset2: $i > $o ).

thf(v3_waybel_8_type,type,
    v3_waybel_8: $i > $o ).

thf(u1_orders_2_type,type,
    u1_orders_2: $i > $i ).

thf(v2_yellow_0_type,type,
    v2_yellow_0: $i > $o ).

thf(v24_waybel_0_type,type,
    v24_waybel_0: $i > $o ).

thf(v2_waybel_3_type,type,
    v2_waybel_3: $i > $o ).

thf(v1_waybel_8_type,type,
    v1_waybel_8: $i > $o ).

thf(v2_waybel_8_type,type,
    v2_waybel_8: $i > $o ).

thf(v1_waybel_5_type,type,
    v1_waybel_5: $i > $o ).

thf(v2_waybel_0_type,type,
    v2_waybel_0: $i > $i > $o ).

thf(k5_waybel_0_type,type,
    k5_waybel_0: $i > $i > $i ).

thf(v13_waybel_0_type,type,
    v13_waybel_0: $i > $i > $o ).

thf(v1_yellow_0_type,type,
    v1_yellow_0: $i > $o ).

thf(v25_waybel_0_type,type,
    v25_waybel_0: $i > $o ).

thf(v1_card_1_type,type,
    v1_card_1: $i > $o ).

thf(k7_waybel_0_type,type,
    k7_waybel_0: $i > $i > $i ).

thf(v3_yellow_0_type,type,
    v3_yellow_0: $i > $o ).

thf(v16_waybel_0_type,type,
    v16_waybel_0: $i > $o ).

thf(v9_waybel_1_type,type,
    v9_waybel_1: $i > $o ).

thf(v2_waybel_1_type,type,
    v2_waybel_1: $i > $o ).

thf(a_1_1_waybel_0_type,type,
    a_1_1_waybel_0: $i > $i ).

thf(v10_waybel_1_type,type,
    v10_waybel_1: $i > $o ).

thf(v11_waybel_1_type,type,
    v11_waybel_1: $i > $o ).

thf(82,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v3_lattice3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow_0) ).

thf(503,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v3_lattice3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

thf(161,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(6,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(138,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(39,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_setfam_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setfam_1) ).

thf(234,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_setfam_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v2_lattice3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).

thf(555,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v2_lattice3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(98,axiom,
    ! [A: $i] :
      ( ( ( v2_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_waybel_8) ).

thf(582,plain,
    ! [A: $i] :
      ( ( ( v2_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(35,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(217,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(43,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(247,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ~ ( v3_struct_0 @ ( k3_yellow_1 @ A ) )
      & ( v1_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( v2_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( v3_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( v4_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( v1_lattice3 @ ( k3_yellow_1 @ A ) )
      & ( v2_lattice3 @ ( k3_yellow_1 @ A ) )
      & ( v3_lattice3 @ ( k3_yellow_1 @ A ) )
      & ( v1_yellow_0 @ ( k3_yellow_1 @ A ) )
      & ( v2_yellow_0 @ ( k3_yellow_1 @ A ) )
      & ( v3_yellow_0 @ ( k3_yellow_1 @ A ) )
      & ( v24_waybel_0 @ ( k3_yellow_1 @ A ) )
      & ( v25_waybel_0 @ ( k3_yellow_1 @ A ) )
      & ( v2_waybel_1 @ ( k3_yellow_1 @ A ) )
      & ( v9_waybel_1 @ ( k3_yellow_1 @ A ) )
      & ( v10_waybel_1 @ ( k3_yellow_1 @ A ) )
      & ( v11_waybel_1 @ ( k3_yellow_1 @ A ) )
      & ( v2_waybel_3 @ ( k3_yellow_1 @ A ) )
      & ( v3_waybel_3 @ ( k3_yellow_1 @ A ) )
      & ( v1_waybel_8 @ ( k3_yellow_1 @ A ) )
      & ( v2_waybel_8 @ ( k3_yellow_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_waybel_8) ).

thf(614,plain,
    ! [A: $i] :
      ( ~ ( v3_struct_0 @ ( k3_yellow_1 @ A ) )
      & ( v1_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( v2_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( v3_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( v4_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( v1_lattice3 @ ( k3_yellow_1 @ A ) )
      & ( v2_lattice3 @ ( k3_yellow_1 @ A ) )
      & ( v3_lattice3 @ ( k3_yellow_1 @ A ) )
      & ( v1_yellow_0 @ ( k3_yellow_1 @ A ) )
      & ( v2_yellow_0 @ ( k3_yellow_1 @ A ) )
      & ( v3_yellow_0 @ ( k3_yellow_1 @ A ) )
      & ( v24_waybel_0 @ ( k3_yellow_1 @ A ) )
      & ( v25_waybel_0 @ ( k3_yellow_1 @ A ) )
      & ( v2_waybel_1 @ ( k3_yellow_1 @ A ) )
      & ( v9_waybel_1 @ ( k3_yellow_1 @ A ) )
      & ( v10_waybel_1 @ ( k3_yellow_1 @ A ) )
      & ( v11_waybel_1 @ ( k3_yellow_1 @ A ) )
      & ( v2_waybel_3 @ ( k3_yellow_1 @ A ) )
      & ( v3_waybel_3 @ ( k3_yellow_1 @ A ) )
      & ( v1_waybel_8 @ ( k3_yellow_1 @ A ) )
      & ( v2_waybel_8 @ ( k3_yellow_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_lattice3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v24_waybel_0 @ A )
          & ( v25_waybel_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_waybel_0) ).

thf(384,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_lattice3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v24_waybel_0 @ A )
          & ( v25_waybel_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v3_lattice3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v3_yellow_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_0) ).

thf(533,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v3_lattice3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v3_yellow_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(174,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(23,axiom,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(185,plain,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(76,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A )
      & ( v1_yellow_0 @ A )
      & ( v2_yellow_0 @ A )
      & ( v3_yellow_0 @ A )
      & ( v16_waybel_0 @ A )
      & ( v24_waybel_0 @ A )
      & ( v25_waybel_0 @ A )
      & ( v2_waybel_1 @ A )
      & ( v9_waybel_1 @ A )
      & ( v1_waybel_5 @ A )
      & ( v3_realset2 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_yellow_7) ).

thf(436,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A )
      & ( v1_yellow_0 @ A )
      & ( v2_yellow_0 @ A )
      & ( v3_yellow_0 @ A )
      & ( v16_waybel_0 @ A )
      & ( v24_waybel_0 @ A )
      & ( v25_waybel_0 @ A )
      & ( v2_waybel_1 @ A )
      & ( v9_waybel_1 @ A )
      & ( v1_waybel_5 @ A )
      & ( v3_realset2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v24_waybel_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v24_waybel_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_waybel_8) ).

thf(389,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v24_waybel_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v24_waybel_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( v1_relat_1 @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(157,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( v1_relat_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(102,axiom,
    ! [A: $i] :
      ( ( ( v1_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_waybel_8) ).

thf(606,plain,
    ! [A: $i] :
      ( ( ( v1_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_setfam_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_setfam_1) ).

thf(152,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_setfam_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( v1_orders_2 @ ( k2_yellow_1 @ A ) )
      & ( l1_orders_2 @ ( k2_yellow_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_1) ).

thf(316,plain,
    ! [A: $i] :
      ( ( v1_orders_2 @ ( k2_yellow_1 @ A ) )
      & ( l1_orders_2 @ ( k2_yellow_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(34,axiom,
    v1_xboole_0 @ k1_xboole_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(216,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( ( k1_struct_0 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).

thf(179,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( ( k1_struct_0 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v1_lattice3 @ A )
       => ~ ( v3_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).

thf(321,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v1_lattice3 @ A )
       => ~ ( v3_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(65,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( m1_subset_1 @ ( k7_waybel_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_waybel_0) ).

thf(376,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( m1_subset_1 @ ( k7_waybel_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).

thf(211,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(45,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice3) ).

thf(253,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(221,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(4,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(132,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(70,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
        & ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).

thf(396,plain,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
        & ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(107,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ ( a_1_0_waybel22 @ B ) )
    <=> ? [C: $i] :
          ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_yellow_1 @ B ) ) )
          & ( A
            = ( k7_waybel_0 @ ( k3_yellow_1 @ B ) @ C ) )
          & ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( C
                = ( k1_tarski @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_waybel22) ).

thf(660,plain,
    ! [A: $i,B: $i] :
      ( ( ( r2_hidden @ A @ ( a_1_0_waybel22 @ B ) )
       => ? [C: $i] :
            ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_yellow_1 @ B ) ) )
            & ( A
              = ( k7_waybel_0 @ ( k3_yellow_1 @ B ) @ C ) )
            & ? [D: $i] :
                ( ( m1_subset_1 @ D @ B )
                & ( C
                  = ( k1_tarski @ D ) ) ) ) )
      & ( ? [C: $i] :
            ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k3_yellow_1 @ B ) ) )
            & ( A
              = ( k7_waybel_0 @ ( k3_yellow_1 @ B ) @ C ) )
            & ? [D: $i] :
                ( ( m1_subset_1 @ D @ B )
                & ( C
                  = ( k1_tarski @ D ) ) ) )
       => ( r2_hidden @ A @ ( a_1_0_waybel22 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(30,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

thf(206,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).

thf(292,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(84,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A )
      & ( v1_yellow_0 @ A )
      & ( v2_yellow_0 @ A )
      & ( v3_yellow_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_yellow_0) ).

thf(512,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A )
      & ( v1_yellow_0 @ A )
      & ( v2_yellow_0 @ A )
      & ( v3_yellow_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_waybel_8) ).

thf(678,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_waybel_8) ).

thf(529,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(56,axiom,
    ! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_card_1) ).

thf(334,plain,
    ! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(113,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
     => ( v13_waybel_0 @ ( k5_waybel_0 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_waybel_0) ).

thf(693,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
     => ( v13_waybel_0 @ ( k5_waybel_0 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v1_yellow_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).

thf(467,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v1_yellow_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(27,axiom,
    ? [A: $i] : ( l1_struct_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(197,plain,
    ? [A: $i] : ( l1_struct_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(63,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v16_waybel_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_waybel_0) ).

thf(361,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v16_waybel_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(77,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A )
      & ( v3_realset2 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_yellow_0) ).

thf(456,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A )
      & ( v3_realset2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
        <=> ( r2_hidden @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

thf(224,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ C @ B ) )
          & ( ( r2_hidden @ C @ B )
           => ( r2_hidden @ C @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(188,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v2_waybel_8 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v24_waybel_0 @ A )
          & ( v1_waybel_8 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel_8) ).

thf(356,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v2_waybel_8 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v24_waybel_0 @ A )
          & ( v1_waybel_8 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).

thf(169,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(7,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(141,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_yellow_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ~ ( v1_xboole_0 @ ( k9_waybel_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel16) ).

thf(610,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_yellow_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ~ ( v1_xboole_0 @ ( k9_waybel_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(79,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A )
      & ( v1_yellow_0 @ A )
      & ( v2_yellow_0 @ A )
      & ( v3_yellow_0 @ A )
      & ( v24_waybel_0 @ A )
      & ( v25_waybel_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_waybel_0) ).

thf(471,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v3_lattice3 @ A )
      & ( v1_yellow_0 @ A )
      & ( v2_yellow_0 @ A )
      & ( v3_yellow_0 @ A )
      & ( v24_waybel_0 @ A )
      & ( v25_waybel_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v1_waybel_5 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_lattice3 @ A )
          & ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A )
          & ( v3_yellow_0 @ A )
          & ( v24_waybel_0 @ A )
          & ( v25_waybel_0 @ A )
          & ( v2_waybel_3 @ A )
          & ( v3_waybel_3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_waybel_5) ).

thf(488,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v1_waybel_5 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_lattice3 @ A )
          & ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A )
          & ( v3_yellow_0 @ A )
          & ( v24_waybel_0 @ A )
          & ( v25_waybel_0 @ A )
          & ( v2_waybel_3 @ A )
          & ( v3_waybel_3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v3_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_waybel_8) ).

thf(339,plain,
    ! [A: $i] :
      ( ( ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v3_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v1_orders_2 @ A )
       => ( A
          = ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).

thf(526,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v1_orders_2 @ A )
       => ( A
          = ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(134,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(42,axiom,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(244,plain,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v1_waybel_5 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_lattice3 @ A )
          & ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A )
          & ( v3_yellow_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_7) ).

thf(541,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v1_waybel_5 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_lattice3 @ A )
          & ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A )
          & ( v3_yellow_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( ( v4_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v4_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_waybel_8) ).

thf(657,plain,
    ! [A: $i] :
      ( ( ( v4_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v4_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(99,axiom,
    ! [A: $i,B: $i] :
      ( ( ( l1_orders_2 @ A )
        & ( l1_orders_2 @ B ) )
     => ( r5_waybel_1 @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r5_waybel_1) ).

thf(586,plain,
    ! [A: $i,B: $i] :
      ( ( ( l1_orders_2 @ A )
        & ( l1_orders_2 @ B ) )
     => ( r5_waybel_1 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(3,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(128,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
        & ( v1_xboole_0 @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

thf(237,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
        & ( v1_xboole_0 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(20,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(176,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(97,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( ~ ( v1_xboole_0 @ ( k7_waybel_0 @ A @ B ) )
        & ( v2_waybel_0 @ ( k7_waybel_0 @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_waybel_0) ).

thf(579,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( ~ ( v1_xboole_0 @ ( k7_waybel_0 @ A @ B ) )
        & ( v2_waybel_0 @ ( k7_waybel_0 @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(204,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_waybel_5 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_waybel_5) ).

thf(350,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_waybel_5 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(159,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( v13_waybel_0 @ ( k7_waybel_0 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_waybel_0) ).

thf(604,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( v13_waybel_0 @ ( k7_waybel_0 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(172,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(111,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ B )
        & ( v2_orders_2 @ B )
        & ( v3_orders_2 @ B )
        & ( l1_orders_2 @ B ) )
     => ( ( r2_hidden @ A @ ( a_1_1_waybel_0 @ B ) )
      <=> ? [C: $i] :
            ( ~ ( v1_xboole_0 @ C )
            & ( v2_waybel_0 @ C @ B )
            & ( v13_waybel_0 @ C @ B )
            & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
            & ( A = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_1_waybel_0) ).

thf(681,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ B )
        & ( v2_orders_2 @ B )
        & ( v3_orders_2 @ B )
        & ( l1_orders_2 @ B ) )
     => ( ( ( r2_hidden @ A @ ( a_1_1_waybel_0 @ B ) )
         => ? [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
              & ( v2_waybel_0 @ C @ B )
              & ( v13_waybel_0 @ C @ B )
              & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
              & ( A = C ) ) )
        & ( ? [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
              & ( v2_waybel_0 @ C @ B )
              & ( v13_waybel_0 @ C @ B )
              & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
              & ( A = C ) )
         => ( r2_hidden @ A @ ( a_1_1_waybel_0 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).

thf(219,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ( v2_waybel_0 @ B @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
     => ( ( v2_waybel_0 @ ( k5_waybel_0 @ A @ B ) @ A )
        & ( v13_waybel_0 @ ( k5_waybel_0 @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_waybel_0) ).

thf(303,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ( v2_waybel_0 @ B @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
     => ( ( v2_waybel_0 @ ( k5_waybel_0 @ A @ B ) @ A )
        & ( v13_waybel_0 @ ( k5_waybel_0 @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( k1_waybel22 @ A )
      = ( a_1_0_waybel22 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_waybel22) ).

thf(208,plain,
    ! [A: $i] :
      ( ( k1_waybel22 @ A )
      = ( a_1_0_waybel22 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ( k9_waybel_0 @ A )
        = ( a_1_1_waybel_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d24_waybel_0) ).

thf(509,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ( k9_waybel_0 @ A )
        = ( a_1_1_waybel_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v2_lattice3 @ A )
       => ~ ( v3_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).

thf(434,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v2_lattice3 @ A )
       => ~ ( v3_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v24_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_yellow_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_waybel_0) ).

thf(345,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v24_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_yellow_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_lattice3 @ A )
        & ( v2_yellow_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v4_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_yellow_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v24_waybel_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v25_waybel_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel16) ).

thf(323,plain,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_lattice3 @ A )
        & ( v2_yellow_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v4_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_yellow_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v24_waybel_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v25_waybel_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(213,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(41,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ ( k1_tarski @ A ) @ ( k1_tarski @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( k1_tarski @ A ) @ B ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( k1_tarski @ A ) @ B ) )
        & ( v3_realset2 @ ( g1_orders_2 @ ( k1_tarski @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow_0) ).

thf(240,plain,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ ( k1_tarski @ A ) @ ( k1_tarski @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( k1_tarski @ A ) @ B ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( k1_tarski @ A ) @ B ) )
        & ( v3_realset2 @ ( g1_orders_2 @ ( k1_tarski @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v2_waybel_8 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v2_yellow_0 @ A )
          & ( v24_waybel_0 @ A )
          & ( v2_waybel_3 @ A )
          & ( v3_waybel_3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel_8) ).

thf(399,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v2_waybel_8 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v2_yellow_0 @ A )
          & ( v24_waybel_0 @ A )
          & ( v2_waybel_3 @ A )
          & ( v3_waybel_3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v2_yellow_0 @ A )
          & ( v24_waybel_0 @ A )
          & ( v2_waybel_3 @ A )
          & ( v3_waybel_3 @ A )
          & ( v1_waybel_8 @ A )
          & ( v2_waybel_8 @ A )
          & ( v3_waybel_8 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_waybel_8) ).

thf(278,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v2_yellow_0 @ A )
          & ( v24_waybel_0 @ A )
          & ( v2_waybel_3 @ A )
          & ( v3_waybel_3 @ A )
          & ( v1_waybel_8 @ A )
          & ( v2_waybel_8 @ A )
          & ( v3_waybel_8 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( k1_card_1 @ ( k1_waybel22 @ A ) )
      = ( k1_card_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_waybel22) ).

thf(431,plain,
    ! [A: $i] :
      ( ( k1_card_1 @ ( k1_waybel22 @ A ) )
      = ( k1_card_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(167,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A ) )
       => ( v3_yellow_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_yellow_0) ).

thf(394,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A ) )
       => ( v3_yellow_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(51,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v3_lattice3 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice3) ).

thf(306,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v3_lattice3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_yellow_0 @ A )
        & ( v2_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v4_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_yellow_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_yellow_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_yellow_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v24_waybel_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v25_waybel_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_waybel_3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel22) ).

thf(589,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_yellow_0 @ A )
        & ( v2_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v4_orders_2 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_yellow_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_yellow_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_yellow_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v24_waybel_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v25_waybel_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v1_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v2_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_lattice3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) )
        & ( v3_waybel_3 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v3_yellow_0 @ A )
       => ( ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_yellow_0) ).

thf(342,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v3_yellow_0 @ A )
       => ( ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(92,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
     => ~ ( v1_xboole_0 @ ( k5_waybel_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_waybel_0) ).

thf(553,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( l1_orders_2 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
     => ~ ( v1_xboole_0 @ ( k5_waybel_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
    <=> ( m1_relset_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

thf(145,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m2_relset_1 @ C @ A @ B )
       => ( m1_relset_1 @ C @ A @ B ) )
      & ( ( m1_relset_1 @ C @ A @ B )
       => ( m2_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(150,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v1_lattice3 @ A )
        & ( v2_lattice3 @ A )
        & ( v3_waybel_8 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v3_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v4_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_yellow_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v24_waybel_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_waybel_3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v3_waybel_3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v3_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_waybel_8) ).

thf(263,plain,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v1_lattice3 @ A )
        & ( v2_lattice3 @ A )
        & ( v3_waybel_8 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v3_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v4_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_lattice3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_yellow_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v24_waybel_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_waybel_3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v3_waybel_3 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v3_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
        & ( v1_setfam_1 @ ( k1_tarski @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_setfam_1) ).

thf(182,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
        & ( v1_setfam_1 @ ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
    <=> ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

thf(199,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
       => ( r1_tarski @ A @ B ) )
      & ( ( r1_tarski @ A @ B )
       => ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(109,axiom,
    ! [A: $i] :
      ( ( v1_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( l1_orders_2 @ ( k3_yellow_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).

thf(673,plain,
    ! [A: $i] :
      ( ( v1_orders_2 @ ( k3_yellow_1 @ A ) )
      & ( l1_orders_2 @ ( k3_yellow_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ( ( k7_waybel_0 @ A @ B )
            = ( k5_waybel_0 @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_waybel_0) ).

thf(336,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ( ( k7_waybel_0 @ A @ B )
            = ( k5_waybel_0 @ A @ ( k1_struct_0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(11,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(154,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(52,axiom,
    ! [A: $i] : ( m1_subset_1 @ ( k1_waybel22 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_yellow_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_waybel22) ).

thf(314,plain,
    ! [A: $i] : ( m1_subset_1 @ ( k1_waybel22 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k3_yellow_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(104,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_yellow_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) ) )
         => ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_waybel22) ).

thf(612,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_yellow_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k2_yellow_1 @ ( k9_waybel_0 @ A ) ) ) )
         => ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(250,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(108,axiom,
    ? [A: $i] : ( l1_orders_2 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).

thf(671,plain,
    ? [A: $i] : ( l1_orders_2 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(85,axiom,
    ! [A: $i] : ( r1_waybel22 @ ( k2_yellow_1 @ ( k9_waybel_0 @ ( k3_yellow_1 @ A ) ) ) @ ( k1_waybel22 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_waybel22) ).

thf(524,plain,
    ! [A: $i] : ( r1_waybel22 @ ( k2_yellow_1 @ ( k9_waybel_0 @ ( k3_yellow_1 @ A ) ) ) @ ( k1_waybel22 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_waybel_8 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v4_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v24_waybel_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_waybel_8) ).

thf(368,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v2_waybel_8 @ A )
        & ( l1_orders_2 @ A ) )
     => ( ~ ( v3_struct_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v4_orders_2 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v24_waybel_0 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v1_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) )
        & ( v2_waybel_8 @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( v2_orders_2 @ B )
        & ( v3_orders_2 @ B )
        & ( v4_orders_2 @ B )
        & ( v1_lattice3 @ B )
        & ( v2_lattice3 @ B )
        & ( v3_lattice3 @ B )
        & ( v3_waybel_3 @ B )
        & ( l1_orders_2 @ B ) )
     => ! [C: $i] :
          ( ( ( r1_waybel22 @ B @ C )
            & ( ( k1_card_1 @ C )
              = ( k1_card_1 @ A ) ) )
         => ( r5_waybel_1 @ B @ ( k2_yellow_1 @ ( k9_waybel_0 @ ( k3_yellow_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_waybel22) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( ( v2_orders_2 @ B )
          & ( v3_orders_2 @ B )
          & ( v4_orders_2 @ B )
          & ( v1_lattice3 @ B )
          & ( v2_lattice3 @ B )
          & ( v3_lattice3 @ B )
          & ( v3_waybel_3 @ B )
          & ( l1_orders_2 @ B ) )
       => ! [C: $i] :
            ( ( ( r1_waybel22 @ B @ C )
              & ( ( k1_card_1 @ C )
                = ( k1_card_1 @ A ) ) )
           => ( r5_waybel_1 @ B @ ( k2_yellow_1 @ ( k9_waybel_0 @ ( k3_yellow_1 @ A ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(114,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( v2_orders_2 @ B )
          & ( v3_orders_2 @ B )
          & ( v4_orders_2 @ B )
          & ( v1_lattice3 @ B )
          & ( v2_lattice3 @ B )
          & ( v3_lattice3 @ B )
          & ( v3_waybel_3 @ B )
          & ( l1_orders_2 @ B ) )
       => ! [C: $i] :
            ( ( ( r1_waybel22 @ B @ C )
              & ( ( k1_card_1 @ C )
                = ( k1_card_1 @ A ) ) )
           => ( r5_waybel_1 @ B @ ( k2_yellow_1 @ ( k9_waybel_0 @ ( k3_yellow_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_waybel_8 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v2_yellow_0 @ A )
          & ( v24_waybel_0 @ A )
          & ( v2_waybel_3 @ A )
          & ( v3_waybel_3 @ A )
          & ( v1_waybel_8 @ A )
          & ( v2_waybel_8 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_waybel_8) ).

thf(418,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_waybel_8 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v2_yellow_0 @ A )
          & ( v24_waybel_0 @ A )
          & ( v2_waybel_3 @ A )
          & ( v3_waybel_3 @ A )
          & ( v1_waybel_8 @ A )
          & ( v2_waybel_8 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v2_yellow_0 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_yellow_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_waybel_0) ).

thf(378,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v2_yellow_0 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_yellow_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v3_lattice3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).

thf(549,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v3_lattice3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v2_waybel_0 @ B @ A )
          & ( v13_waybel_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_waybel_0) ).

thf(536,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( l1_orders_2 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v2_waybel_0 @ B @ A )
          & ( v13_waybel_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v1_waybel_5 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v9_waybel_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_waybel_5) ).

thf(410,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v1_waybel_5 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v9_waybel_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ! [C: $i,D: $i] :
          ( ( ( g1_orders_2 @ A @ B )
            = ( g1_orders_2 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).

thf(190,plain,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ! [C: $i,D: $i] :
          ( ( ( g1_orders_2 @ A @ B )
            = ( g1_orders_2 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v1_yellow_0 @ A )
          & ( v24_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_lattice3 @ A )
          & ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A )
          & ( v3_yellow_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_waybel_0) ).

thf(564,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v1_yellow_0 @ A )
          & ( v24_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v1_lattice3 @ A )
          & ( v2_lattice3 @ A )
          & ( v3_lattice3 @ A )
          & ( v1_yellow_0 @ A )
          & ( v2_yellow_0 @ A )
          & ( v3_yellow_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(49,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v1_waybel_5 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_5) ).

thf(294,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v2_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v4_orders_2 @ A )
      & ( v1_lattice3 @ A )
      & ( v2_lattice3 @ A )
      & ( v1_waybel_5 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(26,axiom,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(195,plain,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v16_waybel_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_waybel_0) ).

thf(575,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v16_waybel_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(163,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).

thf(691,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(80,axiom,
    ! [A: $i,B: $i] :
      ( ( ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
     => ( m1_subset_1 @ ( k5_waybel_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_waybel_0) ).

thf(486,plain,
    ! [A: $i,B: $i] :
      ( ( ( l1_orders_2 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
     => ( m1_subset_1 @ ( k5_waybel_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v1_lattice3 @ A )
        & ( v2_lattice3 @ A )
        & ( v3_lattice3 @ A )
        & ( v3_waybel_3 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( ( v2_orders_2 @ B )
            & ( v3_orders_2 @ B )
            & ( v4_orders_2 @ B )
            & ( v1_lattice3 @ B )
            & ( v2_lattice3 @ B )
            & ( v3_lattice3 @ B )
            & ( v3_waybel_3 @ B )
            & ( l1_orders_2 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( ( r1_waybel22 @ A @ C )
                & ( r1_waybel22 @ B @ D )
                & ( ( k1_card_1 @ C )
                  = ( k1_card_1 @ D ) ) )
             => ( r5_waybel_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_waybel22) ).

thf(560,plain,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v1_lattice3 @ A )
        & ( v2_lattice3 @ A )
        & ( v3_lattice3 @ A )
        & ( v3_waybel_3 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( ( v2_orders_2 @ B )
            & ( v3_orders_2 @ B )
            & ( v4_orders_2 @ B )
            & ( v1_lattice3 @ B )
            & ( v2_lattice3 @ B )
            & ( v3_lattice3 @ B )
            & ( v3_waybel_3 @ B )
            & ( l1_orders_2 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( ( r1_waybel22 @ A @ C )
                & ( r1_waybel22 @ B @ D )
                & ( ( k1_card_1 @ C )
                  = ( k1_card_1 @ D ) ) )
             => ( r5_waybel_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(725,plain,
    $false,
    inference(cvc4,[status(thm)],[503,161,138,234,555,582,217,247,614,384,533,174,185,436,389,157,606,152,316,216,179,321,376,211,253,221,132,396,660,206,292,512,678,529,334,693,467,197,361,456,224,188,356,169,141,610,471,488,339,526,134,244,541,657,586,128,237,176,579,204,350,159,604,172,681,219,303,208,509,434,345,323,213,240,399,278,431,167,394,306,589,342,553,145,150,263,182,199,673,336,154,314,612,250,671,524,368,114,418,378,549,536,410,190,564,294,195,575,163,691,486,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07  % Problem  : LAT351+1 : TPTP v8.1.2. Released v3.4.0.
% 0.04/0.09  % Command  : run_Leo-III %s %d
% 0.09/0.27  % Computer : n032.cluster.edu
% 0.09/0.27  % Model    : x86_64 x86_64
% 0.09/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27  % Memory   : 8042.1875MB
% 0.09/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27  % CPULimit : 300
% 0.09/0.27  % WCLimit  : 300
% 0.09/0.27  % DateTime : Thu May 18 14:39:50 EDT 2023
% 0.09/0.27  % CPUTime  : 
% 0.67/0.66  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.96/0.82  % [INFO] 	 Parsing done (161ms). 
% 0.96/0.83  % [INFO] 	 Running in sequential loop mode. 
% 1.54/1.03  % [INFO] 	 eprover registered as external prover. 
% 1.54/1.03  % [INFO] 	 cvc4 registered as external prover. 
% 1.54/1.04  % [INFO] 	 Scanning for conjecture ... 
% 1.67/1.13  % [INFO] 	 Found a conjecture and 120 axioms. Running axiom selection ... 
% 2.03/1.21  % [INFO] 	 Axiom selection finished. Selected 111 axioms (removed 9 axioms). 
% 2.35/1.31  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.35/1.32  % [INFO] 	 Type checking passed. 
% 2.35/1.33  % [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 ... 
% 9.90/2.97  % External prover 'cvc4' found a proof!
% 9.90/2.97  % [INFO] 	 Killing All external provers ... 
% 9.90/2.97  % Time passed: 2601ms (effective reasoning time: 2145ms)
% 9.90/2.97  % 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)>
% 9.90/2.98  % Axioms used in derivation (111): fc4_subset_1, cc4_waybel_5, dt_l1_orders_2, fc2_waybel16, redefinition_m2_relset_1, dt_k7_waybel_0, fraenkel_a_1_0_waybel22, fc10_waybel_8, cc3_waybel_5, t1_subset, fc12_waybel_8, cc1_setfam_1, fc1_xboole_0, rc2_yellow_0, dt_k1_struct_0, cc2_waybel_8, cc12_waybel_0, rc3_funct_1, d18_waybel_0, cc1_waybel22, cc1_lattice3, dt_m2_relset_1, fc1_waybel16, cc14_waybel_0, d24_waybel_0, cc11_waybel_0, rc13_waybel_0, rc1_waybel_5, rc1_funct_1, cc2_waybel_5, dt_u1_orders_2, fc17_waybel_0, fc14_waybel_0, fc8_waybel_8, fc6_waybel_8, fc1_waybel22, rc1_lattice3, fc2_setfam_1, dt_k3_yellow_1, rc2_lattice3, rc2_subset_1, cc5_waybel_0, t6_boole, dt_k1_card_1, dt_k1_waybel22, t5_subset, cc9_waybel_0, existence_m1_relset_1, cc2_yellow_0, fc7_waybel_8, fc2_subset_1, cc4_waybel_8, t17_waybel22, t2_tarski, t4_subset, fc9_waybel_8, t16_waybel22, t7_boole, existence_l1_orders_2, cc1_funct_1, fc1_subset_1, rc1_yellow_7, rc3_struct_0, cc13_waybel_0, dt_g1_orders_2, rc2_funct_1, rc1_subset_1, reflexivity_r5_waybel_1, abstractness_v1_orders_2, cc4_yellow_0, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, fc14_waybel_8, fc8_waybel_0, dt_k2_yellow_1, cc3_waybel_8, existence_m2_relset_1, fc1_yellow_0, free_g1_orders_2, fc1_struct_0, redefinition_k1_struct_0, d2_waybel22, reflexivity_r1_tarski, rc10_waybel_0, cc10_waybel_0, cc5_yellow_0, fc10_waybel_0, fc11_waybel_8, fc4_waybel_8, cc1_waybel_8, cc1_yellow_0, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, dt_k5_waybel_0, rc1_yellow_0, cc2_lattice3, existence_l1_struct_0, rc12_waybel_0, rc1_setfam_1, fc12_waybel_0, t10_waybel22, rc2_xboole_0, fraenkel_a_1_1_waybel_0, cc1_yellow_7, cc3_yellow_0, fc5_waybel_8, antisymmetry_r2_hidden
% 9.90/2.98  % No. of inferences in proof: 226
% 9.90/2.98  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2601 ms resp. 2145 ms w/o parsing
% 10.08/3.09  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.08/3.09  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------