TSTP Solution File: LCL798-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : LCL798-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 00:07:53 EDT 2024

% Result   : Unsatisfiable 5.07s 2.70s
% Output   : Refutation 5.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  114
% Syntax   : Number of formulae    :  195 (  69 unt;  34 typ;   0 def)
%            Number of atoms       :  309 (  86 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 1158 ( 158   ~; 148   |;   0   &; 852   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   37 (  37   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   36 (  34 usr;  14 con; 0-4 aty)
%            Number of variables   :  336 (   0   ^ 336   !;   0   ?; 336   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_InductTermi_OIT_type,type,
    c_InductTermi_OIT: $i > $o ).

thf(c_Lambda_Osubst_type,type,
    c_Lambda_Osubst: $i > $i > $i > $i ).

thf(v_a_____type,type,
    v_a____: $i ).

thf(v_u_____type,type,
    v_u____: $i ).

thf(v_i_____type,type,
    v_i____: $i ).

thf(class_Nat_Osemiring__char__0_type,type,
    class_Nat_Osemiring__char__0: $i > $o ).

thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).

thf(c_Lambda_OdB_OVar_type,type,
    c_Lambda_OdB_OVar: $i > $i ).

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

thf(c_HOL_Oord__class_Oless_type,type,
    c_HOL_Oord__class_Oless: $i > $i > $i > $o ).

thf(class_Ring__and__Field_Oordered__idom_type,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

thf(c_HOL_Ozero__class_Ozero_type,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

thf(tc_nat_type,type,
    tc_nat: $i ).

thf(c_Lambda_OdB_OApp_type,type,
    c_Lambda_OdB_OApp: $i > $i > $i ).

thf(class_Ring__and__Field_Osemiring__1_type,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

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

thf(class_Orderings_Opreorder_type,type,
    class_Orderings_Opreorder: $i > $o ).

thf(class_Ring__and__Field_Oordered__semidom_type,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

thf(c_Lambda_Obeta_type,type,
    c_Lambda_Obeta: $i > $i > $o ).

thf(c_Lambda_OdB_OAbs_type,type,
    c_Lambda_OdB_OAbs: $i > $i ).

thf(c_Lambda_Olift_type,type,
    c_Lambda_Olift: $i > $i > $i ).

thf(c_Lambda_Osko__Lambda__Xbeta__cases__2__1_type,type,
    c_Lambda_Osko__Lambda__Xbeta__cases__2__1: $i > $i > $i ).

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

thf(v_ua_______type,type,
    v_ua______: $i ).

thf(c_Type_Otyping_type,type,
    c_Type_Otyping: $i > $i > $i > $o ).

thf(v_T_____type,type,
    v_T____: $i ).

thf(c_Type_Oshift_type,type,
    c_Type_Oshift: $i > $i > $i > $i > $i ).

thf(tc_Type_Otype_type,type,
    tc_Type_Otype: $i ).

thf(v_e_____type,type,
    v_e____: $i ).

thf(v_T_H_H_____type,type,
    v_T_H_H____: $i ).

thf(v_rs_____type,type,
    v_rs____: $i ).

thf(v_as_____type,type,
    v_as____: $i ).

thf(tc_Lambda_OdB_type,type,
    tc_Lambda_OdB: $i ).

thf(v_n_____type,type,
    v_n____: $i ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(41,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_Oinject_1) ).

thf(176,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)],[41]) ).

thf(61,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).

thf(226,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(8,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(101,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(75,axiom,
    ( v_rs____
    = ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_0) ).

thf(249,plain,
    ( v_rs____
    = ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(66,axiom,
    c_InductTermi_OIT @ v_u____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

thf(234,plain,
    c_InductTermi_OIT @ v_u____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(115,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) )
      | ~ ( c_InductTermi_OIT @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

thf(247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) )
      | ~ ( c_InductTermi_OIT @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
      | ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(202,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ A @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ A @ B ) )
      | ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).

thf(196,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ A @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ A @ B ) )
      | ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(157,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OApp @ A @ B )
     != ( c_Lambda_OdB_OAbs @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

thf(189,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OApp @ A @ B )
     != ( c_Lambda_OdB_OAbs @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(93,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) )
      | ~ ( c_InductTermi_OIT @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).

thf(228,plain,
    ! [A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) )
      | ~ ( c_InductTermi_OIT @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) )
      | ~ ( c_InductTermi_OIT @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).

thf(261,plain,
    ! [B: $i,A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) )
      | ~ ( c_InductTermi_OIT @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

thf(216,plain,
    ! [B: $i,A: $i] :
      ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OApp @ A @ B )
     != ( c_Lambda_OdB_OVar @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

thf(106,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OApp @ A @ B )
     != ( c_Lambda_OdB_OVar @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
      | ~ ( c_Lambda_Obeta @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).

thf(121,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
      | ~ ( c_Lambda_Obeta @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) @ ( c_Lambda_Olift @ C @ B ) )
      | ~ ( c_Lambda_Obeta @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

thf(147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) @ ( c_Lambda_Olift @ C @ B ) )
      | ~ ( c_Lambda_Obeta @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(133,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

thf(206,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(65,axiom,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).

thf(233,plain,
    c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(47,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

thf(192,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(169,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(25,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(141,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(60,axiom,
    c_InductTermi_OIT @ v_ua______,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).

thf(225,plain,
    c_InductTermi_OIT @ v_ua______,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(56,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_Oinject_0) ).

thf(212,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)],[56]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(96,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OApp @ A @ B )
       != ( c_Lambda_OdB_OApp @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

thf(109,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OApp @ A @ B )
       != ( c_Lambda_OdB_OApp @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(78,axiom,
    v_n____ = v_i____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).

thf(256,plain,
    v_n____ = v_i____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(173,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

thf(129,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(69,axiom,
    ! [B: $i,A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ A @ ( c_Lambda_OdB_OVar @ B ) ) )
      | ~ ( c_InductTermi_OIT @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

thf(237,plain,
    ! [B: $i,A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ A @ ( c_Lambda_OdB_OVar @ B ) ) )
      | ~ ( c_InductTermi_OIT @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(72,axiom,
    ! [B: $i,A: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B ) @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).

thf(244,plain,
    ! [B: $i,A: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B ) @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(53,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(205,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( c_Lambda_OdB_OAbs @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

thf(166,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( c_Lambda_OdB_OAbs @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

thf(180,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(68,axiom,
    c_InductTermi_OIT @ v_u____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).

thf(236,plain,
    c_InductTermi_OIT @ v_u____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OVar @ A )
       != ( c_Lambda_OdB_OVar @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

thf(86,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OVar @ A )
       != ( c_Lambda_OdB_OVar @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(45,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(12,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

thf(113,plain,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(1,negated_conjecture,
    ~ ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_a____ @ v_u____ @ v_i____ ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(81,plain,
    ~ ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_a____ @ v_u____ @ v_i____ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_a____ @ A @ B ) )
      | ~ ( c_Type_Otyping @ C @ A @ v_T____ )
      | ~ ( c_InductTermi_OIT @ A )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ C @ B @ v_T____ @ tc_Type_Otype ) @ v_a____ @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_a____ @ A @ B ) )
      | ~ ( c_Type_Otyping @ C @ A @ v_T____ )
      | ~ ( c_InductTermi_OIT @ A )
      | ~ ( c_Type_Otyping @ ( c_Type_Oshift @ C @ B @ v_T____ @ tc_Type_Otype ) @ v_a____ @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ A @ B ) @ C @ D )
      = ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).

thf(245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ A @ B ) @ C @ D )
      = ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OAbs @ A )
       != ( c_Lambda_OdB_OAbs @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

thf(208,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OAbs @ A )
       != ( c_Lambda_OdB_OAbs @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
      | ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(103,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
      | ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).

thf(251,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(50,axiom,
    ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(198,plain,
    ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( c_Lambda_OdB_OApp @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

thf(123,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( c_Lambda_OdB_OApp @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(48,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

thf(194,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(27,axiom,
    class_Nat_Osemiring__char__0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

thf(145,plain,
    class_Nat_Osemiring__char__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

thf(154,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(40,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(175,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(26,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(143,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(7,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(99,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OApp @ A @ B )
       != ( c_Lambda_OdB_OApp @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

thf(218,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_OdB_OApp @ A @ B )
       != ( c_Lambda_OdB_OApp @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(79,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
      | ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).

thf(258,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
      | ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(13,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(114,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ C @ B ) )
      | ~ ( c_Lambda_Obeta @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).

thf(171,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ C @ B ) )
      | ~ ( c_Lambda_Obeta @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(139,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

thf(119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(67,axiom,
    ! [A: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).

thf(235,plain,
    ! [A: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(28,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(146,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ A @ C ) )
      | ~ ( c_Lambda_Obeta @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).

thf(183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ A @ C ) )
      | ~ ( c_Lambda_Obeta @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ( A = C )
      | ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).

thf(239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
        = ( c_Lambda_OdB_OVar @ A ) )
      | ( A = C )
      | ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).

thf(242,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( c_Lambda_OdB_OApp @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

thf(126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_OdB_OVar @ A )
     != ( c_Lambda_OdB_OApp @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ B @ A ) ) )
      | ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).

thf(136,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ B @ A ) ) )
      | ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ A @ B ) @ C )
      = ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) @ ( c_Lambda_Olift @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

thf(131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ A @ B ) @ C )
      = ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) @ ( c_Lambda_Olift @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(200,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(90,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) @ ( c_Lambda_Osubst @ D @ B @ C ) )
      | ~ ( c_Lambda_Obeta @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

thf(254,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) @ ( c_Lambda_Osubst @ D @ B @ C ) )
      | ~ ( c_Lambda_Obeta @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Nat_Osemiring__char__0 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
       != ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

thf(83,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Nat_Osemiring__char__0 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
       != ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(59,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( c_Lambda_OdB_OVar @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

thf(222,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lambda_OdB_OAbs @ A )
     != ( c_Lambda_OdB_OVar @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(64,axiom,
    c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(232,plain,
    c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(263,plain,
    $false,
    inference(e,[status(thm)],[185,176,226,101,249,234,115,247,202,196,157,189,93,152,228,261,216,106,121,147,133,206,233,117,160,192,169,141,225,212,96,109,256,173,129,237,244,205,166,180,149,236,86,187,113,81,230,245,208,103,251,198,123,194,145,154,175,143,99,218,258,114,171,139,119,235,146,183,239,242,126,136,131,163,200,90,254,83,222,232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : LCL798-1 : TPTP v8.2.0. Released v4.1.0.
% 0.04/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n027.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon May 20 02:36:39 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.91/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.13  % [INFO] 	 Parsing done (202ms). 
% 1.54/1.15  % [INFO] 	 Running in sequential loop mode. 
% 2.06/1.50  % [INFO] 	 eprover registered as external prover. 
% 2.06/1.51  % [INFO] 	 cvc4 registered as external prover. 
% 2.06/1.52  % [INFO] 	 Scanning for conjecture ... 
% 2.24/1.62  % [INFO] 	 Found a conjecture (or negated_conjecture) and 79 axioms. Running axiom selection ... 
% 2.51/1.70  % [INFO] 	 Axiom selection finished. Selected 79 axioms (removed 0 axioms). 
% 2.79/1.78  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.79/1.80  % [INFO] 	 Type checking passed. 
% 2.79/1.80  % [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 ... 
% 5.07/2.69  % External prover 'e' found a proof!
% 5.07/2.69  % [INFO] 	 Killing All external provers ... 
% 5.07/2.69  % Time passed: 2235ms (effective reasoning time: 1542ms)
% 5.07/2.70  % Axioms used in derivation (79): cls_order__less__asym_H_0, cls_subst__Var_1, cls_linorder__neq__iff_1, cls_of__nat__less__0__iff_0, cls_xt1_I9_J_0, cls_subst__lt_0, cls_dB_Osimps_I6_J_0, cls_lift_Osimps_I2_J_0, cls_subst__App_0, cls_of__nat__0_0, cls_subst__eq_0, cls_beta__cases_I2_J_1, cls_dB_Osimps_I8_J_0, cls_list_Oinject_0, cls_linorder__neqE_0, cls_CHAINED_0, cls_of__nat__less__iff_0, cls_uIT_0, cls_not__Cons__self2_0, cls_app__Var__IT_0, cls_appR_0, clsarity_nat__Orderings_Olinorder, cls_order__less__trans_0, cls_of__nat__0__less__iff_0, cls_beta_0, cls_gr0I_0, cls_dB_Osimps_I7_J_0, cls_subst__preserves__beta_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_gr__implies__not0_0, cls_order__less__asym_0, cls_dB_Osimps_I3_J_0, cls_linorder__neqE__nat_0, cls_subst__Var_2, cls_Cons_0, cls_xt1_I10_J_0, cls_not__less__iff__gr__or__eq_0, cls_beta__cases_I2_J_0, cls_CHAINED_0_01, cls_dB_Osimps_I4_J_0, cls_Var__IT_0, cls_Var_I3_J_0, cls_of__nat__eq__iff_0, clsarity_nat__Nat_Osemiring__char__0, cls_True_0, cls_of__nat__0__less__iff_1, cls_not__Cons__self_0, cls_dB_Osimps_I1_J_0, cls_neq0__conv_1, cls_lift__preserves__beta_0, clsarity_nat__Orderings_Opreorder, cls_not__less__iff__gr__or__eq_1, cls_less__not__refl_0, cls_linorder__antisym__conv3_0, cls_linorder__neqE__ordered__idom_0, cls_dB_Osimps_I2_J_1, cls_linorder__less__linear_0, cls_CHAINED_0_02, cls_nat__neq__iff_0, cls_abs_0, cls_lift__IT_0, cls_order__less__irrefl_0, cls_list_Oinject_1, cls_beta__cases_I1_J_0, cls_not__less0_0, cls_dB_Osimps_I2_J_0, cls_dB_Osimps_I5_J_0, cls_subst__Var__IT_0, cls_lift_Osimps_I1_J_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_Lambda_0, cls_CHAINED_0_03, cls_of__nat__less__iff_1, cls_subst__lift_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_appL_0, cls_nat__less__le_1, cls_dB_Osimps_I9_J_0
% 5.07/2.70  % No. of inferences in proof: 161
% 5.07/2.70  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2235 ms resp. 1542 ms w/o parsing
% 5.32/2.78  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.32/2.78  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------