TSTP Solution File: SWV398+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV398+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:15:37 EDT 2023

% Result   : Theorem 113.42s 20.02s
% Output   : Refutation 113.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   76
% Syntax   : Number of formulae    :  350 ( 160 unt;  32 typ;   0 def)
%            Number of atoms       :  642 ( 212 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 3125 ( 212   ~; 128   |;  44   &;2667   @)
%                                         (   8 <=>;  66  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   46 (  46   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   34 (  32 usr;   7 con; 0-3 aty)
%            Number of variables   :  866 (   0   ^; 852   !;  14   ?; 866   :)

% Comments : 
%------------------------------------------------------------------------------
thf(check_cpq_type,type,
    check_cpq: $i > $o ).

thf(triple_type,type,
    triple: $i > $i > $i > $i ).

thf(findmin_cpq_eff_type,type,
    findmin_cpq_eff: $i > $i ).

thf(succ_cpq_type,type,
    succ_cpq: $i > $i > $o ).

thf(removemin_cpq_eff_type,type,
    removemin_cpq_eff: $i > $i ).

thf(strictly_less_than_type,type,
    strictly_less_than: $i > $i > $o ).

thf(less_than_type,type,
    less_than: $i > $i > $o ).

thf(isnonempty_slb_type,type,
    isnonempty_slb: $i > $o ).

thf(insert_slb_type,type,
    insert_slb: $i > $i > $i ).

thf(pair_type,type,
    pair: $i > $i > $i ).

thf(contains_slb_type,type,
    contains_slb: $i > $i > $o ).

thf(create_slb_type,type,
    create_slb: $i ).

thf(insert_cpq_type,type,
    insert_cpq: $i > $i > $i ).

thf(remove_slb_type,type,
    remove_slb: $i > $i > $i ).

thf(bottom_type,type,
    bottom: $i ).

thf(update_slb_type,type,
    update_slb: $i > $i > $i ).

thf(pair_in_list_type,type,
    pair_in_list: $i > $i > $i > $o ).

thf(lookup_slb_type,type,
    lookup_slb: $i > $i > $i ).

thf(remove_cpq_type,type,
    remove_cpq: $i > $i > $i ).

thf(removemin_cpq_res_type,type,
    removemin_cpq_res: $i > $i ).

thf(findmin_cpq_res_type,type,
    findmin_cpq_res: $i > $i ).

thf(insert_pqp_type,type,
    insert_pqp: $i > $i > $i ).

thf(bad_type,type,
    bad: $i ).

thf(remove_pqp_type,type,
    remove_pqp: $i > $i > $i ).

thf(findmin_pqp_res_type,type,
    findmin_pqp_res: $i > $i ).

thf(ok_type,type,
    ok: $i > $o ).

thf(contains_cpq_type,type,
    contains_cpq: $i > $i > $o ).

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

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

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

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

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

thf(16,axiom,
    ! [A: $i] : ( succ_cpq @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).

thf(92,plain,
    ! [A: $i] : ( succ_cpq @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(93,plain,
    ! [A: $i] : ( succ_cpq @ A @ A ),
    inference(cnf,[status(esa)],[92]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( succ_cpq @ A @ B )
     => ( succ_cpq @ A @ ( removemin_cpq_eff @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).

thf(49,plain,
    ! [A: $i,B: $i] :
      ( ( succ_cpq @ A @ B )
     => ( succ_cpq @ A @ ( removemin_cpq_eff @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(50,plain,
    ! [B: $i,A: $i] :
      ( ~ ( succ_cpq @ A @ B )
      | ( succ_cpq @ A @ ( removemin_cpq_eff @ B ) ) ),
    inference(cnf,[status(esa)],[49]) ).

thf(201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ A )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[93,50]) ).

thf(202,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ A ) ),
    inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( succ_cpq @ A @ B )
     => ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).

thf(75,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( succ_cpq @ A @ B )
     => ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(76,plain,
    ! [A: $i,B: $i] :
      ( ( succ_cpq @ A @ B )
     => ! [C: $i] : ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[75]) ).

thf(77,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( succ_cpq @ A @ B )
      | ( succ_cpq @ A @ ( insert_cpq @ B @ C ) ) ),
    inference(cnf,[status(esa)],[76]) ).

thf(1759,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ A ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[202,77]) ).

thf(1760,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ),
    inference(pattern_uni,[status(thm)],[1759:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( removemin_cpq_eff @ E ))]]) ).

thf(1785,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ),
    inference(simp,[status(thm)],[1760]) ).

thf(1814,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1785,50]) ).

thf(1815,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[1814:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( insert_cpq @ ( removemin_cpq_eff @ G ) @ F ))]]) ).

thf(1825,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ),
    inference(simp,[status(thm)],[1815]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
    <=> ( ( contains_slb @ A @ C )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).

thf(59,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
       => ( ( contains_slb @ A @ C )
          | ( B = C ) ) )
      & ( ( ( contains_slb @ A @ C )
          | ( B = C ) )
       => ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(60,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ? [D: $i] : ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
       => ( ( contains_slb @ A @ C )
          | ( B = C ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ( ( contains_slb @ A @ C )
          | ( B = C ) )
       => ! [D: $i] : ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ) ),
    inference(miniscope,[status(thm)],[59]) ).

thf(61,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( contains_slb @ A @ C )
      | ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ),
    inference(cnf,[status(esa)],[60]) ).

thf(64,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( contains_slb @ A @ C )
      | ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ),
    inference(simp,[status(thm)],[61]) ).

thf(7,axiom,
    ! [A: $i] : ( less_than @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

thf(68,plain,
    ! [A: $i] : ( less_than @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

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

thf(39,axiom,
    ! [A: $i,B: $i] :
      ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
      = ( triple @ A @ create_slb @ bad ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).

thf(169,plain,
    ! [A: $i,B: $i] :
      ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
      = ( triple @ A @ create_slb @ bad ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(170,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
      = ( triple @ A @ create_slb @ bad ) ),
    inference(cnf,[status(esa)],[169]) ).

thf(171,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
      = ( triple @ A @ create_slb @ bad ) ),
    inference(lifteq,[status(thm)],[170]) ).

thf(40,axiom,
    ! [A: $i,B: $i] :
      ( ( ok @ ( triple @ A @ B @ bad ) )
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).

thf(172,plain,
    ! [A: $i,B: $i] :
      ~ ( ok @ ( triple @ A @ B @ bad ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(173,plain,
    ~ ? [A: $i,B: $i] : ( ok @ ( triple @ A @ B @ bad ) ),
    inference(miniscope,[status(thm)],[172]) ).

thf(174,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( triple @ A @ B @ bad ) ),
    inference(cnf,[status(esa)],[173]) ).

thf(291,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ok @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ D @ bad ) ) ),
    inference(paramod_ordered,[status(thm)],[171,174]) ).

thf(292,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ),
    inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( create_slb ))]]) ).

thf(350,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,292]) ).

thf(351,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,351]) ).

thf(400,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1334,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,400]) ).

thf(1335,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1334:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1335]) ).

thf(1661,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1660:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(2184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1661]) ).

thf(2185,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2184:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(2411,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,2185]) ).

thf(2412,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2411:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).

thf(57,plain,
    ! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(58,plain,
    ! [C: $i,B: $i,A: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
    inference(cnf,[status(esa)],[57]) ).

thf(15,axiom,
    ~ ( isnonempty_slb @ create_slb ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).

thf(90,plain,
    ~ ( isnonempty_slb @ create_slb ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(91,plain,
    ~ ( isnonempty_slb @ create_slb ),
    inference(polarity_switch,[status(thm)],[90]) ).

thf(233,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) )
     != ( isnonempty_slb @ create_slb ) ),
    inference(paramod_ordered,[status(thm)],[58,91]) ).

thf(234,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( insert_slb @ A @ ( pair @ B @ C ) )
     != create_slb ),
    inference(simp,[status(thm)],[233]) ).

thf(34,axiom,
    ! [A: $i,B: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).

thf(154,plain,
    ! [A: $i,B: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(155,plain,
    ! [B: $i,A: $i] : ( check_cpq @ ( triple @ A @ create_slb @ B ) ),
    inference(cnf,[status(esa)],[154]) ).

thf(312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,155]) ).

thf(313,plain,
    ! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ),
    inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(357,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,313]) ).

thf(358,plain,
    ! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,358]) ).

thf(408,plain,
    ! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
      | ( ( succ_cpq @ A @ A )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[93,77]) ).

thf(1762,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( insert_cpq @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[1761:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(1786,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( insert_cpq @ A @ B ) ),
    inference(simp,[status(thm)],[1762]) ).

thf(1800,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( insert_cpq @ D @ E ) )
      | ( ( succ_cpq @ A @ ( insert_cpq @ A @ B ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1786,77]) ).

thf(1801,plain,
    ! [C: $i,B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( insert_cpq @ B @ C ) @ A ) ),
    inference(pattern_uni,[status(thm)],[1800:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( insert_cpq @ F @ G ))]]) ).

thf(1808,plain,
    ! [C: $i,B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( insert_cpq @ B @ C ) @ A ) ),
    inference(simp,[status(thm)],[1801]) ).

thf(203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ A ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[202,50]) ).

thf(204,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
    inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( removemin_cpq_eff @ D ))]]) ).

thf(205,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ),
    inference(simp,[status(thm)],[204]) ).

thf(216,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[205,50]) ).

thf(217,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ E ) ))]]) ).

thf(218,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ),
    inference(simp,[status(thm)],[217]) ).

thf(220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[218,50]) ).

thf(221,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ F ) ) ))]]) ).

thf(222,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ),
    inference(simp,[status(thm)],[221]) ).

thf(230,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[222,50]) ).

thf(231,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ G ) ) ) ))]]) ).

thf(232,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ),
    inference(simp,[status(thm)],[231]) ).

thf(245,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[232,50]) ).

thf(246,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( H )),bind(B,$thf( H )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ H ) ) ) ) ))]]) ).

thf(247,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ),
    inference(simp,[status(thm)],[246]) ).

thf(1765,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[205,77]) ).

thf(1766,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ),
    inference(pattern_uni,[status(thm)],[1765:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ F ) )),bind(D,$thf( D ))]]) ).

thf(1788,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ),
    inference(simp,[status(thm)],[1766]) ).

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

thf(51,plain,
    ! [A: $i,B: $i] :
      ( ( ( strictly_less_than @ A @ B )
       => ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) ) )
      & ( ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) )
       => ( strictly_less_than @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(52,plain,
    ( ! [A: $i,B: $i] :
        ( ( strictly_less_than @ A @ B )
       => ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) )
       => ( strictly_less_than @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[51]) ).

thf(53,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ( less_than @ B @ A )
      | ( strictly_less_than @ A @ B ) ),
    inference(cnf,[status(esa)],[52]) ).

thf(56,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ( less_than @ B @ A )
      | ( strictly_less_than @ A @ B ) ),
    inference(simp,[status(thm)],[53]) ).

thf(2868,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,2412]) ).

thf(2869,plain,
    ! [B: $i,A: $i] :
      ~ ( ok @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2868:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,408]) ).

thf(1375,plain,
    ! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1375]) ).

thf(1709,plain,
    ! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[1708:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(43,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( check_cpq @ ( triple @ A @ B @ C ) )
    <=> ! [D: $i,E: $i] :
          ( ( pair_in_list @ B @ D @ E )
         => ( less_than @ E @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l26_li4142) ).

thf(184,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( check_cpq @ ( triple @ A @ B @ C ) )
       => ! [D: $i,E: $i] :
            ( ( pair_in_list @ B @ D @ E )
           => ( less_than @ E @ D ) ) )
      & ( ! [D: $i,E: $i] :
            ( ( pair_in_list @ B @ D @ E )
           => ( less_than @ E @ D ) )
       => ( check_cpq @ ( triple @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( removemin_cpq_res @ A )
      = ( findmin_cpq_res @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).

thf(125,plain,
    ! [A: $i] :
      ( ( removemin_cpq_res @ A )
      = ( findmin_cpq_res @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( check_cpq @ ( triple @ A @ B @ C ) )
     => ~ ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l24_co) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ~ ( check_cpq @ ( triple @ A @ B @ C ) )
       => ~ ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ B @ C ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(46,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ~ ( check_cpq @ ( triple @ A @ B @ C ) )
       => ~ ( check_cpq @ ( findmin_cpq_eff @ ( triple @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(48,plain,
    ~ ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[46]) ).

thf(1349,plain,
    ! [B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
     != ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[408,48]) ).

thf(1379,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(simp,[status(thm)],[1349]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
      = bottom ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).

thf(159,plain,
    ! [A: $i,B: $i] :
      ( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
      = bottom ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(160,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
      = bottom ),
    inference(cnf,[status(esa)],[159]) ).

thf(161,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_res @ ( triple @ A @ create_slb @ B ) )
      = bottom ),
    inference(lifteq,[status(thm)],[160]) ).

thf(126,plain,
    ! [A: $i] :
      ( ( removemin_cpq_res @ A )
      = ( findmin_cpq_res @ A ) ),
    inference(cnf,[status(esa)],[125]) ).

thf(127,plain,
    ! [A: $i] :
      ( ( findmin_cpq_res @ A )
      = ( removemin_cpq_res @ A ) ),
    inference(lifteq,[status(thm)],[126]) ).

thf(219,plain,
    ! [B: $i,A: $i] :
      ( ( removemin_cpq_res @ ( triple @ A @ create_slb @ B ) )
      = bottom ),
    inference(rewrite,[status(thm)],[161,127]) ).

thf(293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
        = bottom )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,219]) ).

thf(294,plain,
    ! [B: $i,A: $i] :
      ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
      = bottom ),
    inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(391,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
        = bottom )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,294]) ).

thf(392,plain,
    ! [B: $i,A: $i] :
      ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) )
      = bottom ),
    inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
        = bottom )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,392]) ).

thf(1293,plain,
    ! [B: $i,A: $i] :
      ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
      = bottom ),
    inference(pattern_uni,[status(thm)],[1292:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1610,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
        = bottom )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1293]) ).

thf(1611,plain,
    ! [B: $i,A: $i] :
      ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
      = bottom ),
    inference(pattern_uni,[status(thm)],[1610:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1889,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
        = bottom )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1611]) ).

thf(1890,plain,
    ! [B: $i,A: $i] :
      ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
      = bottom ),
    inference(pattern_uni,[status(thm)],[1889:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(47,plain,
    check_cpq @ ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[46]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( strictly_less_than @ D @ E )
     => ( ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) )
      <=> $false ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).

thf(194,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( strictly_less_than @ D @ E )
     => ~ ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(195,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ D @ E )
      | ~ ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ),
    inference(cnf,[status(esa)],[194]) ).

thf(226,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ D @ E )
      | ( ( check_cpq @ ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) ) )
       != ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47,195]) ).

thf(228,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ D @ E )
      | ( ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) )
       != ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ),
    inference(simp,[status(thm)],[226]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).

thf(78,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1678,plain,
    ! [B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
     != ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[1375,48]) ).

thf(1714,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(simp,[status(thm)],[1678]) ).

thf(42,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( contains_cpq @ ( triple @ A @ B @ C ) @ D )
    <=> ( contains_slb @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).

thf(179,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( contains_cpq @ ( triple @ A @ B @ C ) @ D )
       => ( contains_slb @ B @ D ) )
      & ( ( contains_slb @ B @ D )
       => ( contains_cpq @ ( triple @ A @ B @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(210,plain,
    ! [B: $i,A: $i] :
      ( ( check_cpq @ ( triple @ A @ create_slb @ B ) )
     != ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[155,48]) ).

thf(211,plain,
    ! [B: $i,A: $i] :
      ( ( triple @ A @ create_slb @ B )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(simp,[status(thm)],[210]) ).

thf(2104,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1788,50]) ).

thf(2105,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[2104:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( H )),bind(D,$thf( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ H ) ) @ F ))]]) ).

thf(2122,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) ),
    inference(simp,[status(thm)],[2105]) ).

thf(1977,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) )
       != ( triple @ sk1 @ sk2 @ sk3 ) )
      | ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
       != ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1379]) ).

thf(1978,plain,
    ! [A: $i] :
      ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[1977:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( update_slb @ create_slb @ A )
      = create_slb ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).

thf(119,plain,
    ! [A: $i] :
      ( ( update_slb @ create_slb @ A )
      = create_slb ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(120,plain,
    ! [A: $i] :
      ( ( update_slb @ create_slb @ A )
      = create_slb ),
    inference(cnf,[status(esa)],[119]) ).

thf(121,plain,
    ! [A: $i] :
      ( ( update_slb @ create_slb @ A )
      = create_slb ),
    inference(lifteq,[status(thm)],[120]) ).

thf(32,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( less_than @ E @ D )
     => ( ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) )
      <=> ( check_cpq @ ( triple @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).

thf(147,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( less_than @ E @ D )
     => ( ( ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) )
         => ( check_cpq @ ( triple @ A @ B @ C ) ) )
        & ( ( check_cpq @ ( triple @ A @ B @ C ) )
         => ( check_cpq @ ( triple @ A @ ( insert_slb @ B @ ( pair @ D @ E ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(2344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[2122,50]) ).

thf(2345,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[2344:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( I )),bind(D,$thf( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ I ) ) @ G ) ))]]) ).

thf(2367,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) @ A ) ) ) ),
    inference(simp,[status(thm)],[2345]) ).

thf(1781,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[222,77]) ).

thf(1782,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) ) @ A ) ),
    inference(pattern_uni,[status(thm)],[1781:[bind(A,$thf( H )),bind(B,$thf( H )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ H ) ) ) )),bind(D,$thf( D ))]]) ).

thf(1796,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) ) @ A ) ),
    inference(simp,[status(thm)],[1782]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( succ_cpq @ A @ B )
     => ( succ_cpq @ A @ ( findmin_cpq_eff @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).

thf(132,plain,
    ! [A: $i,B: $i] :
      ( ( succ_cpq @ A @ B )
     => ( succ_cpq @ A @ ( findmin_cpq_eff @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).

thf(86,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(87,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ! [D: $i] :
          ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
          = ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    inference(miniscope,[status(thm)],[86]) ).

thf(88,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( contains_slb @ A @ C )
      | ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    inference(cnf,[status(esa)],[87]) ).

thf(89,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) )
      | ~ ( contains_slb @ A @ C ) ),
    inference(lifteq,[status(thm)],[88]) ).

thf(2240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1709]) ).

thf(2241,plain,
    ! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2240:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(2798,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,2241]) ).

thf(2799,plain,
    ! [B: $i,A: $i] : ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2798:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( less_than @ C @ D )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).

thf(116,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( less_than @ C @ D )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( less_than @ A @ B )
        & ( less_than @ B @ C ) )
     => ( less_than @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).

thf(73,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( less_than @ A @ B )
        & ( less_than @ B @ C ) )
     => ( less_than @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(74,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    inference(cnf,[status(esa)],[73]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( strictly_less_than @ D @ C )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).

thf(83,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( strictly_less_than @ D @ C )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(84,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ D @ C )
      | ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
    inference(cnf,[status(esa)],[83]) ).

thf(85,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) )
      | ~ ( strictly_less_than @ D @ C ) ),
    inference(lifteq,[status(thm)],[84]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ~ ( pair_in_list @ create_slb @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).

thf(100,plain,
    ! [A: $i,B: $i] :
      ~ ( pair_in_list @ create_slb @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(101,plain,
    ~ ? [A: $i,B: $i] : ( pair_in_list @ create_slb @ A @ B ),
    inference(miniscope,[status(thm)],[100]) ).

thf(102,plain,
    ! [B: $i,A: $i] :
      ~ ( pair_in_list @ create_slb @ A @ B ),
    inference(cnf,[status(esa)],[101]) ).

thf(8,axiom,
    ! [A: $i] :
      ~ ( contains_slb @ create_slb @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).

thf(70,plain,
    ! [A: $i] :
      ~ ( contains_slb @ create_slb @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(29,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( contains_slb @ B @ D )
     => ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
        = ( triple @ A @ B @ bad ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).

thf(137,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( contains_slb @ B @ D )
     => ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
        = ( triple @ A @ B @ bad ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(38,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != create_slb )
        & ( contains_slb @ B @ ( findmin_pqp_res @ A ) )
        & ( less_than @ ( lookup_slb @ B @ ( findmin_pqp_res @ A ) ) @ ( findmin_pqp_res @ A ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
        = ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).

thf(165,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B != create_slb )
        & ( contains_slb @ B @ ( findmin_pqp_res @ A ) )
        & ( less_than @ ( lookup_slb @ B @ ( findmin_pqp_res @ A ) ) @ ( findmin_pqp_res @ A ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
        = ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(227,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ F @ G )
      | ( ( check_cpq @ ( triple @ A @ create_slb @ B ) )
       != ( check_cpq @ ( triple @ C @ ( insert_slb @ D @ ( pair @ F @ G ) ) @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[155,195]) ).

thf(229,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ F @ G )
      | ( ( triple @ A @ create_slb @ B )
       != ( triple @ C @ ( insert_slb @ D @ ( pair @ F @ G ) ) @ E ) ) ),
    inference(simp,[status(thm)],[227]) ).

thf(196,plain,
    ( ( check_cpq @ ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) ) )
   != ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[47,48]) ).

thf(197,plain,
    ( ( findmin_cpq_eff @ ( triple @ sk1 @ sk2 @ sk3 ) )
   != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(simp,[status(thm)],[196]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).

thf(97,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(63,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
      | ( contains_slb @ A @ C )
      | ( B = C ) ),
    inference(cnf,[status(esa)],[60]) ).

thf(67,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
      | ( contains_slb @ A @ C ) ),
    inference(lifteq,[status(thm)],[63]) ).

thf(212,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ( sk2 != create_slb )
      | ( B != sk3 ) ),
    inference(simp,[status(thm)],[211]) ).

thf(213,plain,
    sk2 != create_slb,
    inference(simp,[status(thm)],[212]) ).

thf(726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
      | ( contains_slb @ A @ C )
      | ( B != create_slb )
      | ( C != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[67,213]) ).

thf(727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ sk2 )
      | ( contains_slb @ A @ sk2 )
      | ( B != create_slb ) ),
    inference(pattern_uni,[status(thm)],[726:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).

thf(1089,plain,
    ! [B: $i,A: $i] :
      ( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ create_slb @ B ) ) @ sk2 )
      | ( contains_slb @ A @ sk2 ) ),
    inference(simp,[status(thm)],[727]) ).

thf(1777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( insert_cpq @ C @ D ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[218,77]) ).

thf(1778,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) ),
    inference(pattern_uni,[status(thm)],[1777:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ G ) ) )),bind(D,$thf( D ))]]) ).

thf(1794,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) ),
    inference(simp,[status(thm)],[1778]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( removemin_cpq_eff @ A )
      = ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).

thf(156,plain,
    ! [A: $i] :
      ( ( removemin_cpq_eff @ A )
      = ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
       != ( triple @ sk1 @ sk2 @ sk3 ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,211]) ).

thf(303,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(363,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
       != ( triple @ sk1 @ sk2 @ sk3 ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,303]) ).

thf(364,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(1423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) )
       != ( triple @ sk1 @ sk2 @ sk3 ) )
      | ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
       != ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[171,364]) ).

thf(1424,plain,
    ! [A: $i] :
      ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[1423:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(2550,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) )
       != ( triple @ sk1 @ sk2 @ sk3 ) )
      | ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
       != ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1714]) ).

thf(2551,plain,
    ! [A: $i] :
      ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[2550:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( ( pair_in_list @ A @ B @ C )
          & ( strictly_less_than @ B @ C ) )
     => ! [B: $i] :
        ? [C: $i,D: $i] :
          ( ( pair_in_list @ ( update_slb @ A @ B ) @ C @ D )
          & ( strictly_less_than @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_l35) ).

thf(94,plain,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( ( pair_in_list @ A @ B @ C )
          & ( strictly_less_than @ B @ C ) )
     => ! [B: $i] :
        ? [C: $i,D: $i] :
          ( ( pair_in_list @ ( update_slb @ A @ B ) @ C @ D )
          & ( strictly_less_than @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(96,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ A @ B @ C )
      | ~ ( strictly_less_than @ B @ C )
      | ( strictly_less_than @ ( sk4 @ D @ A ) @ ( sk5 @ D @ A ) ) ),
    inference(cnf,[status(esa)],[94]) ).

thf(28,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( insert_cpq @ ( triple @ A @ B @ C ) @ D )
      = ( triple @ ( insert_pqp @ A @ D ) @ ( insert_slb @ B @ ( pair @ D @ bottom ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).

thf(134,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( insert_cpq @ ( triple @ A @ B @ C ) @ D )
      = ( triple @ ( insert_pqp @ A @ D ) @ ( insert_slb @ B @ ( pair @ D @ bottom ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( lookup_slb @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).

thf(128,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( lookup_slb @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(2314,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ B @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1794,50]) ).

thf(2315,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[2314:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( I )),bind(D,$thf( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ I ) ) ) @ F ))]]) ).

thf(2338,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ B ) ) ) @ A ) ) ),
    inference(simp,[status(thm)],[2315]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
    <=> ( ( pair_in_list @ A @ C @ E )
        | ( ( B = C )
          & ( D = E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).

thf(105,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
       => ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) ) )
      & ( ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) )
       => ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(12,axiom,
    ! [A: $i] : ( less_than @ bottom @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).

thf(81,plain,
    ! [A: $i] : ( less_than @ bottom @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(82,plain,
    ! [A: $i] : ( less_than @ bottom @ A ),
    inference(cnf,[status(esa)],[81]) ).

thf(243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( less_than @ C @ B )
      | ( strictly_less_than @ B @ C )
      | ( ( less_than @ bottom @ A )
       != ( less_than @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[82,56]) ).

thf(244,plain,
    ! [A: $i] :
      ( ( less_than @ A @ bottom )
      | ( strictly_less_than @ bottom @ A ) ),
    inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( A )),bind(B,$thf( bottom )),bind(C,$thf( A ))]]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( contains_slb @ B @ D )
        & ( strictly_less_than @ D @ ( lookup_slb @ B @ D ) ) )
     => ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
        = ( triple @ ( remove_pqp @ A @ D ) @ ( remove_slb @ B @ D ) @ bad ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).

thf(191,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( contains_slb @ B @ D )
        & ( strictly_less_than @ D @ ( lookup_slb @ B @ D ) ) )
     => ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
        = ( triple @ ( remove_pqp @ A @ D ) @ ( remove_slb @ B @ D ) @ bad ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(54,plain,
    ! [B: $i,A: $i] :
      ( ~ ( strictly_less_than @ A @ B )
      | ( less_than @ A @ B ) ),
    inference(cnf,[status(esa)],[52]) ).

thf(235,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( less_than @ C @ B )
      | ( strictly_less_than @ B @ C )
      | ( ( less_than @ A @ A )
       != ( less_than @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[69,56]) ).

thf(236,plain,
    ! [A: $i] :
      ( ( less_than @ A @ A )
      | ( strictly_less_than @ A @ A ) ),
    inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(2205,plain,
    ! [B: $i,A: $i] :
      ( ( check_cpq @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) )
     != ( check_cpq @ ( triple @ sk1 @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[1709,48]) ).

thf(2246,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(simp,[status(thm)],[2205]) ).

thf(361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( triple @ A @ create_slb @ bad )
       != ( triple @ sk1 @ sk2 @ sk3 ) )
      | ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
       != ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[171,303]) ).

thf(362,plain,
    ! [A: $i] :
      ( ( triple @ A @ create_slb @ bad )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[361:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( less_than @ A @ B )
      | ( less_than @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).

thf(103,plain,
    ! [A: $i,B: $i] :
      ( ( less_than @ A @ B )
      | ( less_than @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(30,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( contains_slb @ B @ D )
        & ( less_than @ ( lookup_slb @ B @ D ) @ D ) )
     => ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
        = ( triple @ ( remove_pqp @ A @ D ) @ ( remove_slb @ B @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).

thf(140,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( contains_slb @ B @ D )
        & ( less_than @ ( lookup_slb @ B @ D ) @ D ) )
     => ( ( remove_cpq @ ( triple @ A @ B @ C ) @ D )
        = ( triple @ ( remove_pqp @ A @ D ) @ ( remove_slb @ B @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(62,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ),
    inference(cnf,[status(esa)],[60]) ).

thf(65,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B != C )
      | ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ),
    inference(lifteq,[status(thm)],[62]) ).

thf(66,plain,
    ! [C: $i,B: $i,A: $i] : ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B ),
    inference(simp,[status(thm)],[65]) ).

thf(157,plain,
    ! [A: $i] :
      ( ( removemin_cpq_eff @ A )
      = ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) ) ),
    inference(cnf,[status(esa)],[156]) ).

thf(158,plain,
    ! [A: $i] :
      ( ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( findmin_cpq_res @ A ) )
      = ( removemin_cpq_eff @ A ) ),
    inference(lifteq,[status(thm)],[157]) ).

thf(251,plain,
    ! [A: $i] :
      ( ( remove_cpq @ ( findmin_cpq_eff @ A ) @ ( removemin_cpq_res @ A ) )
      = ( removemin_cpq_eff @ A ) ),
    inference(rewrite,[status(thm)],[158,127]) ).

thf(2128,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ B @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1825,50]) ).

thf(2129,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[2128:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H )),bind(D,$thf( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ H ) @ G ) ))]]) ).

thf(2142,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) ),
    inference(simp,[status(thm)],[2129]) ).

thf(2700,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[2142,50]) ).

thf(2701,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2700:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I )),bind(D,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ I ) @ H ) ) ))]]) ).

thf(2725,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ B @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ ( removemin_cpq_eff @ B ) @ A ) ) ) ) ),
    inference(simp,[status(thm)],[2701]) ).

thf(3141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) ) )
       != ( triple @ sk1 @ sk2 @ sk3 ) )
      | ( ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) )
       != ( findmin_cpq_eff @ ( triple @ C @ create_slb @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[171,2246]) ).

thf(3142,plain,
    ! [A: $i] :
      ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ bad ) ) ) ) )
     != ( triple @ sk1 @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[3141:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(79,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = A ),
    inference(cnf,[status(esa)],[78]) ).

thf(80,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = A ),
    inference(lifteq,[status(thm)],[79]) ).

thf(1802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ A @ ( insert_cpq @ A @ B ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1786,50]) ).

thf(1803,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[1802:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( insert_cpq @ E @ F ))]]) ).

thf(1809,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ),
    inference(simp,[status(thm)],[1803]) ).

thf(37,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( ok @ ( triple @ A @ B @ C ) )
     => ( C = bad ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).

thf(162,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( ok @ ( triple @ A @ B @ C ) )
     => ( C = bad ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ~ ( strictly_less_than @ A @ B )
      | ~ ( less_than @ B @ A ) ),
    inference(cnf,[status(esa)],[52]) ).

thf(208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ B @ C )
      | ( ( less_than @ bottom @ A )
       != ( less_than @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[82,55]) ).

thf(209,plain,
    ! [A: $i] :
      ~ ( strictly_less_than @ A @ bottom ),
    inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( bottom ))]]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != create_slb )
        & ~ ( contains_slb @ B @ ( findmin_pqp_res @ A ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
        = ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ bad ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).

thf(150,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B != create_slb )
        & ~ ( contains_slb @ B @ ( findmin_pqp_res @ A ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
        = ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ bad ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(95,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ A @ B @ C )
      | ~ ( strictly_less_than @ B @ C )
      | ( pair_in_list @ ( update_slb @ A @ D ) @ ( sk4 @ D @ A ) @ ( sk5 @ D @ A ) ) ),
    inference(cnf,[status(esa)],[94]) ).

thf(71,plain,
    ~ ? [A: $i] : ( contains_slb @ create_slb @ A ),
    inference(miniscope,[status(thm)],[70]) ).

thf(72,plain,
    ! [A: $i] :
      ~ ( contains_slb @ create_slb @ A ),
    inference(cnf,[status(esa)],[71]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != create_slb )
        & ( contains_slb @ B @ ( findmin_pqp_res @ A ) )
        & ( strictly_less_than @ ( findmin_pqp_res @ A ) @ ( lookup_slb @ B @ ( findmin_pqp_res @ A ) ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
        = ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ bad ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).

thf(175,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B != create_slb )
        & ( contains_slb @ B @ ( findmin_pqp_res @ A ) )
        & ( strictly_less_than @ ( findmin_pqp_res @ A ) @ ( lookup_slb @ B @ ( findmin_pqp_res @ A ) ) ) )
     => ( ( findmin_cpq_eff @ ( triple @ A @ B @ C ) )
        = ( triple @ A @ ( update_slb @ B @ ( findmin_pqp_res @ A ) ) @ bad ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(31,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B != create_slb )
     => ( ( findmin_cpq_res @ ( triple @ A @ B @ C ) )
        = ( findmin_pqp_res @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).

thf(143,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B != create_slb )
     => ( ( findmin_cpq_res @ ( triple @ A @ B @ C ) )
        = ( findmin_pqp_res @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(248,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[247,50]) ).

thf(249,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( I )),bind(B,$thf( I )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ I ) ) ) ) ) ))]]) ).

thf(250,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ),
    inference(simp,[status(thm)],[249]) ).

thf(98,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = C ),
    inference(cnf,[status(esa)],[97]) ).

thf(99,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = C ),
    inference(lifteq,[status(thm)],[98]) ).

thf(1832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1809,50]) ).

thf(1833,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[1832:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( removemin_cpq_eff @ ( insert_cpq @ F @ G ) ))]]) ).

thf(1844,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[1833]) ).

thf(104,plain,
    ! [B: $i,A: $i] :
      ( ( less_than @ A @ B )
      | ( less_than @ B @ A ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(2290,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1844,50]) ).

thf(2291,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2290:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ G @ H ) ) ))]]) ).

thf(2305,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) ),
    inference(simp,[status(thm)],[2291]) ).

thf(206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ B @ C )
      | ( ( less_than @ A @ A )
       != ( less_than @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[69,55]) ).

thf(207,plain,
    ! [A: $i] :
      ~ ( strictly_less_than @ A @ A ),
    inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(380,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
     != ( contains_slb @ create_slb @ D ) ),
    inference(paramod_ordered,[status(thm)],[66,72]) ).

thf(381,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( insert_slb @ A @ ( pair @ B @ C ) )
       != create_slb )
      | ( B != D ) ),
    inference(simp,[status(thm)],[380]) ).

thf(383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( insert_slb @ A @ ( pair @ C @ B ) )
     != create_slb ),
    inference(simp,[status(thm)],[381]) ).

thf(285,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[250,50]) ).

thf(286,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( J )),bind(B,$thf( J )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ J ) ) ) ) ) ) ))]]) ).

thf(287,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) ),
    inference(simp,[status(thm)],[286]) ).

thf(288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ B @ ( removemin_cpq_eff @ C ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) )
       != ( succ_cpq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[287,50]) ).

thf(289,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( K )),bind(B,$thf( K )),bind(C,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ K ) ) ) ) ) ) ) ))]]) ).

thf(290,plain,
    ! [A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ A ) ) ) ) ) ) ) ) ) ),
    inference(simp,[status(thm)],[289]) ).

thf(314,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
        = ( triple @ C @ create_slb @ bad ) )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,171]) ).

thf(315,plain,
    ! [B: $i,A: $i] :
      ( ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) )
      = ( triple @ A @ create_slb @ bad ) ),
    inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(2483,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) )
        = bottom )
      | ( ( triple @ A @ create_slb @ bad )
       != ( triple @ C @ create_slb @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[171,1890]) ).

thf(2484,plain,
    ! [B: $i,A: $i] :
      ( ( removemin_cpq_res @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( findmin_cpq_eff @ ( triple @ A @ create_slb @ B ) ) ) ) ) ) ) )
      = bottom ),
    inference(pattern_uni,[status(thm)],[2483:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( bad ))]]) ).

thf(2730,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( succ_cpq @ C @ ( removemin_cpq_eff @ D ) )
      | ( ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) )
       != ( succ_cpq @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[2305,50]) ).

thf(2731,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2730:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( H )),bind(D,$thf( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ H @ I ) ) ) ))]]) ).

thf(2754,plain,
    ! [B: $i,A: $i] : ( succ_cpq @ A @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( removemin_cpq_eff @ ( insert_cpq @ A @ B ) ) ) ) ) ),
    inference(simp,[status(thm)],[2731]) ).

thf(24,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( succ_cpq @ A @ B )
     => ( succ_cpq @ A @ ( remove_cpq @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).

thf(122,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( succ_cpq @ A @ B )
     => ( succ_cpq @ A @ ( remove_cpq @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( strictly_less_than @ A @ B )
      | ~ ( strictly_less_than @ C @ D )
      | ( ( less_than @ A @ B )
       != ( less_than @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[54,55]) ).

thf(215,plain,
    ! [B: $i,A: $i] :
      ( ~ ( strictly_less_than @ A @ B )
      | ~ ( strictly_less_than @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).

thf(724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
      | ( contains_slb @ A @ C )
      | ( C != create_slb )
      | ( B != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[67,213]) ).

thf(725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ sk2 @ C ) ) @ B )
      | ( contains_slb @ A @ B )
      | ( B != create_slb ) ),
    inference(pattern_uni,[status(thm)],[724:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(1088,plain,
    ! [B: $i,A: $i] :
      ( ~ ( contains_slb @ ( insert_slb @ A @ ( pair @ sk2 @ B ) ) @ create_slb )
      | ( contains_slb @ A @ create_slb ) ),
    inference(simp,[status(thm)],[725]) ).

thf(106,plain,
    ( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
       => ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) ) )
    & ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) )
       => ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
    inference(miniscope,[status(thm)],[105]) ).

thf(107,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ A @ C @ E )
      | ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
    inference(cnf,[status(esa)],[106]) ).

thf(111,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( pair_in_list @ A @ C @ E )
      | ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
    inference(simp,[status(thm)],[107]) ).

thf(41898,plain,
    $false,
    inference(cvc4,[status(thm)],[1825,64,69,2412,234,408,1808,247,202,1788,56,174,2869,1709,184,125,2185,1379,1890,46,93,228,57,78,1714,179,211,2122,1978,121,147,2367,1796,132,89,2799,116,74,292,85,102,392,70,137,165,92,229,197,97,1089,1794,156,1375,169,77,1424,2551,96,134,73,128,205,2338,105,244,191,59,1786,54,313,49,236,86,159,172,219,81,2246,362,303,103,140,213,91,66,251,1293,155,2725,3142,80,1809,162,209,194,48,1611,150,95,50,67,1785,127,154,72,175,143,250,99,1844,218,104,2305,351,55,171,75,207,383,1661,82,287,290,119,58,2142,315,51,294,358,195,1335,400,94,2241,47,68,2484,2754,122,83,215,1088,222,364,232,100,90,111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV398+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n024.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Fri May 19 02:39:23 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.94/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.41/1.07  % [INFO] 	 Parsing done (158ms). 
% 1.41/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.89/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.89/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 1.89/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.08/1.34  % [INFO] 	 Found a conjecture and 43 axioms. Running axiom selection ... 
% 2.20/1.39  % [INFO] 	 Axiom selection finished. Selected 43 axioms (removed 0 axioms). 
% 2.47/1.45  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.47/1.46  % [INFO] 	 Type checking passed. 
% 2.47/1.46  % [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 ... 
% 113.42/20.01  % External prover 'cvc4' found a proof!
% 113.42/20.01  % [INFO] 	 Killing All external provers ... 
% 113.42/20.02  % Time passed: 19477ms (effective reasoning time: 18936ms)
% 113.42/20.02  % 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)>
% 113.42/20.02  % Axioms used in derivation (43): ax28, ax39, ax27, l34_l35, ax32, ax22, ax43, ax19, ax49, ax25, ax53, ax20, ax52, ax24, ax47, ax41, stricly_smaller_definition, ax31, ax45, ax40, ax35, ax51, ax48, ax21, ax38, ax44, reflexivity, ax33, ax26, bottom_smallest, ax50, ax37, l26_li4142, totality, ax46, ax34, ax23, transitivity, ax30, ax42, ax18, ax36, ax29
% 113.42/20.02  % No. of inferences in proof: 318
% 113.42/20.02  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19477 ms resp. 18936 ms w/o parsing
% 113.66/20.09  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 113.66/20.10  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------