%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL771-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:52:49 AM UTC 2026
% Result : Unsatisfiable 17.21s 5.12s
% Output : Refutation 18.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 426
% Syntax : Number of formulae : 853 ( 367 unt; 0 typ; 0 def)
% Number of atoms : 1555 ( 736 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 9924 ( 614 ~; 702 |; 0 &;8608 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 97 ( 95 usr; 11 con; 0-5 aty)
% Number of variables : 2644 ( 0 ^;2644 !; 0 ?;2644 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_List_Olistsp_decl,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_InductTermi_OIT_decl,type,
c_InductTermi_OIT: $i ).
thf(v_rs_decl,type,
v_rs: $i ).
thf(tc_Lambda_OdB_decl,type,
tc_Lambda_OdB: $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(c_Lambda_OdB_OApp_decl,type,
c_Lambda_OdB_OApp: $i ).
thf(c_Lambda_OdB_OVar_decl,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(v_i_decl,type,
v_i: $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_List_Orotate_decl,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(c_List_Omap_decl,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(c_List_Oremove1_decl,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_List_Olist__update_decl,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(c_List_Ofilter_decl,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_List_Oremdups_decl,type,
c_List_Oremdups: $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(c_List_Onull_decl,type,
c_List_Onull: $i > $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_List_Oreplicate_decl,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(c_Map_Omap__upds_decl,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olinorder__class_Osorted_decl,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(c_List_Ofoldr_decl,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Lambda_OdB_OAbs_decl,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(c_ListOrder_Ostep1_decl,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
thf(c_List_Osko__List__XCons__eq__append__conv__1__1_decl,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(c_Lambda_Oliftn_decl,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(c_Lambda_Olift_decl,type,
c_Lambda_Olift: $i > $i > $i ).
thf(c_List_Osko__List__Xappend__eq__Cons__conv__1__1_decl,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Lambda_Osubstn_decl,type,
c_Lambda_Osubstn: $i > $i > $i > $i ).
thf(c_Lambda_Osubst_decl,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(c_List_Olist__ex_decl,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(c_Transitive__Closure_Ortranclp_decl,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(c_List_Ofoldl_decl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(v_sko__List__XdropWhile__Xinduct__2_decl,type,
v_sko__List__XdropWhile__Xinduct__2: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(v_sko__List__Xlist__Xinduct__2_decl,type,
v_sko__List__Xlist__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlist__Xinduct__1_decl,type,
v_sko__List__Xlist__Xinduct__1: $i > $i ).
thf(c_List_Olist_Olist__rec_decl,type,
c_List_Olist_Olist__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Lambda_Obeta_decl,type,
c_Lambda_Obeta: $i ).
thf(c_List_Olist_Olist__case_decl,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).
thf(c_Type_Otyping_decl,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(v_sko__List__Xlistsp__Xcases__2_decl,type,
v_sko__List__Xlistsp__Xcases__2: $i > $i > $i ).
thf(c_Lambda_OdB_OdB__case_decl,type,
c_Lambda_OdB_OdB__case: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__List__Xfilter__eq__Cons__iff__1__3_decl,type,
c_List_Osko__List__Xfilter__eq__Cons__iff__1__3: $i > $i > $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(v_sko__List__Xzip__Xinduct__1_decl,type,
v_sko__List__Xzip__Xinduct__1: $i > $i ).
thf(v_sko__List__Xzip__Xinduct__2_decl,type,
v_sko__List__Xzip__Xinduct__2: $i > $i ).
thf(c_List_Osko__List__XCons__eq__filter__iff__1__3_decl,type,
c_List_Osko__List__XCons__eq__filter__iff__1__3: $i > $i > $i > $i ).
thf(v_sko__List__Xlistsp__Xinduct__1_decl,type,
v_sko__List__Xlistsp__Xinduct__1: $i > $i > $i ).
thf(v_sko__List__Xlistsp__Xinduct__2_decl,type,
v_sko__List__Xlistsp__Xinduct__2: $i > $i > $i ).
thf(v_sko__List__Xremove1__Xinduct__1_decl,type,
v_sko__List__Xremove1__Xinduct__1: $i > $i ).
thf(v_sko__List__Xremove1__Xinduct__2_decl,type,
v_sko__List__Xremove1__Xinduct__2: $i > $i ).
thf(c_Lambda_OdB_OdB__rec_decl,type,
c_Lambda_OdB_OdB__rec: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olistrelp_decl,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(v_sko__List__Xlistset__Xinduct__2_decl,type,
v_sko__List__Xlistset__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistsp__Xcases__1_decl,type,
v_sko__List__Xlistsp__Xcases__1: $i > $i > $i ).
thf(c_List_Ofiltermap_decl,type,
c_List_Ofiltermap: $i > $i > $i > $i > $i ).
thf(v_sko__List__Xconcat__Xinduct__2_decl,type,
v_sko__List__Xconcat__Xinduct__2: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1_decl,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).
thf(v_sko__List__Xtake__Xinduct__2_decl,type,
v_sko__List__Xtake__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistsp__Xinducts__1_decl,type,
v_sko__List__Xlistsp__Xinducts__1: $i > $i > $i ).
thf(v_sko__List__Xlistsp__Xinducts__2_decl,type,
v_sko__List__Xlistsp__Xinducts__2: $i > $i > $i ).
thf(c_List_Osublist_decl,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_decl,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(c_List_Osko__List__Xin__listsp__conv__set__1__1_decl,type,
c_List_Osko__List__Xin__listsp__conv__set__1__1: $i > $i > $i > $i ).
thf(v_sko__List__Xlistset__Xinduct__1_decl,type,
v_sko__List__Xlistset__Xinduct__1: $i > $i ).
thf(v_sko__List__Xmap__Xinduct__2_decl,type,
v_sko__List__Xmap__Xinduct__2: $i > $i ).
thf(v_sko__List__Xdistinct__Xinduct__2_decl,type,
v_sko__List__Xdistinct__Xinduct__2: $i > $i ).
thf(v_sko__List__Xconcat__Xinduct__1_decl,type,
v_sko__List__Xconcat__Xinduct__1: $i > $i ).
thf(v_sko__List__Xmap__Xinduct__1_decl,type,
v_sko__List__Xmap__Xinduct__1: $i > $i ).
thf(v_sko__List__XdropWhile__Xinduct__1_decl,type,
v_sko__List__XdropWhile__Xinduct__1: $i > $i ).
thf(v_sko__List__Xdistinct__Xinduct__1_decl,type,
v_sko__List__Xdistinct__Xinduct__1: $i > $i ).
thf(v_sko__List__Xtake__Xinduct__1_decl,type,
v_sko__List__Xtake__Xinduct__1: $i > $i ).
thf(254,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1024,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Lambda_Olift ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Lambda_Olift ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(909,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ v_sko__List__Xzip__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zip_Oinduct_1) ).
thf(893,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ v_sko__List__Xzip__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( A
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( B @ ( A @ c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 ) ) ) @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( A
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( B @ ( A @ c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 ) ) ) @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listset_Oinduct_0) ).
thf(941,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(666,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(293,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1110,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(479,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(1105,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(333,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Omap ) ) ) )
= ( F @ ( D @ ( A @ hAPP ) @ ( C @ ( F @ ( E @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Olist__update ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__update_0) ).
thf(1200,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Omap ) ) ) )
= ( F @ ( D @ ( A @ hAPP ) @ ( C @ ( F @ ( E @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Olist__update ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(245,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(1005,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(1401,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(1422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(878,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(1173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(741,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(873,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(335,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( F @ ( A @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_ListOrder_Ostep1 ) ) ) )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(1205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( F @ ( A @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_ListOrder_Ostep1 ) ) ) )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(377,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( D @ c_List_Olist_ONil @ ( F @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( D @ ( D @ ( D @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( C @ c_ListOrder_Ostep1 ) ) ) )
| ( D @ ( B @ ( A @ ( C @ c_ListOrder_Ostep1 ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(1305,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( D @ c_List_Olist_ONil @ ( F @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( D @ ( D @ ( D @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( C @ c_ListOrder_Ostep1 ) ) ) )
| ( D @ ( B @ ( A @ ( C @ c_ListOrder_Ostep1 ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1078,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(379,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_List_Olistsp ) ) )
| ~ ( C @ ( D @ ( B @ c_List_Olistsp ) ) )
| ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp__infI_0) ).
thf(1310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_List_Olistsp ) ) )
| ~ ( C @ ( D @ ( B @ c_List_Olistsp ) ) )
| ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(1233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(698,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(1222,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(930,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(197,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( E @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) )
= ( D @ ( D @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) ) )
| ( D @ ( C @ ( A @ c_List_Osko__List__XCons__eq__filter__iff__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filter__iff_5) ).
thf(898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( E @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) )
= ( D @ ( D @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) ) )
| ( D @ ( C @ ( A @ c_List_Osko__List__XCons__eq__filter__iff__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Type_Otyping ) ) )
| ~ ( B @ ( D @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Type_Otyping ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Type_Otyping ) ) )
| ~ ( B @ ( D @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Type_Otyping ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( C @ c_List_Olistsp ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinducts_1) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( C @ c_List_Olistsp ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(709,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(841,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(231,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_1) ).
thf(973,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(1386,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ v_sko__List__Xmap__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Oinduct_1) ).
thf(1366,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ v_sko__List__Xmap__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(5,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(436,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(724,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= C )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= C )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(504,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(304,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Lambda_OdB_OVar @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
thf(1132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Lambda_OdB_OVar @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(13,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(460,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(587,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(1323,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= B )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= B )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(817,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1247,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(229,axiom,
! [A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(969,plain,
! [A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Onull ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_1) ).
thf(1013,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Onull ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(1100,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_0) ).
thf(853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(383,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(1319,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(1398,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(190,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( E @ c_List_Oappend ) ) @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( F @ ( E @ ( D @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(881,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( E @ c_List_Oappend ) ) @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( F @ ( E @ ( D @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(209,axiom,
! [B: $i,A: $i] :
~ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(924,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(789,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(405,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1373,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(1136,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(37,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
thf(514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(1283,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(424,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ v_sko__List__Xdistinct__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).
thf(1418,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ v_sko__List__Xdistinct__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(623,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(1383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(252,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( F @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( F @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(1020,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( F @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( F @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(574,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(266,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1051,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ v_sko__List__Xlist__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).
thf(821,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ v_sko__List__Xlist__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(107,axiom,
tc_nat @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(687,plain,
tc_nat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(127,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( D @ ( D @ ( E @ ( B @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(734,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( D @ ( D @ ( E @ ( B @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(184,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(866,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(144,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(774,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(396,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
| ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).
thf(1351,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
| ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(419,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(1405,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(2,negated_conjecture,
tc_Lambda_OdB @ ( v_rs @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Lambda_OdB @ ( v_i @ c_Lambda_OdB_OVar @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_OdB_OApp @ c_COMBC ) ) ) @ hAPP ) @ ( c_InductTermi_OIT @ c_COMBB ) ) ) ) @ c_List_Olistsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(428,plain,
tc_Lambda_OdB @ ( v_rs @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Lambda_OdB @ ( v_i @ c_Lambda_OdB_OVar @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_OdB_OApp @ c_COMBC ) ) ) @ hAPP ) @ ( c_InductTermi_OIT @ c_COMBB ) ) ) ) @ c_List_Olistsp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubstn ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(1242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubstn ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(981,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(766,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(393,axiom,
! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(1345,plain,
! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(238,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
= ( E @ ( D @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
thf(988,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
= ( E @ ( D @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(207,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).
thf(920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(439,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append1_0) ).
thf(661,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(49,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append_0) ).
thf(546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ v_sko__List__Xconcat__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat_Oinduct_1) ).
thf(1338,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ v_sko__List__Xconcat__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(714,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) )
| ( A
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_5) ).
thf(1153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) )
| ( A
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ c_Lambda_Osubst ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ c_Lambda_Osubst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).
thf(746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
thf(778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinducts_3) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(356,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1255,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(54,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( F @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( E @ c_ListOrder_Ostep1 ) ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(561,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( F @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( E @ c_ListOrder_Ostep1 ) ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(3,negated_conjecture,
~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(429,plain,
~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(151,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(788,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(162,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(815,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(729,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(167,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Orecs_I2_J_0) ).
thf(825,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(1343,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(916,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Ofilter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__filter_0) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Ofilter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(258,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(1032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(373,axiom,
! [A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(1296,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(137,axiom,
tc_nat @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(757,plain,
tc_nat @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(551,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_Type_Otyping ) ) )
| ( C @ ( B @ ( A @ c_Type_Otyping ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(1291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_Type_Otyping ) ) )
| ( C @ ( B @ ( A @ c_Type_Otyping ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(337,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Lambda_OdB_OAbs @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
= ( D @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
thf(1210,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Lambda_OdB_OAbs @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
= ( D @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(682,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_Lambda_OdB_OAbs ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( C @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(1407,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_Lambda_OdB_OAbs ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( C @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(358,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( C @ ( A @ hAPP ) @ ( B @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).
thf(1259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( C @ ( A @ hAPP ) @ ( B @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
thf(1375,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(297,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Lambda_OdB_OAbs @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).
thf(1118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Lambda_OdB_OAbs @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(180,axiom,
! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(857,plain,
! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(39,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(519,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(61,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(578,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ ( A @ ( B @ c_List_Olistsp ) ) )
| ( A
= ( t_a @ c_List_Olist_ONil ) )
| ( A
= ( t_a @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__1 ) @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Ocases_0) ).
thf(948,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ ( A @ ( B @ c_List_Olistsp ) ) )
| ( A
= ( t_a @ c_List_Olist_ONil ) )
| ( A
= ( t_a @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__1 ) @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( D @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(1111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( D @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(1227,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(471,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1329,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__filter_0) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(1361,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(213,axiom,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).
thf(933,plain,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(325,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(1182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(669,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(106,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(686,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(19,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(476,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).
thf(1016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__replicate_0) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(295,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(1114,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(1263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(1060,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping ) ) )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(1002,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping ) ) )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).
thf(1266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(346,axiom,
! [A: $i] :
( ( A @ c_Lambda_OdB_OVar )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(1231,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OVar )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(303,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_0) ).
thf(1131,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(92,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(654,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(73,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).
thf(605,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(414,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(1393,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(805,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(508,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(47,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(541,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(657,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(1054,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(1071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(953,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ v_sko__List__Xremove1__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).
thf(926,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ v_sko__List__Xremove1__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Osubst ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Osubst ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ v_sko__List__Xlistset__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listset_Oinduct_1) ).
thf(1286,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ v_sko__List__Xlistset__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(65,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(586,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(120,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(718,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Orecs_I1_J_0) ).
thf(906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(1278,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(618,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinducts_0) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(179,axiom,
! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(856,plain,
! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(375,axiom,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__ex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I1_J_0) ).
thf(1301,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__ex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(227,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(965,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(134,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(750,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(36,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(513,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(584,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).
thf(819,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(732,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( C @ c_List_Olistsp ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinduct_1) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( C @ c_List_Olistsp ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(411,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1388,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(743,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(1124,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).
thf(958,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinduct_2) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_Olift ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_Olift ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(936,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(380,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Lambda_OdB_OAbs @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).
thf(1312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Lambda_OdB_OAbs @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(29,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(498,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(1239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(1332,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(1092,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(285,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(1090,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(704,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Olift ) )
= ( C @ ( B @ c_Lambda_Olift ) @ ( C @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(1356,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Olift ) )
= ( C @ ( B @ c_Lambda_Olift ) @ ( C @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).
thf(1271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(1371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubst ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubst ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubst ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubst ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubst ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubst ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( C @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( C @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(784,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(1011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(1349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_1) ).
thf(567,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping ) ) )
| ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(990,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping ) ) )
| ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(616,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(299,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Lambda_OdB_OAbs @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( D @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
thf(1122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Lambda_OdB_OAbs @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( D @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_1) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(322,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( F @ ( E @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
thf(1175,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( F @ ( E @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(1080,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(631,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(138,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(758,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(181,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(858,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_0) ).
thf(799,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(176,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(848,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(196,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(895,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(82,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(626,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(1293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(14,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(462,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs )
= B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(943,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs )
= B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(253,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(1022,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(521,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
| ( B
= ( t_a @ c_List_Olist_ONil ) )
| ( B @ ( A @ v_sko__List__Xlistsp__Xcases__1 ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Ocases_1) ).
thf(983,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
| ( B
= ( t_a @ c_List_Olist_ONil ) )
| ( B @ ( A @ v_sko__List__Xlistsp__Xcases__1 ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(185,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Lambda_OdB_OVar @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
= ( D @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
thf(868,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Lambda_OdB_OVar @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
= ( D @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(780,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(986,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(243,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( D @ ( E @ ( B @ ( E @ ( C @ c_List_Orev ) @ ( D @ ( E @ ( D @ ( A @ c_COMBC ) ) ) @ c_List_Ofoldr ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr_0) ).
thf(1000,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( D @ ( E @ ( B @ ( E @ ( C @ c_List_Orev ) @ ( D @ ( E @ ( D @ ( A @ c_COMBC ) ) ) @ c_List_Ofoldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(431,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(208,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).
thf(922,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(142,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(768,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(827,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(352,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1245,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).
thf(1044,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( E @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) )
| ( D @ ( C @ ( A @ c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__Cons__iff_5) ).
thf(883,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( E @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) )
| ( D @ ( C @ ( A @ c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(1364,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(1250,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Olistsp ) ) )
| ~ ( D @ ( C @ ( A @ c_List_Olistsp ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Olistsp ) ) )
| ~ ( D @ ( C @ ( A @ c_List_Olistsp ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinduct_0) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ v_sko__List__Xtake__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take_Oinduct_1) ).
thf(1420,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ v_sko__List__Xtake__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(1340,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(251,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( F @ ( E @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
thf(1018,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( F @ ( E @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(836,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(1049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(422,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( E @ ( E @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( F @ c_List_Oappend ) ) @ ( E @ ( E @ ( E @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( B = C )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(1413,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( E @ ( E @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( F @ c_List_Oappend ) ) @ ( E @ ( E @ ( E @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( B = C )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).
thf(675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(305,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
= ( F @ ( E @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
thf(1134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
= ( F @ ( E @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orotate ) ) )
= ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Orotate ) ) @ ( B @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__map_0) ).
thf(458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orotate ) ) )
= ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Orotate ) ) @ ( B @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(62,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(580,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(109,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(690,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take_Oinduct_0) ).
thf(971,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OVar )
= B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OVar )
= B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(993,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Oliftn ) ) )
= ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(1225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Oliftn ) ) )
= ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(115,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( D @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(707,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( D @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(673,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).
thf(1317,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
thf(576,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(88,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(48,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(328,axiom,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(1188,plain,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofiltermap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofiltermap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(808,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(1358,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(357,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).
thf(1257,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(1141,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(76,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(613,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(267,axiom,
! [A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
= ( A @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(1052,plain,
! [A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
= ( A @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(124,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ c_Suc @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( C @ ( E @ ( D @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(727,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ c_Suc @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( C @ ( E @ ( D @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(287,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( D @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( E @ c_ListOrder_Ostep1 ) ) ) )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(1094,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( D @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( E @ c_ListOrder_Ostep1 ) ) ) )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(595,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1353,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(71,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( E @ ( C @ c_List_Oappend ) ) @ ( D @ ( E @ ( B @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(600,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( E @ ( C @ c_List_Oappend ) ) @ ( D @ ( E @ ( B @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1084,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(556,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
= ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
= ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(671,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(108,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(688,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(27,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(495,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_List_Osko__List__Xin__listsp__conv__set__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_List_Osko__List__Xin__listsp__conv__set__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).
thf(844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(771,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( C @ c_Lambda_OdB_OVar ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(1216,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( C @ c_Lambda_OdB_OVar ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_0) ).
thf(891,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(365,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1276,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1326,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(1253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(748,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(652,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(150,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(786,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).
thf(1030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(35,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).
thf(510,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinducts_2) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(338,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Lambda_OdB_OVar @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
thf(1212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Lambda_OdB_OVar @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(140,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( F @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( C = B )
| ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(763,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( F @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
| ( C = B )
| ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__Suc_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate_0) ).
thf(716,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( B @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(1161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( B @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(1280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(1395,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).
thf(1303,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(170,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(833,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(967,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(55,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(506,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(1335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(421,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(960,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(696,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(394,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(1346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(796,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinduct_3) ).
thf(918,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
| ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(157,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(801,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(269,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zip_Oinduct_0) ).
thf(1056,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( C @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(1288,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( C @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( D
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ ( A @ c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 ) ) ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_1) ).
thf(1197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( D
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ ( A @ c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 ) ) ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(211,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Lambda_OdB_OVar @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
= ( D @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
thf(928,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Lambda_OdB_OVar @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
= ( D @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(839,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(1236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__last_0) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(359,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(1261,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(362,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(1268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(1,negated_conjecture,
tc_Lambda_OdB @ ( v_rs @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(427,plain,
tc_Lambda_OdB @ ( v_rs @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
| ( B
= ( t_a @ c_List_Olist_ONil ) )
| ( t_a @ ( B @ ( A @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_Ocases_2) ).
thf(860,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
| ( B
= ( t_a @ c_List_Olist_ONil ) )
| ( t_a @ ( B @ ( A @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(407,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( D @ ( E @ ( D @ ( B @ c_List_Orev ) @ ( C @ ( E @ ( E @ ( D @ ( A @ c_COMBC ) ) ) @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
thf(1378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( D @ ( E @ ( D @ ( B @ c_List_Orev ) @ ( C @ ( E @ ( E @ ( D @ ( A @ c_COMBC ) ) ) @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(691,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(442,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1120,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(30,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(501,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(803,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(1009,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(326,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(1184,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Orev ) )
= ( D @ ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__map_0) ).
thf(659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Orev ) )
= ( D @ ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(260,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).
thf(1037,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ v_sko__List__XdropWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_1) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ v_sko__List__XdropWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ c_Transitive__Closure_Ortranclp ) )
= ( B @ ( A @ c_Transitive__Closure_Ortranclp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(755,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ c_Transitive__Closure_Ortranclp ) )
= ( B @ ( A @ c_Transitive__Closure_Ortranclp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osublist ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sublist__nil_0) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osublist ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(275,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(1069,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1438,plain,
$false,
inference(e,[status(thm)],[1024,1168,846,909,893,962,941,1179,666,1110,479,1105,1200,977,1005,1401,1422,878,1173,523,582,741,1073,873,1205,449,614,677,1305,597,1078,1310,1164,1233,698,913,1222,930,898,1127,1391,782,709,841,973,1386,1366,436,724,570,1298,504,1132,460,587,1323,934,1191,817,1247,969,1013,1100,638,853,1319,870,1398,881,924,789,1373,1136,514,1283,1418,623,1383,1020,574,1051,821,687,734,866,774,1351,998,1405,428,1242,602,981,766,1345,988,452,920,439,661,546,1338,534,1067,714,1047,1153,761,746,778,1042,1255,561,429,788,815,729,825,1343,916,484,1032,1296,830,1159,1027,757,551,1291,493,1210,682,1407,1143,1259,1375,593,610,1118,857,519,578,650,948,1111,1227,471,1329,1082,488,1361,933,753,1182,669,1214,901,686,476,1016,590,679,1039,1114,1263,701,1150,1060,911,1002,1266,1231,1131,654,605,1393,1202,633,805,508,541,657,1054,1170,1071,530,953,926,1086,938,1286,1035,794,586,718,888,906,1278,618,1103,1219,1273,856,1301,965,750,513,1146,584,819,1007,732,1389,1388,743,1124,904,975,958,1403,641,1139,936,572,1312,498,1058,1239,1332,1092,1090,704,1356,1271,1371,979,1194,784,1011,736,1349,567,990,996,616,1122,863,1175,1080,631,758,858,799,848,895,626,1293,1177,462,943,1022,521,983,868,780,608,986,1000,851,431,922,768,827,1245,636,1044,455,883,1364,1250,722,1166,1208,1420,1340,1018,553,836,1049,1413,473,1076,490,675,1134,648,458,823,776,525,712,580,690,1025,1156,971,739,1368,993,1225,707,673,791,502,1317,576,643,544,1188,1186,951,808,1358,1257,1141,613,1052,727,1094,595,876,1353,600,1084,556,482,671,1321,688,495,1189,844,771,1108,1216,891,1276,1326,1253,813,517,748,1062,946,652,1244,786,1030,510,1308,1212,763,684,549,536,716,1161,1116,620,447,1280,1097,1229,1395,1380,1303,1148,833,967,564,1314,506,1335,1410,960,696,720,955,1346,796,918,801,1056,664,1288,1197,532,1065,886,928,839,1236,464,1129,1261,1268,427,860,1378,908,691,442,1120,501,486,803,469,1009,1184,659,1037,1416,755,1088,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL771-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.47 % Computer : n002.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Fri Sep 25 23:34:50 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.14/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.35/1.46 % [INFO] Parsing done (363ms).
% 2.35/1.47 % [INFO] Running in sequential loop mode.
% 4.15/1.81 % [INFO] eprover registered as external prover.
% 4.15/1.82 % [INFO] Scanning for conjecture ...
% 4.63/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 425 axioms. Running axiom selection ...
% 5.86/2.18 % [INFO] Axiom selection finished. Selected 423 axioms (removed 2 axioms).
% 7.47/2.52 % [INFO] Problem is propositional (TPTP CNF).
% 7.47/2.56 % [INFO] Type checking passed.
% 7.47/2.57 % [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 ...
% 17.21/5.11 % External prover 'e' found a proof!
% 17.21/5.11 % [INFO] Killing All external provers ...
% 17.21/5.11 % Time passed: 4431ms (effective reasoning time: 3633ms)
% 17.21/5.12 % Axioms used in derivation (423): clsarity_fun__Lattices_Olower__semilattice, cls_butlast__snoc_0, cls_inf__sup__aci_I2_J_0, cls_dB_Orecs_I1_J_0, cls_xt1_I9_J_0, cls_list_Orecs_I1_J_0, cls_subst__lt_0, cls_listsp_Oinduct_0, cls_App__eq__foldl__conv_3, cls_concat_Oinduct_1, cls_dB_Osimps_I6_J_0, cls_length__0__conv_1, cls_last_Osimps_1, cls_distinct_Oinduct_0, cls_Nil__is__rev__conv_1, cls_Nil__is__map__conv_1, cls_last_Osimps_0, cls_dB_Osplit_0, cls_apps__eq__Abs__conv_0, cls_rev__swap_1, cls_lift_Osimps_I2_J_0, cls_Cons__eq__append__conv_2, cls_Suc__inject_0, cls_subst__App_0, cls_Cons__step1__Cons_0, cls_Suc__mono_0, cls_Cons__eq__append__conv_5, cls_Var__eq__apps__conv_1, cls_remove1_Osimps_I2_J_0, cls_listrelp_OCons_0, cls_list__update__overwrite_0, cls_subst__eq_0, cls_COMBC__def_0, cls_map__replicate_0, cls_append__self__conv_0, cls_dB_Osimps_I8_J_0, cls_butlast_Osimps_I1_J_0, cls_subject__reduction_0, cls_Suc__n__not__n_0, cls_append__step1I_0, clsarity_bool__Lattices_Olower__semilattice, cls_replicate__empty_0, cls_linorder__neqE_0, cls_less__antisym_0, clsarity_fun__Orderings_Oorder, cls_rotate__map_0, cls_rev__singleton__conv_1, cls_listsp_Oinduct_3, cls_list_Oinject_0, cls_map_Oinduct_1, cls_liftn_Osimps_I2_J_0, cls_Cons__eq__map__conv_3, cls_listsp__infI_0, cls_substn__subst__0_0, cls_rtrancl__beta__Abs_0, cls_Snoc__step1__SnocD_2, cls_not__Cons__self2_0, cls_Suc__lessI_0, cls_less__Suc__eq_2, cls_dB_Osimps_I12_J_0, cls_rev__is__rev__conv_0, clsarity_nat__Orderings_Olinorder, cls_not__less__eq_1, cls_remove1__filter__not_0, cls_not__step1__Nil_0, cls_appR_0, cls_list__update__nonempty_1, cls_dB_Osplit__asm_0, cls_filter__eq__ConsD_2, cls_order__less__trans_0, cls_self__append__conv_0, cls_zip_Oinduct_0, cls_substn_Osimps_I1_J_2, cls_same__append__eq_0, cls_list_Osimps_I5_J_0, cls_inf__left__commute_0, cls_head__Var__reduction_1, cls_listsp_ONil_0, cls_inf1E_1, cls_remdups__filter_0, cls_append__eq__Cons__conv_4, cls_eq__Nil__appendI_0, cls_list_Oinduct_1, cls_rtranclp__trans_0, cls_Cons__step1__Cons_5, cls_beta_0, cls_COMBB__def_0, cls_butlast_Osimps_I2_J_1, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_Nil__is__map__conv_0, cls_dB_Orecs_I3_J_0, cls_replicate__eq__replicate_0, cls_append__Cons_0, cls_listset_Oinduct_1, cls_gr0I_0, cls_inf__commute_0, cls_length__map_0, cls_filter_Osimps_I2_J_0, cls_foldr_Osimps_I1_J_0, cls_nat__less__cases_0, cls_append__eq__append__conv2_4, cls_append__eq__Cons__conv_0, cls_Var__apps__eq__Var__apps__conv_0, cls_gr__implies__not0_0, cls_sorted_Osimps_I3_J_1, cls_order__less__asym_0, cls_append1__eq__conv_1, cls_filter__append_0, cls_order__less__asym_H_0, cls_foldl__foldr_0, cls_length__greater__0__conv_1, cls_substn__subst__n_0, cls_liftn__0_0, cls_empty__null_0, cls_concat_Oinduct_0, cls_length__remdups__eq_0, cls_dB_Osimps_I3_J_0, cls_replicate__append__same_0, cls_listsp_Ocases_0, cls_listsp_Oinducts_1, cls_rev__map_0, cls_linorder__neqE__nat_0, cls_list__update__append1_0, cls_list_Osimps_I4_J_0, cls_filter_Osimps_I1_J_0, cls_rev__singleton__conv_0, cls_listset_Oinduct_0, cls_rev_Osimps_I2_J_0, clsarity_bool__Orderings_Oorder, cls_subst__Var_2, cls_xt1_I10_J_0, cls_append__Nil2_0, cls_listrelp_ONil_0, cls_append__self__conv2_0, cls_Var__eq__apps__conv_2, cls_dB_Osimps_I11_J_0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_Var__apps__eq__Var__apps__conv_1, cls_not__less__iff__gr__or__eq_0, cls_ATP__Linkup_OCOMBC__def_0, cls_rotate__is__Nil__conv_0, cls_self__append__conv2_0, cls_listsp_Ocases_2, cls_length__0__conv_0, cls_App__eq__foldl__conv_0, cls_remdups__eq__nil__iff_1, cls_Cons__eq__append__conv_3, cls_map__eq__Cons__conv_3, cls_remove1_Oinduct_0, cls_self__append__conv2_1, cls_dB_Osimps_I4_J_0, cls_Cons__step1__Cons_1, cls_typing__elims_I1_J_0, cls_map__update_0, cls_replicate__Suc_0, cls_append__is__Nil__conv_2, cls_Suc__neq__Zero_0, cls_list_Osplit_0, cls_append__Nil_0, cls_map__is__Nil__conv_0, cls_append__eq__append__conv2_5, cls_Var__IT_0, cls_Cons__step1__Cons_3, cls_append__eq__Cons__conv_5, cls_converse__rtranclp__into__rtranclp_0, cls_append__in__listsp__conv_1, cls_subject__reduction_H_0, cls_length__list__update_0, cls_append__in__listsp__conv_0, cls_last__append_1, cls_append__butlast__last__id_0, cls_singleton__rev__conv_0, cls_dB_Osimps_I10_J_0, clsarity_nat__Lattices_Olower__semilattice, cls_apps__preserves__betas_0, cls_zip_Oinduct_1, cls_rev__is__Nil__conv_0, cls_inf__sup__aci_I3_J_0, cls_less__infI1_0, cls_filter__replicate_1, cls_Snoc__step1__SnocD_3, cls_map__upds__Nil2_0, cls_list__ex_Osimps_I1_J_0, cls_length__remdups__eq_1, cls_foldl__Cons_0, cls_replicate__app__Cons__same_0, cls_rotate__simps_0, cls_ATP__Linkup_OCOMBB__def_0, cls_lessI_0, cls_replicate__eq__replicate_1, cls_head__Var__reduction_0, clsarity_fun__Lattices_Olattice, cls_filter__replicate_0, cls_append__eq__Cons__conv_1, cls_list__update__append_0, cls_Int__assoc_0, cls_fun__upds__append2__drop_0, cls_list__update_Osimps_I1_J_0, cls_butlast__append_0, cls_take_Oinduct_1, cls_list__update__code_I2_J_0, cls_append__step1I_1, cls_sublist__nil_0, cls_dB_Osimps_I1_J_0, cls_self__append__conv_1, cls_rev__filter_0, cls_apps__eq__Abs__conv_2, cls_Abs__App__neq__Var__apps_0, cls_map__eq__imp__length__eq_0, cls_rtrancl__beta__App_0, cls_less__Suc__eq__0__disj_3, cls_rotate1__is__Nil__conv_0, cls_rotate1__rotate__swap_0, cls_not__Cons__self_0, cls_append__same__eq_0, cls_last__snoc_0, cls_subst__Var_1, clsarity_bool__Orderings_Opreorder, cls_fun__upds__append__drop_0, cls_Cons__step1__Cons_2, cls_rtrancl__beta__AppL_0, cls_neq__Nil__conv_1, cls_sorted__Cons_0, cls_list__update__swap_0, cls_length__rev_0, cls_length__greater__0__conv_0, cls_listsp_Oinduct_1, cls_Nil__is__append__conv_1, cls_list__update__length_0, cls_Nitpick_Ortranclp__def_1, cls_last__append_0, cls_neq0__conv_1, cls_append__assoc_0, cls_inf__sup__aci_I1_J_0, cls_not__Nil__step1_0, cls_foldr_Osimps_I2_J_0, cls_apps__eq__Abs__conv_1, cls_Int__commute_0, cls_butlast__append_1, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_map__upds__Nil1_0, cls_not__less__iff__gr__or__eq_1, cls_Cons__eq__append__conv_0, clsarity_nat__Lattices_Olattice, cls_remove1_Oinduct_1, cls_Var__apps__neq__Abs__apps_0, cls_remove1_Osimps_I1_J_0, clsarity_nat__Orderings_Opreorder, cls_Cons__step1__Cons_4, cls_less__not__refl_0, cls_linorder__antisym__conv3_0, cls_Int__absorb_0, cls_inf__assoc_0, cls_append__in__listsp__conv_2, cls_rotate__Suc_0, cls_gr0__conv__Suc_1, cls_dB_Osimps_I2_J_1, cls_foldr__foldl_0, cls_take_Oinduct_0, cls_listsp_Oinducts_2, cls_linorder__neqE__ordered__idom_0, cls_map__append_0, cls_Int__left__absorb_0, cls_sorted__remdups_0, cls_empty__replicate_0, cls_dB_Osplit__asm_2, cls_nat_Oinject_0, cls_in__listsp__conv__set_2, cls_rev__replicate_0, cls_List_Onull_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_1, cls_append__eq__Cons__conv_2, cls_foldr__append_0, cls_linorder__neq__iff_1, cls_sorted_Osimps_I1_J_0, cls_sorted__remove1_0, cls_rotate__simps_1, cls_less__SucE_0, cls_lift__preserves__beta_H_0, cls_rev__eq__Cons__iff_1, cls_list_Osplit__asm_1, clsarity_bool__Lattices_Olattice, cls_Cons__eq__filter__iff_5, cls_listsp_Oinducts_0, cls_rtranclp_Ortrancl__refl_0, cls_rotate__is__Nil__conv_1, cls_liftn__lift_0, cls_map__is__Nil__conv_1, cls_Suc__lessD_0, cls_substn_Osimps_I2_J_0, cls_not__less__less__Suc__eq_1, cls_list_Orecs_I2_J_0, cls_sorted__append_0, cls_linorder__less__linear_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_rev__is__Nil__conv_1, cls_App__eq__foldl__conv_2, cls_last__replicate_0, cls_app__last_0, cls_length__rotate1_0, cls_listsp_Ocases_1, cls_inf__idem_0, cls_list__ex_Osimps_I2_J_1, cls_inf1I_0, cls_Suc__length__conv_2, cls_Int__left__commute_0, cls_map_Osimps_I2_J_0, cls_filter__eq__Cons__iff_5, cls_abs_0, cls_less__Suc0_0, cls_apps__eq__tail__conv_0, cls_Abs__eq__apps__conv_2, cls_dB_Orecs_I2_J_0, cls_rtranclp__idemp_0, cls_append__is__Nil__conv_1, cls_typing_OVar_0, cls_dB_Osplit_1, cls_lift__IT_0, cls_replicate__eq__replicate_2, cls_IT_OVar_0, cls_inf__sup__aci_I4_J_0, cls_length__rotate_0, cls_Snoc__step1__SnocD_0, cls_dropWhile_Oinduct_0, cls_not__less__eq_0, cls_nat_Osimps_I3_J_0, cls_apps__preserves__beta2_0, cls_liftn_Osimps_I1_J_0, cls_Cons__eq__appendI_0, cls_less__trans__Suc_0, cls_Nil__is__rev__conv_0, cls_apps__preserves__beta_0, cls_order__less__irrefl_0, cls_length__Suc__conv_2, cls_append__is__Nil__conv_0, cls_less__infI2_0, cls_append__eq__appendI_0, cls_list_Oinject_1, cls_listsp_Oinduct_2, cls_App__eq__foldl__conv_5, cls_butlast_Osimps_I2_J_0, cls_Cons__eq__append__conv_4, cls_App__eq__foldl__conv_4, cls_Abs__eq__apps__conv_0, cls_singleton__rev__conv_1, cls_foldl__append_0, cls_substn_Osimps_I1_J_1, cls_rev__append_0, cls_n__not__Suc__n_0, cls_listsp_Oinducts_3, cls_Cons__eq__append__conv_1, cls_less__SucI_0, cls_map_Oinduct_0, clsarity_fun__Orderings_Opreorder, cls_remove1_Osimps_I2_J_1, cls_not__less0_0, cls_dB_Osimps_I5_J_0, cls_rev__swap_0, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_Nil__is__append__conv_2, cls_append__replicate__commute_0, cls_list_Osplit_1, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_replicate__empty_1, cls_subst__Var__IT_0, cls_inf__left__idem_0, cls_sorted_Osimps_I2_J_0, cls_filtermap_Osimps_I1_J_0, cls_foldl__Nil_0, cls_Lambda_0, cls_Suc__less__eq_0, cls_length__replicate_0, cls_lift_Osimps_I1_J_0, cls_rtranclp_Ortrancl__into__rtrancl_0, cls_dB_Osplit__asm_1, cls_list_Oinduct_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_list__ex_Osimps_I2_J_0, cls_list__ex_Osimps_I2_J_2, cls_dB_Osplit_2, cls_less__Suc0_1, cls_subst__lift_0, cls_Abs__eq__apps__conv_1, cls_subst__preserves__beta2_0, cls_append__eq__Cons__conv_3, cls_list__update__code_I3_J_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_remdups__eq__nil__iff_0, cls_filter_Osimps_I2_J_1, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_subst__preserves__beta2_H_0, cls_rev__rev__ident_0, cls_dropWhile_Oinduct_1, cls_Snoc__step1__SnocD_1, cls_dB_Osimps_I9_J_0, cls_zero__less__Suc_0, cls_append1__eq__conv_0, cls_distinct_Oinduct_1, cls_empty__replicate_1, cls_Cons__eq__filterD_2, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_inf1E_0, cls_list__update__nonempty_0, cls_App__eq__foldl__conv_1, cls_Abs__apps__eq__Abs__apps__conv_0, cls_r__into__rtranclp_0, cls_subst__preserves__beta_H_0, cls_rtrancl__beta__AppR_0, cls_empty__null_1
% 17.21/5.12 % No. of inferences in proof: 853
% 17.21/5.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4431 ms resp. 3633 ms w/o parsing
% 18.84/5.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.84/5.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------