TSTP Solution File: SWW096+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWW096+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 : Tue May 21 06:47:08 EDT 2024

% Result   : Theorem 195.20s 36.69s
% Output   : Refutation 195.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   89
% Syntax   : Number of formulae    :  654 ( 229 unt;  44 typ;   0 def)
%            Number of atoms       : 1470 ( 885 equ;   0 cnn)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives : 5910 ( 715   ~; 610   |;  92   &;4433   @)
%                                         (   5 <=>;  55  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   65 (  65   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   47 (  44 usr;  10 con; 0-3 aty)
%            Number of variables   :  724 (   0   ^ 696   !;  28   ?; 724   :)

% Comments : 
%------------------------------------------------------------------------------
thf(and1_type,type,
    and1: $i > $i > $i ).

thf(and2_type,type,
    and2: $i > $i > $i ).

thf(f2_type,type,
    f2: $i > $i > $i > $i ).

thf(lazy_impl_type,type,
    lazy_impl: $i > $i > $i ).

thf(prop_type,type,
    prop: $i > $i ).

thf(impl_type,type,
    impl: $i > $i > $i ).

thf(f6_type,type,
    f6: $i > $i > $i ).

thf(f5_type,type,
    f5: $i > $i > $i ).

thf(not2_type,type,
    not2: $i > $i ).

thf(false2_type,type,
    false2: $i ).

thf(f1_type,type,
    f1: $i > $i > $i > $i ).

thf(f4_type,type,
    f4: $i > $i > $i > $i ).

thf(apply_type,type,
    apply: $i > $i > $i ).

thf(f3_type,type,
    f3: $i > $i > $i > $i ).

thf(f7_type,type,
    f7: $i > $i ).

thf(d_type,type,
    d: $i > $o ).

thf(phi_type,type,
    phi: $i > $i ).

thf(err_type,type,
    err: $i ).

thf(false_type,type,
    false: $i ).

thf(true_type,type,
    true: $i ).

thf(bool_type,type,
    bool: $i > $o ).

thf(or1_type,type,
    or1: $i > $i > $i ).

thf(lazy_and2_type,type,
    lazy_and2: $i > $i > $i ).

thf(forallprefers_type,type,
    forallprefers: $i > $i > $o ).

thf(lazy_and1_type,type,
    lazy_and1: $i > $i > $i ).

thf(exists1_type,type,
    exists1: $i > $i ).

thf(existsprefers_type,type,
    existsprefers: $i > $i > $o ).

thf(exists2_type,type,
    exists2: $i > $i ).

thf(or2_type,type,
    or2: $i > $i > $i ).

thf(not1_type,type,
    not1: $i > $i ).

thf(false1_type,type,
    false1: $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i > $i > $i ).

thf(sk4_type,type,
    sk4: $i > $i > $i ).

thf(sk5_type,type,
    sk5: $i > $i ).

thf(sk6_type,type,
    sk6: $i > $i > $o ).

thf(sk7_type,type,
    sk7: $i > $i > $o ).

thf(sk8_type,type,
    sk8: $i > $i ).

thf(sk9_type,type,
    sk9: $i > $i > $i ).

thf(sk10_type,type,
    sk10: $i > $i > $o ).

thf(sk11_type,type,
    sk11: $i > $i > $o ).

thf(sk12_type,type,
    sk12: $i ).

thf(sk13_type,type,
    sk13: $i > $i > $i ).

thf(10,axiom,
    ! [A: $i] :
      ( ( ( d @ A )
        & ( ( phi @ A )
          = A ) )
      | ( ~ ( d @ A )
        & ( ( phi @ A )
          = err ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_phi) ).

thf(71,plain,
    ! [A: $i] :
      ( ( ( d @ A )
        & ( ( phi @ A )
          = A ) )
      | ( ~ ( d @ A )
        & ( ( phi @ A )
          = err ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(75,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = A )
      | ( ( phi @ A )
        = err ) ),
    inference(cnf,[status(esa)],[71]) ).

thf(78,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = A )
      | ( ( phi @ A )
        = err ) ),
    inference(lifteq,[status(thm)],[75]) ).

thf(700,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = A )
      | ( ( phi @ A )
       != ( phi @ A ) )
      | ( err != A ) ),
    inference(eqfactor_ordered,[status(thm)],[78]) ).

thf(701,plain,
    ( ( phi @ err )
    = err ),
    inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( err ))]]) ).

thf(42,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( ( and2 @ A @ B )
        = ( phi @ ( f1 @ A @ B @ C ) ) )
      & ~ ? [D: $i] : ( forallprefers @ ( f1 @ A @ B @ D ) @ ( f1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_and2) ).

thf(231,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( ( and2 @ A @ B )
        = ( phi @ ( f1 @ A @ B @ C ) ) )
      & ~ ? [D: $i] : ( forallprefers @ ( f1 @ A @ B @ D ) @ ( f1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(233,plain,
    ! [B: $i,A: $i] :
      ( ( and2 @ A @ B )
      = ( phi @ ( f1 @ A @ B @ ( sk13 @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[231]) ).

thf(234,plain,
    ! [B: $i,A: $i] :
      ( ( and2 @ A @ B )
      = ( phi @ ( f1 @ A @ B @ ( sk13 @ B @ A ) ) ) ),
    inference(lifteq,[status(thm)],[233]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( f1 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f1) ).

thf(59,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( f1 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(60,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f1 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
    inference(cnf,[status(esa)],[59]) ).

thf(61,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f1 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
    inference(lifteq,[status(thm)],[60]) ).

thf(1672,plain,
    ! [B: $i,A: $i] :
      ( ( and2 @ A @ B )
      = ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( impl @ B @ ( sk13 @ B @ A ) ) ) @ ( sk13 @ B @ A ) ) ) ) ),
    inference(rewrite,[status(thm)],[234,61]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( and1 @ A @ B )
      = ( and2 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_and2) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( and1 @ A @ B )
        = ( and2 @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(47,plain,
    ~ ! [A: $i,B: $i] :
        ( ( and1 @ A @ B )
        = ( and2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(48,plain,
    ( ( and1 @ sk1 @ sk2 )
   != ( and2 @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[47]) ).

thf(49,plain,
    ( ( and2 @ sk1 @ sk2 )
   != ( and1 @ sk1 @ sk2 ) ),
    inference(lifteq,[status(thm)],[48]) ).

thf(1699,plain,
    ! [B: $i,A: $i] :
      ( ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( impl @ B @ ( sk13 @ B @ A ) ) ) @ ( sk13 @ B @ A ) ) ) )
       != ( and1 @ sk1 @ sk2 ) )
      | ( ( and2 @ A @ B )
       != ( and2 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[1672,49]) ).

thf(1700,plain,
    ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) )
   != ( and1 @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[1699:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(1799,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != err )
    | ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) )
     != ( phi @ err ) ) ),
    inference(paramod_ordered,[status(thm)],[701,1700]) ).

thf(1879,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != err )
    | ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) )
     != err ) ),
    inference(simp,[status(thm)],[1799]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( ( prop @ A )
        = false )
    <=> ~ ( bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop_false) ).

thf(202,plain,
    ! [A: $i] :
      ( ( ( ( prop @ A )
          = false )
       => ~ ( bool @ A ) )
      & ( ~ ( bool @ A )
       => ( ( prop @ A )
          = false ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(203,plain,
    ( ! [A: $i] :
        ( ( ( prop @ A )
          = false )
       => ~ ( bool @ A ) )
    & ! [A: $i] :
        ( ~ ( bool @ A )
       => ( ( prop @ A )
          = false ) ) ),
    inference(miniscope,[status(thm)],[202]) ).

thf(204,plain,
    ! [A: $i] :
      ( ( bool @ A )
      | ( ( prop @ A )
        = false ) ),
    inference(cnf,[status(esa)],[203]) ).

thf(206,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
        = false )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[204]) ).

thf(207,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
        = false )
      | ( bool @ A ) ),
    inference(simp,[status(thm)],[206]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( lazy_impl @ false @ A )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom2) ).

thf(79,plain,
    ! [A: $i] :
      ( ( lazy_impl @ false @ A )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(80,plain,
    ! [A: $i] :
      ( ( lazy_impl @ false @ A )
      = true ),
    inference(cnf,[status(esa)],[79]) ).

thf(81,plain,
    ! [A: $i] :
      ( ( lazy_impl @ false @ A )
      = true ),
    inference(lifteq,[status(thm)],[80]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( forallprefers @ A @ B )
    <=> ( ( ~ ( d @ A )
          & ( d @ B ) )
        | ( ( d @ A )
          & ( d @ B )
          & ~ ( bool @ A )
          & ( bool @ B ) )
        | ( ( A = false )
          & ( B = true ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_forallprefers) ).

thf(176,plain,
    ! [A: $i,B: $i] :
      ( ( ( forallprefers @ A @ B )
       => ( ( ~ ( d @ A )
            & ( d @ B ) )
          | ( ( d @ A )
            & ( d @ B )
            & ~ ( bool @ A )
            & ( bool @ B ) )
          | ( ( A = false )
            & ( B = true ) ) ) )
      & ( ( ( ~ ( d @ A )
            & ( d @ B ) )
          | ( ( d @ A )
            & ( d @ B )
            & ~ ( bool @ A )
            & ( bool @ B ) )
          | ( ( A = false )
            & ( B = true ) ) )
       => ( forallprefers @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(177,plain,
    ( ! [A: $i,B: $i] :
        ( ( forallprefers @ A @ B )
       => ( ( ~ ( d @ A )
            & ( d @ B ) )
          | ( ( d @ A )
            & ( d @ B )
            & ~ ( bool @ A )
            & ( bool @ B ) )
          | ( ( A = false )
            & ( B = true ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( ~ ( d @ A )
            & ( d @ B ) )
          | ( ( d @ A )
            & ( d @ B )
            & ~ ( bool @ A )
            & ( bool @ B ) )
          | ( ( A = false )
            & ( B = true ) ) )
       => ( forallprefers @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[176]) ).

thf(187,plain,
    ! [B: $i,A: $i] :
      ( ( A != false )
      | ( B != true )
      | ( forallprefers @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(192,plain,
    ! [B: $i,A: $i] :
      ( ( A != false )
      | ( B != true )
      | ( forallprefers @ A @ B ) ),
    inference(lifteq,[status(thm)],[187]) ).

thf(193,plain,
    forallprefers @ false @ true,
    inference(simp,[status(thm)],[192]) ).

thf(20,axiom,
    ( ( d @ true )
    & ( d @ false )
    & ( d @ err ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_true_err_in_d) ).

thf(123,plain,
    ( ( d @ true )
    & ( d @ false )
    & ( d @ err ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(125,plain,
    d @ false,
    inference(cnf,[status(esa)],[123]) ).

thf(74,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = A )
      | ~ ( d @ A ) ),
    inference(cnf,[status(esa)],[71]) ).

thf(77,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = A )
      | ~ ( d @ A ) ),
    inference(lifteq,[status(thm)],[74]) ).

thf(760,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = A )
      | ( ( d @ false )
       != ( d @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[125,77]) ).

thf(761,plain,
    ( ( phi @ false )
    = false ),
    inference(pattern_uni,[status(thm)],[760:[bind(A,$thf( false ))]]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( bool @ A )
    <=> ( ( A = false )
        | ( A = true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_bool) ).

thf(85,plain,
    ! [A: $i] :
      ( ( ( bool @ A )
       => ( ( A = false )
          | ( A = true ) ) )
      & ( ( ( A = false )
          | ( A = true ) )
       => ( bool @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(86,plain,
    ( ! [A: $i] :
        ( ( bool @ A )
       => ( ( A = false )
          | ( A = true ) ) )
    & ! [A: $i] :
        ( ( ( A = false )
          | ( A = true ) )
       => ( bool @ A ) ) ),
    inference(miniscope,[status(thm)],[85]) ).

thf(87,plain,
    ! [A: $i] :
      ( ( A != false )
      | ( bool @ A ) ),
    inference(cnf,[status(esa)],[86]) ).

thf(90,plain,
    ! [A: $i] :
      ( ( A != false )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[87]) ).

thf(91,plain,
    bool @ false,
    inference(simp,[status(thm)],[90]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( ( prop @ A )
        = true )
    <=> ( bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop_true) ).

thf(112,plain,
    ! [A: $i] :
      ( ( ( ( prop @ A )
          = true )
       => ( bool @ A ) )
      & ( ( bool @ A )
       => ( ( prop @ A )
          = true ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(113,plain,
    ( ! [A: $i] :
        ( ( ( prop @ A )
          = true )
       => ( bool @ A ) )
    & ! [A: $i] :
        ( ( bool @ A )
       => ( ( prop @ A )
          = true ) ) ),
    inference(miniscope,[status(thm)],[112]) ).

thf(114,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
      | ( ( prop @ A )
        = true ) ),
    inference(cnf,[status(esa)],[113]) ).

thf(116,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
        = true )
      | ~ ( bool @ A ) ),
    inference(lifteq,[status(thm)],[114]) ).

thf(117,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
        = true )
      | ~ ( bool @ A ) ),
    inference(simp,[status(thm)],[116]) ).

thf(2901,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
        = true )
      | ( ( bool @ false )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[91,117]) ).

thf(2902,plain,
    ( ( prop @ false )
    = true ),
    inference(pattern_uni,[status(thm)],[2901:[bind(A,$thf( false ))]]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( f7 @ A )
      = ( lazy_impl @ ( prop @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f7) ).

thf(68,plain,
    ! [A: $i] :
      ( ( f7 @ A )
      = ( lazy_impl @ ( prop @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(69,plain,
    ! [A: $i] :
      ( ( f7 @ A )
      = ( lazy_impl @ ( prop @ A ) @ A ) ),
    inference(cnf,[status(esa)],[68]) ).

thf(70,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ A ) @ A )
      = ( f7 @ A ) ),
    inference(lifteq,[status(thm)],[69]) ).

thf(3032,plain,
    ! [A: $i] :
      ( ( ( lazy_impl @ true @ A )
        = ( f7 @ A ) )
      | ( ( prop @ false )
       != ( prop @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2902,70]) ).

thf(3033,plain,
    ( ( lazy_impl @ true @ false )
    = ( f7 @ false ) ),
    inference(pattern_uni,[status(thm)],[3032:[bind(A,$thf( false ))]]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( lazy_impl @ true @ A )
      = ( phi @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom3) ).

thf(102,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ A )
      = ( phi @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(103,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ A )
      = ( phi @ A ) ),
    inference(cnf,[status(esa)],[102]) ).

thf(104,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ A )
      = ( phi @ A ) ),
    inference(lifteq,[status(thm)],[103]) ).

thf(3645,plain,
    ( ( phi @ false )
    = ( f7 @ false ) ),
    inference(rewrite,[status(thm)],[3033,104]) ).

thf(3646,plain,
    ( ( f7 @ false )
    = false ),
    inference(rewrite,[status(thm)],[761,3645]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( impl @ true @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom4) ).

thf(95,plain,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( impl @ true @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(96,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
      | ( ( impl @ true @ A )
        = A ) ),
    inference(cnf,[status(esa)],[95]) ).

thf(97,plain,
    ! [A: $i] :
      ( ( ( impl @ true @ A )
        = A )
      | ~ ( bool @ A ) ),
    inference(lifteq,[status(thm)],[96]) ).

thf(2107,plain,
    ! [A: $i] :
      ( ( ( impl @ true @ A )
        = A )
      | ( ( bool @ false )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[91,97]) ).

thf(2108,plain,
    ( ( impl @ true @ false )
    = false ),
    inference(pattern_uni,[status(thm)],[2107:[bind(A,$thf( false ))]]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( ( lazy_and2 @ A @ B )
        = ( phi @ ( f2 @ A @ B @ C ) ) )
      & ~ ? [D: $i] : ( forallprefers @ ( f2 @ A @ B @ D ) @ ( f2 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_lazy_and2) ).

thf(119,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( ( lazy_and2 @ A @ B )
        = ( phi @ ( f2 @ A @ B @ C ) ) )
      & ~ ? [D: $i] : ( forallprefers @ ( f2 @ A @ B @ D ) @ ( f2 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(120,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( forallprefers @ ( f2 @ A @ B @ C ) @ ( f2 @ A @ B @ ( sk3 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[119]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( f2 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f2) ).

thf(50,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( f2 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(51,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f2 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
    inference(cnf,[status(esa)],[50]) ).

thf(52,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f2 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) ),
    inference(lifteq,[status(thm)],[51]) ).

thf(3453,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ C ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ C ) ) @ C ) ) @ ( lazy_impl @ ( prop @ ( sk3 @ B @ A ) ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ ( sk3 @ B @ A ) ) ) @ ( sk3 @ B @ A ) ) ) ),
    inference(rewrite,[status(thm)],[120,52]) ).

thf(3489,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( lazy_impl @ ( prop @ D ) @ ( impl @ ( lazy_impl @ B @ ( impl @ C @ D ) ) @ D ) ) @ ( lazy_impl @ ( prop @ ( sk3 @ C @ B ) ) @ ( impl @ true @ ( sk3 @ C @ B ) ) ) )
      | ( ( lazy_impl @ false @ A )
       != ( lazy_impl @ B @ ( impl @ C @ ( sk3 @ C @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[81,3453]) ).

thf(3490,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ A ) @ ( impl @ ( lazy_impl @ false @ ( impl @ B @ A ) ) @ A ) ) @ ( lazy_impl @ ( prop @ ( sk3 @ B @ false ) ) @ ( impl @ true @ ( sk3 @ B @ false ) ) ) ),
    inference(pattern_uni,[status(thm)],[3489:[bind(A,$thf( impl @ G @ ( sk3 @ G @ false ) )),bind(B,$thf( false )),bind(C,$thf( G )),bind(D,$thf( D ))]]) ).

thf(3610,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ A ) @ ( impl @ ( lazy_impl @ false @ ( impl @ B @ A ) ) @ A ) ) @ ( lazy_impl @ ( prop @ ( sk3 @ B @ false ) ) @ ( impl @ true @ ( sk3 @ B @ false ) ) ) ),
    inference(simp,[status(thm)],[3490]) ).

thf(27216,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ A ) @ ( impl @ true @ A ) ) @ ( lazy_impl @ ( prop @ ( sk3 @ B @ false ) ) @ ( impl @ true @ ( sk3 @ B @ false ) ) ) ),
    inference(rewrite,[status(thm)],[3610,81]) ).

thf(27242,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ ( lazy_impl @ ( prop @ A ) @ false ) @ ( lazy_impl @ ( prop @ ( sk3 @ B @ false ) ) @ ( impl @ true @ ( sk3 @ B @ false ) ) ) )
      | ( ( impl @ true @ false )
       != ( impl @ true @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2108,27216]) ).

thf(27243,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ false ) @ false ) @ ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) ) ),
    inference(pattern_uni,[status(thm)],[27242:[bind(A,$thf( false ))]]) ).

thf(27498,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ false ) @ false ) @ ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) ) ),
    inference(simp,[status(thm)],[27243]) ).

thf(27552,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( f7 @ false ) @ ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) ) ),
    inference(rewrite,[status(thm)],[27498,70]) ).

thf(27587,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ false @ ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) ) )
      | ( ( f7 @ false )
       != ( f7 @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[3646,27552]) ).

thf(27588,plain,
    ! [A: $i] :
      ~ ( forallprefers @ false @ ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) ) ),
    inference(pattern_uni,[status(thm)],[27587:[]]) ).

thf(27797,plain,
    ! [A: $i] :
      ( ( forallprefers @ false @ ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) ) )
     != ( forallprefers @ false @ true ) ),
    inference(paramod_ordered,[status(thm)],[193,27588]) ).

thf(27944,plain,
    ! [A: $i] :
      ( ( false != false )
      | ( ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) )
       != true ) ),
    inference(simp,[status(thm)],[27797]) ).

thf(27968,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) )
     != true ),
    inference(simp,[status(thm)],[27944]) ).

thf(28040,plain,
    ! [B: $i,A: $i] :
      ( ( lazy_impl @ false @ A )
     != ( lazy_impl @ ( prop @ ( sk3 @ B @ false ) ) @ ( impl @ true @ ( sk3 @ B @ false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[81,27968]) ).

thf(28138,plain,
    ! [B: $i,A: $i] :
      ( ( ( prop @ ( sk3 @ B @ false ) )
       != false )
      | ( A
       != ( impl @ true @ ( sk3 @ B @ false ) ) ) ),
    inference(simp,[status(thm)],[28040]) ).

thf(28177,plain,
    ! [A: $i] :
      ( ( prop @ ( sk3 @ A @ false ) )
     != false ),
    inference(simp,[status(thm)],[28138]) ).

thf(28217,plain,
    ! [B: $i,A: $i] :
      ( ( bool @ A )
      | ( ( prop @ A )
       != ( prop @ ( sk3 @ B @ false ) ) ) ),
    inference(paramod_ordered,[status(thm)],[207,28177]) ).

thf(28218,plain,
    ! [A: $i] : ( bool @ ( sk3 @ A @ false ) ),
    inference(pattern_uni,[status(thm)],[28217:[bind(A,$thf( sk3 @ C @ false )),bind(B,$thf( C ))]]) ).

thf(28238,plain,
    ! [A: $i] : ( bool @ ( sk3 @ A @ false ) ),
    inference(simp,[status(thm)],[28218]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( and1 @ false @ A )
        = false ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom3) ).

thf(242,plain,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( and1 @ false @ A )
        = false ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(243,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
      | ( ( and1 @ false @ A )
        = false ) ),
    inference(cnf,[status(esa)],[242]) ).

thf(244,plain,
    ! [A: $i] :
      ( ( ( and1 @ false @ A )
        = false )
      | ~ ( bool @ A ) ),
    inference(lifteq,[status(thm)],[243]) ).

thf(33646,plain,
    ! [B: $i,A: $i] :
      ( ( ( and1 @ false @ B )
        = false )
      | ( ( bool @ ( sk3 @ A @ false ) )
       != ( bool @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[28238,244]) ).

thf(33647,plain,
    ! [A: $i] :
      ( ( and1 @ false @ ( sk3 @ A @ false ) )
      = false ),
    inference(pattern_uni,[status(thm)],[33646:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C @ false ))]]) ).

thf(33839,plain,
    ! [A: $i] :
      ( ( and1 @ false @ ( sk3 @ A @ false ) )
      = false ),
    inference(simp,[status(thm)],[33647]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( ( f5 @ A @ B )
        = ( phi @ ( f4 @ A @ C @ B ) ) )
      & ~ ? [D: $i] : ( forallprefers @ ( f4 @ A @ D @ B ) @ ( f4 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f5) ).

thf(137,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( ( f5 @ A @ B )
        = ( phi @ ( f4 @ A @ C @ B ) ) )
      & ~ ? [D: $i] : ( forallprefers @ ( f4 @ A @ D @ B ) @ ( f4 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(139,plain,
    ! [B: $i,A: $i] :
      ( ( f5 @ A @ B )
      = ( phi @ ( f4 @ A @ ( sk4 @ B @ A ) @ B ) ) ),
    inference(cnf,[status(esa)],[137]) ).

thf(140,plain,
    ! [B: $i,A: $i] :
      ( ( f5 @ A @ B )
      = ( phi @ ( f4 @ A @ ( sk4 @ B @ A ) @ B ) ) ),
    inference(lifteq,[status(thm)],[139]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( f4 @ A @ B @ C )
      = ( impl @ ( apply @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f4) ).

thf(62,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( f4 @ A @ B @ C )
      = ( impl @ ( apply @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(63,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f4 @ A @ B @ C )
      = ( impl @ ( apply @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[62]) ).

thf(64,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f4 @ A @ B @ C )
      = ( impl @ ( apply @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[63]) ).

thf(539,plain,
    ! [B: $i,A: $i] :
      ( ( f5 @ A @ B )
      = ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) ),
    inference(rewrite,[status(thm)],[140,64]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( f6 @ A @ B )
      = ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f6) ).

thf(53,plain,
    ! [A: $i,B: $i] :
      ( ( f6 @ A @ B )
      = ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(54,plain,
    ! [B: $i,A: $i] :
      ( ( f6 @ A @ B )
      = ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) ),
    inference(cnf,[status(esa)],[53]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ( f6 @ A @ B )
      = ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) ),
    inference(lifteq,[status(thm)],[54]) ).

thf(3041,plain,
    ! [B: $i,A: $i] :
      ( ( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ B ) @ B ) )
        = ( f6 @ A @ B ) )
      | ( ( prop @ false )
       != ( prop @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2902,55]) ).

thf(3042,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ false ) @ false ) )
      = ( f6 @ A @ false ) ),
    inference(pattern_uni,[status(thm)],[3041:[bind(A,$thf( A )),bind(B,$thf( false ))]]) ).

thf(4045,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) )
      = ( f6 @ A @ false ) ),
    inference(rewrite,[status(thm)],[3042,104]) ).

thf(4100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ false ) )
        = ( f6 @ C @ false ) )
      | ( ( f5 @ A @ B )
       != ( f5 @ C @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[539,4045]) ).

thf(4101,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) )
      = ( f6 @ A @ false ) ),
    inference(pattern_uni,[status(thm)],[4100:[bind(A,$thf( A )),bind(B,$thf( false )),bind(C,$thf( A ))]]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( or1 @ A @ B )
        = ( phi @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom1) ).

thf(98,plain,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( or1 @ A @ B )
        = ( phi @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(99,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
     => ! [B: $i] :
          ( ( or1 @ A @ B )
          = ( phi @ A ) ) ),
    inference(miniscope,[status(thm)],[98]) ).

thf(100,plain,
    ! [B: $i,A: $i] :
      ( ( bool @ A )
      | ( ( or1 @ A @ B )
        = ( phi @ A ) ) ),
    inference(cnf,[status(esa)],[99]) ).

thf(101,plain,
    ! [B: $i,A: $i] :
      ( ( ( or1 @ A @ B )
        = ( phi @ A ) )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[100]) ).

thf(89,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
      | ( A = false )
      | ( A = true ) ),
    inference(cnf,[status(esa)],[86]) ).

thf(94,plain,
    ! [A: $i] :
      ( ( A = false )
      | ( A = true )
      | ~ ( bool @ A ) ),
    inference(lifteq,[status(thm)],[89]) ).

thf(1384,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( A
       != ( and2 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[94,49]) ).

thf(1385,plain,
    ( ( ( and2 @ sk1 @ sk2 )
      = false )
    | ~ ( bool @ ( and2 @ sk1 @ sk2 ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true ) ),
    inference(pattern_uni,[status(thm)],[1384:[bind(A,$thf( and2 @ sk1 @ sk2 ))]]) ).

thf(5259,plain,
    ( ~ ( bool @ ( and2 @ sk1 @ sk2 ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( and2 @ sk1 @ sk2 )
     != ( and2 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[1385,49]) ).

thf(5260,plain,
    ( ~ ( bool @ ( and2 @ sk1 @ sk2 ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false ) ),
    inference(pattern_uni,[status(thm)],[5259:[]]) ).

thf(1814,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != ( phi @ true ) )
      | ( ( lazy_impl @ false @ A )
       != ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[81,1700]) ).

thf(1880,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != ( phi @ true ) )
      | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
       != false )
      | ( A
       != ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) ),
    inference(simp,[status(thm)],[1814]) ).

thf(1893,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != ( phi @ true ) )
    | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
     != false ) ),
    inference(simp,[status(thm)],[1880]) ).

thf(126,plain,
    d @ true,
    inference(cnf,[status(esa)],[123]) ).

thf(810,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = A )
      | ( ( d @ true )
       != ( d @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[126,77]) ).

thf(811,plain,
    ( ( phi @ true )
    = true ),
    inference(pattern_uni,[status(thm)],[810:[bind(A,$thf( true ))]]) ).

thf(1899,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
     != false ) ),
    inference(rewrite,[status(thm)],[1893,811]) ).

thf(554,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( lazy_impl @ ( prop @ D ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ D ) )
        = ( f6 @ C @ D ) )
      | ( ( f5 @ A @ B )
       != ( f5 @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[539,55]) ).

thf(555,plain,
    ! [B: $i,A: $i] :
      ( ( lazy_impl @ ( prop @ B ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ B ) )
      = ( f6 @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[554:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(1900,plain,
    ! [A: $i] :
      ( ( bool @ A )
      | ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( prop @ A )
       != ( prop @ ( sk13 @ sk2 @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[207,1899]) ).

thf(1901,plain,
    ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true ) ),
    inference(pattern_uni,[status(thm)],[1900:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( or1 @ true @ A )
        = true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom3) ).

thf(228,plain,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( or1 @ true @ A )
        = true ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(229,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
      | ( ( or1 @ true @ A )
        = true ) ),
    inference(cnf,[status(esa)],[228]) ).

thf(230,plain,
    ! [A: $i] :
      ( ( ( or1 @ true @ A )
        = true )
      | ~ ( bool @ A ) ),
    inference(lifteq,[status(thm)],[229]) ).

thf(31326,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( or1 @ true @ A )
        = true )
      | ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1901,230]) ).

thf(31327,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( or1 @ true @ ( sk13 @ sk2 @ sk1 ) )
      = true ) ),
    inference(pattern_uni,[status(thm)],[31326:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).

thf(88,plain,
    ! [A: $i] :
      ( ( A != true )
      | ( bool @ A ) ),
    inference(cnf,[status(esa)],[86]) ).

thf(92,plain,
    ! [A: $i] :
      ( ( A != true )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[88]) ).

thf(93,plain,
    bool @ true,
    inference(simp,[status(thm)],[92]) ).

thf(2057,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( bool @ ( sk13 @ sk2 @ true ) )
      | ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[94,1901]) ).

thf(2058,plain,
    ( ( sk1 = false )
    | ~ ( bool @ sk1 )
    | ( bool @ ( sk13 @ sk2 @ true ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true ) ),
    inference(pattern_uni,[status(thm)],[2057:[bind(A,$thf( sk1 ))]]) ).

thf(7275,plain,
    ( ( sk1 = false )
    | ( bool @ ( sk13 @ sk2 @ true ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( bool @ sk1 )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,2058]) ).

thf(7322,plain,
    ( ( sk1 = false )
    | ( bool @ ( sk13 @ sk2 @ true ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( sk1 != true ) ),
    inference(simp,[status(thm)],[7275]) ).

thf(2095,plain,
    ! [A: $i] :
      ( ( ( impl @ true @ A )
        = A )
      | ( ( bool @ true )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,97]) ).

thf(2096,plain,
    ( ( impl @ true @ true )
    = true ),
    inference(pattern_uni,[status(thm)],[2095:[bind(A,$thf( true ))]]) ).

thf(2883,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
        = true )
      | ( ( bool @ true )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,117]) ).

thf(2884,plain,
    ( ( prop @ true )
    = true ),
    inference(pattern_uni,[status(thm)],[2883:[bind(A,$thf( true ))]]) ).

thf(2967,plain,
    ! [A: $i] :
      ( ( ( lazy_impl @ true @ A )
        = ( f7 @ A ) )
      | ( ( prop @ true )
       != ( prop @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2884,70]) ).

thf(2968,plain,
    ( ( lazy_impl @ true @ true )
    = ( f7 @ true ) ),
    inference(pattern_uni,[status(thm)],[2967:[bind(A,$thf( true ))]]) ).

thf(3253,plain,
    ( ( phi @ true )
    = ( f7 @ true ) ),
    inference(rewrite,[status(thm)],[2968,104]) ).

thf(3254,plain,
    ( ( f7 @ true )
    = true ),
    inference(rewrite,[status(thm)],[811,3253]) ).

thf(3331,plain,
    ( ( phi @ true )
    = true ),
    inference(rewrite,[status(thm)],[3253,3254]) ).

thf(2907,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( prop @ A )
        = true )
      | ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1901,117]) ).

thf(2908,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
      = true ) ),
    inference(pattern_uni,[status(thm)],[2907:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).

thf(1817,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) )
     != ( phi @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[811,1700]) ).

thf(1886,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) )
     != true ) ),
    inference(simp,[status(thm)],[1817]) ).

thf(3164,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( lazy_impl @ true @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) )
     != true )
    | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
     != ( prop @ ( sk13 @ sk2 @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2908,1886]) ).

thf(3165,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( lazy_impl @ true @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) )
     != true ) ),
    inference(pattern_uni,[status(thm)],[3164:[]]) ).

thf(16651,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( phi @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) )
     != true ) ),
    inference(rewrite,[status(thm)],[3165,104]) ).

thf(16761,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( phi @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) )
     != ( phi @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[3331,16651]) ).

thf(16812,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) )
     != true ) ),
    inference(simp,[status(thm)],[16761]) ).

thf(17611,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) )
     != ( impl @ true @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[2096,16812]) ).

thf(17686,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true ) ),
    inference(simp,[status(thm)],[17611]) ).

thf(17748,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) )
     != ( impl @ true @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[2096,17686]) ).

thf(17815,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( sk1 != true )
    | ( ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) )
     != true ) ),
    inference(simp,[status(thm)],[17748]) ).

thf(28,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( ( exists2 @ A )
        = ( phi @ ( f6 @ A @ B ) ) )
      & ~ ? [C: $i] : ( forallprefers @ ( f6 @ A @ C ) @ ( f6 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_exists2) ).

thf(168,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( ( exists2 @ A )
        = ( phi @ ( f6 @ A @ B ) ) )
      & ~ ? [C: $i] : ( forallprefers @ ( f6 @ A @ C ) @ ( f6 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(169,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( f6 @ A @ B ) @ ( f6 @ A @ ( sk8 @ A ) ) ),
    inference(cnf,[status(esa)],[168]) ).

thf(4074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) @ ( f6 @ B @ ( sk8 @ B ) ) )
      | ( ( f6 @ A @ false )
       != ( f6 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[4045,169]) ).

thf(4075,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) @ ( f6 @ A @ ( sk8 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[4074:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( false ))]]) ).

thf(37,axiom,
    ? [A: $i] :
      ( ( false2
        = ( phi @ ( f7 @ A ) ) )
      & ~ ? [B: $i] : ( forallprefers @ ( f7 @ B ) @ ( f7 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_false2) ).

thf(217,plain,
    ? [A: $i] :
      ( ( false2
        = ( phi @ ( f7 @ A ) ) )
      & ~ ? [B: $i] : ( forallprefers @ ( f7 @ B ) @ ( f7 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(2061,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( bool @ ( sk13 @ sk2 @ sk1 ) )
      | ( ( and1 @ true @ sk2 )
       != true )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[94,1901]) ).

thf(2062,plain,
    ( ( sk1 = false )
    | ~ ( bool @ sk1 )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( and1 @ true @ sk2 )
     != true ) ),
    inference(pattern_uni,[status(thm)],[2061:[bind(A,$thf( sk1 ))]]) ).

thf(2063,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( bool @ ( sk13 @ sk2 @ sk1 ) )
      | ( ( and1 @ sk1 @ true )
       != true )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[94,1901]) ).

thf(2064,plain,
    ( ( sk2 = false )
    | ~ ( bool @ sk2 )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( and1 @ sk1 @ true )
     != true ) ),
    inference(pattern_uni,[status(thm)],[2063:[bind(A,$thf( sk2 ))]]) ).

thf(8045,plain,
    ( ( sk2 = false )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( and1 @ sk1 @ true )
     != true )
    | ( ( bool @ sk2 )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,2064]) ).

thf(8101,plain,
    ( ( sk2 = false )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( and1 @ sk1 @ true )
     != true )
    | ( sk2 != true ) ),
    inference(simp,[status(thm)],[8045]) ).

thf(25,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( ( exists1 @ A )
        = ( phi @ ( apply @ A @ B ) ) )
      & ~ ? [C: $i] : ( existsprefers @ ( apply @ A @ C ) @ ( apply @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists1_axiom1) ).

thf(141,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( ( exists1 @ A )
        = ( phi @ ( apply @ A @ B ) ) )
      & ~ ? [C: $i] : ( existsprefers @ ( apply @ A @ C ) @ ( apply @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(142,plain,
    ! [B: $i,A: $i] :
      ~ ( existsprefers @ ( apply @ A @ B ) @ ( apply @ A @ ( sk5 @ A ) ) ),
    inference(cnf,[status(esa)],[141]) ).

thf(2055,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( bool @ ( sk13 @ true @ sk1 ) )
      | ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[94,1901]) ).

thf(2056,plain,
    ( ( sk2 = false )
    | ~ ( bool @ sk2 )
    | ( bool @ ( sk13 @ true @ sk1 ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true ) ),
    inference(pattern_uni,[status(thm)],[2055:[bind(A,$thf( sk2 ))]]) ).

thf(6625,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( sk2 = false )
      | ~ ( bool @ sk2 )
      | ( bool @ ( sk13 @ true @ sk1 ) )
      | ( ( and1 @ sk1 @ true )
       != true )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[94,2056]) ).

thf(6626,plain,
    ( ( sk2 = false )
    | ~ ( bool @ sk2 )
    | ( sk2 = false )
    | ~ ( bool @ sk2 )
    | ( bool @ ( sk13 @ true @ sk1 ) )
    | ( ( and1 @ sk1 @ true )
     != true ) ),
    inference(pattern_uni,[status(thm)],[6625:[bind(A,$thf( sk2 ))]]) ).

thf(6640,plain,
    ( ( sk2 = false )
    | ~ ( bool @ sk2 )
    | ( bool @ ( sk13 @ true @ sk1 ) )
    | ( ( and1 @ sk1 @ true )
     != true ) ),
    inference(simp,[status(thm)],[6626]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( not2 @ A )
      = ( impl @ A @ false2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_not2) ).

thf(56,plain,
    ! [A: $i] :
      ( ( not2 @ A )
      = ( impl @ A @ false2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(57,plain,
    ! [A: $i] :
      ( ( not2 @ A )
      = ( impl @ A @ false2 ) ),
    inference(cnf,[status(esa)],[56]) ).

thf(58,plain,
    ! [A: $i] :
      ( ( impl @ A @ false2 )
      = ( not2 @ A ) ),
    inference(lifteq,[status(thm)],[57]) ).

thf(558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( not2 @ A ) )
        = ( f5 @ B @ C ) )
      | ( ( impl @ A @ false2 )
       != ( impl @ ( apply @ B @ ( sk4 @ C @ B ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[58,539]) ).

thf(559,plain,
    ! [A: $i] :
      ( ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) )
      = ( f5 @ A @ false2 ) ),
    inference(pattern_uni,[status(thm)],[558:[bind(A,$thf( apply @ G @ ( sk4 @ false2 @ G ) )),bind(B,$thf( G )),bind(C,$thf( false2 ))]]) ).

thf(574,plain,
    ! [A: $i] :
      ( ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) )
      = ( f5 @ A @ false2 ) ),
    inference(simp,[status(thm)],[559]) ).

thf(260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( lazy_impl @ ( prop @ C ) @ ( not2 @ A ) )
        = ( f6 @ B @ C ) )
      | ( ( impl @ A @ false2 )
       != ( impl @ ( f5 @ B @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[58,55]) ).

thf(261,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
      = ( f6 @ A @ false2 ) ),
    inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( f5 @ D @ false2 )),bind(B,$thf( D )),bind(C,$thf( false2 ))]]) ).

thf(262,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
      = ( f6 @ A @ false2 ) ),
    inference(simp,[status(thm)],[261]) ).

thf(575,plain,
    ! [B: $i,A: $i] :
      ( ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) ) ) )
        = ( f6 @ B @ false2 ) )
      | ( ( f5 @ A @ false2 )
       != ( f5 @ B @ false2 ) ) ),
    inference(paramod_ordered,[status(thm)],[574,262]) ).

thf(576,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) ) ) )
      = ( f6 @ A @ false2 ) ),
    inference(pattern_uni,[status(thm)],[575:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(15783,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( lazy_impl @ ( prop @ B ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ B ) )
        = ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ C @ ( sk4 @ false2 @ C ) ) ) ) ) ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ false2 ) ) ),
    inference(paramod_ordered,[status(thm)],[555,576]) ).

thf(15784,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ false2 ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false2 @ A ) ) @ false2 ) ) @ false2 ) )
      = ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[15783:[bind(A,$thf( A )),bind(B,$thf( false2 )),bind(C,$thf( A ))]]) ).

thf(26657,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false2 @ A ) ) @ false2 ) ) ) )
      = ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[15784,58]) ).

thf(2976,plain,
    ! [B: $i,A: $i] :
      ( ( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ B ) @ B ) )
        = ( f6 @ A @ B ) )
      | ( ( prop @ true )
       != ( prop @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2884,55]) ).

thf(2977,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ true ) @ true ) )
      = ( f6 @ A @ true ) ),
    inference(pattern_uni,[status(thm)],[2976:[bind(A,$thf( A )),bind(B,$thf( true ))]]) ).

thf(3885,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) )
      = ( f6 @ A @ true ) ),
    inference(rewrite,[status(thm)],[2977,104]) ).

thf(3914,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) @ ( f6 @ B @ ( sk8 @ B ) ) )
      | ( ( f6 @ A @ true )
       != ( f6 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[3885,169]) ).

thf(3915,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) @ ( f6 @ A @ ( sk8 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[3914:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( true ))]]) ).

thf(1807,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( phi @ ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) ) )
     != ( phi @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[761,1700]) ).

thf(1887,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( lazy_impl @ ( prop @ ( sk13 @ sk2 @ sk1 ) ) @ ( impl @ ( impl @ sk1 @ ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) ) ) @ ( sk13 @ sk2 @ sk1 ) ) )
     != false ) ),
    inference(simp,[status(thm)],[1807]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( impl @ false @ A )
        = true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom3) ).

thf(212,plain,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( impl @ false @ A )
        = true ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(213,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
      | ( ( impl @ false @ A )
        = true ) ),
    inference(cnf,[status(esa)],[212]) ).

thf(214,plain,
    ! [A: $i] :
      ( ( ( impl @ false @ A )
        = true )
      | ~ ( bool @ A ) ),
    inference(lifteq,[status(thm)],[213]) ).

thf(28690,plain,
    ! [A: $i] :
      ( ( ( impl @ false @ A )
        = true )
      | ( ( bool @ false )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[91,214]) ).

thf(28691,plain,
    ( ( impl @ false @ false )
    = true ),
    inference(pattern_uni,[status(thm)],[28690:[bind(A,$thf( false ))]]) ).

thf(115,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
       != true )
      | ( bool @ A ) ),
    inference(cnf,[status(esa)],[113]) ).

thf(118,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
       != true )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[115]) ).

thf(7240,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
       != true )
      | ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( and1 @ sk1 @ sk2 )
       != false )
      | ( ( bool @ A )
       != ( bool @ ( and2 @ sk1 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[118,5260]) ).

thf(7241,plain,
    ( ( ( prop @ ( and2 @ sk1 @ sk2 ) )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false ) ),
    inference(pattern_uni,[status(thm)],[7240:[bind(A,$thf( and2 @ sk1 @ sk2 ))]]) ).

thf(218,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( f7 @ A ) @ ( f7 @ sk12 ) ),
    inference(cnf,[status(esa)],[217]) ).

thf(3734,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ false @ ( f7 @ sk12 ) )
      | ( ( f7 @ false )
       != ( f7 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3646,218]) ).

thf(3735,plain,
    ~ ( forallprefers @ false @ ( f7 @ sk12 ) ),
    inference(pattern_uni,[status(thm)],[3734:[bind(A,$thf( false ))]]) ).

thf(3839,plain,
    ( ~ ( forallprefers @ false @ false )
    | ( ( f7 @ sk12 )
     != ( f7 @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[3646,3735]) ).

thf(3845,plain,
    ( ~ ( forallprefers @ false @ false )
    | ( sk12 != false ) ),
    inference(simp,[status(thm)],[3839]) ).

thf(26,axiom,
    ! [A: $i,B: $i] :
      ( ( existsprefers @ A @ B )
    <=> ( ( ~ ( d @ A )
          & ( d @ B ) )
        | ( ( d @ A )
          & ( d @ B )
          & ~ ( bool @ A )
          & ( bool @ B ) )
        | ( ( A = true )
          & ( B = false ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_existsprefers) ).

thf(145,plain,
    ! [A: $i,B: $i] :
      ( ( ( existsprefers @ A @ B )
       => ( ( ~ ( d @ A )
            & ( d @ B ) )
          | ( ( d @ A )
            & ( d @ B )
            & ~ ( bool @ A )
            & ( bool @ B ) )
          | ( ( A = true )
            & ( B = false ) ) ) )
      & ( ( ( ~ ( d @ A )
            & ( d @ B ) )
          | ( ( d @ A )
            & ( d @ B )
            & ~ ( bool @ A )
            & ( bool @ B ) )
          | ( ( A = true )
            & ( B = false ) ) )
       => ( existsprefers @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(146,plain,
    ( ! [A: $i,B: $i] :
        ( ( existsprefers @ A @ B )
       => ( ( ~ ( d @ A )
            & ( d @ B ) )
          | ( ( d @ A )
            & ( d @ B )
            & ~ ( bool @ A )
            & ( bool @ B ) )
          | ( ( A = true )
            & ( B = false ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( ~ ( d @ A )
            & ( d @ B ) )
          | ( ( d @ A )
            & ( d @ B )
            & ~ ( bool @ A )
            & ( bool @ B ) )
          | ( ( A = true )
            & ( B = false ) ) )
       => ( existsprefers @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[145]) ).

thf(157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( existsprefers @ A @ B )
      | ( d @ B )
      | ( sk6 @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( ( or2 @ A @ B )
        = ( phi @ ( f3 @ A @ B @ C ) ) )
      & ~ ? [D: $i] : ( forallprefers @ ( f3 @ A @ B @ D ) @ ( f3 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_or2) ).

thf(172,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( ( or2 @ A @ B )
        = ( phi @ ( f3 @ A @ B @ C ) ) )
      & ~ ? [D: $i] : ( forallprefers @ ( f3 @ A @ B @ D ) @ ( f3 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(174,plain,
    ! [B: $i,A: $i] :
      ( ( or2 @ A @ B )
      = ( phi @ ( f3 @ A @ B @ ( sk9 @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(175,plain,
    ! [B: $i,A: $i] :
      ( ( or2 @ A @ B )
      = ( phi @ ( f3 @ A @ B @ ( sk9 @ B @ A ) ) ) ),
    inference(lifteq,[status(thm)],[174]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( f3 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f3) ).

thf(65,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( f3 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(66,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f3 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) ),
    inference(cnf,[status(esa)],[65]) ).

thf(67,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f3 @ A @ B @ C )
      = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) ),
    inference(lifteq,[status(thm)],[66]) ).

thf(1055,plain,
    ! [B: $i,A: $i] :
      ( ( or2 @ A @ B )
      = ( phi @ ( lazy_impl @ ( prop @ ( sk9 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( sk9 @ B @ A ) ) @ ( impl @ ( impl @ B @ ( sk9 @ B @ A ) ) @ ( sk9 @ B @ A ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[175,67]) ).

thf(28601,plain,
    ! [A: $i] :
      ( ( ( impl @ false @ A )
        = true )
      | ( ( bool @ true )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,214]) ).

thf(28602,plain,
    ( ( impl @ false @ true )
    = true ),
    inference(pattern_uni,[status(thm)],[28601:[bind(A,$thf( true ))]]) ).

thf(17,axiom,
    ( ( true != false )
    & ( true != err )
    & ( false != err ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct_false_true_err) ).

thf(105,plain,
    ( ( true != false )
    & ( true != err )
    & ( false != err ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(107,plain,
    true != err,
    inference(cnf,[status(esa)],[105]) ).

thf(110,plain,
    true != err,
    inference(lifteq,[status(thm)],[107]) ).

thf(1906,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( ( and1 @ sk1 @ true )
       != true )
      | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
       != false )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[94,1899]) ).

thf(1907,plain,
    ( ( sk2 = false )
    | ~ ( bool @ sk2 )
    | ( ( and1 @ sk1 @ true )
     != true )
    | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
     != false ) ),
    inference(pattern_uni,[status(thm)],[1906:[bind(A,$thf( sk2 ))]]) ).

thf(2109,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( impl @ true @ A )
        = A )
      | ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1901,97]) ).

thf(2110,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ true @ ( sk13 @ sk2 @ sk1 ) )
      = ( sk13 @ sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[2109:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).

thf(17642,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ ( impl @ sk1 @ ( sk13 @ sk2 @ sk1 ) ) @ ( sk13 @ sk2 @ sk1 ) )
     != true )
    | ( ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) )
     != ( impl @ true @ ( sk13 @ sk2 @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2110,16812]) ).

thf(17684,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ ( impl @ sk1 @ ( sk13 @ sk2 @ sk1 ) ) @ ( sk13 @ sk2 @ sk1 ) )
     != true )
    | ( sk2 != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != ( sk13 @ sk2 @ sk1 ) ) ),
    inference(simp,[status(thm)],[17642]) ).

thf(17694,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ ( impl @ sk1 @ ( sk13 @ sk2 @ sk1 ) ) @ ( sk13 @ sk2 @ sk1 ) )
     != true )
    | ( sk2 != true ) ),
    inference(simp,[status(thm)],[17684]) ).

thf(368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( f6 @ B @ ( sk8 @ B ) ) )
      | ( ( f6 @ A @ false2 )
       != ( f6 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[262,169]) ).

thf(369,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( f6 @ A @ ( sk8 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( false2 ))]]) ).

thf(387,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ true @ ( f6 @ B @ ( sk8 @ B ) ) )
      | ( ( lazy_impl @ false @ A )
       != ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[81,369]) ).

thf(393,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ true @ ( f6 @ B @ ( sk8 @ B ) ) )
      | ( ( prop @ false2 )
       != false )
      | ( A
       != ( not2 @ ( f5 @ B @ false2 ) ) ) ),
    inference(simp,[status(thm)],[387]) ).

thf(400,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ true @ ( f6 @ A @ ( sk8 @ A ) ) )
      | ( ( prop @ false2 )
       != false ) ),
    inference(simp,[status(thm)],[393]) ).

thf(408,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
      | ( ( prop @ false2 )
       != false )
      | ( ( f6 @ A @ false2 )
       != ( f6 @ B @ ( sk8 @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[262,400]) ).

thf(412,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
      | ( ( prop @ false2 )
       != false )
      | ( A != B )
      | ( ( sk8 @ B )
       != false2 ) ),
    inference(simp,[status(thm)],[408]) ).

thf(415,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ true @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) )
      | ( ( prop @ false2 )
       != false )
      | ( ( sk8 @ A )
       != false2 ) ),
    inference(simp,[status(thm)],[412]) ).

thf(621,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ true @ true )
      | ( ( prop @ false2 )
       != false )
      | ( ( sk8 @ B )
       != false2 )
      | ( ( lazy_impl @ false @ A )
       != ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[81,415]) ).

thf(632,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ true @ true )
      | ( ( prop @ false2 )
       != false )
      | ( ( sk8 @ B )
       != false2 )
      | ( ( prop @ false2 )
       != false )
      | ( A
       != ( not2 @ ( f5 @ B @ false2 ) ) ) ),
    inference(simp,[status(thm)],[621]) ).

thf(638,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ true @ true )
      | ( ( prop @ false2 )
       != false )
      | ( ( sk8 @ A )
       != false2 ) ),
    inference(simp,[status(thm)],[632]) ).

thf(3936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ true ) )
        = ( f6 @ C @ true ) )
      | ( ( f5 @ A @ B )
       != ( f5 @ C @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[539,3885]) ).

thf(3937,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) )
      = ( f6 @ A @ true ) ),
    inference(pattern_uni,[status(thm)],[3936:[bind(A,$thf( A )),bind(B,$thf( true )),bind(C,$thf( A ))]]) ).

thf(4787,plain,
    ! [B: $i,A: $i] :
      ( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) )
        = ( phi @ ( impl @ ( f5 @ B @ true ) @ true ) ) )
      | ( ( f6 @ A @ true )
       != ( f6 @ B @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[3937,3885]) ).

thf(4788,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) )
      = ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) ),
    inference(pattern_uni,[status(thm)],[4787:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(185,plain,
    ! [B: $i,A: $i] :
      ( ( d @ A )
      | ~ ( d @ B )
      | ( forallprefers @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(189,plain,
    ! [B: $i,A: $i] :
      ( ( d @ A )
      | ~ ( d @ B )
      | ( forallprefers @ A @ B ) ),
    inference(simp,[status(thm)],[185]) ).

thf(152,plain,
    ! [B: $i,A: $i] :
      ( ~ ( existsprefers @ A @ B )
      | ~ ( sk6 @ A @ B )
      | ( bool @ B )
      | ( sk7 @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(36,axiom,
    ( ( not1 @ true )
    = false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom3) ).

thf(215,plain,
    ( ( not1 @ true )
    = false ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(216,plain,
    ( ( not1 @ true )
    = false ),
    inference(lifteq,[status(thm)],[215]) ).

thf(219,plain,
    ( false2
    = ( phi @ ( f7 @ sk12 ) ) ),
    inference(cnf,[status(esa)],[217]) ).

thf(220,plain,
    ( ( phi @ ( f7 @ sk12 ) )
    = false2 ),
    inference(lifteq,[status(thm)],[219]) ).

thf(662,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = err )
      | ( A = false2 )
      | ( ( phi @ A )
       != ( phi @ ( f7 @ sk12 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[78,220]) ).

thf(663,plain,
    ( ( ( phi @ ( f7 @ sk12 ) )
      = err )
    | ( ( f7 @ sk12 )
      = false2 ) ),
    inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( f7 @ sk12 ))]]) ).

thf(2567,plain,
    ( ( err = false2 )
    | ( ( f7 @ sk12 )
      = false2 ) ),
    inference(rewrite,[status(thm)],[663,220]) ).

thf(73,plain,
    ! [A: $i] :
      ( ( d @ A )
      | ( ( phi @ A )
        = err ) ),
    inference(cnf,[status(esa)],[71]) ).

thf(76,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = err )
      | ( d @ A ) ),
    inference(lifteq,[status(thm)],[73]) ).

thf(285,plain,
    ! [A: $i] :
      ( ( d @ A )
      | ( err = false2 )
      | ( ( phi @ A )
       != ( phi @ ( f7 @ sk12 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[76,220]) ).

thf(286,plain,
    ( ( d @ ( f7 @ sk12 ) )
    | ( err = false2 ) ),
    inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( f7 @ sk12 ))]]) ).

thf(124,plain,
    d @ err,
    inference(cnf,[status(esa)],[123]) ).

thf(289,plain,
    ( ( d @ ( f7 @ sk12 ) )
    | ( d @ false2 )
    | ( err != err ) ),
    inference(paramod_ordered,[status(thm)],[286,124]) ).

thf(290,plain,
    ( ( d @ ( f7 @ sk12 ) )
    | ( d @ false2 ) ),
    inference(pattern_uni,[status(thm)],[289:[]]) ).

thf(379,plain,
    ( ( d @ false2 )
    | ( ( d @ ( f7 @ sk12 ) )
     != ( d @ false2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[290]) ).

thf(381,plain,
    ( ( d @ false2 )
    | ( ( f7 @ sk12 )
     != false2 ) ),
    inference(simp,[status(thm)],[379]) ).

thf(2572,plain,
    ( ( err = false2 )
    | ( d @ false2 )
    | ( ( f7 @ sk12 )
     != ( f7 @ sk12 ) ) ),
    inference(paramod_ordered,[status(thm)],[2567,381]) ).

thf(2573,plain,
    ( ( err = false2 )
    | ( d @ false2 ) ),
    inference(pattern_uni,[status(thm)],[2572:[]]) ).

thf(2838,plain,
    ( ( d @ false2 )
    | ( err != err ) ),
    inference(paramod_ordered,[status(thm)],[2573,124]) ).

thf(2839,plain,
    d @ false2,
    inference(pattern_uni,[status(thm)],[2838:[]]) ).

thf(2949,plain,
    ! [A: $i] :
      ( ( ( phi @ A )
        = A )
      | ( ( d @ false2 )
       != ( d @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2839,77]) ).

thf(2950,plain,
    ( ( phi @ false2 )
    = false2 ),
    inference(pattern_uni,[status(thm)],[2949:[bind(A,$thf( false2 ))]]) ).

thf(179,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ A @ B )
      | ~ ( d @ A )
      | ( sk10 @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(248,plain,
    ! [A: $i] :
      ( ( forallprefers @ ( f7 @ A ) @ ( f7 @ sk12 ) )
     != ( forallprefers @ false @ true ) ),
    inference(paramod_ordered,[status(thm)],[193,218]) ).

thf(249,plain,
    ! [A: $i] :
      ( ( ( f7 @ A )
       != false )
      | ( ( f7 @ sk12 )
       != true ) ),
    inference(simp,[status(thm)],[248]) ).

thf(3723,plain,
    ! [A: $i] :
      ( ( ( f7 @ sk12 )
       != true )
      | ( ( f7 @ false )
       != ( f7 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3646,249]) ).

thf(3724,plain,
    ( ( f7 @ sk12 )
   != true ),
    inference(pattern_uni,[status(thm)],[3723:[bind(A,$thf( false ))]]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( lazy_and1 @ true @ A )
      = ( phi @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom3) ).

thf(209,plain,
    ! [A: $i] :
      ( ( lazy_and1 @ true @ A )
      = ( phi @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(210,plain,
    ! [A: $i] :
      ( ( lazy_and1 @ true @ A )
      = ( phi @ A ) ),
    inference(cnf,[status(esa)],[209]) ).

thf(211,plain,
    ! [A: $i] :
      ( ( lazy_and1 @ true @ A )
      = ( phi @ A ) ),
    inference(lifteq,[status(thm)],[210]) ).

thf(44,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( and1 @ A @ B )
        = ( phi @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom1) ).

thf(238,plain,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( and1 @ A @ B )
        = ( phi @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( or1 @ false @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom4) ).

thf(82,plain,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( or1 @ false @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(83,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
      | ( ( or1 @ false @ A )
        = A ) ),
    inference(cnf,[status(esa)],[82]) ).

thf(84,plain,
    ! [A: $i] :
      ( ( ( or1 @ false @ A )
        = A )
      | ~ ( bool @ A ) ),
    inference(lifteq,[status(thm)],[83]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( lazy_impl @ A @ B )
        = ( phi @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom1) ).

thf(164,plain,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( lazy_impl @ A @ B )
        = ( phi @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(7243,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
     != ( bool @ ( and2 @ sk1 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1901,5260]) ).

thf(7268,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( sk13 @ sk2 @ sk1 )
     != ( and2 @ sk1 @ sk2 ) ) ),
    inference(simp,[status(thm)],[7243]) ).

thf(6588,plain,
    ( ( sk2 = false )
    | ( bool @ ( sk13 @ true @ sk1 ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( bool @ sk2 )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,2056]) ).

thf(6631,plain,
    ( ( sk2 = false )
    | ( bool @ ( sk13 @ true @ sk1 ) )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( sk2 != true ) ),
    inference(simp,[status(thm)],[6588]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( ( bool @ A )
        & ~ ( bool @ B ) )
     => ( ( impl @ A @ B )
        = ( phi @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom2) ).

thf(221,plain,
    ! [A: $i,B: $i] :
      ( ( ( bool @ A )
        & ~ ( bool @ B ) )
     => ( ( impl @ A @ B )
        = ( phi @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( lazy_and1 @ A @ B )
        = ( phi @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom1) ).

thf(130,plain,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( lazy_and1 @ A @ B )
        = ( phi @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(131,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
     => ! [B: $i] :
          ( ( lazy_and1 @ A @ B )
          = ( phi @ A ) ) ),
    inference(miniscope,[status(thm)],[130]) ).

thf(132,plain,
    ! [B: $i,A: $i] :
      ( ( bool @ A )
      | ( ( lazy_and1 @ A @ B )
        = ( phi @ A ) ) ),
    inference(cnf,[status(esa)],[131]) ).

thf(133,plain,
    ! [B: $i,A: $i] :
      ( ( ( lazy_and1 @ A @ B )
        = ( phi @ A ) )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[132]) ).

thf(4800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) )
        = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( f5 @ B @ C ) @ C ) ) )
      | ( ( f6 @ A @ true )
       != ( f6 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[3937,55]) ).

thf(4801,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) )
      = ( lazy_impl @ ( prop @ true ) @ ( impl @ ( f5 @ A @ true ) @ true ) ) ),
    inference(pattern_uni,[status(thm)],[4800:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( true ))]]) ).

thf(6863,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) )
      = ( lazy_impl @ true @ ( impl @ ( f5 @ A @ true ) @ true ) ) ),
    inference(rewrite,[status(thm)],[4801,2884]) ).

thf(4349,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ C @ false ) @ false ) ) @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ ( sk8 @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[55,4075]) ).

thf(4350,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[4349:[bind(A,$thf( D )),bind(B,$thf( sk8 @ D )),bind(C,$thf( D ))]]) ).

thf(4407,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) ),
    inference(simp,[status(thm)],[4350]) ).

thf(3720,plain,
    ( ( phi @ false )
    = false ),
    inference(rewrite,[status(thm)],[3645,3646]) ).

thf(1386,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( ( and2 @ true @ sk2 )
       != ( and1 @ sk1 @ sk2 ) )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[94,49]) ).

thf(1387,plain,
    ( ( sk1 = false )
    | ~ ( bool @ sk1 )
    | ( ( and2 @ true @ sk2 )
     != ( and1 @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[1386:[bind(A,$thf( sk1 ))]]) ).

thf(2065,plain,
    ( ( sk1 = false )
    | ( ( and2 @ true @ sk2 )
     != ( and1 @ sk1 @ sk2 ) )
    | ( ( bool @ sk1 )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,1387]) ).

thf(2083,plain,
    ( ( sk1 = false )
    | ( ( and2 @ true @ sk2 )
     != ( and1 @ sk1 @ sk2 ) )
    | ( sk1 != true ) ),
    inference(simp,[status(thm)],[2065]) ).

thf(29617,plain,
    ! [B: $i,A: $i] :
      ( ( ( prop @ B )
        = true )
      | ( ( bool @ ( sk3 @ A @ false ) )
       != ( bool @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[28238,117]) ).

thf(29618,plain,
    ! [A: $i] :
      ( ( prop @ ( sk3 @ A @ false ) )
      = true ),
    inference(pattern_uni,[status(thm)],[29617:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C @ false ))]]) ).

thf(29698,plain,
    ! [A: $i] :
      ( ( prop @ ( sk3 @ A @ false ) )
      = true ),
    inference(simp,[status(thm)],[29618]) ).

thf(29704,plain,
    ! [A: $i] :
      ~ ( forallprefers @ false @ ( lazy_impl @ true @ ( impl @ true @ ( sk3 @ A @ false ) ) ) ),
    inference(rewrite,[status(thm)],[27588,29698]) ).

thf(31608,plain,
    ! [A: $i] :
      ~ ( forallprefers @ false @ ( phi @ ( impl @ true @ ( sk3 @ A @ false ) ) ) ),
    inference(rewrite,[status(thm)],[29704,104]) ).

thf(29621,plain,
    ! [B: $i,A: $i] :
      ( ( ( impl @ true @ B )
        = B )
      | ( ( bool @ ( sk3 @ A @ false ) )
       != ( bool @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[28238,97]) ).

thf(29622,plain,
    ! [A: $i] :
      ( ( impl @ true @ ( sk3 @ A @ false ) )
      = ( sk3 @ A @ false ) ),
    inference(pattern_uni,[status(thm)],[29621:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C @ false ))]]) ).

thf(29699,plain,
    ! [A: $i] :
      ( ( impl @ true @ ( sk3 @ A @ false ) )
      = ( sk3 @ A @ false ) ),
    inference(simp,[status(thm)],[29622]) ).

thf(32249,plain,
    ! [A: $i] :
      ~ ( forallprefers @ false @ ( phi @ ( sk3 @ A @ false ) ) ),
    inference(rewrite,[status(thm)],[31608,29699]) ).

thf(29734,plain,
    ! [B: $i,A: $i] :
      ( ( ( lazy_impl @ true @ B )
        = ( f7 @ B ) )
      | ( ( prop @ ( sk3 @ A @ false ) )
       != ( prop @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[29698,70]) ).

thf(29735,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( sk3 @ A @ false ) )
      = ( f7 @ ( sk3 @ A @ false ) ) ),
    inference(pattern_uni,[status(thm)],[29734:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C @ false ))]]) ).

thf(29857,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( sk3 @ A @ false ) )
      = ( f7 @ ( sk3 @ A @ false ) ) ),
    inference(simp,[status(thm)],[29735]) ).

thf(32969,plain,
    ! [A: $i] :
      ( ( phi @ ( sk3 @ A @ false ) )
      = ( f7 @ ( sk3 @ A @ false ) ) ),
    inference(rewrite,[status(thm)],[29857,104]) ).

thf(32971,plain,
    ! [A: $i] :
      ~ ( forallprefers @ false @ ( f7 @ ( sk3 @ A @ false ) ) ),
    inference(rewrite,[status(thm)],[32249,32969]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ~ ( bool @ A )
     => ( ( not1 @ A )
        = ( phi @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom1) ).

thf(199,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
     => ( ( not1 @ A )
        = ( phi @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(200,plain,
    ! [A: $i] :
      ( ( bool @ A )
      | ( ( not1 @ A )
        = ( phi @ A ) ) ),
    inference(cnf,[status(esa)],[199]) ).

thf(201,plain,
    ! [A: $i] :
      ( ( ( not1 @ A )
        = ( phi @ A ) )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[200]) ).

thf(7242,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( bool @ ( and2 @ sk1 @ sk2 ) )
     != ( bool @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[91,5260]) ).

thf(7269,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( and2 @ sk1 @ sk2 )
     != false ) ),
    inference(simp,[status(thm)],[7242]) ).

thf(1914,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( prop @ ( sk13 @ sk2 @ true ) )
       != false )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[94,1899]) ).

thf(1915,plain,
    ( ( sk1 = false )
    | ~ ( bool @ sk1 )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( prop @ ( sk13 @ sk2 @ true ) )
     != false ) ),
    inference(pattern_uni,[status(thm)],[1914:[bind(A,$thf( sk1 ))]]) ).

thf(33695,plain,
    ! [A: $i] :
      ( ( ( and1 @ false @ A )
        = false )
      | ( ( bool @ false )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[91,244]) ).

thf(33696,plain,
    ( ( and1 @ false @ false )
    = false ),
    inference(pattern_uni,[status(thm)],[33695:[bind(A,$thf( false ))]]) ).

thf(2051,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( A = false )
      | ( A = true )
      | ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1901,94]) ).

thf(2052,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
      = false )
    | ( ( sk13 @ sk2 @ sk1 )
      = true ) ),
    inference(pattern_uni,[status(thm)],[2051:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).

thf(17747,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ sk1 @ true )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( ( impl @ sk2 @ ( sk13 @ sk2 @ sk1 ) )
     != ( impl @ true @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[2096,17686]) ).

thf(17809,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ sk1 @ true )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( sk2 != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true ) ),
    inference(simp,[status(thm)],[17747]) ).

thf(17819,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ sk1 @ true )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( sk2 != true ) ),
    inference(simp,[status(thm)],[17809]) ).

thf(18195,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( sk2 != true )
    | ( ( impl @ sk1 @ true )
     != ( impl @ true @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[2096,17819]) ).

thf(18246,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( sk2 != true )
    | ( sk1 != true )
    | ( true != true ) ),
    inference(simp,[status(thm)],[18195]) ).

thf(18255,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( sk2 != true )
    | ( sk1 != true ) ),
    inference(simp,[status(thm)],[18246]) ).

thf(18267,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
      = false )
    | ( sk2 != true )
    | ( sk1 != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != ( sk13 @ sk2 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[2052,18255]) ).

thf(18268,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
      = false )
    | ( sk2 != true )
    | ( sk1 != true ) ),
    inference(pattern_uni,[status(thm)],[18267:[]]) ).

thf(5037,plain,
    ! [B: $i,A: $i] :
      ( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) )
        = ( phi @ ( impl @ ( f5 @ B @ false ) @ false ) ) )
      | ( ( f6 @ A @ false )
       != ( f6 @ B @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[4101,4045]) ).

thf(5038,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) )
      = ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) ),
    inference(pattern_uni,[status(thm)],[5037:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(138,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( forallprefers @ ( f4 @ A @ C @ B ) @ ( f4 @ A @ ( sk4 @ B @ A ) @ B ) ),
    inference(cnf,[status(esa)],[137]) ).

thf(4559,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( forallprefers @ ( impl @ ( apply @ A @ C ) @ B ) @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ),
    inference(rewrite,[status(thm)],[138,64]) ).

thf(4569,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( impl @ ( apply @ B @ D ) @ C ) @ ( not2 @ A ) )
      | ( ( impl @ A @ false2 )
       != ( impl @ ( apply @ B @ ( sk4 @ C @ B ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[58,4559]) ).

thf(4570,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( impl @ ( apply @ B @ A ) @ false2 ) @ ( not2 @ ( apply @ B @ ( sk4 @ false2 @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[4569:[bind(A,$thf( apply @ H @ ( sk4 @ false2 @ H ) )),bind(B,$thf( H )),bind(C,$thf( false2 )),bind(D,$thf( D ))]]) ).

thf(4598,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( impl @ ( apply @ B @ A ) @ false2 ) @ ( not2 @ ( apply @ B @ ( sk4 @ false2 @ B ) ) ) ),
    inference(simp,[status(thm)],[4570]) ).

thf(5330,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( not2 @ ( apply @ B @ A ) ) @ ( not2 @ ( apply @ B @ ( sk4 @ false2 @ B ) ) ) ),
    inference(rewrite,[status(thm)],[4598,58]) ).

thf(39,axiom,
    ( ( not1 @ false )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom2) ).

thf(224,plain,
    ( ( not1 @ false )
    = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(7504,plain,
    ( ( sk1 = false )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( and1 @ true @ sk2 )
     != true )
    | ( ( bool @ sk1 )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,2062]) ).

thf(7555,plain,
    ( ( sk1 = false )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( and1 @ true @ sk2 )
     != true )
    | ( sk1 != true ) ),
    inference(simp,[status(thm)],[7504]) ).

thf(577,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) ) ) ) @ ( f6 @ B @ ( sk8 @ B ) ) )
      | ( ( f5 @ A @ false2 )
       != ( f5 @ B @ false2 ) ) ),
    inference(paramod_ordered,[status(thm)],[574,369]) ).

thf(578,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) ) ) ) @ ( f6 @ A @ ( sk8 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[577:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(7311,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( sk1 = false )
      | ~ ( bool @ sk1 )
      | ( bool @ ( sk13 @ sk2 @ true ) )
      | ( ( and1 @ true @ sk2 )
       != true )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[94,2058]) ).

thf(7312,plain,
    ( ( sk1 = false )
    | ~ ( bool @ sk1 )
    | ( sk1 = false )
    | ~ ( bool @ sk1 )
    | ( bool @ ( sk13 @ sk2 @ true ) )
    | ( ( and1 @ true @ sk2 )
     != true ) ),
    inference(pattern_uni,[status(thm)],[7311:[bind(A,$thf( sk1 ))]]) ).

thf(7329,plain,
    ( ( sk1 = false )
    | ~ ( bool @ sk1 )
    | ( bool @ ( sk13 @ sk2 @ true ) )
    | ( ( and1 @ true @ sk2 )
     != true ) ),
    inference(simp,[status(thm)],[7312]) ).

thf(156,plain,
    ! [B: $i,A: $i] :
      ( ~ ( existsprefers @ A @ B )
      | ~ ( sk6 @ A @ B )
      | ( d @ B )
      | ( sk7 @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(188,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ A @ B )
      | ~ ( sk10 @ A @ B )
      | ( d @ B )
      | ( sk11 @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(106,plain,
    false != err,
    inference(cnf,[status(esa)],[105]) ).

thf(109,plain,
    false != err,
    inference(lifteq,[status(thm)],[106]) ).

thf(29614,plain,
    ! [B: $i,A: $i] :
      ( ( ( or1 @ false @ B )
        = B )
      | ( ( bool @ ( sk3 @ A @ false ) )
       != ( bool @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[28238,84]) ).

thf(29615,plain,
    ! [A: $i] :
      ( ( or1 @ false @ ( sk3 @ A @ false ) )
      = ( sk3 @ A @ false ) ),
    inference(pattern_uni,[status(thm)],[29614:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C @ false ))]]) ).

thf(29697,plain,
    ! [A: $i] :
      ( ( or1 @ false @ ( sk3 @ A @ false ) )
      = ( sk3 @ A @ false ) ),
    inference(simp,[status(thm)],[29615]) ).

thf(33649,plain,
    ! [A: $i] :
      ( ( ( and1 @ false @ A )
        = false )
      | ( ( bool @ true )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,244]) ).

thf(33650,plain,
    ( ( and1 @ false @ true )
    = false ),
    inference(pattern_uni,[status(thm)],[33649:[bind(A,$thf( true ))]]) ).

thf(225,plain,
    ( ( not1 @ false )
    = true ),
    inference(lifteq,[status(thm)],[224]) ).

thf(205,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
       != false )
      | ~ ( bool @ A ) ),
    inference(cnf,[status(esa)],[203]) ).

thf(208,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
       != false )
      | ~ ( bool @ A ) ),
    inference(lifteq,[status(thm)],[205]) ).

thf(3241,plain,
    ! [B: $i,A: $i] :
      ( ( ( prop @ A )
       != true )
      | ( ( prop @ B )
       != false )
      | ( ( bool @ A )
       != ( bool @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[118,208]) ).

thf(3242,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
       != true )
      | ( ( prop @ A )
       != false ) ),
    inference(pattern_uni,[status(thm)],[3241:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(1388,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( ( and2 @ sk1 @ true )
       != ( and1 @ sk1 @ sk2 ) )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[94,49]) ).

thf(1389,plain,
    ( ( sk2 = false )
    | ~ ( bool @ sk2 )
    | ( ( and2 @ sk1 @ true )
     != ( and1 @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[1388:[bind(A,$thf( sk2 ))]]) ).

thf(2597,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
        = false )
      | ( sk2 = false )
      | ( ( and2 @ sk1 @ true )
       != ( and1 @ sk1 @ sk2 ) )
      | ( ( bool @ A )
       != ( bool @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[207,1389]) ).

thf(2598,plain,
    ( ( ( prop @ sk2 )
      = false )
    | ( sk2 = false )
    | ( ( and2 @ sk1 @ true )
     != ( and1 @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[2597:[bind(A,$thf( sk2 ))]]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( ( bool @ A )
        & ~ ( bool @ B ) )
     => ( ( or1 @ A @ B )
        = ( phi @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom2) ).

thf(127,plain,
    ! [A: $i,B: $i] :
      ( ( ( bool @ A )
        & ~ ( bool @ B ) )
     => ( ( or1 @ A @ B )
        = ( phi @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(128,plain,
    ! [B: $i,A: $i] :
      ( ~ ( bool @ A )
      | ( bool @ B )
      | ( ( or1 @ A @ B )
        = ( phi @ B ) ) ),
    inference(cnf,[status(esa)],[127]) ).

thf(129,plain,
    ! [B: $i,A: $i] :
      ( ( ( or1 @ A @ B )
        = ( phi @ B ) )
      | ~ ( bool @ A )
      | ( bool @ B ) ),
    inference(lifteq,[status(thm)],[128]) ).

thf(4346,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ false ) ) @ ( f6 @ C @ ( sk8 @ C ) ) )
      | ( ( f5 @ A @ B )
       != ( f5 @ C @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[539,4075]) ).

thf(4347,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) ) @ ( f6 @ A @ ( sk8 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[4346:[bind(A,$thf( A )),bind(B,$thf( false )),bind(C,$thf( A ))]]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( lazy_and1 @ false @ A )
      = false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom2) ).

thf(134,plain,
    ! [A: $i] :
      ( ( lazy_and1 @ false @ A )
      = false ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(43,axiom,
    ! [A: $i,B: $i] :
      ( ( ( bool @ A )
        & ~ ( bool @ B ) )
     => ( ( and1 @ A @ B )
        = ( phi @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom2) ).

thf(235,plain,
    ! [A: $i,B: $i] :
      ( ( ( bool @ A )
        & ~ ( bool @ B ) )
     => ( ( and1 @ A @ B )
        = ( phi @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(236,plain,
    ! [B: $i,A: $i] :
      ( ~ ( bool @ A )
      | ( bool @ B )
      | ( ( and1 @ A @ B )
        = ( phi @ B ) ) ),
    inference(cnf,[status(esa)],[235]) ).

thf(237,plain,
    ! [B: $i,A: $i] :
      ( ( ( and1 @ A @ B )
        = ( phi @ B ) )
      | ~ ( bool @ A )
      | ( bool @ B ) ),
    inference(lifteq,[status(thm)],[236]) ).

thf(239,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
     => ! [B: $i] :
          ( ( and1 @ A @ B )
          = ( phi @ A ) ) ),
    inference(miniscope,[status(thm)],[238]) ).

thf(240,plain,
    ! [B: $i,A: $i] :
      ( ( bool @ A )
      | ( ( and1 @ A @ B )
        = ( phi @ A ) ) ),
    inference(cnf,[status(esa)],[239]) ).

thf(241,plain,
    ! [B: $i,A: $i] :
      ( ( ( and1 @ A @ B )
        = ( phi @ A ) )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[240]) ).

thf(32811,plain,
    ! [B: $i,A: $i] :
      ( ( bool @ A )
      | ( bool @ ( sk13 @ sk2 @ sk1 ) )
      | ( ( phi @ A )
       != true )
      | ( ( and1 @ A @ B )
       != ( and1 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[241,1901]) ).

thf(32812,plain,
    ( ( bool @ sk1 )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( phi @ sk1 )
     != true ) ),
    inference(pattern_uni,[status(thm)],[32811:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(33421,plain,
    ( ( bool @ sk1 )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( ( phi @ sk1 )
     != ( phi @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[3331,32812]) ).

thf(33452,plain,
    ( ( bool @ sk1 )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) )
    | ( sk1 != true ) ),
    inference(simp,[status(thm)],[33421]) ).

thf(232,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( forallprefers @ ( f1 @ A @ B @ C ) @ ( f1 @ A @ B @ ( sk13 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[231]) ).

thf(12577,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ ( impl @ B @ C ) ) @ C ) ) @ ( lazy_impl @ ( prop @ ( sk13 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( impl @ B @ ( sk13 @ B @ A ) ) ) @ ( sk13 @ B @ A ) ) ) ),
    inference(rewrite,[status(thm)],[232,61]) ).

thf(5245,plain,
    ( ( ( and2 @ sk1 @ sk2 )
      = false )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( bool @ ( and2 @ sk1 @ sk2 ) )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,1385]) ).

thf(5295,plain,
    ( ( ( and2 @ sk1 @ sk2 )
      = false )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and2 @ sk1 @ sk2 )
     != true ) ),
    inference(simp,[status(thm)],[5245]) ).

thf(389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ C @ false2 ) ) ) @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ ( sk8 @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[55,369]) ).

thf(390,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( D )),bind(B,$thf( sk8 @ D )),bind(C,$thf( D ))]]) ).

thf(398,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) ),
    inference(simp,[status(thm)],[390]) ).

thf(1034,plain,
    ! [A: $i] :
      ( ( ( or1 @ false @ A )
        = A )
      | ( ( bool @ true )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,84]) ).

thf(1035,plain,
    ( ( or1 @ false @ true )
    = true ),
    inference(pattern_uni,[status(thm)],[1034:[bind(A,$thf( true ))]]) ).

thf(148,plain,
    ! [B: $i,A: $i] :
      ( ~ ( existsprefers @ A @ B )
      | ~ ( sk6 @ A @ B )
      | ( d @ A )
      | ( sk7 @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(154,plain,
    ! [B: $i,A: $i] :
      ( ( A != true )
      | ( B != false )
      | ( existsprefers @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(160,plain,
    ! [B: $i,A: $i] :
      ( ( A != true )
      | ( B != false )
      | ( existsprefers @ A @ B ) ),
    inference(lifteq,[status(thm)],[154]) ).

thf(161,plain,
    existsprefers @ true @ false,
    inference(simp,[status(thm)],[160]) ).

thf(3342,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ true @ ( f7 @ sk12 ) )
      | ( ( f7 @ true )
       != ( f7 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3254,218]) ).

thf(3343,plain,
    ~ ( forallprefers @ true @ ( f7 @ sk12 ) ),
    inference(pattern_uni,[status(thm)],[3342:[bind(A,$thf( true ))]]) ).

thf(180,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ A @ B )
      | ~ ( sk10 @ A @ B )
      | ~ ( sk11 @ A @ B )
      | ( B = true ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(191,plain,
    ! [B: $i,A: $i] :
      ( ( B = true )
      | ~ ( forallprefers @ A @ B )
      | ~ ( sk10 @ A @ B )
      | ~ ( sk11 @ A @ B ) ),
    inference(lifteq,[status(thm)],[180]) ).

thf(2047,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( or1 @ false @ A )
        = A )
      | ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1901,84]) ).

thf(2048,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( or1 @ false @ ( sk13 @ sk2 @ sk1 ) )
      = ( sk13 @ sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[2047:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).

thf(3239,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
       != true )
      | ( sk2 = false )
      | ( ( and2 @ sk1 @ true )
       != ( and1 @ sk1 @ sk2 ) )
      | ( ( bool @ A )
       != ( bool @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[118,1389]) ).

thf(3240,plain,
    ( ( ( prop @ sk2 )
     != true )
    | ( sk2 = false )
    | ( ( and2 @ sk1 @ true )
     != ( and1 @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[3239:[bind(A,$thf( sk2 ))]]) ).

thf(729,plain,
    ( ( err = false2 )
    | ( ( phi @ ( f7 @ sk12 ) )
     != ( phi @ err ) ) ),
    inference(paramod_ordered,[status(thm)],[220,701]) ).

thf(743,plain,
    ( ( err = false2 )
    | ( ( f7 @ sk12 )
     != err ) ),
    inference(simp,[status(thm)],[729]) ).

thf(13955,plain,
    ( ( sk2 = false )
    | ( bool @ ( sk13 @ true @ sk1 ) )
    | ( ( and1 @ sk1 @ true )
     != true )
    | ( ( bool @ sk2 )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,6640]) ).

thf(14044,plain,
    ( ( sk2 = false )
    | ( bool @ ( sk13 @ true @ sk1 ) )
    | ( ( and1 @ sk1 @ true )
     != true )
    | ( sk2 != true ) ),
    inference(simp,[status(thm)],[13955]) ).

thf(29703,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( impl @ true @ ( sk3 @ A @ false ) ) )
     != true ),
    inference(rewrite,[status(thm)],[27968,29698]) ).

thf(30959,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ true @ ( sk3 @ A @ false ) ) )
     != true ),
    inference(rewrite,[status(thm)],[29703,104]) ).

thf(32247,plain,
    ! [A: $i] :
      ( ( phi @ ( sk3 @ A @ false ) )
     != true ),
    inference(rewrite,[status(thm)],[30959,29699]) ).

thf(32970,plain,
    ! [A: $i] :
      ( ( f7 @ ( sk3 @ A @ false ) )
     != true ),
    inference(rewrite,[status(thm)],[32247,32969]) ).

thf(143,plain,
    ! [A: $i] :
      ( ( exists1 @ A )
      = ( phi @ ( apply @ A @ ( sk5 @ A ) ) ) ),
    inference(cnf,[status(esa)],[141]) ).

thf(144,plain,
    ! [A: $i] :
      ( ( exists1 @ A )
      = ( phi @ ( apply @ A @ ( sk5 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[143]) ).

thf(170,plain,
    ! [A: $i] :
      ( ( exists2 @ A )
      = ( phi @ ( f6 @ A @ ( sk8 @ A ) ) ) ),
    inference(cnf,[status(esa)],[168]) ).

thf(171,plain,
    ! [A: $i] :
      ( ( exists2 @ A )
      = ( phi @ ( f6 @ A @ ( sk8 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[170]) ).

thf(327,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) )
        = ( exists2 @ C ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ ( sk8 @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[55,171]) ).

thf(328,plain,
    ! [A: $i] :
      ( ( phi @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) )
      = ( exists2 @ A ) ),
    inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( D )),bind(B,$thf( sk8 @ D )),bind(C,$thf( D ))]]) ).

thf(335,plain,
    ! [A: $i] :
      ( ( phi @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) )
      = ( exists2 @ A ) ),
    inference(simp,[status(thm)],[328]) ).

thf(3825,plain,
    ( ( f7 @ sk12 )
   != ( f7 @ true ) ),
    inference(paramod_ordered,[status(thm)],[3254,3724]) ).

thf(3832,plain,
    sk12 != true,
    inference(simp,[status(thm)],[3825]) ).

thf(181,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ A @ B )
      | ~ ( sk10 @ A @ B )
      | ~ ( bool @ A )
      | ( sk11 @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(147,plain,
    ! [B: $i,A: $i] :
      ( ~ ( existsprefers @ A @ B )
      | ~ ( sk6 @ A @ B )
      | ~ ( sk7 @ A @ B )
      | ( A = true ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(159,plain,
    ! [B: $i,A: $i] :
      ( ( A = true )
      | ~ ( existsprefers @ A @ B )
      | ~ ( sk6 @ A @ B )
      | ~ ( sk7 @ A @ B ) ),
    inference(lifteq,[status(thm)],[147]) ).

thf(3237,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
       != true )
      | ( sk1 = false )
      | ( ( and2 @ true @ sk2 )
       != ( and1 @ sk1 @ sk2 ) )
      | ( ( bool @ A )
       != ( bool @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[118,1387]) ).

thf(3238,plain,
    ( ( ( prop @ sk1 )
     != true )
    | ( sk1 = false )
    | ( ( and2 @ true @ sk2 )
     != ( and1 @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[3237:[bind(A,$thf( sk1 ))]]) ).

thf(371,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( f6 @ C @ D ) @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ ( sk8 @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[55,169]) ).

thf(372,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( f6 @ B @ A ) @ ( lazy_impl @ ( prop @ ( sk8 @ B ) ) @ ( impl @ ( f5 @ B @ ( sk8 @ B ) ) @ ( sk8 @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[371:[bind(A,$thf( E )),bind(B,$thf( sk8 @ E )),bind(C,$thf( E ))]]) ).

thf(377,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( f6 @ B @ A ) @ ( lazy_impl @ ( prop @ ( sk8 @ B ) ) @ ( impl @ ( f5 @ B @ ( sk8 @ B ) ) @ ( sk8 @ B ) ) ) ),
    inference(simp,[status(thm)],[372]) ).

thf(4103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) )
        = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( f5 @ B @ C ) @ C ) ) )
      | ( ( f6 @ A @ false )
       != ( f6 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[4045,55]) ).

thf(4104,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ false ) @ ( impl @ ( f5 @ A @ false ) @ false ) )
      = ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) ),
    inference(pattern_uni,[status(thm)],[4103:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( false ))]]) ).

thf(4601,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ false ) @ false ) )
      = ( phi @ ( impl @ ( f5 @ A @ false ) @ false ) ) ),
    inference(rewrite,[status(thm)],[4104,2902]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( and1 @ true @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom4) ).

thf(245,plain,
    ! [A: $i] :
      ( ( bool @ A )
     => ( ( and1 @ true @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(173,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( forallprefers @ ( f3 @ A @ B @ C ) @ ( f3 @ A @ B @ ( sk9 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[172]) ).

thf(12248,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ C ) @ ( impl @ ( impl @ A @ C ) @ ( impl @ ( impl @ B @ C ) @ C ) ) ) @ ( lazy_impl @ ( prop @ ( sk9 @ B @ A ) ) @ ( impl @ ( impl @ A @ ( sk9 @ B @ A ) ) @ ( impl @ ( impl @ B @ ( sk9 @ B @ A ) ) @ ( sk9 @ B @ A ) ) ) ) ),
    inference(rewrite,[status(thm)],[173,67]) ).

thf(3729,plain,
    ( ~ ( forallprefers @ true @ false )
    | ( ( f7 @ sk12 )
     != ( f7 @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[3646,3343]) ).

thf(3747,plain,
    ( ~ ( forallprefers @ true @ false )
    | ( sk12 != false ) ),
    inference(simp,[status(thm)],[3729]) ).

thf(2592,plain,
    ( ( sk2 = false )
    | ( ( and2 @ sk1 @ true )
     != ( and1 @ sk1 @ sk2 ) )
    | ( ( bool @ sk2 )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,1389]) ).

thf(2610,plain,
    ( ( sk2 = false )
    | ( ( and2 @ sk1 @ true )
     != ( and1 @ sk1 @ sk2 ) )
    | ( sk2 != true ) ),
    inference(simp,[status(thm)],[2592]) ).

thf(837,plain,
    ( ( false = false2 )
    | ( ( phi @ ( f7 @ sk12 ) )
     != ( phi @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[220,761]) ).

thf(858,plain,
    ( ( false = false2 )
    | ( ( f7 @ sk12 )
     != false ) ),
    inference(simp,[status(thm)],[837]) ).

thf(155,plain,
    ! [B: $i,A: $i] :
      ( ~ ( existsprefers @ A @ B )
      | ~ ( d @ A )
      | ( sk6 @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( impl @ A @ B )
        = ( phi @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom1) ).

thf(195,plain,
    ! [A: $i,B: $i] :
      ( ~ ( bool @ A )
     => ( ( impl @ A @ B )
        = ( phi @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(196,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
     => ! [B: $i] :
          ( ( impl @ A @ B )
          = ( phi @ A ) ) ),
    inference(miniscope,[status(thm)],[195]) ).

thf(197,plain,
    ! [B: $i,A: $i] :
      ( ( bool @ A )
      | ( ( impl @ A @ B )
        = ( phi @ A ) ) ),
    inference(cnf,[status(esa)],[196]) ).

thf(198,plain,
    ! [B: $i,A: $i] :
      ( ( ( impl @ A @ B )
        = ( phi @ A ) )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[197]) ).

thf(4231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ true ) ) @ ( f6 @ C @ ( sk8 @ C ) ) )
      | ( ( f5 @ A @ B )
       != ( f5 @ C @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[539,3915]) ).

thf(4232,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) ) @ ( f6 @ A @ ( sk8 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[4231:[bind(A,$thf( A )),bind(B,$thf( true )),bind(C,$thf( A ))]]) ).

thf(15696,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( lazy_impl @ ( prop @ B ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ B ) )
        = ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ C @ ( sk4 @ true @ C ) ) @ true ) ) @ true ) ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[555,3937]) ).

thf(15697,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ true ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) )
      = ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) ) ),
    inference(pattern_uni,[status(thm)],[15696:[bind(A,$thf( A )),bind(B,$thf( true )),bind(C,$thf( A ))]]) ).

thf(26239,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) )
      = ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ true @ A ) ) @ true ) ) @ true ) ) ),
    inference(rewrite,[status(thm)],[15697,2884]) ).

thf(222,plain,
    ! [B: $i,A: $i] :
      ( ~ ( bool @ A )
      | ( bool @ B )
      | ( ( impl @ A @ B )
        = ( phi @ B ) ) ),
    inference(cnf,[status(esa)],[221]) ).

thf(223,plain,
    ! [B: $i,A: $i] :
      ( ( ( impl @ A @ B )
        = ( phi @ B ) )
      | ~ ( bool @ A )
      | ( bool @ B ) ),
    inference(lifteq,[status(thm)],[222]) ).

thf(40,axiom,
    false1 = false,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_false1) ).

thf(226,plain,
    false1 = false,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(31312,plain,
    ! [A: $i] :
      ( ( ( or1 @ true @ A )
        = true )
      | ( ( bool @ false )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[91,230]) ).

thf(31313,plain,
    ( ( or1 @ true @ false )
    = true ),
    inference(pattern_uni,[status(thm)],[31312:[bind(A,$thf( false ))]]) ).

thf(165,plain,
    ! [A: $i] :
      ( ~ ( bool @ A )
     => ! [B: $i] :
          ( ( lazy_impl @ A @ B )
          = ( phi @ A ) ) ),
    inference(miniscope,[status(thm)],[164]) ).

thf(166,plain,
    ! [B: $i,A: $i] :
      ( ( bool @ A )
      | ( ( lazy_impl @ A @ B )
        = ( phi @ A ) ) ),
    inference(cnf,[status(esa)],[165]) ).

thf(167,plain,
    ! [B: $i,A: $i] :
      ( ( ( lazy_impl @ A @ B )
        = ( phi @ A ) )
      | ( bool @ A ) ),
    inference(lifteq,[status(thm)],[166]) ).

thf(5055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) )
        = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( f5 @ B @ C ) @ C ) ) )
      | ( ( f6 @ A @ false )
       != ( f6 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[4101,55]) ).

thf(5056,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) )
      = ( lazy_impl @ ( prop @ false ) @ ( impl @ ( f5 @ A @ false ) @ false ) ) ),
    inference(pattern_uni,[status(thm)],[5055:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( false ))]]) ).

thf(7630,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) )
      = ( lazy_impl @ true @ ( impl @ ( f5 @ A @ false ) @ false ) ) ),
    inference(rewrite,[status(thm)],[5056,2902]) ).

thf(4234,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ C @ true ) @ true ) ) @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ ( sk8 @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[55,3915]) ).

thf(4235,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[4234:[bind(A,$thf( D )),bind(B,$thf( sk8 @ D )),bind(C,$thf( D ))]]) ).

thf(4282,plain,
    ! [A: $i] :
      ~ ( forallprefers @ ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) ),
    inference(simp,[status(thm)],[4235]) ).

thf(151,plain,
    ! [B: $i,A: $i] :
      ( ~ ( existsprefers @ A @ B )
      | ~ ( sk6 @ A @ B )
      | ~ ( sk7 @ A @ B )
      | ( B = false ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(162,plain,
    ! [B: $i,A: $i] :
      ( ( B = false )
      | ~ ( existsprefers @ A @ B )
      | ~ ( sk6 @ A @ B )
      | ~ ( sk7 @ A @ B ) ),
    inference(lifteq,[status(thm)],[151]) ).

thf(1904,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( ( and1 @ true @ sk2 )
       != true )
      | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
       != false )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[94,1899]) ).

thf(1905,plain,
    ( ( sk1 = false )
    | ~ ( bool @ sk1 )
    | ( ( and1 @ true @ sk2 )
     != true )
    | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
     != false ) ),
    inference(pattern_uni,[status(thm)],[1904:[bind(A,$thf( sk1 ))]]) ).

thf(373,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( forallprefers @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) @ ( f6 @ C @ ( sk8 @ C ) ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[55,169]) ).

thf(374,plain,
    ! [B: $i,A: $i] :
      ~ ( forallprefers @ ( lazy_impl @ ( prop @ B ) @ ( impl @ ( f5 @ A @ B ) @ B ) ) @ ( f6 @ A @ ( sk8 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(616,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ true @ ( f6 @ A @ false2 ) )
      | ( ( prop @ false2 )
       != false )
      | ( ( sk8 @ B )
       != false2 )
      | ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) )
       != ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[262,415]) ).

thf(617,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ true @ ( f6 @ A @ false2 ) )
      | ( ( prop @ false2 )
       != false )
      | ( ( sk8 @ A )
       != false2 ) ),
    inference(pattern_uni,[status(thm)],[616:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(28727,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( impl @ false @ A )
        = true )
      | ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1901,214]) ).

thf(28728,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( impl @ false @ ( sk13 @ sk2 @ sk1 ) )
      = true ) ),
    inference(pattern_uni,[status(thm)],[28727:[bind(A,$thf( sk13 @ sk2 @ sk1 ))]]) ).

thf(182,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ A @ B )
      | ~ ( sk10 @ A @ B )
      | ~ ( sk11 @ A @ B )
      | ( A = false ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(194,plain,
    ! [B: $i,A: $i] :
      ( ( A = false )
      | ~ ( forallprefers @ A @ B )
      | ~ ( sk10 @ A @ B )
      | ~ ( sk11 @ A @ B ) ),
    inference(lifteq,[status(thm)],[182]) ).

thf(31047,plain,
    ! [A: $i] :
      ( ( phi @ ( impl @ true @ ( sk3 @ A @ false ) ) )
     != ( phi @ true ) ),
    inference(paramod_ordered,[status(thm)],[3331,30959]) ).

thf(31070,plain,
    ! [A: $i] :
      ( ( impl @ true @ ( sk3 @ A @ false ) )
     != true ),
    inference(simp,[status(thm)],[31047]) ).

thf(31180,plain,
    ! [A: $i] :
      ( ( impl @ true @ ( sk3 @ A @ false ) )
     != ( impl @ true @ true ) ),
    inference(paramod_ordered,[status(thm)],[2096,31070]) ).

thf(31194,plain,
    ! [A: $i] :
      ( ( true != true )
      | ( ( sk3 @ A @ false )
       != true ) ),
    inference(simp,[status(thm)],[31180]) ).

thf(31210,plain,
    ! [A: $i] :
      ( ( sk3 @ A @ false )
     != true ),
    inference(simp,[status(thm)],[31194]) ).

thf(150,plain,
    ! [B: $i,A: $i] :
      ( ~ ( existsprefers @ A @ B )
      | ~ ( sk6 @ A @ B )
      | ~ ( bool @ A )
      | ( sk7 @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(2059,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( bool @ ( sk13 @ sk2 @ sk1 ) )
      | ( A
       != ( and1 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[94,1901]) ).

thf(2060,plain,
    ( ( ( and1 @ sk1 @ sk2 )
      = false )
    | ~ ( bool @ ( and1 @ sk1 @ sk2 ) )
    | ( bool @ ( sk13 @ sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[2059:[bind(A,$thf( and1 @ sk1 @ sk2 ))]]) ).

thf(32607,plain,
    ! [A: $i] :
      ( ( true != false2 )
      | ( ( phi @ ( sk3 @ A @ false ) )
       != ( phi @ false2 ) ) ),
    inference(paramod_ordered,[status(thm)],[2950,32247]) ).

thf(32676,plain,
    ! [A: $i] :
      ( ( true != false2 )
      | ( ( sk3 @ A @ false )
       != false2 ) ),
    inference(simp,[status(thm)],[32607]) ).

thf(3939,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) )
        = ( lazy_impl @ ( prop @ C ) @ ( impl @ ( f5 @ B @ C ) @ C ) ) )
      | ( ( f6 @ A @ true )
       != ( f6 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[3885,55]) ).

thf(3940,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ true ) @ ( impl @ ( f5 @ A @ true ) @ true ) )
      = ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) ),
    inference(pattern_uni,[status(thm)],[3939:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( true ))]]) ).

thf(4409,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( impl @ ( f5 @ A @ true ) @ true ) )
      = ( phi @ ( impl @ ( f5 @ A @ true ) @ true ) ) ),
    inference(rewrite,[status(thm)],[3940,2884]) ).

thf(33590,plain,
    ( ( bool @ sk1 )
    | ( sk1 != true )
    | ( ( bool @ ( sk13 @ sk2 @ sk1 ) )
     != ( bool @ sk1 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[33452]) ).

thf(33598,plain,
    ( ( bool @ sk1 )
    | ( sk1 != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != sk1 ) ),
    inference(simp,[status(thm)],[33590]) ).

thf(15636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( lazy_impl @ ( prop @ B ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ B @ A ) ) @ B ) ) @ B ) )
        = ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ C @ ( sk4 @ false @ C ) ) @ false ) ) @ false ) ) )
      | ( ( f6 @ A @ B )
       != ( f6 @ C @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[555,4101]) ).

thf(15637,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ false ) @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) )
      = ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) ) ),
    inference(pattern_uni,[status(thm)],[15636:[bind(A,$thf( A )),bind(B,$thf( false )),bind(C,$thf( A ))]]) ).

thf(25023,plain,
    ! [A: $i] :
      ( ( lazy_impl @ true @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) )
      = ( phi @ ( impl @ ( phi @ ( impl @ ( apply @ A @ ( sk4 @ false @ A ) ) @ false ) ) @ false ) ) ),
    inference(rewrite,[status(thm)],[15637,2902]) ).

thf(121,plain,
    ! [B: $i,A: $i] :
      ( ( lazy_and2 @ A @ B )
      = ( phi @ ( f2 @ A @ B @ ( sk3 @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[119]) ).

thf(122,plain,
    ! [B: $i,A: $i] :
      ( ( lazy_and2 @ A @ B )
      = ( phi @ ( f2 @ A @ B @ ( sk3 @ B @ A ) ) ) ),
    inference(lifteq,[status(thm)],[121]) ).

thf(437,plain,
    ! [B: $i,A: $i] :
      ( ( lazy_and2 @ A @ B )
      = ( phi @ ( lazy_impl @ ( prop @ ( sk3 @ B @ A ) ) @ ( impl @ ( lazy_impl @ A @ ( impl @ B @ ( sk3 @ B @ A ) ) ) @ ( sk3 @ B @ A ) ) ) ) ),
    inference(rewrite,[status(thm)],[122,52]) ).

thf(453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( lazy_impl @ ( prop @ ( sk3 @ C @ B ) ) @ ( impl @ ( phi @ A ) @ ( sk3 @ C @ B ) ) ) )
        = ( lazy_and2 @ B @ C ) )
      | ( ( lazy_impl @ true @ A )
       != ( lazy_impl @ B @ ( impl @ C @ ( sk3 @ C @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[104,437]) ).

thf(454,plain,
    ! [A: $i] :
      ( ( phi @ ( lazy_impl @ ( prop @ ( sk3 @ A @ true ) ) @ ( impl @ ( phi @ ( impl @ A @ ( sk3 @ A @ true ) ) ) @ ( sk3 @ A @ true ) ) ) )
      = ( lazy_and2 @ true @ A ) ),
    inference(pattern_uni,[status(thm)],[453:[bind(A,$thf( impl @ F @ ( sk3 @ F @ true ) )),bind(B,$thf( true )),bind(C,$thf( F ))]]) ).

thf(482,plain,
    ! [A: $i] :
      ( ( phi @ ( lazy_impl @ ( prop @ ( sk3 @ A @ true ) ) @ ( impl @ ( phi @ ( impl @ A @ ( sk3 @ A @ true ) ) ) @ ( sk3 @ A @ true ) ) ) )
      = ( lazy_and2 @ true @ A ) ),
    inference(simp,[status(thm)],[454]) ).

thf(1912,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( prop @ ( sk13 @ true @ sk1 ) )
       != false )
      | ( A != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[94,1899]) ).

thf(1913,plain,
    ( ( sk2 = false )
    | ~ ( bool @ sk2 )
    | ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( prop @ ( sk13 @ true @ sk1 ) )
     != false ) ),
    inference(pattern_uni,[status(thm)],[1912:[bind(A,$thf( sk2 ))]]) ).

thf(2070,plain,
    ! [A: $i] :
      ( ( ( prop @ A )
        = false )
      | ( sk1 = false )
      | ( ( and2 @ true @ sk2 )
       != ( and1 @ sk1 @ sk2 ) )
      | ( ( bool @ A )
       != ( bool @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[207,1387]) ).

thf(2071,plain,
    ( ( ( prop @ sk1 )
      = false )
    | ( sk1 = false )
    | ( ( and2 @ true @ sk2 )
     != ( and1 @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[2070:[bind(A,$thf( sk1 ))]]) ).

thf(1902,plain,
    ! [A: $i] :
      ( ( A = false )
      | ~ ( bool @ A )
      | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
       != false )
      | ( A
       != ( and1 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[94,1899]) ).

thf(1903,plain,
    ( ( ( and1 @ sk1 @ sk2 )
      = false )
    | ~ ( bool @ ( and1 @ sk1 @ sk2 ) )
    | ( ( prop @ ( sk13 @ sk2 @ sk1 ) )
     != false ) ),
    inference(pattern_uni,[status(thm)],[1902:[bind(A,$thf( and1 @ sk1 @ sk2 ))]]) ).

thf(153,plain,
    ! [B: $i,A: $i] :
      ( ~ ( d @ A )
      | ~ ( d @ B )
      | ( bool @ A )
      | ~ ( bool @ B )
      | ( existsprefers @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(158,plain,
    ! [B: $i,A: $i] :
      ( ~ ( d @ A )
      | ~ ( d @ B )
      | ( bool @ A )
      | ~ ( bool @ B )
      | ( existsprefers @ A @ B ) ),
    inference(simp,[status(thm)],[153]) ).

thf(186,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ A @ B )
      | ~ ( sk10 @ A @ B )
      | ( bool @ B )
      | ( sk11 @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(29660,plain,
    ! [B: $i,A: $i] :
      ( ( ( impl @ false @ B )
        = true )
      | ( ( bool @ ( sk3 @ A @ false ) )
       != ( bool @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[28238,214]) ).

thf(29661,plain,
    ! [A: $i] :
      ( ( impl @ false @ ( sk3 @ A @ false ) )
      = true ),
    inference(pattern_uni,[status(thm)],[29660:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C @ false ))]]) ).

thf(29693,plain,
    ! [A: $i] :
      ( ( impl @ false @ ( sk3 @ A @ false ) )
      = true ),
    inference(simp,[status(thm)],[29661]) ).

thf(3733,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ ( f7 @ A ) @ false )
      | ( ( f7 @ sk12 )
       != ( f7 @ false ) ) ),
    inference(paramod_ordered,[status(thm)],[3646,218]) ).

thf(3748,plain,
    ! [A: $i] :
      ( ~ ( forallprefers @ ( f7 @ A ) @ false )
      | ( sk12 != false ) ),
    inference(simp,[status(thm)],[3733]) ).

thf(31276,plain,
    ! [A: $i] :
      ( ( ( or1 @ true @ A )
        = true )
      | ( ( bool @ true )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,230]) ).

thf(31277,plain,
    ( ( or1 @ true @ true )
    = true ),
    inference(pattern_uni,[status(thm)],[31276:[bind(A,$thf( true ))]]) ).

thf(184,plain,
    ! [B: $i,A: $i] :
      ( ~ ( d @ A )
      | ~ ( d @ B )
      | ( bool @ A )
      | ~ ( bool @ B )
      | ( forallprefers @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(190,plain,
    ! [B: $i,A: $i] :
      ( ~ ( d @ A )
      | ~ ( d @ B )
      | ( bool @ A )
      | ~ ( bool @ B )
      | ( forallprefers @ A @ B ) ),
    inference(simp,[status(thm)],[184]) ).

thf(183,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ A @ B )
      | ~ ( sk10 @ A @ B )
      | ( d @ A )
      | ( sk11 @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(14832,plain,
    ( ( sk1 = false )
    | ( bool @ ( sk13 @ sk2 @ true ) )
    | ( ( and1 @ true @ sk2 )
     != true )
    | ( ( bool @ sk1 )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,7329]) ).

thf(14924,plain,
    ( ( sk1 = false )
    | ( bool @ ( sk13 @ sk2 @ true ) )
    | ( ( and1 @ true @ sk2 )
     != true )
    | ( sk1 != true ) ),
    inference(simp,[status(thm)],[14832]) ).

thf(6728,plain,
    ! [B: $i,A: $i] :
      ( ( ( phi @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) )
        = ( phi @ ( f6 @ B @ ( sk8 @ B ) ) ) )
      | ( ( exists2 @ A )
       != ( exists2 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[335,171]) ).

thf(6729,plain,
    ! [A: $i] :
      ( ( phi @ ( lazy_impl @ ( prop @ ( sk8 @ A ) ) @ ( impl @ ( f5 @ A @ ( sk8 @ A ) ) @ ( sk8 @ A ) ) ) )
      = ( phi @ ( f6 @ A @ ( sk8 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[6728:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(18221,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( not2 @ A )
       != true )
      | ( ( sk13 @ sk2 @ sk1 )
       != true )
      | ( sk2 != true )
      | ( ( impl @ A @ false2 )
       != ( impl @ sk1 @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[58,17819]) ).

thf(18249,plain,
    ! [A: $i] :
      ( ( ( and1 @ sk1 @ sk2 )
       != true )
      | ( ( not2 @ A )
       != true )
      | ( ( sk13 @ sk2 @ sk1 )
       != true )
      | ( sk2 != true )
      | ( A != sk1 )
      | ( true != false2 ) ),
    inference(simp,[status(thm)],[18221]) ).

thf(18259,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( not2 @ sk1 )
     != true )
    | ( ( sk13 @ sk2 @ sk1 )
     != true )
    | ( sk2 != true )
    | ( true != false2 ) ),
    inference(simp,[status(thm)],[18249]) ).

thf(135,plain,
    ! [A: $i] :
      ( ( lazy_and1 @ false @ A )
      = false ),
    inference(cnf,[status(esa)],[134]) ).

thf(136,plain,
    ! [A: $i] :
      ( ( lazy_and1 @ false @ A )
      = false ),
    inference(lifteq,[status(thm)],[135]) ).

thf(31274,plain,
    ! [B: $i,A: $i] :
      ( ( ( or1 @ true @ B )
        = true )
      | ( ( bool @ ( sk3 @ A @ false ) )
       != ( bool @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[28238,230]) ).

thf(31275,plain,
    ! [A: $i] :
      ( ( or1 @ true @ ( sk3 @ A @ false ) )
      = true ),
    inference(pattern_uni,[status(thm)],[31274:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C @ false ))]]) ).

thf(31356,plain,
    ! [A: $i] :
      ( ( or1 @ true @ ( sk3 @ A @ false ) )
      = true ),
    inference(simp,[status(thm)],[31275]) ).

thf(927,plain,
    ! [B: $i,A: $i] :
      ( ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) ) ) )
        = ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ B @ false2 ) ) ) )
      | ( ( f6 @ A @ false2 )
       != ( f6 @ B @ false2 ) ) ),
    inference(paramod_ordered,[status(thm)],[576,262]) ).

thf(928,plain,
    ! [A: $i] :
      ( ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( phi @ ( not2 @ ( apply @ A @ ( sk4 @ false2 @ A ) ) ) ) ) )
      = ( lazy_impl @ ( prop @ false2 ) @ ( not2 @ ( f5 @ A @ false2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[927:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(149,plain,
    ! [B: $i,A: $i] :
      ( ( d @ A )
      | ~ ( d @ B )
      | ( existsprefers @ A @ B ) ),
    inference(cnf,[status(esa)],[146]) ).

thf(163,plain,
    ! [B: $i,A: $i] :
      ( ( d @ A )
      | ~ ( d @ B )
      | ( existsprefers @ A @ B ) ),
    inference(simp,[status(thm)],[149]) ).

thf(178,plain,
    ! [B: $i,A: $i] :
      ( ~ ( forallprefers @ A @ B )
      | ( d @ B )
      | ( sk10 @ A @ B ) ),
    inference(cnf,[status(esa)],[177]) ).

thf(108,plain,
    true != false,
    inference(cnf,[status(esa)],[105]) ).

thf(111,plain,
    true != false,
    inference(lifteq,[status(thm)],[108]) ).

thf(227,plain,
    false1 = false,
    inference(lifteq,[status(thm)],[226]) ).

thf(446,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( phi @ ( lazy_impl @ ( prop @ ( sk3 @ C @ B ) ) @ ( impl @ true @ ( sk3 @ C @ B ) ) ) )
        = ( lazy_and2 @ B @ C ) )
      | ( ( lazy_impl @ false @ A )
       != ( lazy_impl @ B @ ( impl @ C @ ( sk3 @ C @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[81,437]) ).

thf(447,plain,
    ! [A: $i] :
      ( ( phi @ ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) ) )
      = ( lazy_and2 @ false @ A ) ),
    inference(pattern_uni,[status(thm)],[446:[bind(A,$thf( impl @ F @ ( sk3 @ F @ false ) )),bind(B,$thf( false )),bind(C,$thf( F ))]]) ).

thf(492,plain,
    ! [A: $i] :
      ( ( phi @ ( lazy_impl @ ( prop @ ( sk3 @ A @ false ) ) @ ( impl @ true @ ( sk3 @ A @ false ) ) ) )
      = ( lazy_and2 @ false @ A ) ),
    inference(simp,[status(thm)],[447]) ).

thf(29705,plain,
    ! [A: $i] :
      ( ( phi @ ( lazy_impl @ true @ ( impl @ true @ ( sk3 @ A @ false ) ) ) )
      = ( lazy_and2 @ false @ A ) ),
    inference(rewrite,[status(thm)],[492,29698]) ).

thf(34380,plain,
    ! [A: $i] :
      ( ( phi @ ( phi @ ( impl @ true @ ( sk3 @ A @ false ) ) ) )
      = ( lazy_and2 @ false @ A ) ),
    inference(rewrite,[status(thm)],[29705,104]) ).

thf(1036,plain,
    ! [A: $i] :
      ( ( ( or1 @ false @ A )
        = A )
      | ( ( bool @ false )
       != ( bool @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[91,84]) ).

thf(1037,plain,
    ( ( or1 @ false @ false )
    = false ),
    inference(pattern_uni,[status(thm)],[1036:[bind(A,$thf( false ))]]) ).

thf(7237,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( bool @ ( and2 @ sk1 @ sk2 ) )
     != ( bool @ true ) ) ),
    inference(paramod_ordered,[status(thm)],[93,5260]) ).

thf(7267,plain,
    ( ( ( and1 @ sk1 @ sk2 )
     != true )
    | ( ( and1 @ sk1 @ sk2 )
     != false )
    | ( ( and2 @ sk1 @ sk2 )
     != true ) ),
    inference(simp,[status(thm)],[7237]) ).

thf(67969,plain,
    $false,
    inference(cvc4,[status(thm)],[1879,33839,4101,101,5260,1899,555,31327,7322,17815,202,4075,217,2908,2062,8101,142,6640,26657,56,16651,3915,1887,28691,7241,125,3845,157,52,1055,28602,110,1907,28238,17694,638,4788,189,93,152,228,78,216,2950,179,3724,3453,211,238,574,84,164,7268,2058,6631,61,221,1886,133,6863,2884,117,4407,3720,220,102,2083,32971,85,201,7269,1915,3735,1387,70,137,97,33696,18268,5038,5330,224,65,7555,578,7329,3254,156,169,141,188,1672,17819,53,109,77,29697,193,33650,1700,2108,212,124,225,3242,701,2598,3937,129,4347,2052,134,237,33452,12577,16812,5295,105,244,398,1035,18255,148,161,64,3343,176,191,2048,1389,3240,743,14044,286,32970,59,118,71,17686,3646,144,49,335,3832,181,159,172,3238,81,377,76,98,208,230,4601,245,2839,12248,3747,2610,858,91,155,198,130,4232,26239,2064,223,226,31313,167,7630,4282,241,29698,162,1905,374,209,112,617,123,28728,2096,194,145,4045,2567,31210,150,2060,32676,95,50,4409,33598,67,199,3885,127,1901,576,2056,25023,231,539,482,1913,4559,218,104,2110,2071,32969,1385,1903,158,186,171,3331,29693,3748,55,235,207,31277,2902,82,214,119,58,190,183,168,262,242,14924,79,195,29699,437,6729,400,18259,126,136,94,31356,928,415,47,32812,163,68,62,178,369,111,227,34380,215,1037,7267]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SWW096+1 : TPTP v8.2.0. Released v5.2.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n002.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sat May 18 19:30:39 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.87/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.12  % [INFO] 	 Parsing done (189ms). 
% 1.47/1.14  % [INFO] 	 Running in sequential loop mode. 
% 2.04/1.48  % [INFO] 	 eprover registered as external prover. 
% 2.04/1.48  % [INFO] 	 cvc4 registered as external prover. 
% 2.04/1.49  % [INFO] 	 Scanning for conjecture ... 
% 2.26/1.58  % [INFO] 	 Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ... 
% 2.45/1.66  % [INFO] 	 Axiom selection finished. Selected 44 axioms (removed 0 axioms). 
% 2.55/1.73  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.55/1.74  % [INFO] 	 Type checking passed. 
% 2.73/1.74  % [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 ... 
% 195.20/36.68  % External prover 'cvc4' found a proof!
% 195.20/36.68  % [INFO] 	 Killing All external provers ... 
% 195.20/36.69  % Time passed: 36215ms (effective reasoning time: 35546ms)
% 195.20/36.69  % 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)>
% 195.20/36.69  % Axioms used in derivation (44): or1_axiom2, def_or2, distinct_false_true_err, def_f3, prop_false, impl_axiom1, def_f5, lazy_impl_axiom1, def_f7, def_existsprefers, not1_axiom2, lazy_impl_axiom3, lazy_and1_axiom1, and1_axiom3, false_true_err_in_d, impl_axiom4, def_f4, def_f6, and1_axiom4, prop_true, or1_axiom3, or1_axiom4, def_false2, not1_axiom3, lazy_and1_axiom3, def_exists2, def_false1, and1_axiom1, impl_axiom2, def_f2, exists1_axiom1, def_not2, def_bool, def_f1, and1_axiom2, def_lazy_and2, impl_axiom3, def_phi, def_and2, not1_axiom1, lazy_and1_axiom2, or1_axiom1, def_forallprefers, lazy_impl_axiom2
% 195.20/36.69  % No. of inferences in proof: 610
% 195.20/36.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 36215 ms resp. 35546 ms w/o parsing
% 195.59/36.92  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 195.59/36.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------