TSTP Solution File: LAT296+1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : LAT296+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 23:28:50 EDT 2024

% Result   : Theorem 7.47s 3.38s
% Output   : Refutation 7.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  108
% Syntax   : Number of formulae    :  176 (  25 unt;  42 typ;   0 def)
%            Number of atoms       :  680 (  32 equ;   0 cnn)
%            Maximal formula atoms :   19 (   5 avg)
%            Number of connectives : 1920 ( 104   ~;   2   |; 407   &;1270   @)
%                                         (   3 <=>; 134  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   60 (  60   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  42 usr;   2 con; 0-3 aty)
%            Number of variables   :  225 (   0   ^ 179   !;  46   ?; 225   :)

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

thf(v10_lattices_type,type,
    v10_lattices: $i > $o ).

thf(v17_lattices_type,type,
    v17_lattices: $i > $o ).

thf(l3_lattices_type,type,
    l3_lattices: $i > $o ).

thf(g3_lattices_type,type,
    g3_lattices: $i > $i > $i > $i ).

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

thf(u2_lattices_type,type,
    u2_lattices: $i > $i ).

thf(u1_lattices_type,type,
    u1_lattices: $i > $i ).

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

thf(k7_lattices_type,type,
    k7_lattices: $i > $i > $i ).

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

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

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

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

thf(l2_lattices_type,type,
    l2_lattices: $i > $o ).

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

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

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

thf(l1_lattices_type,type,
    l1_lattices: $i > $o ).

thf(v1_relat_1_type,type,
    v1_relat_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_funct_2_type,type,
    v1_funct_2: $i > $i > $i > $o ).

thf(v13_lattices_type,type,
    v13_lattices: $i > $o ).

thf(v14_lattices_type,type,
    v14_lattices: $i > $o ).

thf(v15_lattices_type,type,
    v15_lattices: $i > $o ).

thf(v3_lattices_type,type,
    v3_lattices: $i > $o ).

thf(v4_lattices_type,type,
    v4_lattices: $i > $o ).

thf(v5_lattices_type,type,
    v5_lattices: $i > $o ).

thf(v6_lattices_type,type,
    v6_lattices: $i > $o ).

thf(v7_lattices_type,type,
    v7_lattices: $i > $o ).

thf(v8_lattices_type,type,
    v8_lattices: $i > $o ).

thf(v9_lattices_type,type,
    v9_lattices: $i > $o ).

thf(v2_binop_1_type,type,
    v2_binop_1: $i > $i > $o ).

thf(v1_partfun1_type,type,
    v1_partfun1: $i > $i > $i > $o ).

thf(v16_lattices_type,type,
    v16_lattices: $i > $o ).

thf(r2_lattices_type,type,
    r2_lattices: $i > $i > $i > $o ).

thf(v1_binop_1_type,type,
    v1_binop_1: $i > $i > $o ).

thf(v11_lattices_type,type,
    v11_lattices: $i > $o ).

thf(v12_lattices_type,type,
    v12_lattices: $i > $o ).

thf(25,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(142,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v15_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).

thf(157,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v15_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(24,axiom,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(139,plain,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( l1_lattices @ A )
        & ( l2_lattices @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).

thf(346,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( l1_lattices @ A )
        & ( l2_lattices @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(15,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(115,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v11_lattices @ A )
          & ( v15_lattices @ A )
          & ( v16_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v17_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).

thf(217,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v11_lattices @ A )
          & ( v15_lattices @ A )
          & ( v16_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v17_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v15_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).

thf(308,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v15_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(17,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(120,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(37,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/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).

thf(185,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)],[37]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).

thf(320,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).

thf(106,plain,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v5_lattices @ A )
        & ( l2_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice2) ).

thf(353,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v5_lattices @ A )
        & ( l2_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(21,axiom,
    ? [A: $i] : ( l1_lattices @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).

thf(132,plain,
    ? [A: $i] : ( l1_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(312,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)],[58]) ).

thf(49,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A )
      & ( v17_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_lattices) ).

thf(233,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A )
      & ( v17_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
    <=> ( m1_relset_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

thf(85,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)],[3]) ).

thf(45,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
    <=> ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

thf(220,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)],[45]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(102,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v6_lattices @ A )
        & ( l1_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice2) ).

thf(302,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v6_lattices @ A )
        & ( l1_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(65,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).

thf(349,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).

thf(160,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)],[30]) ).

thf(23,axiom,
    ? [A: $i] : ( l2_lattices @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).

thf(137,plain,
    ? [A: $i] : ( l2_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(32,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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(165,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)],[32]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

thf(92,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(47,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

thf(229,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
        & ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).

thf(197,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
        & ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(60,axiom,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(317,plain,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(38,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
        & ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).

thf(188,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
        & ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( v3_lattices @ A )
       => ( A
          = ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).

thf(169,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( v3_lattices @ A )
       => ( A
          = ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(96,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(18,axiom,
    ? [A: $i] : ( l1_struct_0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(124,plain,
    ? [A: $i] : ( l1_struct_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( ( v1_funct_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).

thf(225,plain,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( ( v1_funct_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(22,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(134,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(20,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/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(128,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)],[20]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g3_lattices @ A @ B @ C )
            = ( g3_lattices @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).

thf(148,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g3_lattices @ A @ B @ C )
            = ( g3_lattices @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v17_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v11_lattices @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A )
          & ( v15_lattices @ A )
          & ( v16_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).

thf(264,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v17_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v11_lattices @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A )
          & ( v15_lattices @ A )
          & ( v16_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(54,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/sandbox/benchmark/theBenchmark.p',t5_subset) ).

thf(296,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)],[54]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v7_lattices @ A )
        & ( l1_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_lattice2) ).

thf(191,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v7_lattices @ A )
        & ( l1_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).

thf(118,plain,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(53,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_lattices) ).

thf(281,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v4_lattices @ A )
        & ( l2_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice2) ).

thf(204,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v4_lattices @ A )
        & ( l2_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(35,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).

thf(172,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(98,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( v11_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A )
          & ( v10_lattices @ A )
          & ( v12_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).

thf(271,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( v11_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A )
          & ( v10_lattices @ A )
          & ( v12_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(62,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v12_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_lattices) ).

thf(323,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v12_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l3_lattices @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_lattices) ).

thf(155,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l3_lattices @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
     => ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

thf(108,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(55,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ( v3_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).

thf(299,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ( v3_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(33,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(167,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)],[33]) ).

thf(31,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(162,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)],[31]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

thf(112,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).

thf(338,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( ( v1_funct_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).

thf(359,plain,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( ( v1_funct_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(10,axiom,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(104,plain,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(50,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_lattices) ).

thf(250,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(48,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/sandbox/benchmark/theBenchmark.p',t4_subset) ).

thf(231,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)],[48]) ).

thf(59,axiom,
    ? [A: $i] : ( l3_lattices @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).

thf(315,plain,
    ? [A: $i] : ( l3_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(26,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(146,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

thf(183,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)],[36]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ( ( ~ ( v3_struct_0 @ A )
              & ( v10_lattices @ A )
              & ( v11_lattices @ A )
              & ( v16_lattices @ A )
              & ( l3_lattices @ A ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
               => ( ( C
                    = ( k7_lattices @ A @ B ) )
                <=> ( r2_lattices @ A @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattices) ).

thf(210,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ( ( ~ ( v3_struct_0 @ A )
              & ( v10_lattices @ A )
              & ( v11_lattices @ A )
              & ( v16_lattices @ A )
              & ( l3_lattices @ A ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
               => ( ( ( C
                      = ( k7_lattices @ A @ B ) )
                   => ( r2_lattices @ A @ C @ B ) )
                  & ( ( r2_lattices @ A @ C @ B )
                   => ( C
                      = ( k7_lattices @ A @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(19,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(126,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v15_lattices @ A )
        & ( v16_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v3_struct_0 @ B )
            & ( v10_lattices @ B )
            & ( v15_lattices @ B )
            & ( v16_lattices @ B )
            & ( l3_lattices @ B ) )
         => ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
              = ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
                           => ( ( ( C = E )
                                & ( D = F )
                                & ( r2_lattices @ A @ C @ D ) )
                             => ( r2_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_filter_2) ).

thf(200,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v15_lattices @ A )
        & ( v16_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v3_struct_0 @ B )
            & ( v10_lattices @ B )
            & ( v15_lattices @ B )
            & ( v16_lattices @ B )
            & ( l3_lattices @ B ) )
         => ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
              = ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
                           => ( ( ( C = E )
                                & ( D = F )
                                & ( r2_lattices @ A @ C @ D ) )
                             => ( r2_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v3_struct_0 @ B )
            & ( v10_lattices @ B )
            & ( v17_lattices @ B )
            & ( l3_lattices @ B ) )
         => ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
              = ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
                   => ( ( C = D )
                     => ( ( k7_lattices @ A @ C )
                        = ( k7_lattices @ B @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_2) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( v17_lattices @ A )
          & ( l3_lattices @ A ) )
       => ! [B: $i] :
            ( ( ~ ( v3_struct_0 @ B )
              & ( v10_lattices @ B )
              & ( v17_lattices @ B )
              & ( l3_lattices @ B ) )
           => ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
                = ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
                     => ( ( C = D )
                       => ( ( k7_lattices @ A @ C )
                          = ( k7_lattices @ B @ D ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(68,plain,
    ~ ! [A: $i] :
        ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( v17_lattices @ A )
          & ( l3_lattices @ A ) )
       => ! [B: $i] :
            ( ( ~ ( v3_struct_0 @ B )
              & ( v10_lattices @ B )
              & ( v17_lattices @ B )
              & ( l3_lattices @ B ) )
           => ( ( ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) )
                = ( g3_lattices @ ( u1_struct_0 @ B ) @ ( u2_lattices @ B ) @ ( u1_lattices @ B ) ) )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
                     => ( ( C = D )
                       => ( ( k7_lattices @ A @ C )
                          = ( k7_lattices @ B @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(100,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(90,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)],[4]) ).

thf(13,axiom,
    v1_xboole_0 @ k1_xboole_0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(111,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(363,plain,
    $false,
    inference(e,[status(thm)],[142,157,139,346,115,217,308,120,185,320,106,353,132,312,233,85,220,102,302,349,160,137,165,92,229,197,317,188,169,96,124,225,134,128,148,264,296,191,118,281,204,172,98,271,323,155,108,299,167,162,112,338,359,104,250,231,315,146,183,210,126,200,68,100,90,111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT296+1 : TPTP v8.2.0. Released v3.4.0.
% 0.03/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun May 19 19:59:54 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 1.12/1.03  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.69/1.26  % [INFO] 	 Parsing done (231ms). 
% 1.69/1.27  % [INFO] 	 Running in sequential loop mode. 
% 2.31/1.64  % [INFO] 	 eprover registered as external prover. 
% 2.31/1.64  % [INFO] 	 cvc4 registered as external prover. 
% 2.31/1.65  % [INFO] 	 Scanning for conjecture ... 
% 2.65/1.79  % [INFO] 	 Found a conjecture (or negated_conjecture) and 72 axioms. Running axiom selection ... 
% 2.74/1.90  % [INFO] 	 Axiom selection finished. Selected 65 axioms (removed 7 axioms). 
% 3.16/2.02  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.16/2.04  % [INFO] 	 Type checking passed. 
% 3.16/2.04  % [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 ... 
% 7.47/3.38  % External prover 'e' found a proof!
% 7.47/3.38  % [INFO] 	 Killing All external provers ... 
% 7.47/3.38  % Time passed: 2865ms (effective reasoning time: 2103ms)
% 7.47/3.38  % 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)>
% 7.47/3.38  % Axioms used in derivation (65): rc1_funct_1, t5_subset, dt_l2_lattices, d21_lattices, cc3_lattices, existence_m2_relset_1, rc2_xboole_0, redefinition_m2_relset_1, t11_filter_2, fc1_xboole_0, rc12_lattices, cc6_lattices, existence_l1_lattices, t1_subset, fc4_subset_1, existence_l3_lattices, fc4_lattice2, cc4_lattices, rc3_funct_1, fc2_lattice2, dt_m2_relset_1, fc3_lattice2, rc11_lattices, rc3_lattices, dt_l1_lattices, dt_k7_lattices, t6_boole, rc2_subset_1, existence_l2_lattices, existence_m1_relset_1, dt_l3_lattices, rc13_lattices, cc5_lattices, t4_subset, t7_boole, cc1_funct_1, rc3_struct_0, fc1_subset_1, fc5_lattice2, rc2_funct_1, rc1_subset_1, cc1_lattices, cc2_funct_1, t3_subset, cc1_relset_1, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, fc1_struct_0, reflexivity_r1_tarski, dt_g3_lattices, rc6_lattices, free_g3_lattices, cc7_lattices, abstractness_v3_lattices, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, existence_l1_struct_0, rc10_lattices, dt_u2_lattices, fc3_lattices, antisymmetry_r2_hidden, cc2_lattices
% 7.47/3.38  % No. of inferences in proof: 134
% 7.47/3.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2865 ms resp. 2103 ms w/o parsing
% 7.78/3.48  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.78/3.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------