%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT262-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:27:09 EDT 2023

% Result   : Unsatisfiable 7.91s 2.83s
% Output   : Refutation 8.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  291
% Syntax   : Number of formulae    :  525 ( 133 unt;  58 typ;   0 def)
%            Number of atoms       : 1085 ( 314 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 5298 ( 574   ~; 618   |;   0   &;4106   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  115 ( 115   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   60 (  58 usr;  11 con; 0-5 aty)
%            Number of variables   : 1372 (   0   ^;1372   !;   0   ?;1372   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
    c_lessequals: $i > $i > $i > $o ).

thf(v_S_type,type,
    v_S: $i ).

thf(c_Tarski_Opotype_Opset_type,type,
    c_Tarski_Opotype_Opset: $i > $i > $i > $i ).

thf(v_cl_type,type,
    v_cl: $i ).

thf(t_a_type,type,
    t_a: $i ).

thf(tc_Product__Type_Ounit_type,type,
    tc_Product__Type_Ounit: $i ).

thf(tc_set_type,type,
    tc_set: $i > $i ).

thf(c_Tarski_Odual_type,type,
    c_Tarski_Odual: $i > $i > $i ).

thf(class_Orderings_Olinorder_type,type,
    class_Orderings_Olinorder: $i > $o ).

thf(c_in_type,type,
    c_in: $i > $i > $i > $o ).

thf(c_Finite__Set_OFinites_type,type,
    c_Finite__Set_OFinites: $i ).

thf(c_emptyset_type,type,
    c_emptyset: $i ).

thf(c_Orderings_Omin_type,type,
    c_Orderings_Omin: $i > $i > $i > $i ).

thf(c_Finite__Set_OMax_type,type,
    c_Finite__Set_OMax: $i > $i > $i ).

thf(c_less_type,type,
    c_less: $i > $i > $i > $o ).

thf(c_Orderings_Omax_type,type,
    c_Orderings_Omax: $i > $i > $i > $i ).

thf(c_Finite__Set_OMin_type,type,
    c_Finite__Set_OMin: $i > $i > $i ).

thf(class_Orderings_Oord_type,type,
    class_Orderings_Oord: $i > $o ).

thf(c_SetInterval_OatLeastAtMost_type,type,
    c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).

thf(c_SetInterval_OatLeastLessThan_type,type,
    c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).

thf(c_insert_type,type,
    c_insert: $i > $i > $i > $i ).

thf(c_SetInterval_OgreaterThanAtMost_type,type,
    c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).

thf(c_Main_OMax__le__iff__1_type,type,
    c_Main_OMax__le__iff__1: $i > $i > $i > $i ).

thf(c_Union_type,type,
    c_Union: $i > $i > $i ).

thf(c_Inter_type,type,
    c_Inter: $i > $i > $i ).

thf(c_UNIV_type,type,
    c_UNIV: $i ).

thf(c_SetInterval_OlessThan_type,type,
    c_SetInterval_OlessThan: $i > $i > $i ).

thf(c_Main_OMin__gr__iff__1_type,type,
    c_Main_OMin__gr__iff__1: $i > $i > $i > $i ).

thf(c_union_type,type,
    c_union: $i > $i > $i > $i ).

thf(c_Main_OMax__less__iff__1_type,type,
    c_Main_OMax__less__iff__1: $i > $i > $i > $i ).

thf(c_inter_type,type,
    c_inter: $i > $i > $i > $i ).

thf(c_Pow_type,type,
    c_Pow: $i > $i > $i ).

thf(class_Orderings_Oorder_type,type,
    class_Orderings_Oorder: $i > $o ).

thf(c_Main_OMin__ge__iff__1_type,type,
    c_Main_OMin__ge__iff__1: $i > $i > $i > $i ).

thf(c_Tarski_Opotype_Opotype__ext_type,type,
    c_Tarski_Opotype_Opotype__ext: $i > $i > $i > $i > $i > $i ).

thf(c_SetInterval_OatLeast_type,type,
    c_SetInterval_OatLeast: $i > $i > $i ).

thf(c_uminus_type,type,
    c_uminus: $i > $i > $i ).

thf(c_List_Olist_OCons_type,type,
    c_List_Olist_OCons: $i > $i > $i > $i ).

thf(c_SetInterval_OatMost_type,type,
    c_SetInterval_OatMost: $i > $i > $i ).

thf(c_SetInterval_OgreaterThan_type,type,
    c_SetInterval_OgreaterThan: $i > $i > $i ).

thf(c_Tarski_Opotype_Oorder_type,type,
    c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).

thf(c_Tarski_OCompleteLattice_type,type,
    c_Tarski_OCompleteLattice: $i ).

thf(tc_Tarski_Opotype_Opotype__ext__type_type,type,
    tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).

thf(c_Relation_Oantisym_type,type,
    c_Relation_Oantisym: $i > $i > $o ).

thf(c_Main_Oall__not__in__conv__1_type,type,
    c_Main_Oall__not__in__conv__1: $i > $i > $i ).

thf(c_Relation_Otrans_type,type,
    c_Relation_Otrans: $i > $i > $o ).

thf(c_Set_Ocontents_type,type,
    c_Set_Ocontents: $i > $i > $i ).

thf(c_Main_OsubsetI__1_type,type,
    c_Main_OsubsetI__1: $i > $i > $i > $i ).

thf(c_Tarski_OPartialOrder_type,type,
    c_Tarski_OPartialOrder: $i ).

thf(c_Tarski_Olub_type,type,
    c_Tarski_Olub: $i > $i > $i > $i ).

thf(class_Nat_Opower_type,type,
    class_Nat_Opower: $i > $o ).

thf(v_A_type,type,
    v_A: $i ).

thf(class_HOL_Ominus_type,type,
    class_HOL_Ominus: $i > $o ).

thf(class_Finite__Set_Ofinite_type,type,
    class_Finite__Set_Ofinite: $i > $o ).

thf(c_Tarski_Oglb_type,type,
    c_Tarski_Oglb: $i > $i > $i > $i ).

thf(c_Relation_Orefl_type,type,
    c_Relation_Orefl: $i > $i > $i > $o ).

thf(c_List_Olistset_type,type,
    c_List_Olistset: $i > $i > $i ).

thf(c_List_Oset__Cons_type,type,
    c_List_Oset__Cons: $i > $i > $i > $i ).

thf(165,axiom,
    ! [B: $i,A: $i] :
      ( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).

thf(629,plain,
    ! [B: $i,A: $i] :
      ( ( c_inter @ ( c_uminus @ A @ ( tc_set @ B ) ) @ A @ B )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Arefl_A_Ipset_Acl1_J_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).

thf(760,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Orefl @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OatLeast @ B @ A )
       != ( c_SetInterval_OatLeast @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).

thf(479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OatLeast @ B @ A )
       != ( c_SetInterval_OatLeast @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(1,negated_conjecture,
    c_lessequals @ v_S @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(234,plain,
    c_lessequals @ v_S @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(44,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ E @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).

thf(333,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ E @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ D @ C @ A )
      | ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).

thf(249,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ D @ C @ A )
      | ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ B @ A )
      | ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).

thf(408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ B @ A )
      | ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(188,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ B @ C )
       != c_emptyset )
      | ( c_in @ D @ A @ C )
      | ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
        = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).

thf(683,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ B @ C )
       != c_emptyset )
      | ( c_in @ D @ A @ C )
      | ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
      | ( c_less @ B @ D @ A )
      | ( C = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).

thf(308,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
      | ( c_less @ B @ D @ A )
      | ( C = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(217,axiom,
    ! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).

thf(741,plain,
    ! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).

thf(449,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).

thf(247,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(64,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).

thf(379,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).

thf(597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(123,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).

thf(523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

thf(582,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olistset @ ( c_List_Olist_OCons @ A @ B @ ( tc_set @ C ) ) @ C )
      = ( c_List_Oset__Cons @ A @ ( c_List_Olistset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).

thf(762,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olistset @ ( c_List_Olist_OCons @ A @ B @ ( tc_set @ C ) ) @ C )
      = ( c_List_Oset__Cons @ A @ ( c_List_Olistset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).

thf(730,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( C = c_emptyset )
      | ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).

thf(276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( C = c_emptyset )
      | ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ( c_UNIV
       != ( c_Inter @ B @ C ) )
      | ( A = c_UNIV ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).

thf(614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ( c_UNIV
       != ( c_Inter @ B @ C ) )
      | ( A = c_UNIV ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).

thf(677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_lessequals @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
      | ( c_lessequals @ B @ D @ A )
      | ( C = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).

thf(385,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_lessequals @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
      | ( c_lessequals @ B @ D @ A )
      | ( C = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).

thf(472,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(194,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
      | ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).

thf(698,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
      | ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).

thf(301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_inter @ A @ B @ C ) )
      | ( c_in @ D @ B @ C )
      | ( c_emptyset
        = ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_2) ).

thf(436,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_inter @ A @ B @ C ) )
      | ( c_in @ D @ B @ C )
      | ( c_emptyset
        = ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ c_UNIV @ B )
      = c_UNIV ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).

thf(651,plain,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ c_UNIV @ B )
      = c_UNIV ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
      | ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).

thf(320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
      | ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).

thf(565,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(208,axiom,
    ! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(724,plain,
    ! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).

thf(570,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
      = ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).

thf(587,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
      = ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(222,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(751,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).

thf(344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OgreaterThanAtMost @ C @ D @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Finite__Set_OMax @ B @ A ) @ B @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).

thf(357,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Finite__Set_OMax @ B @ A ) @ B @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).

thf(542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(97,axiom,
    ! [B: $i,A: $i] :
      ( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).

thf(460,plain,
    ! [B: $i,A: $i] :
      ( ( c_inter @ A @ ( c_uminus @ A @ ( tc_set @ B ) ) @ B )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).

thf(559,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).

thf(638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
      | ( c_less @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).

thf(325,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
      | ( c_less @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).

thf(289,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ( c_in @ C @ ( c_SetInterval_OgreaterThanAtMost @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
      | ( c_in @ D @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).

thf(316,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
      | ( c_in @ D @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(284,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(233,axiom,
    c_in @ v_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0) ).

thf(770,plain,
    c_in @ v_cl @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).

thf(492,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      | ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).

thf(756,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      | ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).

thf(591,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(163,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).

thf(623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( C = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( c_Union @ c_UNIV @ A )
      = c_UNIV ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).

thf(348,plain,
    ! [A: $i] :
      ( ( c_Union @ c_UNIV @ A )
      = c_UNIV ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_lessequals @ ( c_Finite__Set_OMin @ C @ A ) @ B @ A )
      | ( C = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).

thf(353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_lessequals @ ( c_Finite__Set_OMin @ C @ A ) @ B @ A )
      | ( C = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(692,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
      | ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).

thf(396,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
      | ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_uminus @ A @ ( tc_set @ B ) )
       != ( c_uminus @ C @ ( tc_set @ B ) ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).

thf(660,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_uminus @ A @ ( tc_set @ B ) )
       != ( c_uminus @ C @ ( tc_set @ B ) ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(77,axiom,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).

thf(411,plain,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_uminus @ ( c_inter @ A @ B @ C ) @ ( tc_set @ C ) )
      = ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).

thf(428,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_uminus @ ( c_inter @ A @ B @ C ) @ ( tc_set @ C ) )
      = ( c_union @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
        = ( c_Orderings_Omax @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).

thf(265,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
        = ( c_Orderings_Omax @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).

thf(602,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(766,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(452,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).

thf(439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D ) )
      | ( c_emptyset
        = ( c_inter @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).

thf(546,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D ) )
      | ( c_emptyset
        = ( c_inter @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).

thf(381,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).

thf(714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_less @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).

thf(270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_less @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).

thf(529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

thf(746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).

thf(260,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Inter @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
      = ( c_inter @ A @ ( c_Inter @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).

thf(561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Inter @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
      = ( c_inter @ A @ ( c_Inter @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).

thf(392,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( c_Inter @ c_emptyset @ A )
      = c_UNIV ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).

thf(297,plain,
    ! [A: $i] :
      ( ( c_Inter @ c_emptyset @ A )
      = c_UNIV ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).

thf(424,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Pow @ ( c_inter @ A @ B @ C ) @ C )
      = ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).

thf(467,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Pow @ ( c_inter @ A @ B @ C ) @ C )
      = ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).

thf(484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(180,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).

thf(665,plain,
    ! [B: $i,A: $i] :
      ( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(148,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).

thf(583,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
      = ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).

thf(551,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
      = ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).

thf(710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(173,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(650,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).

thf(725,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( c_Inter @ c_UNIV @ A )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).

thf(388,plain,
    ! [A: $i] :
      ( ( c_Inter @ c_UNIV @ A )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(53,axiom,
    ! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(356,plain,
    ! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ( c_union @ c_emptyset @ c_emptyset @ A )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).

thf(593,plain,
    ! [A: $i] :
      ( ( c_union @ c_emptyset @ c_emptyset @ A )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ( ( c_Inter @ B @ C )
       != c_UNIV )
      | ( A = c_UNIV ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).

thf(499,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ( ( c_Inter @ B @ C )
       != c_UNIV )
      | ( A = c_UNIV ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(218,axiom,
    ! [A: $i] :
      ( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
      | ~ ( class_Finite__Set_Ofinite @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).

thf(742,plain,
    ! [A: $i] :
      ( ( class_Finite__Set_Ofinite @ ( tc_set @ A ) )
      | ~ ( class_Finite__Set_Ofinite @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(145,axiom,
    ! [B: $i,A: $i] :
      ( ( c_inter @ A @ c_UNIV @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).

thf(578,plain,
    ! [B: $i,A: $i] :
      ( ( c_inter @ A @ c_UNIV @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).

thf(256,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ( c_inter @ c_emptyset @ A @ B )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).

thf(488,plain,
    ! [B: $i,A: $i] :
      ( ( c_inter @ c_emptyset @ A @ B )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(128,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).

thf(537,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(182,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

thf(669,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(189,axiom,
    ! [A: $i] :
      ( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
      = c_UNIV ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).

thf(686,plain,
    ! [A: $i] :
      ( ( c_uminus @ c_emptyset @ ( tc_set @ A ) )
      = c_UNIV ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(124,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
        = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).

thf(526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
      | ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).

thf(706,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
      | ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
      | ( ( c_insert @ B @ c_emptyset @ C )
        = ( c_insert @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).

thf(647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
      | ( ( c_insert @ B @ c_emptyset @ C )
        = ( c_insert @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(196,axiom,
    ( v_A
    = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).

thf(701,plain,
    ( v_A
    = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(120,axiom,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ c_emptyset @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).

thf(515,plain,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ c_emptyset @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( C = c_emptyset )
      | ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).

thf(237,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( C = c_emptyset )
      | ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
        = ( c_Orderings_Omin @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).

thf(244,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
        = ( c_Orderings_Omin @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).

thf(508,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
      | ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).

thf(311,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
      | ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_emptyset
     != ( c_insert @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).

thf(657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_emptyset
     != ( c_insert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).

thf(718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(167,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).

thf(633,plain,
    c_UNIV != c_emptyset,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(55,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ D @ B @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).

thf(360,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ D @ B @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).

thf(279,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(143,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).

thf(573,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).

thf(444,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).

thf(513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).

thf(430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(62,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Union @ ( c_union @ A @ B @ ( tc_set @ C ) ) @ C )
      = ( c_union @ ( c_Union @ A @ C ) @ ( c_Union @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).

thf(375,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Union @ ( c_union @ A @ B @ ( tc_set @ C ) ) @ C )
      = ( c_union @ ( c_Union @ A @ C ) @ ( c_Union @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).

thf(733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ~ ( c_lessequals @ C @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ ( tc_set @ B ) )
      | ( c_in @ ( c_Tarski_Olub @ C @ A @ B ) @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__in__lattice_0) ).

thf(694,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ~ ( c_lessequals @ C @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ ( tc_set @ B ) )
      | ( c_in @ ( c_Tarski_Olub @ C @ A @ B ) @ ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( B = c_emptyset )
      | ( ( c_Finite__Set_OMax @ ( c_insert @ C @ B @ A ) @ A )
        = ( c_Orderings_Omax @ C @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).

thf(402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( B = c_emptyset )
      | ( ( c_Finite__Set_OMax @ ( c_insert @ C @ B @ A ) @ A )
        = ( c_Orderings_Omax @ C @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
      | ( c_lessequals @ D @ B @ A )
      | ( C = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).

thf(286,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
      | ( c_lessequals @ D @ B @ A )
      | ( C = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
      | ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).

thf(291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
      | ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(22,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ E @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).

thf(281,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ E @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( c_Pow @ c_emptyset @ A )
      = ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).

thf(413,plain,
    ! [A: $i] :
      ( ( c_Pow @ c_emptyset @ A )
      = ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_uminus @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
        = ( c_SetInterval_OatLeast @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).

thf(641,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_uminus @ ( c_SetInterval_OlessThan @ B @ A ) @ ( tc_set @ A ) )
        = ( c_SetInterval_OatLeast @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_emptyset
       != ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).

thf(611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_emptyset
       != ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_less @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
      | ( c_less @ D @ B @ A )
      | ( C = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).

thf(335,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_less @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
      | ( c_less @ D @ B @ A )
      | ( C = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Finite__Set_OMin @ B @ A ) @ B @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).

thf(350,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Finite__Set_OMin @ B @ A ) @ B @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(129,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).

thf(540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).

thf(274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(80,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
       != c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).

thf(419,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).

thf(377,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_uminus @ ( c_union @ A @ B @ C ) @ ( tc_set @ C ) )
      = ( c_inter @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).

thf(434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_uminus @ ( c_union @ A @ B @ C ) @ ( tc_set @ C ) )
      = ( c_inter @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
      | ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).

thf(303,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
      | ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ B @ C )
       != c_emptyset )
      | ( c_in @ D @ B @ C )
      | ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
        = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).

thf(599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ B @ C )
       != c_emptyset )
      | ( c_in @ D @ B @ C )
      | ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(230,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).

thf(764,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(157,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
      | ( ( c_insert @ B @ A @ C )
        = ( c_insert @ B @ c_emptyset @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).

thf(604,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
      | ( ( c_insert @ B @ A @ C )
        = ( c_insert @ B @ c_emptyset @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).

thf(362,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ C @ D @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(141,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).

thf(567,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
      | ( c_lessequals @ A @ C @ ( tc_set @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).

thf(737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
      | ( c_lessequals @ A @ C @ ( tc_set @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(318,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(104,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E ) @ D @ E )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__2_0) ).

thf(477,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E ) @ D @ E )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(112,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).

thf(494,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(166,axiom,
    ! [B: $i,A: $i] :
      ( ( c_union @ c_emptyset @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).

thf(631,plain,
    ! [B: $i,A: $i] :
      ( ( c_union @ c_emptyset @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(758,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(367,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( class_Orderings_Oord @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).

thf(535,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C ) )
      | ( c_emptyset
        = ( c_inter @ B @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).

thf(626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C ) )
      | ( c_emptyset
        = ( c_inter @ B @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(232,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(769,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_less @ C @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ A )
      | ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).

thf(330,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_less @ C @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ A )
      | ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ( c_union @ c_UNIV @ A @ B )
      = c_UNIV ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).

thf(462,plain,
    ! [B: $i,A: $i] :
      ( ( c_union @ c_UNIV @ A @ B )
      = c_UNIV ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(195,axiom,
    ! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(700,plain,
    ! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ B @ C )
       != c_UNIV )
      | ( B = c_UNIV ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).

thf(520,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ B @ C )
       != c_UNIV )
      | ( B = c_UNIV ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_less @ C @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).

thf(240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_less @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Orderings_Omin @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).

thf(251,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Orderings_Omin @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).

thf(399,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Union @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
      = ( c_union @ A @ ( c_Union @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).

thf(636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Union @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
      = ( c_union @ A @ ( c_Union @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(95,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_emptyset
       != ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).

thf(455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_emptyset
       != ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(139,axiom,
    ! [B: $i,A: $i] :
      ( ( c_inter @ c_UNIV @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).

thf(563,plain,
    ! [B: $i,A: $i] :
      ( ( c_inter @ c_UNIV @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).

thf(299,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_inter @ A @ B @ C ) )
      | ( c_in @ D @ A @ C )
      | ( c_emptyset
        = ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).

thf(505,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_inter @ A @ B @ C ) )
      | ( c_in @ D @ A @ C )
      | ( c_emptyset
        = ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Finite__Set_OMax @ ( c_insert @ B @ c_emptyset @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).

thf(653,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Finite__Set_OMax @ ( c_insert @ B @ c_emptyset @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).

thf(394,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
      | ( c_less @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( c_Union @ c_emptyset @ A )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).

thf(306,plain,
    ! [A: $i] :
      ( ( c_Union @ c_emptyset @ A )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

thf(722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
      = ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).

thf(490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
      = ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).

thf(426,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(150,axiom,
    ! [B: $i,A: $i] :
      ( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).

thf(589,plain,
    ! [B: $i,A: $i] :
      ( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).

thf(680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(179,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).

thf(663,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_less @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
        = ( c_insert @ B @ c_emptyset @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).

thf(617,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
        = ( c_insert @ B @ c_emptyset @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(224,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).

thf(754,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ c_UNIV @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(135,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
       != ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
      | ( B = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_1) ).

thf(553,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
       != ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
      | ( B = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).

thf(458,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(146,axiom,
    ! [A: $i] :
      ( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).

thf(580,plain,
    ! [A: $i] :
      ( ( c_uminus @ c_UNIV @ ( tc_set @ A ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(198,axiom,
    c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).

thf(705,plain,
    c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( B = c_emptyset )
      | ( ( c_Finite__Set_OMin @ ( c_insert @ C @ B @ A ) @ A )
        = ( c_Orderings_Omin @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).

thf(327,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( B = c_emptyset )
      | ( ( c_Finite__Set_OMin @ ( c_insert @ C @ B @ A ) @ A )
        = ( c_Orderings_Omin @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Oglb @ A @ B @ C )
      = ( c_Tarski_Olub @ A @ ( c_Tarski_Odual @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).

thf(739,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Oglb @ A @ B @ C )
      = ( c_Tarski_Olub @ A @ ( c_Tarski_Odual @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(202,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ A @ B ) @ B @ tc_Product__Type_Ounit )
      = ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).

thf(712,plain,
    ! [B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ A @ B ) @ B @ tc_Product__Type_Ounit )
      = ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(136,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).

thf(557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
      | ( c_less @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OatMost @ B @ A )
       != ( c_SetInterval_OatMost @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).

thf(673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OatMost @ B @ A )
       != ( c_SetInterval_OatMost @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
       != c_emptyset )
      | ( ( c_inter @ A @ C @ D )
        = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).

thf(502,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
       != c_emptyset )
      | ( ( c_inter @ A @ C @ D )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
      | ( C = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).

thf(338,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ C @ A )
      | ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ( c_lessequals @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
      | ( C = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).

thf(544,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).

thf(744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ ( c_inter @ D @ B @ C ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).

thf(703,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ ( c_inter @ D @ B @ C ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(176,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(656,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(210,axiom,
    class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).

thf(727,plain,
    class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(36,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).

thf(314,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).

thf(446,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(153,axiom,
    ! [B: $i,A: $i] :
      ( ( c_inter @ A @ c_emptyset @ B )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__right_0) ).

thf(595,plain,
    ! [B: $i,A: $i] :
      ( ( c_inter @ A @ c_emptyset @ B )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(106,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Aantisym_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).

thf(482,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Oantisym @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ( c_Pow @ c_UNIV @ A )
      = c_UNIV ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).

thf(671,plain,
    ! [A: $i] :
      ( ( c_Pow @ c_UNIV @ A )
      = c_UNIV ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(190,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
       != ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
      | ( A = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_0) ).

thf(688,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
       != ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
      | ( A = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OgreaterThan @ B @ A )
       != ( c_SetInterval_OgreaterThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).

thf(517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OgreaterThan @ B @ A )
       != ( c_SetInterval_OgreaterThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
      | ( c_less @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).

thf(258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
      | ( c_less @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).

thf(390,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ( c_in @ B @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(2,negated_conjecture,
    ~ ( c_lessequals @ v_S @ ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(235,plain,
    ~ ( c_lessequals @ v_S @ ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ B @ C )
       != c_UNIV )
      | ( A = c_UNIV ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).

thf(510,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ A @ B @ C )
       != c_UNIV )
      | ( A = c_UNIV ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(667,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).

thf(272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).

thf(383,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Union @ ( c_Pow @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).

thf(346,plain,
    ! [B: $i,A: $i] :
      ( ( c_Union @ ( c_Pow @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ( c_inter @ c_UNIV @ c_UNIV @ A )
      = c_UNIV ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_2) ).

thf(549,plain,
    ! [A: $i] :
      ( ( c_inter @ c_UNIV @ c_UNIV @ A )
      = c_UNIV ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).

thf(716,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ c_emptyset @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ c_emptyset @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(223,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E ) @ D @ E )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__1_0) ).

thf(752,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E ) @ D @ E )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(86,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(432,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Orderings_Omax @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).

thf(262,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Orderings_Omax @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_lessequals @ C @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ A )
      | ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).

thf(405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
      | ~ ( c_lessequals @ C @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ A )
      | ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
      = ( c_insert @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).

thf(422,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
      = ( c_insert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).

thf(373,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
      | ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(214,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).

thf(735,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).

thf(242,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ( ( c_Union @ B @ C )
       != c_emptyset )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).

thf(294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ( ( c_Union @ B @ C )
       != c_emptyset )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OlessThan @ B @ A )
       != ( c_SetInterval_OlessThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).

thf(341,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_OlessThan @ B @ A )
       != ( c_SetInterval_OlessThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ B @ D @ A )
      | ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).

thf(268,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_less @ B @ C @ A )
      | ~ ( c_less @ B @ D @ A )
      | ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_insert @ A @ B @ C )
     != c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).

thf(474,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_insert @ A @ B @ C )
     != c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
       != c_emptyset )
      | ( ( c_inter @ B @ D @ C )
        = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).

thf(532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
       != c_emptyset )
      | ( ( c_inter @ B @ D @ C )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(193,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(696,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(23,axiom,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(283,plain,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(79,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
       != ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
      | ( C = H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_2) ).

thf(415,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Tarski_Opotype_Opotype__ext @ A @ B @ C @ D @ E )
       != ( c_Tarski_Opotype_Opotype__ext @ F @ G @ H @ D @ E ) )
      | ( C = H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

thf(728,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
        = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).

thf(464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
        = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).

thf(575,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( ( c_SetInterval_OgreaterThanAtMost @ C @ B @ A )
        = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_uminus @ ( c_SetInterval_OatMost @ B @ A ) @ ( tc_set @ A ) )
        = ( c_SetInterval_OgreaterThan @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).

thf(644,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_uminus @ ( c_SetInterval_OatMost @ B @ A ) @ ( tc_set @ A ) )
        = ( c_SetInterval_OgreaterThan @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(90,axiom,
    ! [B: $i,A: $i] :
      ( ( c_inter @ A @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).

thf(442,plain,
    ! [B: $i,A: $i] :
      ( ( c_inter @ A @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).

thf(369,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_OatLeastAtMost @ C @ D @ A ) @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(158,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).

thf(607,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).

thf(254,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).

thf(486,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(101,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
        = ( c_SetInterval_OatMost @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).

thf(469,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_uminus @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) )
        = ( c_SetInterval_OatMost @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(113,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
        = ( c_SetInterval_OlessThan @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).

thf(496,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_uminus @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) )
        = ( c_SetInterval_OlessThan @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(57,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ( c_emptyset
       != ( c_Union @ B @ C ) )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).

thf(364,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ( c_emptyset
       != ( c_Union @ B @ C ) )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).

thf(708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
      | ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(225,axiom,
    c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).

thf(755,plain,
    c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(185,axiom,
    ! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(676,plain,
    ! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(771,plain,
    $false,
    inference(e,[status(thm)],[629,760,479,234,333,249,408,683,308,741,449,247,379,597,523,582,762,730,276,614,677,385,472,698,301,436,651,320,565,724,570,587,751,344,357,542,460,559,638,325,289,316,284,770,492,756,591,623,348,353,692,396,660,411,428,265,602,766,452,439,546,381,714,270,529,746,260,561,392,297,424,467,484,665,583,551,710,650,725,388,356,593,499,742,578,256,488,537,669,686,526,706,647,701,515,371,237,244,508,311,657,718,633,360,279,573,444,513,430,375,733,694,402,286,291,281,413,641,611,335,350,540,274,419,377,434,303,599,764,604,362,567,737,318,477,494,631,758,367,535,323,626,769,330,462,700,520,240,251,399,636,455,563,299,505,653,394,306,722,490,426,589,680,663,749,617,754,553,458,580,705,327,739,712,557,673,502,338,544,744,703,656,727,314,446,595,482,671,688,517,258,390,235,510,667,272,383,346,549,716,620,752,432,262,405,422,373,735,242,294,341,268,474,532,696,720,283,415,728,464,575,644,442,369,607,254,486,469,496,364,708,755,676]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LAT262-1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n011.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.21/0.36  % WCLimit  : 300
% 0.21/0.36  % DateTime : Thu May 18 14:21:33 EDT 2023
% 0.21/0.36  % CPUTime  : 
% 0.98/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.06/1.26  % [INFO] 	 Parsing done (297ms). 
% 2.06/1.27  % [INFO] 	 Running in sequential loop mode. 
% 2.63/1.46  % [INFO] 	 eprover registered as external prover. 
% 2.63/1.46  % [INFO] 	 cvc4 registered as external prover. 
% 2.63/1.47  % [INFO] 	 Scanning for conjecture ... 
% 2.93/1.61  % [INFO] 	 Found a conjecture and 2746 axioms. Running axiom selection ... 
% 3.56/1.74  % [INFO] 	 Axiom selection finished. Selected 231 axioms (removed 2515 axioms). 
% 4.15/1.83  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.15/1.85  % [INFO] 	 Type checking passed. 
% 4.15/1.85  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 7.91/2.83  % External prover 'e' found a proof!
% 7.91/2.83  % [INFO] 	 Killing All external provers ... 
% 7.91/2.83  % Time passed: 2202ms (effective reasoning time: 1553ms)
% 7.91/2.83  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.91/2.83  % Axioms used in derivation (231): cls_Set_OPow__UNIV_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_Set_OCompl__subset__Compl__iff_1, cls_Set_OPow__iff_1, cls_Set_Oinsert__disjoint__1_1, cls_Tarski_Opotype_Oselect__convs__2_0, cls_Finite__Set_OMin__gr__iff_2, cls_SetInterval_OgreaterThanAtMost__iff_2, cls_Set_Osingleton__insert__inj__eq_0, cls_Tarski_Opotype_Oext__inject_1, cls_Finite__Set_OMin__insert_0, cls_Set_OInt__iff_2, cls_Set_OUNIV__not__empty_0, cls_Set_OsubsetI_1, cls_Set_Osubset__UNIV_0, cls_Finite__Set_OMin__singleton_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2, cls_Finite__Set_OFinites_OemptyI_0, cls_Finite__Set_OMax__less__iff_2, cls_Set_OInt__UNIV__left_0, clsrel_Orderings_Olinorder_4, cls_SetInterval_OCompl__atLeast_0, cls_SetInterval_OgreaterThan__subset__iff_1, cls_Orderings_Oorder__less__irrefl_0, cls_SetInterval_OatLeast__iff_1, cls_Set_Oinsert__disjoint__2_2, cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0, cls_Set_Osingleton__inject__dest_0, cls_Set_OInt__subset__iff_0, cls_Set_OCompl__iff_1, cls_List_Olist_Oinject_1, cls_Finite__Set_OFinites_OinsertI_0, cls_Set_OUn__subset__iff_2, clsarity_set_2, cls_Set_OInt__UNIV_2, cls_Set_OUn__UNIV__left_0, cls_SetInterval_OlessThan__subset__iff_1, cls_Set_OPow__iff_0, cls_SetInterval_OatMost__iff_1, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Set_Odisjoint__insert__2_1, cls_Finite__Set_Ofinite__Int_0, cls_Set_OInter__UNIV_0, cls_Set_OInter__iff_0, cls_Set_Osubset__refl_0, cls_SetInterval_Oivl__subset_1, cls_Finite__Set_Ofinite__Pow__iff_1, cls_Set_OCompl__eq__Compl__iff_0, cls_Finite__Set_Ofinite__Un_2, cls_Set_OpsubsetI_0, cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0, cls_SetInterval_OatLeastLessThan__iff_2, cls_Finite__Set_Ofinite__Un_0, cls_Set_OUnion__insert_0, cls_Set_Odisjoint__insert__1_1, cls_Orderings_Omax__less__iff__conj_0, cls_SetInterval_OatLeastAtMost__iff_2, cls_Set_Osubset__empty_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_SetInterval_OatLeastAtMost__empty_0, cls_Set_OsubsetI_0, cls_Set_OUNIV__I_0, cls_SetInterval_OatLeastAtMost__singleton_0, cls_Finite__Set_OMin__ge__iff_2, cls_Finite__Set_OMax__le__iff_2, cls_SetInterval_OgreaterThan__subset__iff_0, cls_Set_Oinsert__subset_2, cls_Set_OUn__UNIV__right_0, cls_Tarski_Opotype_Oext__inject_2, cls_Set_OUn__iff_0, cls_Set_Osingleton__insert__inj__eq_H_1, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OUn__empty_1, cls_Tarski_OCL_Olub__in__lattice_0, cls_Set_OInter__UNIV__conv__1_0, cls_Set_Oinsert__disjoint__2_1, cls_Orderings_Omin__less__iff__conj_2, cls_Finite__Set_OMin__gr__iff_1, cls_SetInterval_OatLeast__subset__iff_0, cls_Finite__Set_Ofinite__insert_0, cls_Set_Oinsert__iff_2, cls_SetInterval_OlessThan__subset__iff_0, cls_Set_OCompl__Un_0, cls_Set_OCompl__subset__Compl__iff_0, clsarity_set_3, cls_Set_Oinsert__not__empty_0, cls_SetInterval_OgreaterThan__iff_0, cls_Set_OsingletonD__dest_0, cls_Finite__Set_OMax__less__iff_1, cls_SetInterval_OlessThan__iff_0, cls_SetInterval_OCompl__greaterThan_0, cls_Set_OUn__subset__iff_0, cls_Finite__Set_Ofinite__Int_1, cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0, cls_SetInterval_OCompl__lessThan_0, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_Finite__Set_OMin__le_0, cls_List_Olist_Oinject_0, cls_Set_Oempty__iff_0, cls_Set_Oempty__subsetI_0, cls_Set_OInt__UNIV__right_0, cls_Set_OsubsetD_0, cls_SetInterval_OatLeastLessThan__iff_1, cls_Set_Odisjoint__insert__2_2, cls_Set_OUnion__empty__conv_0, cls_Set_OsingletonI_0, cls_SetInterval_OCompl__atMost_0, cls_Set_OCompl__empty__eq_0, cls_Finite__Set_OMax__ge_0, cls_Set_Osubset__antisym_0, cls_Set_OInt__empty__left_0, cls_SetInterval_OatLeastLessThan__iff_0, cls_SetInterval_OatMost__iff_0, clsrel_Orderings_Oorder_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1, cls_Set_OUnion__Un__distrib_0, cls_Tarski_Odual_Acl_A_58_APartialOrder_0, cls_Set_OCompl__iff_0, cls_Set_Oall__not__in__conv_0, cls_Set_Oinsert__iff_1, cls_Finite__Set_Ofinite__Un_1, cls_Finite__Set_OMax__singleton_0, cls_Set_Osubset__empty_1, cls_Set_Osingleton__insert__inj__eq_1, cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0, cls_Finite__Set_Ofinite__Pow__iff_0, cls_Set_Oinsert__disjoint__1_0, cls_Set_Oempty__Union__conv_0, cls_SetInterval_Oivl__subset_0, cls_Set_Odisjoint__insert__1_2, cls_SetInterval_OatLeastAtMost__iff_1, cls_Set_Oinsert__subset_1, cls_Finite__Set_OMin__ge__iff_1, cls_SetInterval_OatLeastLessThan__empty_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0, clsarity_set_1, cls_SetInterval_OgreaterThanAtMost__iff_0, cls_Set_OInt__UNIV_0, cls_Set_Oinsert__disjoint__2_0, cls_SetInterval_OatLeast__eq__iff_0, cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0, cls_Set_OCompl__UNIV__eq_0, cls_Set_OUn__insert__left_0, cls_Set_OInt__empty__right_0, cls_Finite__Set_OMin__ge__iff_0, cls_Orderings_Omax__less__iff__conj_1, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Set_OUn__insert__right_0, cls_SetInterval_OatLeast__subset__iff_1, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Aantisym_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_Set_OCompl__Int_0, cls_Finite__Set_OMax__less__iff_0, cls_Set_OUnion__iff_2, cls_Finite__Set_OMax__le__iff_0, cls_Finite__Set_OMin__gr__iff_0, cls_List_Onot__Cons__self_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0, cls_Set_OUn__iff_1, cls_Finite__Set_OMax__le__iff_1, cls_SetInterval_OlessThan__iff_1, cls_Set_OUnion__empty_0, cls_SetInterval_Oivl__subset_3, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0, cls_Set_Oempty__not__insert_0, cls_Set_OpsubsetE_0, cls_SetInterval_OgreaterThan__iff_1, cls_Orderings_Omin__less__iff__conj_0, cls_Set_OInt__subset__iff_2, cls_Set_OInt__iff_0, cls_SetInterval_OatMost__eq__iff_0, cls_Finite__Set_OMax__in_0, cls_Set_Oinsert__disjoint__1_2, cls_SetInterval_OatLeast__iff_0, cls_Set_OUn__empty__right_0, cls_Tarski_Oglb__dual__lub_0, cls_Set_OInt__iff_1, cls_Set_OInt__UNIV_1, cls_Set_OUn__empty__left_0, cls_Set_Ocontents__eq_0, cls_Set_OPow__Int__eq_0, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Arefl_A_Ipset_Acl1_J_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_SetInterval_OgreaterThanAtMost__iff_1, cls_Finite__Set_OMin__in_0, cls_Set_OInter__insert_0, cls_Orderings_Oorder__class_Oaxioms__1_0, clsarity_Product____Type__Ounit_0, clsrel_Orderings_Olinorder_3, cls_SetInterval_OatMost__subset__iff_0, cls_SetInterval_OgreaterThan__eq__iff_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0, cls_Set_OCompl__disjoint_0, cls_Set_OInter__empty_0, clsarity_set_0, cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0, cls_Set_OInt__absorb_0, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__iff_0, cls_List_Olistset_Osimps__2_0, cls_Set_Oinsert__absorb2_0, cls_SetInterval_OlessThan__eq__iff_0, cls_Set_OUn__subset__iff_1, cls_Set_OUnion__Pow__eq_0, cls_Set_Onot__psubset__empty_0, cls_SetInterval_OgreaterThanAtMost__empty_0, cls_Set_Odisjoint__insert__2_0, cls_Set_OUn__empty_2, cls_Finite__Set_OMax__insert_0, cls_Set_OUn__iff_2, cls_Tarski_Opotype_Oselect__convs__1_0, cls_Set_OpsubsetE_1, cls_Orderings_Omax__less__iff__conj_2, cls_Set_OPow__empty_0, cls_Set_Osingleton__insert__inj__eq_2, cls_Set_Oinsert__inter__insert_0, cls_SetInterval_OatMost__subset__iff_1, cls_Set_OInter__UNIV__conv__2_0, cls_SetInterval_Oivl__subset_2, clsarity_set_4, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1, cls_Set_Odisjoint__insert__1_0, cls_Set_OUnion__UNIV_0, cls_SetInterval_OatLeastAtMost__iff_0, cls_Set_Odouble__complement_0, cls_Set_Oinsert__subset_0, cls_Set_OUn__absorb_0, cls_Tarski_Opotype_Oext__inject_0, cls_Orderings_Omin__less__iff__conj_1, cls_Set_OInt__subset__iff_1, cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0, cls_Set_OCompl__disjoint2_0
% 7.91/2.83  % No. of inferences in proof: 467
% 7.91/2.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2202 ms resp. 1553 ms w/o parsing
% 8.34/2.93  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.34/2.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------