TSTP Solution File: LCL764-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL764-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:31:31 EDT 2023
% Result : Unsatisfiable 7.44s 2.65s
% Output : Refutation 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 438
% Syntax : Number of formulae : 768 ( 249 unt; 109 typ; 0 def)
% Number of atoms : 1265 ( 432 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 7630 ( 528 ~; 606 |; 0 &;6496 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 201 ( 201 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 109 usr; 7 con; 0-5 aty)
% Number of variables : 2078 ( 0 ^;2078 !; 0 ?;2078 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_List_Ofoldr_type,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_List_Otake_type,type,
c_List_Otake: $i > $i > $i > $i ).
thf(c_List_Otl_type,type,
c_List_Otl: $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_List_Orotate_type,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_List_Olist_Olist__rec_type,type,
c_List_Olist_Olist__rec: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olist__all2_type,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(c_List_Ofilter_type,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_List_Orev_type,type,
c_List_Orev: $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_List_Olinorder__class_Osorted_type,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(c_List_OdropWhile_type,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_ListOrder_Ostep1_type,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
thf(c_List_Oremove1_type,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(c_List_Olist__update_type,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(c_List_Osplice_type,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(c_List_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Onull_type,type,
c_List_Onull: $i > $i > $o ).
thf(c_List_Olist__all_type,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_List_Olist_Olist__case_type,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_List_Oconcat__map_type,type,
c_List_Oconcat__map: $i > $i > $i > $i > $i ).
thf(c_List_Orotate1_type,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_List_Omember_type,type,
c_List_Omember: $i > $i > $i > $o ).
thf(c_List_Osublist_type,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(c_List_Olist__ex_type,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(c_List_Olinorder__class_Osort__key_type,type,
c_List_Olinorder__class_Osort__key: $i > $i > $i > $i > $i ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(c_List_Ohd_type,type,
c_List_Ohd: $i > $i > $i ).
thf(c_List_Olistrelp_type,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(v_sko__List__Xremdups__Xinduct__2_type,type,
v_sko__List__Xremdups__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlist__Xinduct__2_type,type,
v_sko__List__Xlist__Xinduct__2: $i > $i ).
thf(v_sko__List__XdropWhile__Xinduct__2_type,type,
v_sko__List__XdropWhile__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlist__Xinduct__1_type,type,
v_sko__List__Xlist__Xinduct__1: $i > $i ).
thf(v_sko__List__Xtl__Xinduct__2_type,type,
v_sko__List__Xtl__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlist__update__Xinduct__2_type,type,
v_sko__List__Xlist__update__Xinduct__2: $i > $i ).
thf(c_List_Osko__List__Xrev__induct__1__2_type,type,
c_List_Osko__List__Xrev__induct__1__2: $i > $i > $i ).
thf(v_sko__List__Xdrop__Xinduct__2_type,type,
v_sko__List__Xdrop__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistsp__Xcases__2_type,type,
v_sko__List__Xlistsp__Xcases__2: $i > $i > $i ).
thf(v_sko__List__Xtl__Xinduct__1_type,type,
v_sko__List__Xtl__Xinduct__1: $i > $i ).
thf(c_List_Osko__List__Xrev__induct__1__1_type,type,
c_List_Osko__List__Xrev__induct__1__1: $i > $i > $i ).
thf(v_sko__List__Xdrop__Xinduct__1_type,type,
v_sko__List__Xdrop__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlist__Xinducts__2_type,type,
v_sko__List__Xlist__Xinducts__2: $i > $i ).
thf(v_sko__List__Xzip__Xinduct__1_type,type,
v_sko__List__Xzip__Xinduct__1: $i > $i ).
thf(v_sko__List__Xzip__Xinduct__2_type,type,
v_sko__List__Xzip__Xinduct__2: $i > $i ).
thf(v_sko__List__Xrev__Xinduct__2_type,type,
v_sko__List__Xrev__Xinduct__2: $i > $i ).
thf(v_sko__List__Xrev__Xinduct__1_type,type,
v_sko__List__Xrev__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlistsp__Xinduct__1_type,type,
v_sko__List__Xlistsp__Xinduct__1: $i > $i > $i ).
thf(v_sko__List__Xlistsp__Xinduct__2_type,type,
v_sko__List__Xlistsp__Xinduct__2: $i > $i > $i ).
thf(v_sko__List__Xremove1__Xinduct__1_type,type,
v_sko__List__Xremove1__Xinduct__1: $i > $i ).
thf(v_sko__List__Xremove1__Xinduct__2_type,type,
v_sko__List__Xremove1__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistset__Xinduct__2_type,type,
v_sko__List__Xlistset__Xinduct__2: $i > $i ).
thf(v_sko__List__Xhd__Xinduct__1_type,type,
v_sko__List__Xhd__Xinduct__1: $i > $i ).
thf(v_sko__List__Xhd__Xinduct__2_type,type,
v_sko__List__Xhd__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistsp__Xcases__1_type,type,
v_sko__List__Xlistsp__Xcases__1: $i > $i > $i ).
thf(c_List_Ofiltermap_type,type,
c_List_Ofiltermap: $i > $i > $i > $i > $i ).
thf(v_sko__List__Xconcat__Xinduct__2_type,type,
v_sko__List__Xconcat__Xinduct__2: $i > $i ).
thf(v_sko__List__Xtake__Xinduct__2_type,type,
v_sko__List__Xtake__Xinduct__2: $i > $i ).
thf(v_sko__List__XremoveAll__Xinduct__1_type,type,
v_sko__List__XremoveAll__Xinduct__1: $i > $i ).
thf(v_sko__List__XremoveAll__Xinduct__2_type,type,
v_sko__List__XremoveAll__Xinduct__2: $i > $i ).
thf(v_sko__List__Xset__Xinduct__2_type,type,
v_sko__List__Xset__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistsp__Xinducts__1_type,type,
v_sko__List__Xlistsp__Xinducts__1: $i > $i > $i ).
thf(v_sko__List__Xlistsp__Xinducts__2_type,type,
v_sko__List__Xlistsp__Xinducts__2: $i > $i > $i ).
thf(v_sko__List__Xlist__Xinducts__1_type,type,
v_sko__List__Xlist__Xinducts__1: $i > $i ).
thf(v_sko__List__Xlast__Xinduct__1_type,type,
v_sko__List__Xlast__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlast__Xinduct__2_type,type,
v_sko__List__Xlast__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistsum__Xinduct__2_type,type,
v_sko__List__Xlistsum__Xinduct__2: $i > $i ).
thf(v_sko__List__Xfoldl__Xinduct__1_type,type,
v_sko__List__Xfoldl__Xinduct__1: $i > $i ).
thf(v_sko__List__Xfoldl__Xinduct__2_type,type,
v_sko__List__Xfoldl__Xinduct__2: $i > $i ).
thf(v_sko__List__Xset__Xinduct__1_type,type,
v_sko__List__Xset__Xinduct__1: $i > $i ).
thf(c_List_Olist__inter_type,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i > $i > $i ).
thf(c_List_Osko__List__Xin__listsp__conv__set__1__1_type,type,
c_List_Osko__List__Xin__listsp__conv__set__1__1: $i > $i > $i > $i ).
thf(v_sko__List__Xlist__update__Xinduct__1_type,type,
v_sko__List__Xlist__update__Xinduct__1: $i > $i ).
thf(v_sko__List__Xsplice__Xinduct__2_type,type,
v_sko__List__Xsplice__Xinduct__2: $i > $i ).
thf(c_Map_Omap__upds_type,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(v_sko__List__Xlistset__Xinduct__1_type,type,
v_sko__List__Xlistset__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlistsum__Xinduct__1_type,type,
v_sko__List__Xlistsum__Xinduct__1: $i > $i ).
thf(v_sko__List__Xmap__Xinduct__2_type,type,
v_sko__List__Xmap__Xinduct__2: $i > $i ).
thf(v_sko__List__Xsplice__Xinduct__1_type,type,
v_sko__List__Xsplice__Xinduct__1: $i > $i ).
thf(v_sko__List__Xdistinct__Xinduct__2_type,type,
v_sko__List__Xdistinct__Xinduct__2: $i > $i ).
thf(v_sko__List__XtakeWhile__Xinduct__1_type,type,
v_sko__List__XtakeWhile__Xinduct__1: $i > $i ).
thf(v_sko__List__XtakeWhile__Xinduct__2_type,type,
v_sko__List__XtakeWhile__Xinduct__2: $i > $i ).
thf(v_sko__List__Xremdups__Xinduct__1_type,type,
v_sko__List__Xremdups__Xinduct__1: $i > $i ).
thf(v_sko__List__Xconcat__Xinduct__1_type,type,
v_sko__List__Xconcat__Xinduct__1: $i > $i ).
thf(v_sko__List__Xmap__Xinduct__1_type,type,
v_sko__List__Xmap__Xinduct__1: $i > $i ).
thf(v_sko__List__XdropWhile__Xinduct__1_type,type,
v_sko__List__XdropWhile__Xinduct__1: $i > $i ).
thf(v_sko__List__Xdistinct__Xinduct__1_type,type,
v_sko__List__Xdistinct__Xinduct__1: $i > $i ).
thf(v_sko__List__Xtake__Xinduct__1_type,type,
v_sko__List__Xtake__Xinduct__1: $i > $i ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(892,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_ONil @ B ) @ C @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_ONil @ B ) @ C @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(216,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(809,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B )
| ~ ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B )
| ~ ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(194,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(760,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_List_Olistsp @ C @ ( v_sko__List__Xlistsp__Xinducts__2 @ C @ A ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_1) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_List_Olistsp @ C @ ( v_sko__List__Xlistsp__Xinducts__2 @ C @ A ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Omap__upds @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Omap__upds @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(277,axiom,
! [B: $i,A: $i] :
~ ( c_List_Omember @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I1_J_0) ).
thf(941,plain,
! [B: $i,A: $i] :
~ ( c_List_Omember @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(555,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__tl_0) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(160,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( C = B )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(683,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( C = B )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
= ( c_List_Oappend @ ( c_List_Otl @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(730,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
= ( c_List_Oappend @ ( c_List_Otl @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ohd @ ( c_List_OdropWhile @ A @ B @ C ) @ C ) ) )
| ( ( c_List_OdropWhile @ A @ B @ C )
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).
thf(873,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ohd @ ( c_List_OdropWhile @ A @ B @ C ) @ C ) ) )
| ( ( c_List_OdropWhile @ A @ B @ C )
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(24,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(379,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Otake @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
thf(597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Otake @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(861,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Odistinct @ B @ C )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ D @ B @ C @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__sort_0) ).
thf(523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Odistinct @ B @ C )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ D @ B @ C @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ C ) @ D @ C @ E )
| ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Orev @ D @ E ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev1_1) ).
thf(582,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ C ) @ D @ C @ E )
| ~ ( c_List_Olist__all2 @ A @ B @ ( c_List_Orev @ D @ E ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(878,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C )
= ( c_List_Orotate @ A @ ( c_List_Orotate1 @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C )
= ( c_List_Orotate @ A @ ( c_List_Orotate1 @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(614,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
= ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(384,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
= ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ B @ A ) @ ( v_sko__List__Xlistsp__Xcases__2 @ B @ A ) @ t_a ) )
| ( A
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ B @ A @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_0) ).
thf(797,plain,
! [B: $i,A: $i] :
( ( A
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ B @ A ) @ ( v_sko__List__Xlistsp__Xcases__2 @ B @ A ) @ t_a ) )
| ( A
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ B @ A @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( c_List_OdropWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).
thf(747,plain,
! [B: $i,A: $i] :
( ( c_List_OdropWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(93,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(538,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ ( v_sko__List__Xlistsp__Xinduct__1 @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_0) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ ( v_sko__List__Xlistsp__Xinduct__1 @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1001,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(204,axiom,
! [B: $i,A: $i] : ( c_List_Olistrelp @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).
thf(782,plain,
! [B: $i,A: $i] : ( c_List_Olistrelp @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(841,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(40,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ D ) @ ( c_List_Orev @ C @ E ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev_0) ).
thf(417,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ D ) @ ( c_List_Orev @ C @ E ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(251,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ A ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl_Oinduct_1) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ A ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(323,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1046,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ D @ ( c_List_Osplice @ B @ E @ C ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(389,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ D @ ( c_List_Osplice @ B @ E @ C ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xdrop__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop_Oinduct_0) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xdrop__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B )
| ~ ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(570,plain,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B )
| ~ ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).
thf(702,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__Xinducts__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinducts_0) ).
thf(751,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__Xinducts__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orotate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(802,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orotate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(9,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Orotate @ A @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__map_0) ).
thf(344,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Orotate @ A @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xzip__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zip_Oinduct_0) ).
thf(853,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xzip__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc_0) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(870,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(124,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Otake @ B @ C @ D ) @ ( c_List_Otake @ B @ E @ F ) @ D @ F )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__takeI_0) ).
thf(606,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Otake @ B @ C @ D ) @ ( c_List_Otake @ B @ E @ F ) @ D @ F )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(924,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(72,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(492,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_0) ).
thf(756,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omember @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Omember @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_2) ).
thf(443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omember @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Omember @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XtakeWhile__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_0) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XtakeWhile__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(142,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
= ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(646,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
= ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
= A )
| ~ ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
= A )
| ~ ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(966,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(574,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Olist__all2 @ C @ ( c_List_Olist_ONil @ D ) @ A @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).
thf(1020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Olist__all2 @ C @ ( c_List_Olist_ONil @ D ) @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(11,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).
thf(348,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oremove1 @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ B @ C @ D ) )
| ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oremove1 @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ B @ C @ D ) )
| ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Orev @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Orev @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(660,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_List_Olinorder__class_Osort__key @ B @ ( c_List_Olist_ONil @ C ) @ C @ A )
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sort__key_Osimps_I1_J_0) ).
thf(988,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_List_Olinorder__class_Osort__key @ B @ ( c_List_Olist_ONil @ C ) @ C @ A )
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(849,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xmap__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).
thf(981,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xmap__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__filter_0) ).
thf(439,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(89,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ E @ D ) @ ( c_List_Oappend @ C @ E @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(529,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ E @ D ) @ ( c_List_Oappend @ C @ E @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__all @ A @ C @ D )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__all @ A @ C @ D )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(714,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ A ) @ ( v_sko__List__Xhd__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Oinduct_1) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ A ) @ ( v_sko__List__Xhd__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(3,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(334,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(910,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ D @ B ) )
| ( A
= ( c_List_Oappend @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ D @ B ) )
| ( A
= ( c_List_Oappend @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ C @ A ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ C @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_3) ).
thf(778,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ C @ A ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ C @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(321,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(1042,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Orev @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(788,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Orev @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(847,plain,
! [B: $i,A: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(49,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oconcat__map @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( hAPP @ A @ B ) @ ( c_List_Oconcat__map @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat__map_Osimps_I2_J_0) ).
thf(435,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oconcat__map @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( hAPP @ A @ B ) @ ( c_List_Oconcat__map @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(253,axiom,
! [A: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_0) ).
thf(889,plain,
! [A: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(73,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Olist_OCons @ B @ D @ F ) @ ( c_List_Olist_OCons @ A @ C @ F ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(493,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Olist_OCons @ B @ D @ F ) @ ( c_List_Olist_OCons @ A @ C @ F ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).
thf(710,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ A ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Oinduct_1) ).
thf(974,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ A ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ A ) @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Oinduct_1) ).
thf(1012,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ A ) @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(916,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(62,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(467,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Orev @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__rev_0) ).
thf(403,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Orev @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ D @ E ) @ C @ E )
| ~ ( c_List_Olist__all2 @ A @ B @ D @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev_1) ).
thf(356,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ D @ E ) @ C @ E )
| ~ ( c_List_Olist__all2 @ A @ B @ D @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ B @ C @ D @ A ) @ D )
| ~ ( c_List_Odistinct @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__sort_1) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ B @ C @ D @ A ) @ D )
| ~ ( c_List_Odistinct @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).
thf(610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ ( c_List_Ohd @ D @ C ) @ ( c_List_Osplice @ B @ ( c_List_Otl @ D @ C ) @ C ) @ C ) @ C ) )
| ( D
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
thf(783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_OCons @ ( c_List_Ohd @ D @ C ) @ ( c_List_Osplice @ B @ ( c_List_Otl @ D @ C ) @ C ) @ C ) @ C ) )
| ( D
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).
thf(499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinducts__1 @ A ) @ ( v_sko__List__Xlist__Xinducts__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinducts_1) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinducts__1 @ A ) @ ( v_sko__List__Xlist__Xinducts__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
= ( c_List_Omap @ A @ ( c_List_Orev @ B @ C ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__map_0) ).
thf(578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
= ( c_List_Omap @ A @ ( c_List_Orev @ B @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(144,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ E @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist__update @ B @ D @ E @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ E @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist__update @ B @ D @ E @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oremdups @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oremdups @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(314,axiom,
! [B: $i,A: $i] : ( c_List_Olist__all @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I1_J_0) ).
thf(1028,plain,
! [B: $i,A: $i] : ( c_List_Olist__all @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Olist__all2 @ C @ A @ ( c_List_Olist_ONil @ D ) @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).
thf(753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Olist__all2 @ C @ A @ ( c_List_Olist_ONil @ D ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Odrop @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(669,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Odrop @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__take_0) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ A ) @ ( v_sko__List__Xmap__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Oinduct_1) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ A ) @ ( v_sko__List__Xmap__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).
thf(679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XdropWhile__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_0) ).
thf(706,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XdropWhile__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(66,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(476,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ A @ C @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ A @ C @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlast__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Oinduct_0) ).
thf(997,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlast__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(82,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ ( c_List_Orev @ C @ D ) @ E @ D )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ E ) @ C @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev1_0) ).
thf(515,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ ( c_List_Orev @ C @ D ) @ E @ D )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Orev @ B @ E ) @ C @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(184,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_ListOrder_Ostep1 @ A @ D @ E @ F )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(738,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_ListOrder_Ostep1 @ A @ D @ E @ F )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(654,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(123,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(605,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(131,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).
thf(622,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).
thf(837,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(329,axiom,
! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1060,plain,
! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(58,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_1) ).
thf(457,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(276,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( A
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( A
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).
thf(805,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(79,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(508,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(921,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(95,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(541,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(398,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ C ) @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).
thf(953,plain,
! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ C ) @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).
thf(926,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ C @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).
thf(360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ C @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xrev__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Oinduct_0) ).
thf(765,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xrev__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ A ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ A ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(114,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ A @ F @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(586,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ A @ F @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(412,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ C @ A @ B @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__map_0) ).
thf(425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ C @ A @ B @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Otake @ A @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__map_0) ).
thf(513,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Otake @ A @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_ONil @ C ) @ C )
= ( c_List_Olist_OCons @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_ONil @ C ) @ C )
= ( c_List_Olist_OCons @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ A ) @ ( v_sko__List__Xdrop__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop_Oinduct_1) ).
thf(745,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ A ) @ ( v_sko__List__Xdrop__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( v_sko__List__Xlistsp__Xcases__2 @ A @ B ) @ t_a )
| ( B
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ A @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_2) ).
thf(733,plain,
! [B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( v_sko__List__Xlistsp__Xcases__2 @ A @ B ) @ t_a )
| ( B
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ A @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(113,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist__update @ B @ C @ D @ E ) @ E @ F )
= ( c_List_Olist__update @ ( c_List_Omap @ A @ B @ E @ F ) @ C @ ( hAPP @ A @ D ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__update_0) ).
thf(584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist__update @ B @ C @ D @ E ) @ E @ F )
= ( c_List_Olist__update @ ( c_List_Omap @ A @ B @ E @ F ) @ C @ ( hAPP @ A @ D ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ A ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Oinduct_1) ).
thf(826,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ A ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ A @ B @ C ) @ C )
= ( c_List_Ofilter @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__filter_0) ).
thf(391,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ A @ B @ C ) @ C )
= ( c_List_Ofilter @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(4,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(335,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(266,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(919,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(704,plain,
! [B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Ofilter @ A @ B @ D ) @ ( c_List_Ofilter @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Ofilter @ A @ B @ D ) @ ( c_List_Ofilter @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_OdropWhile @ A @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).
thf(445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_OdropWhile @ A @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Oinduct_1) ).
thf(936,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(122,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(604,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
!= ( c_List_Orev @ C @ B ) )
| ( C
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
!= ( c_List_Orev @ C @ B ) )
| ( C
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xset__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set_Oinduct_0) ).
thf(831,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xset__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(159,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).
thf(681,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(41,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).
thf(419,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ A ) @ ( v_sko__List__Xtl__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Oinduct_1) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ A ) @ ( v_sko__List__Xtl__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(377,plain,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsum__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Oinduct_0) ).
thf(880,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsum__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(129,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(616,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sublist__nil_0) ).
thf(863,plain,
! [B: $i,A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ A ) @ ( v_sko__List__Xset__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set_Oinduct_1) ).
thf(890,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ A ) @ ( v_sko__List__Xset__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_0) ).
thf(631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ A ) @ ( v_sko__List__Xzip__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zip_Oinduct_1) ).
thf(758,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ A ) @ ( v_sko__List__Xzip__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(816,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).
thf(726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(483,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xremdups__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Oinduct_0) ).
thf(700,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xremdups__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ A ) @ ( v_sko__List__Xlistset__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listset_Oinduct_1) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ A ) @ ( v_sko__List__Xlistset__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oconcat__map @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat__map_Osimps_I1_J_0) ).
thf(769,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oconcat__map @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xsplice__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Oinduct_0) ).
thf(943,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xsplice__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1,negated_conjecture,
~ ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(330,plain,
~ ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(273,axiom,
! [A: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(932,plain,
! [A: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xtake__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take_Oinduct_0) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xtake__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ A @ B @ C ) @ C )
= ( c_List_Ofilter @ A @ ( c_List_Orev @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__filter_0) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ A @ B @ C ) @ C )
= ( c_List_Ofilter @ A @ ( c_List_Orev @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_List_Olistsp @ C @ ( v_sko__List__Xlistsp__Xinduct__2 @ C @ A ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_1) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_List_Olistsp @ C @ ( v_sko__List__Xlistsp__Xinduct__2 @ C @ A ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(295,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_ListOrder_Ostep1 @ C @ A @ B @ D )
| ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ F @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(983,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_ListOrder_Ostep1 @ C @ A @ B @ D )
| ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ F @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ A ) @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).
thf(780,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ A ) @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(125,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).
thf(608,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsp__Xinducts__2 @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_2) ).
thf(986,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsp__Xinducts__2 @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(104,axiom,
! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).
thf(563,plain,
! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(851,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(47,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(431,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ ( c_List_Olinorder__class_Osort__key @ B @ C @ D @ A ) @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__sort__key_0) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ B @ ( c_List_Olinorder__class_Osort__key @ B @ C @ D @ A ) @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olistsp @ A @ C @ D )
| ~ ( c_List_Olistsp @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olistsp @ A @ C @ D )
| ~ ( c_List_Olistsp @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(521,plain,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(165,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Odrop @ B @ C @ D ) @ ( c_List_Odrop @ B @ E @ F ) @ D @ F )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__dropI_0) ).
thf(695,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Odrop @ B @ C @ D ) @ ( c_List_Odrop @ B @ E @ F ) @ D @ F )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(137,axiom,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(636,plain,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xhd__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Oinduct_0) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xhd__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xrev__induct__1__2 @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__induct_0) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xrev__induct__1__2 @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_1) ).
thf(675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(115,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).
thf(589,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(531,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(795,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] : ( c_List_Omember @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_1) ).
thf(663,plain,
! [C: $i,B: $i,A: $i] : ( c_List_Omember @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ B @ E @ D ) @ D )
| ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(648,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ B @ E @ D ) @ D )
| ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
= ( c_List_Ohd @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(749,plain,
! [B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
= ( c_List_Ohd @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(310,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1018,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(100,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(553,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(324,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(1049,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xtl__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Oinduct_0) ).
thf(712,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xtl__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(163,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(690,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(139,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) @ D )
| ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) @ D )
| ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(887,plain,
! [B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ B @ C ) @ ( c_List_Otake @ A @ ( c_List_Otl @ B @ C ) @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc_0) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ B @ C ) @ ( c_List_Otake @ A @ ( c_List_Otl @ B @ C ) @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C )
| ~ ( c_List_Olistsp @ B @ D @ C )
| ~ ( c_List_Olistsp @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__infI_0) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C )
| ~ ( c_List_Olistsp @ B @ D @ C )
| ~ ( c_List_Olistsp @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(238,axiom,
! [A: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(855,plain,
! [A: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(155,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistrelp @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ D ) @ D )
| ~ ( c_List_Olistrelp @ A @ C @ F @ D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).
thf(673,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistrelp @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ D ) @ D )
| ~ ( c_List_Olistrelp @ A @ C @ F @ D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistset__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listset_Oinduct_0) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistset__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsp__Xinduct__2 @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_2) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsp__Xinduct__2 @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ A ) @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__tl_0) ).
thf(338,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ A ) @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(281,axiom,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(951,plain,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(96,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ B @ E @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).
thf(544,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ B @ E @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(5,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(336,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ A ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_1) ).
thf(1052,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ A ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Ohd @ A @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Ohd @ A @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).
thf(595,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ ( v_sko__List__Xlistsp__Xinducts__1 @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_0) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ ( v_sko__List__Xlistsp__Xinducts__1 @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(859,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ A ) @ ( v_sko__List__Xsplice__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Oinduct_1) ).
thf(991,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ A ) @ ( v_sko__List__Xsplice__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(147,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Odrop @ A @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__map_0) ).
thf(656,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Odrop @ A @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1023,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(233,axiom,
! [A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(845,plain,
! [A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(61,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).
thf(465,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(627,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).
thf(450,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(94,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
= ( c_List_Olist__update @ A @ B @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(539,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
= ( c_List_Olist__update @ A @ B @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Orev @ B @ C ) @ C )
| ~ ( c_List_Olist__all @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__rev_1) ).
thf(671,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Orev @ B @ C ) @ C )
| ~ ( c_List_Olist__all @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ A ) @ ( v_sko__List__Xremdups__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Oinduct_1) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ A ) @ ( v_sko__List__Xremdups__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ A ) @ ( v_sko__List__Xrev__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Oinduct_1) ).
thf(771,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ A ) @ ( v_sko__List__Xrev__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(292,axiom,
! [B: $i,A: $i] :
~ ( c_List_Olist__ex @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I1_J_0) ).
thf(976,plain,
! [B: $i,A: $i] :
~ ( c_List_Olist__ex @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(688,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsp__Xcases__1 @ A @ B ) ) )
| ( B
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ A @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_1) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsp__Xcases__1 @ A @ B ) ) )
| ( B
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ A @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__all @ A @ C @ D )
| ~ ( c_List_Olist__all @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_2) ).
thf(517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__all @ A @ C @ D )
| ~ ( c_List_Olist__all @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(652,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
thf(401,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ B @ ( c_List_Olist_ONil @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(786,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ B @ ( c_List_Olist_ONil @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).
thf(995,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ B @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(433,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ B @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__ex @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).
thf(667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__ex @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ B @ C )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).
thf(478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ B @ C )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(763,plain,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(10,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__rec @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_List_Olist_Olist__rec @ A @ B @ D @ F @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Orecs_I2_J_0) ).
thf(346,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__rec @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_List_Olist_Olist__rec @ A @ B @ D @ F @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__take_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ofiltermap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ofiltermap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XremoveAll__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Oinduct_0) ).
thf(835,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XremoveAll__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(244,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(867,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ A ) @ ( v_sko__List__Xlast__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Oinduct_1) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ A ) @ ( v_sko__List__Xlast__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ A ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_1) ).
thf(999,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ A ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(833,plain,
! [B: $i,A: $i] :
( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).
thf(410,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(506,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) )
| ( A
= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) )
| ( A
= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Onull @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_1) ).
thf(828,plain,
! [B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Onull @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Omap__upds @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).
thf(960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Omap__upds @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__update__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Oinduct_0) ).
thf(720,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__update__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ( c_List_Osplice @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(928,plain,
! [B: $i,A: $i] :
( ( c_List_Osplice @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__drop_0) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(215,axiom,
! [A: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(807,plain,
! [A: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__Suc_0) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__rec @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Orecs_I1_J_0) ).
thf(767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__rec @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ A ) @ ( v_sko__List__Xtake__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take_Oinduct_1) ).
thf(1056,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ A ) @ ( v_sko__List__Xtake__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(151,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Ofilter @ D @ E @ C ) )
| ( hBOOL @ ( hAPP @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Ofilter @ D @ E @ C ) )
| ( hBOOL @ ( hAPP @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
= ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(427,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
= ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(644,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(222,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(822,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(76,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(501,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__drop_0) ).
thf(369,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omember @ A @ B @ C )
| ( A = D )
| ~ ( c_List_Omember @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_0) ).
thf(624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omember @ A @ B @ C )
| ( A = D )
| ~ ( c_List_Omember @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ C @ A ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ C @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_3) ).
thf(839,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ C @ A ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ C @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(728,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ A @ C ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ A @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__induct_1) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ A @ C ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ A @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__sublistI_0) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__drop_0) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(268,axiom,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(923,plain,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Omap @ B @ C @ D @ A ) )
| ( C
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Omap @ B @ C @ D @ A ) )
| ( C
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xfoldl__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl_Oinduct_0) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xfoldl__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(972,plain,
! [B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1061,plain,
$false,
inference(e,[status(thm)],[892,1036,809,629,365,760,1031,962,941,555,352,408,683,730,873,379,597,861,523,582,878,511,614,677,384,797,747,945,340,538,930,898,1001,782,841,417,885,1046,389,724,570,504,934,702,751,802,344,853,448,421,870,969,606,924,492,756,591,443,1040,646,485,966,480,574,1020,348,692,453,396,660,988,849,527,602,981,439,529,381,534,714,546,793,334,910,957,778,1042,820,561,429,788,847,435,889,461,493,551,710,974,1012,916,467,697,403,356,593,610,783,499,857,519,742,578,650,948,471,1028,488,753,669,642,637,1016,679,706,686,476,393,997,515,738,654,371,605,622,837,1060,457,938,805,508,921,541,398,558,1026,953,926,633,360,765,1054,773,586,906,412,425,513,824,745,375,733,584,423,1007,843,826,391,572,1058,335,919,704,350,445,936,604,900,831,681,419,736,377,880,616,599,863,890,631,758,816,726,483,700,964,769,943,330,932,811,387,1029,895,983,780,608,986,563,851,431,658,912,521,695,636,1044,722,675,589,531,795,663,648,749,342,1018,553,1049,776,525,712,690,640,887,414,954,993,580,855,673,791,441,1038,717,338,951,544,336,1052,978,595,612,876,859,991,656,1023,845,465,627,450,363,539,671,1010,771,976,688,903,813,517,652,401,786,995,568,914,433,667,478,763,346,549,536,800,835,818,405,867,865,999,620,833,410,564,506,437,1033,828,960,720,928,358,807,474,767,1056,664,332,427,644,459,908,822,1004,501,369,624,839,728,740,469,354,923,496,708,882,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL764-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 16:16:20 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.05 % [INFO] Parsing done (206ms).
% 1.53/1.06 % [INFO] Running in sequential loop mode.
% 2.16/1.27 % [INFO] eprover registered as external prover.
% 2.16/1.27 % [INFO] cvc4 registered as external prover.
% 2.16/1.28 % [INFO] Scanning for conjecture ...
% 2.43/1.37 % [INFO] Found a conjecture and 328 axioms. Running axiom selection ...
% 2.93/1.47 % [INFO] Axiom selection finished. Selected 328 axioms (removed 0 axioms).
% 3.26/1.59 % [INFO] Problem is propositional (TPTP CNF).
% 3.26/1.60 % [INFO] Type checking passed.
% 3.26/1.60 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.44/2.64 % External prover 'e' found a proof!
% 7.44/2.64 % [INFO] Killing All external provers ...
% 7.44/2.65 % Time passed: 2123ms (effective reasoning time: 1585ms)
% 7.44/2.65 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.44/2.65 % Axioms used in derivation (328): clsarity_fun__Lattices_Olower__semilattice, cls_inf__sup__aci_I2_J_0, cls_list_Orecs_I1_J_0, cls_listsp_Oinduct_0, cls_concat_Oinduct_1, cls_rev__swap_1, cls_takeWhile_Oinduct_1, cls_distinct_Oinduct_0, cls_Nil__is__rev__conv_1, cls_Nil__is__map__conv_1, cls_dropWhile_Osimps_I1_J_0, cls_Suc__inject_0, cls_Cons__step1__Cons_0, cls_Cons__eq__append__conv_5, cls_remove1_Osimps_I2_J_0, cls_listrelp_OCons_0, cls_list__all__append_1, cls_list__all2__Cons_2, cls_listsum_Oinduct_0, cls_list__update__overwrite_0, cls_list__all_Osimps_I2_J_1, cls_splice_Osimps_I2_J_1, cls_list__all2__eq_1, cls_append__self__conv_0, cls_Suc__n__not__n_0, cls_splice__Cons__Cons_0, cls_take__tl_0, cls_append__step1I_0, clsarity_bool__Lattices_Olower__semilattice, cls_tl_Osimps_I1_J_0, cls_rev__induct_0, cls_map_Oinduct_1, cls_distinct__sort_0, cls_rotate__map_0, cls_rev__singleton__conv_1, cls_drop_Oinduct_1, cls_listsp_Oinduct_3, cls_list_Oinject_0, cls_Cons__eq__map__conv_3, cls_listsp__infI_0, cls_distinct__filter_0, cls_Snoc__step1__SnocD_2, cls_not__Cons__self2_0, cls_remove1__filter__not_0, cls_rev__is__rev__conv_0, cls_not__step1__Nil_0, cls_distinct__rev_1, clsarity_nat__Orderings_Olinorder, cls_list__update__nonempty_1, cls_filter__eq__ConsD_2, cls_zip_Oinduct_0, cls_Cons__step1__Cons_5, cls_list_Osimps_I5_J_0, cls_inf__left__commute_0, cls_sort__key_Osimps_I1_J_0, cls_listsp_ONil_0, cls_inf1E_1, cls_remdups__filter_0, cls_append__eq__Cons__conv_4, cls_list__update_Oinduct_1, cls_eq__Nil__appendI_0, cls_list_Oinduct_1, cls_self__append__conv_0, cls_distinct__sort_1, cls_List_Omember_Osimps_I2_J_0, cls_same__append__eq_0, cls_list__all_Osimps_I2_J_0, cls_inf__commute_0, cls_hd__append_0, cls_filter_Osimps_I2_J_0, cls_append__Cons_0, cls_listset_Oinduct_1, cls_Nil__is__map__conv_0, cls_drop__map_0, cls_foldr_Osimps_I1_J_0, cls_append__eq__append__conv2_4, cls_rev_Oinduct_1, cls_sorted_Osimps_I3_J_1, cls_list__all__rev_0, cls_append1__eq__conv_1, cls_list__all2__rev_1, cls_filter__append_0, cls_splice_Osimps_I2_J_0, cls_sorted__take_0, cls_distinct_Osimps_I2_J_1, cls_list__all2__rev_0, cls_list__all2__Cons_1, cls_distinct_Osimps_I1_J_0, cls_empty__null_0, cls_concat_Oinduct_0, cls_dB_Osimps_I3_J_0, cls_listsp_Oinducts_1, cls_rev__map_0, cls_hd__append_1, cls_filter_Osimps_I1_J_0, cls_rev__induct_1, cls_drop__Suc__Cons_0, cls_hd_Oinduct_1, cls_last_Oinduct_1, cls_takeWhile_Oinduct_0, cls_listsp_Ocases_0, cls_listset_Oinduct_0, cls_rev_Osimps_I2_J_0, cls_distinct__remove1_0, cls_list_Osimps_I4_J_0, cls_removeAll_Oinduct_0, cls_rev__singleton__conv_0, cls_remdups_Oinduct_1, cls_listrelp_ONil_0, cls_append__self__conv2_0, cls_remdups__id__iff__distinct_0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_list__all__append_2, cls_dropWhile__eq__Cons__conv_1, cls_append__Nil2_0, cls_rotate__is__Nil__conv_0, cls_self__append__conv2_0, cls_distinct__map_0, cls_drop__tl_0, cls_listsp_Ocases_2, cls_distinct__append_0, cls_remdups__eq__nil__iff_1, cls_map__eq__Cons__conv_3, cls_remove1_Oinduct_0, cls_self__append__conv2_1, cls_sorted__drop_0, cls_Cons__step1__Cons_1, cls_map__update_0, cls_List_Omember_Osimps_I2_J_1, cls_append__is__Nil__conv_2, cls_list_Osplit_0, cls_append__Nil_0, cls_sorted__sort__key_0, cls_map__is__Nil__conv_0, cls_append__in__listsp__conv_0, cls_append__eq__append__conv2_5, cls_Cons__step1__Cons_3, cls_singleton__rev__conv_0, cls_rev_Oinduct_0, cls_append__eq__Cons__conv_5, cls_take__map_0, cls_append__in__listsp__conv_1, cls_list__all__rev_1, clsarity_nat__Lattices_Olower__semilattice, cls_zip_Oinduct_1, cls_List_Omember_Osimps_I1_J_0, cls_Snoc__step1__SnocD_3, cls_map__upds__Nil2_0, cls_foldl__Cons_0, cls_rev__is__Nil__conv_0, cls_list__all2__Cons_0, cls_inf__sup__aci_I3_J_0, cls_distinct__rev_0, cls_list__ex_Osimps_I1_J_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_hd__dropWhile_0, cls_distinct__rotate_1, clsarity_fun__Lattices_Olattice, cls_rotate__simps_0, cls_distinct__sublistI_0, cls_list__update_Osimps_I1_J_0, cls_rotate1__is__Nil__conv_0, cls_take_Oinduct_1, cls_list__all2__appendI_0, cls_sublist__nil_0, cls_self__append__conv_1, cls_rev__filter_0, cls_Int__assoc_0, cls_splice__Nil2_0, cls_append__step1I_1, cls_list__all2__Nil_1, cls_rotate1__rotate__swap_0, cls_not__Cons__self_0, cls_listsp_Oinduct_1, cls_append__same__eq_0, cls_splice_Oinduct_1, cls_append__take__drop__id_0, cls_list__all2__rev1_1, cls_hd_Oinduct_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__swap_0, cls_Cons__step1__Cons_2, cls_splice_Osimps_I1_J_0, cls_sorted__Cons_0, cls_list__inter_Osimps_I1_J_0, cls_distinct1__rotate_0, cls_drop__Nil_0, cls_append__assoc_0, cls_inf__sup__aci_I1_J_0, cls_not__Nil__step1_0, cls_foldr_Osimps_I2_J_0, cls_Int__commute_0, cls_concat__map_Osimps_I2_J_0, cls_map__upds__Nil1_0, cls_list__all2__Nil2_0, cls_remove1_Osimps_I1_J_0, cls_remove1_Oinduct_1, clsarity_nat__Lattices_Olattice, cls_tl_Oinduct_0, cls_Cons__step1__Cons_4, cls_Int__absorb_0, cls_inf__assoc_0, cls_append__in__listsp__conv_2, cls_map__append_0, cls_rotate__Suc_0, cls_remdups_Oinduct_0, cls_list__all2__dropI_0, cls_take__eq__Nil_2, cls_distinct__append_1, cls_take_Oinduct_0, cls_listsp_Oinducts_2, cls_Int__left__absorb_0, cls_sorted__remdups_0, cls_distinct__remdups__id_0, cls_remdups__eq__nil__right__iff_1, cls_set_Oinduct_0, cls_foldr__append_0, cls_sorted_Osimps_I1_J_0, cls_tl__append2_0, cls_nat_Oinject_0, cls_list__all2__Nil_0, cls_in__listsp__conv__set_2, cls_sorted__remove1_0, cls_rotate__simps_1, cls_List_Onull_Osimps_I2_J_0, cls_foldl_Oinduct_1, cls_rev__eq__Cons__iff_1, cls_list_Osplit__asm_1, cls_distinct__dropWhile_0, clsarity_bool__Lattices_Olattice, cls_sorted__append_0, cls_listsp_Oinducts_0, cls_rotate__is__Nil__conv_1, cls_map__is__Nil__conv_1, cls_list_Osimps_I3_J_0, cls_tl_Oinduct_1, cls_drop_Oinduct_0, cls_list_Orecs_I2_J_0, cls_drop__Suc_0, cls_inf1I_0, cls_rotate1__hd__tl_0, cls_listsp_Ocases_1, cls_inf__idem_0, cls_list__ex_Osimps_I2_J_1, cls_rev__is__Nil__conv_1, cls_list__all2__Cons1_3, cls_Int__left__commute_0, cls_map_Osimps_I2_J_0, cls_take__Suc__Cons_0, cls_listsum_Oinduct_1, cls_distinct__rotate_0, cls_append__is__Nil__conv_1, cls_lift__IT_0, cls_inf__sup__aci_I4_J_0, cls_Snoc__step1__SnocD_0, cls_dropWhile_Osimps_I2_J_1, cls_list__all2__takeI_0, cls_list_Oinducts_0, cls_dropWhile_Oinduct_0, cls_Nil__is__rev__conv_0, cls_Cons__eq__appendI_0, cls_Cons__eq__append__conv_4, cls_append__is__Nil__conv_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_distinct__take_0, cls_singleton__rev__conv_1, cls_list_Oinject_1, cls_listsp_Oinduct_2, cls_splice_Oinduct_0, cls_append__eq__appendI_0, cls_list__all_Osimps_I2_J_2, cls_remove1_Osimps_I2_J_1, cls_list__update_Oinduct_0, cls_list__all_Osimps_I1_J_0, cls_hd_Osimps_0, cls_rev__append_0, cls_n__not__Suc__n_0, cls_listsp_Oinducts_3, cls_map_Oinduct_0, cls_foldl__append_0, cls_distinct__remdups_0, cls_Nil__is__append__conv_2, cls_list_Osplit_1, cls_List_Omember_Osimps_I2_J_2, cls_list_Oinducts_1, cls_list__all2__eq_0, cls_tl__drop_0, cls_inf__left__idem_0, cls_rev__swap_0, cls_concat__map_Osimps_I1_J_0, cls_sorted_Osimps_I2_J_0, cls_filtermap_Osimps_I1_J_0, cls_tl_Osimps_I2_J_0, cls_foldl__Nil_0, cls_distinct__drop_0, cls_Lambda_0, cls_last_Oinduct_0, cls_take__Suc_0, 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_set_Oinduct_1, cls_list__update__code_I3_J_0, cls_remdups__eq__nil__iff_0, cls_filter_Osimps_I2_J_1, cls_rev__rev__ident_0, cls_distinct1__rotate_1, cls_Snoc__step1__SnocD_1, cls_list__all2__Cons2_3, cls_append1__eq__conv_0, cls_sorted__dropWhile_0, cls_dropWhile_Oinduct_1, cls_distinct_Oinduct_1, cls_Cons__eq__filterD_2, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_removeAll_Oinduct_1, cls_dropWhile_Osimps_I2_J_0, cls_list__all__append_0, cls_foldl_Oinduct_0, cls_inf1E_0, cls_list__update__nonempty_0, cls_empty__null_1, cls_list__all2__rev1_0
% 7.44/2.65 % No. of inferences in proof: 659
% 7.44/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2123 ms resp. 1585 ms w/o parsing
% 8.04/2.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.04/2.78 % [INFO] Killing All external provers ...
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