TSTP Solution File: LCL787-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL787-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:31:41 EDT 2023
% Result : Unsatisfiable 5.74s 2.24s
% Output : Refutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 173
% Syntax : Number of formulae : 296 ( 111 unt; 51 typ; 0 def)
% Number of atoms : 417 ( 178 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 3168 ( 206 ~; 172 |; 0 &;2790 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 24 con; 0-5 aty)
% Number of variables : 810 ( 0 ^; 810 !; 0 ?; 810 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____type,type,
v_thesis____: $o ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i ).
thf(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(c_Type_Otyping_type,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
thf(c_List_Ofoldr_type,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_type,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i > $i > $i ).
thf(c_Type_Otypings_type,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(c_Type_Otype_OFun_type,type,
c_Type_Otype_OFun: $i ).
thf(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
thf(c_Type_Osko__Type__Xlist__app__typeD__1__1_type,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xvar__app__types__1__1_type,type,
c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).
thf(v_rs_____type,type,
v_rs____: $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(v_as_____type,type,
v_as____: $i ).
thf(c_Type_Otype_Otype__case_type,type,
c_Type_Otype_Otype__case: $i > $i > $i > $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
thf(c_Lambda_OdB_OdB__case_type,type,
c_Lambda_OdB_OdB__case: $i > $i > $i > $i > $i > $i ).
thf(c_Type_Oshift_type,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
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_Type_Osko__Type__Xtyping__elims__3__1_type,type,
c_Type_Osko__Type__Xtyping__elims__3__1: $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xtyping__elims__3__2_type,type,
c_Type_Osko__Type__Xtyping__elims__3__2: $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xlist__app__typeE__1__1_type,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).
thf(v_ua_______type,type,
v_ua______: $i ).
thf(c_Lambda_OdB_OdB__rec_type,type,
c_Lambda_OdB_OdB__rec: $i > $i > $i > $i > $i > $i ).
thf(v_u_____type,type,
v_u____: $i ).
thf(c_Type_Otype_OAtom_type,type,
c_Type_Otype_OAtom: $i > $i ).
thf(c_Type_Otype_Otype__rec_type,type,
c_Type_Otype_Otype__rec: $i > $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xvar__app__typesE__1__1_type,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).
thf(v_ea_______type,type,
v_ea______: $i ).
thf(v_T_____type,type,
v_T____: $i ).
thf(c_Type_Osko__Type__Xtyping__elims__2__1_type,type,
c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).
thf(v_ia_______type,type,
v_ia______: $i ).
thf(v_n_____type,type,
v_n____: $i ).
thf(v_T_Ha_______type,type,
v_T_Ha______: $i ).
thf(v_e_____type,type,
v_e____: $i ).
thf(v_i_____type,type,
v_i____: $i ).
thf(v_Ts_____type,type,
v_Ts____: $i ).
thf(v_T_H_____type,type,
v_T_H____: $i ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ B @ D ) ) @ C ) )
| ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
thf(352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ B @ D ) ) @ C ) )
| ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(115,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
thf(384,plain,
v_n____ = v_i____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(9,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(142,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_0) ).
thf(174,plain,
( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(320,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)],[86]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(102,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(357,plain,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(216,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)],[42]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(51,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(238,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( B
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( B
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(43,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ D ) @ E ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ D @ F ) ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
thf(220,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ D ) @ E ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ D @ F ) ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( c_Type_Otype_OAtom @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( c_Type_Otype_OAtom @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(90,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(334,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(118,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ C @ D @ E ) ) )
| ~ ( c_Type_Otyping @ F @ D @ B )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ B @ tc_Type_Otype ) @ C @ G )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(392,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ C @ D @ E ) ) )
| ~ ( c_Type_Otyping @ F @ D @ B )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ B @ tc_Type_Otype ) @ C @ G )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(33,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(197,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_Type_Otype ) @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_Type_Otype ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(70,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ C @ D @ A @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
| ~ ( c_Type_Otypings @ A @ F @ G )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).
thf(285,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ C @ D @ A @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
| ~ ( c_Type_Otypings @ A @ F @ G )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
| ~ ( c_Type_Otypings @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ E @ D @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(156,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
| ~ ( c_Type_Otypings @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ E @ D @ tc_Type_Otype @ tc_Type_Otype ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ B @ A @ C @ D ) @ B @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A )
| ~ ( c_Type_Otypings @ C @ F @ G )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).
thf(169,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ B @ A @ C @ D ) @ B @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A )
| ~ ( c_Type_Otypings @ C @ F @ G )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).
thf(256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(193,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)],[32]) ).
thf(40,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
thf(212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(109,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
= ( hAPP @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
thf(371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
= ( hAPP @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
thf(343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(120,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).
thf(398,plain,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(111,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
= ( hAPP @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
thf(375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
= ( hAPP @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(26,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(180,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(296,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)],[75]) ).
thf(24,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_1) ).
thf(176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
thf(191,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_0) ).
thf(281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(83,axiom,
! [A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(313,plain,
! [A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).
thf(236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(98,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
| ~ ( c_Type_Otyping @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
thf(350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
| ~ ( c_Type_Otyping @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ B @ A @ C ) @ tc_Type_Otype ) @ C @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ B @ A @ C ) )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ B @ A @ C ) @ tc_Type_Otype ) @ C @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ B @ A @ C ) )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( ( c_Type_Otype_OAtom @ A )
!= ( c_Type_Otype_OAtom @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( c_Type_Otype_OAtom @ A )
!= ( c_Type_Otype_OAtom @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otype_OAtom @ A )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otype_OAtom @ A )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
thf(303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(38,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(208,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(57,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OVar @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(251,plain,
! [A: $i] :
( ( c_Lambda_OdB_OVar @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(330,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)],[89]) ).
thf(121,axiom,
c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argsT_0) ).
thf(399,plain,
c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(63,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(267,plain,
! [A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
thf(241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(123,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_Lambda_Olift @ D @ B ) @ E )
| ~ ( c_Type_Otyping @ A @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(355,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_Lambda_Olift @ D @ B ) @ E )
| ~ ( c_Type_Otyping @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(150,plain,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(27,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ B @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
thf(182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ B @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(91,axiom,
c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
thf(336,plain,
c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) ) @ ( c_Lambda_Olift @ C @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) ) @ ( c_Lambda_Olift @ C @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(116,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ C @ D @ E ) ) )
| ~ ( c_Type_Otyping @ F @ D @ A )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ A @ tc_Type_Otype ) @ C @ G )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(386,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ C @ D @ E ) ) )
| ~ ( c_Type_Otyping @ F @ D @ A )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ A @ tc_Type_Otype ) @ C @ G )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(48,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
thf(231,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(105,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
thf(363,plain,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).
thf(203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__rec @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
= ( hAPP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__rec @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
= ( hAPP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(114,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_headT_0) ).
thf(383,plain,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(41,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
= ( hAPP @ ( hAPP @ C @ D ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
thf(214,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
= ( hAPP @ ( hAPP @ C @ D ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(71,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ 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/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(287,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ 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)],[71]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__case @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
= ( hAPP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__case @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
= ( hAPP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__rec @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_Type_Otype_Otype__rec @ A @ B @ C @ E ) ) @ ( c_Type_Otype_Otype__rec @ A @ B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).
thf(373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__rec @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_Type_Otype_Otype__rec @ A @ B @ C @ E ) ) @ ( c_Type_Otype_Otype__rec @ A @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(79,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(305,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(52,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
= ( hAPP @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
thf(239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
= ( hAPP @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
thf(341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(122,axiom,
! [A: $i] :
( v_thesis____
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ A )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
thf(400,plain,
! [A: $i] :
( v_thesis____
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ A )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).
thf(283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) ) @ ( c_Lambda_Olift @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(294,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) ) @ ( c_Lambda_Olift @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ A @ B @ C ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ A @ B @ C ) ) )
| ~ ( c_Type_Otyping @ B @ ( c_Lambda_OdB_OAbs @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ A @ B @ C ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ A @ B @ C ) ) )
| ~ ( c_Type_Otyping @ B @ ( c_Lambda_OdB_OAbs @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(108,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
| ( c_Type_Otyping @ A @ ( c_Lambda_Osubst @ E @ B @ D ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(369,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
| ( c_Type_Otyping @ A @ ( c_Lambda_Osubst @ E @ B @ D ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(92,axiom,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(337,plain,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(100,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_ea______ @ v_ia______ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_Ha______,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).
thf(354,plain,
c_Type_Otyping @ ( c_Type_Oshift @ v_ea______ @ v_ia______ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_Ha______,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(106,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__case @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
= ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
thf(364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__case @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
= ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(402,plain,
$false,
inference(e,[status(thm)],[243,347,352,308,269,384,142,174,288,320,389,184,125,357,189,261,216,164,253,238,233,248,380,220,366,334,392,229,197,361,324,285,224,317,156,169,256,193,212,129,371,134,343,205,311,398,298,148,264,161,375,180,296,176,191,291,281,313,144,236,350,187,172,274,377,303,208,345,251,198,330,399,278,306,226,267,241,167,123,355,150,327,182,127,338,336,154,386,231,363,203,258,158,139,246,272,383,214,287,151,300,315,146,373,305,210,239,341,358,400,283,294,136,395,131,200,178,369,337,354,222,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL787-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 15:47:10 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.87/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.60/1.03 % [INFO] Parsing done (202ms).
% 1.60/1.04 % [INFO] Running in sequential loop mode.
% 2.25/1.24 % [INFO] eprover registered as external prover.
% 2.25/1.24 % [INFO] cvc4 registered as external prover.
% 2.25/1.24 % [INFO] Scanning for conjecture ...
% 2.54/1.34 % [INFO] Found a conjecture and 377 axioms. Running axiom selection ...
% 2.81/1.43 % [INFO] Axiom selection finished. Selected 121 axioms (removed 256 axioms).
% 3.26/1.51 % [INFO] Problem is propositional (TPTP CNF).
% 3.26/1.52 % [INFO] Type checking passed.
% 3.26/1.52 % [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 ...
% 5.74/2.24 % External prover 'e' found a proof!
% 5.74/2.24 % [INFO] Killing All external provers ...
% 5.74/2.24 % Time passed: 1732ms (effective reasoning time: 1196ms)
% 5.74/2.24 % 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)>
% 5.74/2.24 % Axioms used in derivation (121): cls_dB_Osimps_I2_J_1, cls_type_Orecs_I2_J_0, cls_dB_Osplit_0, cls_dB_Orecs_I1_J_0, cls_MI1_0, cls_dB_Osimps_I6_J_0, cls_apps__eq__Abs__conv_0, cls_lift_Osimps_I2_J_0, cls_subst__App_0, cls_Var__eq__apps__conv_1, cls_subst__eq_0, cls_dB_Osimps_I8_J_0, cls_type_Osimps_I3_J_0, cls_typing__elims_I3_J_0, cls_subject__reduction_0, cls_list_Oinject_0, cls_CHAINED_0, cls_var__app__typesE_0, cls_MI2_0, cls_uIT_0, cls_not__Cons__self2_0, cls_app__Var__IT_0, cls_type_Osimps_I4_J_0, cls_dB_Osimps_I12_J_0, cls_appR_0, cls_listsp_ONil_0, cls_dB_Osplit__asm_0, cls_type_Osplit__asm_1, cls_head__Var__reduction_1, cls_beta_0, cls_lift__type_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_Abs_0, cls_dB_Orecs_I3_J_0, cls_foldr_Osimps_I1_J_0, cls_Var__apps__eq__Var__apps__conv_0, cls_headT_0, cls_shift__eq_0, cls_Var_I2_J_0, cls_dB_Osimps_I3_J_0, cls_Cons_0, cls_Var__apps__eq__Var__apps__conv_1, cls_typing__elims_I2_J_0, cls_typing__elims_I3_J_1, cls_Var__eq__apps__conv_2, cls_dB_Osimps_I11_J_0, cls_App__eq__foldl__conv_0, cls_dB_Osimps_I4_J_0, cls_type_Osimps_I5_J_0, cls_type_Osimps_I2_J_1, cls_typing__elims_I1_J_0, cls_var__app__typesE_1, cls_var__app__types_0, cls_Var__IT_0, cls_Var_I3_J_0, cls_list__app__typeD_1, cls_dB_Osimps_I10_J_0, cls_App_0, cls_foldl__Cons_0, cls_nT_0, cls_True_0, cls_apps__eq__Abs__conv_2, cls_Abs__App__neq__Var__apps_0, cls_uT_0, cls_type_Osplit_0, cls_not__Cons__self_0, cls_dB_Osimps_I1_J_0, cls_type_Osimps_I1_J_0, cls_neq__Nil__conv_1, cls_type_Osimps_I2_J_0, cls_type_Orecs_I1_J_0, cls_foldr_Osimps_I2_J_0, cls_apps__eq__Abs__conv_1, cls_type_Osplit_1, cls_lift__preserves__beta_0, cls_Var__apps__neq__Abs__apps_0, cls_subst__lemma_0, cls_var__app__types_1, cls_dB_Osplit__asm_2, cls_list__app__typeD_0, cls_list_Osimps_I3_J_0, cls_abs_0, cls_Abs__eq__apps__conv_2, cls_dB_Orecs_I2_J_0, cls_list__app__typeE_1, cls_typing_OVar_0, cls_dB_Osplit_1, cls_lift__IT_0, cls_IT_OVar_0, cls_Var_I4_J_0, cls_apps__eq__tail__conv_0, cls_typing__elims_I2_J_1, cls_list__app__typeI_0, cls_apps__preserves__beta_0, cls_App__eq__foldl__conv_4, cls_Abs__eq__apps__conv_0, cls_list_Oinject_1, cls_dB_Osimps_I5_J_0, cls_subst__Var__IT_0, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_foldl__Nil_0, cls_Lambda_0, cls_type_Osplit__asm_0, cls_list__app__typeE_0, cls_that_0, cls_dB_Osplit__asm_1, cls_dB_Osplit_2, cls_subst__lift_0, cls_Abs__eq__apps__conv_1, cls_appL_0, cls_Beta_0, cls_list_Osimps_I2_J_0, cls_dB_Osimps_I9_J_0, cls_argsT_0, cls_type_Osimps_I6_J_0, cls_Abs__apps__eq__Abs__apps__conv_0
% 5.74/2.24 % No. of inferences in proof: 245
% 5.74/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1732 ms resp. 1196 ms w/o parsing
% 6.05/2.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.05/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------