%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV938-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:01:04 AM UTC 2026
% Result : Unsatisfiable 18.02s 7.92s
% Output : Refutation 19.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 501
% Syntax : Number of formulae : 1003 ( 387 unt; 0 typ; 0 def)
% Number of atoms : 2468 (1293 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 15465 (1062 ~;1465 |; 0 &;12938 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 106 ( 104 usr; 26 con; 0-8 aty)
% Number of variables : 5082 ( 0 ^;5082 !; 0 ?;5082 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_WellTypeRT_OWTrt_decl,type,
c_WellTypeRT_OWTrt: $i > $i > $i > $i > $i > $o ).
thf(v_P_decl,type,
v_P: $i ).
thf(v_ha_____decl,type,
v_ha____: $i ).
thf(c_Map_Omap__upds_decl,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(v_E_____decl,type,
v_E____: $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_Type_Othis_decl,type,
c_Type_Othis: $i ).
thf(v_pns_____decl,type,
v_pns____: $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(tc_String_Ochar_decl,type,
tc_String_Ochar: $i ).
thf(c_Type_Oty_OClass_decl,type,
c_Type_Oty_OClass: $i > $i ).
thf(v_D_____decl,type,
v_D____: $i ).
thf(v_Ts_____decl,type,
v_Ts____: $i ).
thf(tc_Type_Oty_decl,type,
tc_Type_Oty: $i ).
thf(v_body_____decl,type,
v_body____: $i ).
thf(v_T_H_H_____decl,type,
v_T_H_H____: $i ).
thf(c_Type_Oty_OBoolean_decl,type,
c_Type_Oty_OBoolean: $i ).
thf(c_Type_Oty_OVoid_decl,type,
c_Type_Oty_OVoid: $i ).
thf(c_Type_Oty_Oty__case_decl,type,
c_Type_Oty_Oty__case: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xty__Xcase__cong__1__1_decl,type,
c_Type_Osko__Type__Xty__Xcase__cong__1__1: $i > $i > $i > $i > $i ).
thf(c_Type_Oty_ONT_decl,type,
c_Type_Oty_ONT: $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_TypeRel_Owiden_decl,type,
c_TypeRel_Owiden: $i > $i > $i ).
thf(c_List_Ofilter_decl,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_sko__Type__Xty__Xsplit__asm__1_decl,type,
v_sko__Type__Xty__Xsplit__asm__1: $i > $i > $i > $i ).
thf(c_Type_Oty_OInteger_decl,type,
c_Type_Oty_OInteger: $i ).
thf(v_sko__Type__Xty__Xsplit__1_decl,type,
v_sko__Type__Xty__Xsplit__1: $i > $i > $i > $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_List_Olinorder__class_Osorted_decl,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(c_List_OtakeWhile_decl,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i > $i ).
thf(c_Expr_Oexp_OFAss_decl,type,
c_Expr_Oexp_OFAss: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_decl,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Option_Ooption_OSome_decl,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(c_Map_Omap__add_decl,type,
c_Map_Omap__add: $i > $i > $i > $i > $i ).
thf(c_Option_Ooption_ONone_decl,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_Expr_Oexp_OCast_decl,type,
c_Expr_Oexp_OCast: $i > $i > $i > $i ).
thf(c_Expr_Oexp_OVal_decl,type,
c_Expr_Oexp_OVal: $i > $i ).
thf(c_Expr_Oexp_OFAcc_decl,type,
c_Expr_Oexp_OFAcc: $i > $i > $i > $i > $i ).
thf(c_Map_Omap__le_decl,type,
c_Map_Omap__le: $i > $i > $i > $i > $o ).
thf(c_List_Olist_Olist__case_decl,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_OCall_decl,type,
c_Expr_Oexp_OCall: $i > $i > $i > $i > $i ).
thf(c_List_Omap_decl,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_OSeq_decl,type,
c_Expr_Oexp_OSeq: $i > $i > $i > $i ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_Oremove1_decl,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(c_List_OdropWhile_decl,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_List_Ohd_decl,type,
c_List_Ohd: $i > $i > $i ).
thf(c_List_Olist__all2_decl,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_Expr_Oexp_Onew_decl,type,
c_Expr_Oexp_Onew: $i > $i > $i ).
thf(c_Type_Oty_Oty__rec_decl,type,
c_Type_Oty_Oty__rec: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Type_Ois__refT_decl,type,
c_Type_Ois__refT: $i > $o ).
thf(c_Decl_Ois__class_decl,type,
c_Decl_Ois__class: $i > $i > $i > $o ).
thf(c_TypeRel_OMethod_decl,type,
c_TypeRel_OMethod: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_List_Olist_Olist__rec_decl,type,
c_List_Olist_Olist__rec: $i > $i > $i > $i > $i > $i ).
thf(c_fequal_decl,type,
c_fequal: $i > $i ).
thf(c_List_Olistrelp_decl,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_List_Ofoldr_decl,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_List_OremoveAll_decl,type,
c_List_OremoveAll: $i > $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_List_Ofoldl_decl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(c_List_Onull_decl,type,
c_List_Onull: $i > $i > $o ).
thf(c_Objects_Ohext_decl,type,
c_Objects_Ohext: $i > $i > $o ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_List_Olist__all_decl,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(c_List_Osplice_decl,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(c_WellTypeRT_OWTrts_decl,type,
c_WellTypeRT_OWTrts: $i > $i > $i > $i > $i > $o ).
thf(c_Progress_OWTrts_H_decl,type,
c_Progress_OWTrts_H: $i > $i > $i > $i > $i > $o ).
thf(c_List_Otl_decl,type,
c_List_Otl: $i > $i > $i ).
thf(c_List_Omap__filter_decl,type,
c_List_Omap__filter: $i > $i > $i > $i > $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_List_Omember_decl,type,
c_List_Omember: $i > $i > $i > $o ).
thf(c_WellType_OWTs_decl,type,
c_WellType_OWTs: $i > $i > $i > $i > $o ).
thf(c_List_Olist__ex_decl,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_Expr_Oexp_decl,type,
tc_Expr_Oexp: $i > $i ).
thf(c_WellType_OWT_decl,type,
c_WellType_OWT: $i > $i > $i > $i > $o ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(c_Progress_OWTrt_H_decl,type,
c_Progress_OWTrt_H: $i > $i > $i > $i > $i > $o ).
thf(c_TypeRel_Ohas__field_decl,type,
c_TypeRel_Ohas__field: $i > $i > $i > $i > $i > $i > $o ).
thf(v_sko__Type__Xty__Xinducts__1_decl,type,
v_sko__Type__Xty__Xinducts__1: $i > $i ).
thf(c_List_OListMem_decl,type,
c_List_OListMem: $i > $i > $i > $o ).
thf(v_vs_____decl,type,
v_vs____: $i ).
thf(tc_Value_Oval_decl,type,
tc_Value_Oval: $i ).
thf(v_Ts_H_____decl,type,
v_Ts_H____: $i ).
thf(c_List_Oconcat_decl,type,
c_List_Oconcat: $i > $i > $i ).
thf(c_Type_Osko__Type__Xty__Xexhaust__1__1_decl,type,
c_Type_Osko__Type__Xty__Xexhaust__1__1: $i > $i ).
thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1_decl,type,
c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xty__Xnchotomy__1__1_decl,type,
c_Type_Osko__Type__Xty__Xnchotomy__1__1: $i > $i ).
thf(v_sko__Value__Xdefault__val__Xinduct__1_decl,type,
v_sko__Value__Xdefault__val__Xinduct__1: $i > $i ).
thf(v_C_____decl,type,
v_C____: $i ).
thf(v_M_____decl,type,
v_M____: $i ).
thf(v_T_____decl,type,
v_T____: $i ).
thf(c_TypeSafe__Mirabelle_Osconf_decl,type,
c_TypeSafe__Mirabelle_Osconf: $i > $i > $i > $o ).
thf(v_la_____decl,type,
v_la____: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(v_sko__Type__Xty__Xinduct__1_decl,type,
v_sko__Type__Xty__Xinduct__1: $i > $i ).
thf(54,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).
thf(645,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(441,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_0) ).
thf(1665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(198,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I29_J_0) ).
thf(1036,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(305,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_31) ).
thf(1337,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(335,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( E @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_6) ).
thf(1411,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( E @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWTs ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__implies__WTrts_0) ).
thf(1168,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWTs ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(352,axiom,
! [A: $i] : ( A @ c_Type_Oty_OClass @ c_Type_Ois__refT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__refT__def_2) ).
thf(1454,plain,
! [A: $i] : ( A @ c_Type_Oty_OClass @ c_Type_Ois__refT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(398,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ hAPP ) @ hBOOL )
| ( ( F @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) )
= ( F @ ( F @ ( E @ ( D @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) @ ( C @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__filter_Osimps_I2_J_0) ).
thf(1559,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ hAPP ) @ hBOOL )
| ( ( F @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) )
= ( F @ ( F @ ( E @ ( D @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) @ ( C @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(132,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(846,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(250,axiom,
c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I11_J_0) ).
thf(1179,plain,
c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(223,axiom,
c_Type_Oty_ONT != c_Type_Oty_OVoid,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I7_J_0) ).
thf(1110,plain,
c_Type_Oty_ONT != c_Type_Oty_OVoid,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(450,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtFAcc_0) ).
thf(1686,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(409,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I7_J_0) ).
thf(1586,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(373,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt__env__mono_0) ).
thf(1501,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(154,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).
thf(909,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__takeWhile_0) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(196,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_34) ).
thf(1031,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Orecs_I1_J_0) ).
thf(666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(290,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(1295,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_0) ).
thf(1200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(262,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_9) ).
thf(1211,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_1) ).
thf(1596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(210,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).
thf(1068,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(1522,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(348,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( B @ ( D @ ( A @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( B @ ( D @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append1_5) ).
thf(1443,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( B @ ( D @ ( A @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( B @ ( D @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
| ~ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__le ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).
thf(994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
| ~ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__le ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(92,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( D @ tc_Option_Ooption @ ( E @ ( D @ ( G @ c_Option_Ooption_OSome ) @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).
thf(741,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( D @ tc_Option_Ooption @ ( E @ ( D @ ( G @ c_Option_Ooption_OSome ) @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(411,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).
thf(1591,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(144,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_33) ).
thf(878,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(142,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).
thf(873,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(260,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_30) ).
thf(1205,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
thf(614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).
thf(677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).
thf(1705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(341,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__map_0) ).
thf(1671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1655,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(19,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
| ( C @ ( D @ ( C @ tc_Option_Ooption @ ( D @ ( C @ ( F @ c_Option_Ooption_OSome ) @ ( B @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__imp__upd__le_0) ).
thf(550,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
| ( C @ ( D @ ( C @ tc_Option_Ooption @ ( D @ ( C @ ( F @ c_Option_Ooption_OSome ) @ ( B @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(797,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(82,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_7) ).
thf(715,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(75,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_10) ).
thf(698,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1761,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(208,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(1063,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(354,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
| ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_WellType_OWTs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTCons_0) ).
thf(1458,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( F @ ( D @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
| ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_WellType_OWTs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__le ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__empty_0) ).
thf(1354,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__le ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(376,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(1507,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(265,axiom,
c_Type_Oty_OBoolean != c_Type_Oty_ONT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I12_J_0) ).
thf(1222,plain,
c_Type_Oty_OBoolean != c_Type_Oty_ONT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(476,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
| ( ( C @ ( A @ ( B @ c_List_OdropWhile ) ) )
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
!= ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( B @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_2) ).
thf(1746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
| ( ( C @ ( A @ ( B @ c_List_OdropWhile ) ) )
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
!= ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( B @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(347,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(1441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(267,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_13) ).
thf(1228,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(327,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(1391,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(405,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( F @ ( E @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I26_J_0) ).
thf(1576,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( F @ ( E @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(1601,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(325,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I10_J_1) ).
thf(1386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(280,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = c_Type_Oty_OBoolean )
| ( F = c_Type_Oty_OInteger )
| ( F = c_Type_Oty_ONT )
| ( F
= ( G @ ( K @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( K @ ( J @ ( I @ ( H @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_16) ).
thf(1265,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = c_Type_Oty_OBoolean )
| ( F = c_Type_Oty_OInteger )
| ( F = c_Type_Oty_ONT )
| ( F
= ( G @ ( K @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( K @ ( J @ ( I @ ( H @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(458,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).
thf(1703,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(205,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_16) ).
thf(1055,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(2,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = c_Type_Oty_ONT )
| ( A
= ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( K @ ( J @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_4) ).
thf(504,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = c_Type_Oty_ONT )
| ( A
= ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( K @ ( J @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(300,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_7) ).
thf(1323,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(113,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_29) ).
thf(802,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(353,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(1455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(162,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_15) ).
thf(934,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(356,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I10_J_0) ).
thf(1462,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(231,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1132,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(392,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCallNT_0) ).
thf(1545,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(51,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_32) ).
thf(638,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(322,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_28) ).
thf(1379,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(379,axiom,
v_Ts_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( v_vs____ @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wtes_0) ).
thf(1514,plain,
v_Ts_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( v_vs____ @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
| ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I1_J_0) ).
thf(1479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
| ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(175,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Orecs_I3_J_0) ).
thf(969,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(403,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Map_Omap__upds ) ) ) ) )
= ( G @ ( D @ ( F @ ( C @ ( G @ tc_Option_Ooption @ ( D @ ( G @ ( E @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Cons_0) ).
thf(1572,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Map_Omap__upds ) ) ) ) )
= ( G @ ( D @ ( F @ ( C @ ( G @ tc_Option_Ooption @ ( D @ ( G @ ( E @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(473,axiom,
tc_Type_Oty @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_Ts_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subs_0) ).
thf(1741,plain,
tc_Type_Oty @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_Ts_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(330,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Orecs_I2_J_0) ).
thf(1398,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(145,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_24) ).
thf(881,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(97,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_31) ).
thf(756,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(222,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1109,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(45,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( K @ ( E @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_2) ).
thf(623,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( K @ ( E @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).
thf(1334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(163,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( E @ ( D @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( D @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_2) ).
thf(937,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( E @ ( D @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( D @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(446,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Map_Omap__le ) ) ) )
| ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( F @ c_Map_Omap__upds ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__upds_0) ).
thf(1677,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Map_Omap__le ) ) ) )
| ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( F @ c_Map_Omap__upds ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(174,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_13) ).
thf(966,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(286,axiom,
c_Type_Oty_OInteger != c_Type_Oty_OVoid,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I5_J_0) ).
thf(1283,plain,
c_Type_Oty_OInteger != c_Type_Oty_OVoid,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__add ) ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__map__add_0) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__add ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(448,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtSeq_0) ).
thf(1682,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(127,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( J @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OInteger )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_25) ).
thf(834,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( J @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OInteger )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(71,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).
thf(687,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(170,axiom,
c_Type_Oty_OInteger != c_Type_Oty_ONT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I16_J_0) ).
thf(956,plain,
c_Type_Oty_OInteger != c_Type_Oty_ONT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(309,axiom,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I1_J_0) ).
thf(1351,plain,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(1405,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__refl_0) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(400,axiom,
! [A: $i] :
( ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger )
| ( A = c_Type_Oty_ONT )
| ( A
= ( A @ c_Type_Osko__Type__Xty__Xexhaust__1__1 @ c_Type_Oty_OClass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Oexhaust_0) ).
thf(1564,plain,
! [A: $i] :
( ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger )
| ( A = c_Type_Oty_ONT )
| ( A
= ( A @ c_Type_Osko__Type__Xty__Xexhaust__1__1 @ c_Type_Oty_OClass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(37,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_34) ).
thf(602,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(178,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).
thf(981,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(100,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).
thf(766,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(220,axiom,
c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I10_J_0) ).
thf(1104,plain,
c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(455,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__implies__WTrt_0) ).
thf(1697,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(272,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_9) ).
thf(1242,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(849,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(434,axiom,
( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) )
= ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__pns_0) ).
thf(1651,plain,
( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) )
= ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(12,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ tc_Option_Ooption @ ( F @ ( E @ ( A @ c_Option_Ooption_OSome ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( E @ ( B @ c_Option_Ooption_OSome ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).
thf(529,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ tc_Option_Ooption @ ( F @ ( E @ ( A @ c_Option_Ooption_OSome ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( E @ ( B @ c_Option_Ooption_OSome ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I16_J_0) ).
thf(793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(159,axiom,
c_Type_Oty_OVoid != c_Type_Oty_ONT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I6_J_0) ).
thf(925,plain,
c_Type_Oty_OVoid != c_Type_Oty_ONT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(99,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(761,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).
thf(1311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(487,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I15_J_0) ).
thf(1768,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(428,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1636,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I35_J_0) ).
thf(1074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(416,axiom,
! [A: $i] :
( ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger )
| ( A = c_Type_Oty_ONT )
| ( A
= ( A @ c_Type_Osko__Type__Xty__Xnchotomy__1__1 @ c_Type_Oty_OClass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Onchotomy_0) ).
thf(1604,plain,
! [A: $i] :
( ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger )
| ( A = c_Type_Oty_ONT )
| ( A
= ( A @ c_Type_Osko__Type__Xty__Xnchotomy__1__1 @ c_Type_Oty_OClass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(359,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).
thf(1470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(1708,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(202,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__trans_0) ).
thf(1047,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
| ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(468,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).
thf(1730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(243,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1163,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(1274,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(149,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_OInteger )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_3) ).
thf(894,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_OInteger )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(307,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_12) ).
thf(1343,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(200,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_27) ).
thf(1042,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(1255,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(402,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCons_0) ).
thf(1570,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).
thf(1217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(478,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(1751,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
thf(729,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(192,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_21) ).
thf(1021,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(104,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_10) ).
thf(778,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(312,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
= ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_0) ).
thf(1355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
= ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(407,axiom,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_OVoid ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I9_J_0) ).
thf(1580,plain,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_OVoid ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(73,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Type_Oty_OInteger @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_2) ).
thf(693,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Type_Oty_OInteger @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).
thf(630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(422,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(1619,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(1370,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(25,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_28) ).
thf(566,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(316,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(1365,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oconcat ) )
= ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Osimps_I2_J_0) ).
thf(1555,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oconcat ) )
= ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_OBoolean ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I15_J_0) ).
thf(1624,plain,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_OBoolean ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(496,axiom,
( ( tc_Value_Oval @ tc_List_Olist @ ( v_vs____ @ c_Nat_Osize__class_Osize ) )
= ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RedCall_I3_J_0) ).
thf(1787,plain,
( ( tc_Value_Oval @ tc_List_Olist @ ( v_vs____ @ c_Nat_Osize__class_Osize ) )
= ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(69,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_36) ).
thf(682,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(1634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(80,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_OInteger )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_19) ).
thf(710,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_OInteger )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ tc_Option_Ooption @ ( B @ c_Option_Ooption_ONone @ c_COMBK ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__empty_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ tc_Option_Ooption @ ( B @ c_Option_Ooption_ONone @ c_COMBK ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(472,axiom,
tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_D____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_body____ @ ( v_pns____ @ c_Pair ) ) ) @ ( v_T____ @ ( v_Ts____ @ ( v_M____ @ ( v_C____ @ ( v_P @ c_TypeRel_OMethod ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_method_0) ).
thf(1740,plain,
tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_D____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_body____ @ ( v_pns____ @ c_Pair ) ) ) @ ( v_T____ @ ( v_Ts____ @ ( v_M____ @ ( v_C____ @ ( v_P @ c_TypeRel_OMethod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(842,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(332,axiom,
! [A: $i] :
( c_Type_Oty_OVoid
!= ( A @ c_Type_Oty_OClass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I8_J_0) ).
thf(1402,plain,
! [A: $i] :
( c_Type_Oty_OVoid
!= ( A @ c_Type_Oty_OClass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(314,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_32) ).
thf(1360,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(30,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_0) ).
thf(578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( E @ ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__add ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).
thf(1234,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( E @ ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__add ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(235,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = c_Type_Oty_OVoid )
| ( F = c_Type_Oty_OBoolean )
| ( F = c_Type_Oty_OInteger )
| ( F = c_Type_Oty_ONT )
| ( F
= ( G @ ( L @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( L @ ( K @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_0) ).
thf(1143,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = c_Type_Oty_OVoid )
| ( F = c_Type_Oty_OBoolean )
| ( F = c_Type_Oty_OInteger )
| ( F = c_Type_Oty_ONT )
| ( F
= ( G @ ( L @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( L @ ( K @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(489,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
| ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).
thf(1772,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
| ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(56,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OInteger )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_11) ).
thf(650,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OInteger )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(499,axiom,
v_T_H_H____ @ ( v_body____ @ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_Type_Oty @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__upds ) ) ) ) @ ( v_P @ c_WellType_OWT ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wtabody_0) ).
thf(1794,plain,
v_T_H_H____ @ ( v_body____ @ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_Type_Oty @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__upds ) ) ) ) @ ( v_P @ c_WellType_OWT ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(218,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(1096,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__dropWhile__id_0) ).
thf(1006,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( D @ ( B @ ( A @ c_List_OremoveAll ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll__append_0) ).
thf(1138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( D @ ( B @ ( A @ c_List_OremoveAll ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( C @ ( A @ c_Expr_Oexp_OVal @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( C @ ( A @ c_Expr_Oexp_OVal @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(481,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(1755,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(226,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).
thf(1118,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(136,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_35) ).
thf(857,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(320,axiom,
! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__refl_0) ).
thf(1375,plain,
! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(227,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).
thf(1121,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(401,axiom,
! [A: $i] :
( c_Type_Oty_OBoolean
!= ( A @ c_Type_Oty_OClass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I14_J_0) ).
thf(1567,plain,
! [A: $i] :
( c_Type_Oty_OBoolean
!= ( A @ c_Type_Oty_OClass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( E @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).
thf(1493,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( E @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(289,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_6) ).
thf(1292,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(21,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).
thf(554,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(251,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( E @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome ) @ ( C @ ( E @ ( F @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upd_0) ).
thf(1182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( E @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome ) @ ( C @ ( E @ ( F @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(340,axiom,
( ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) )
= ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RedCall_I4_J_0) ).
thf(1424,plain,
( ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) )
= ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(498,axiom,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_OInteger ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I19_J_0) ).
thf(1791,plain,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_OInteger ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(349,axiom,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_ONT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I21_J_0) ).
thf(1446,plain,
! [A: $i] :
( ( A @ c_Type_Oty_OClass )
!= c_Type_Oty_ONT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(190,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_22) ).
thf(1016,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(431,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).
thf(1644,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(338,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCall_0) ).
thf(1419,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(884,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(302,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1329,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(419,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I18_J_0) ).
thf(1612,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(199,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ tc_Option_Ooption @ ( G @ ( D @ ( F @ c_Option_Ooption_OSome ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) )
| ( B = E )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).
thf(1039,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ tc_Option_Ooption @ ( G @ ( D @ ( F @ c_Option_Ooption_OSome ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) )
| ( B = E )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(18,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_30) ).
thf(547,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(1744,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(128,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_6) ).
thf(837,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(76,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Type_Oty_OVoid @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_0) ).
thf(701,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Type_Oty_OVoid @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(91,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OInteger )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_27) ).
thf(738,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OInteger )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(268,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(1231,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(442,axiom,
! [A: $i] :
( c_Type_Oty_OInteger
!= ( A @ c_Type_Oty_OClass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I18_J_0) ).
thf(1668,plain,
! [A: $i] :
( c_Type_Oty_OInteger
!= ( A @ c_Type_Oty_OClass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(1552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
thf(1192,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(414,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTSeq_0) ).
thf(1599,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(462,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).
thf(1715,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(464,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtFAss_0) ).
thf(1720,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(425,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( F @ ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I7_J_1) ).
thf(1627,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( F @ ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(491,axiom,
v_T____ @ ( v_T_H_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_H_HsubT_0) ).
thf(1776,plain,
v_T____ @ ( v_T_H_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(184,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_12) ).
thf(997,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(410,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = c_Type_Oty_OInteger )
| ( F = c_Type_Oty_ONT )
| ( F
= ( G @ ( J @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( J @ ( I @ ( H @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_24) ).
thf(1588,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = c_Type_Oty_OInteger )
| ( F = c_Type_Oty_ONT )
| ( F
= ( G @ ( J @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( J @ ( I @ ( H @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(219,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = I )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).
thf(1099,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = I )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_0) ).
thf(1530,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(389,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OVoid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_0) ).
thf(1539,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(323,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_29) ).
thf(1382,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(1429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(605,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(483,axiom,
! [B: $i,A: $i] :
( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
| ~ ( A @ v_sko__Type__Xty__Xinduct__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Oinduct_0) ).
thf(1759,plain,
! [B: $i,A: $i] :
( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
| ~ ( A @ v_sko__Type__Xty__Xinduct__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(328,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( B @ c_Expr_Oexp_OCast ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_2) ).
thf(1393,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( B @ c_Expr_Oexp_OCast ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I17_J_0) ).
thf(1318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(114,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OBoolean )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_23) ).
thf(805,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OBoolean )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(454,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I11_J_0) ).
thf(1695,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).
thf(541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(246,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Type_Oty_OBoolean @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_1) ).
thf(1170,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Type_Oty_OBoolean @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(287,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( K @ ( B @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__fun_1) ).
thf(1286,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( K @ ( B @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(211,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( D @ ( F @ c_Option_Ooption_OSome ) ) )
| ( ( E @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ ( F @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).
thf(1071,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( D @ ( F @ c_Option_Ooption_OSome ) ) )
| ( ( E @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ ( F @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(66,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( I @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_29) ).
thf(674,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( I @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(440,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( L @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( K @ ( J @ c_Pair ) ) ) @ ( F @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( G @ ( E @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( H @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTCall_0) ).
thf(1663,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( L @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( K @ ( J @ c_Pair ) ) ) @ ( F @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( G @ ( E @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( H @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(380,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).
thf(1515,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(169,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_22) ).
thf(953,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).
thf(1732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(493,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).
thf(1779,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(83,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).
thf(718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(153,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_5) ).
thf(906,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(433,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append_1) ).
thf(1648,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(467,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( E = c_Type_Oty_OVoid )
| ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_1) ).
thf(1727,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( E = c_Type_Oty_OVoid )
| ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(28,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( K @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OInteger )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_9) ).
thf(573,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( K @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OInteger )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(89,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(733,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).
thf(618,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(485,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_4) ).
thf(1764,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(6,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_26) ).
thf(513,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).
thf(1146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(480,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_1) ).
thf(1754,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1154,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(495,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F
= ( G @ ( H @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( H @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_30) ).
thf(1784,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F
= ( G @ ( H @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( H @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(326,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( E @ ( I @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_18) ).
thf(1388,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( E @ ( I @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__le__mapE_0) ).
thf(826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(382,axiom,
( ( t_a @ ( v_P @ c_COMBI ) )
= v_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(1520,plain,
( ( t_a @ ( v_P @ c_COMBI ) )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OdropWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).
thf(1124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OdropWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(367,axiom,
! [B: $i,A: $i] :
( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
| ~ ( A @ v_sko__Type__Xty__Xinducts__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Oinducts_0) ).
thf(1488,plain,
! [B: $i,A: $i] :
( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
| ~ ( A @ v_sko__Type__Xty__Xinducts__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(500,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1795,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(457,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtFAccNT_0) ).
thf(1701,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(1503,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1271,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__map_0) ).
thf(713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(216,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_18) ).
thf(1090,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(78,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_11) ).
thf(704,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(1675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(40,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( K @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_OInteger )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_17) ).
thf(611,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( K @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_OInteger )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(206,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1058,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__filter__conv_0) ).
thf(1107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(357,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( A
= ( B @ c_Type_Oty_OClass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I10_J_0) ).
thf(1464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( A
= ( B @ c_Type_Oty_OClass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(167,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_27) ).
thf(947,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(256,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).
thf(1194,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).
thf(1408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(106,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( K @ ( J @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__fun_0) ).
thf(784,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( K @ ( J @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(384,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ hBOOL )
| ( ( F @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) )
= ( F @ ( E @ ( D @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__filter_Osimps_I2_J_1) ).
thf(1524,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ hBOOL )
| ( ( F @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) )
= ( F @ ( E @ ( D @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OListMem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_elem_0) ).
thf(1492,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OListMem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] : ( C @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__Class_2) ).
thf(1542,plain,
! [C: $i,B: $i,A: $i] : ( C @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(465,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
| ( A
= ( B @ c_Type_Oty_OClass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_0) ).
thf(1722,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
| ( A
= ( B @ c_Type_Oty_OClass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(42,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I22_J_0) ).
thf(616,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(452,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( I @ ( E @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_14) ).
thf(1690,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( I @ ( E @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(404,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_3) ).
thf(1574,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(189,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).
thf(1011,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
!= ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).
thf(599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
!= ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(321,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).
thf(1376,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(346,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I13_J_0) ).
thf(1439,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(138,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Type_Oty_ONT @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_3) ).
thf(863,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Type_Oty_ONT @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).
thf(1175,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Objects_Ohext ) )
| ~ ( B @ ( C @ c_Objects_Ohext ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__trans_0) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Objects_Ohext ) )
| ~ ( B @ ( C @ c_Objects_Ohext ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(1080,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(14,axiom,
c_Type_Oty_ONT != c_Type_Oty_OBoolean,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I13_J_0) ).
thf(535,plain,
c_Type_Oty_ONT != c_Type_Oty_OBoolean,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(119,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I27_J_0) ).
thf(816,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) )
= ( D @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__filter_Osimps_I1_J_0) ).
thf(1029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Omap__filter ) ) ) ) )
= ( D @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(355,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( F @ c_Type_Ois__refT )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
| ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I2_J_0) ).
thf(1460,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( F @ c_Type_Ois__refT )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
| ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(165,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).
thf(943,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(64,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_11) ).
thf(668,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(451,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(1688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).
thf(1557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).
thf(552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(112,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_23) ).
thf(799,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(86,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_23) ).
thf(726,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Ohd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Ohd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( D @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( D @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(155,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( B @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__fun_2) ).
thf(912,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( L @ ( B @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( C @ ( D @ c_List_Otl ) @ ( B @ c_List_Osplice ) ) @ ( C @ ( D @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
thf(1474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( C @ ( D @ c_List_Otl ) @ ( B @ c_List_Osplice ) ) @ ( C @ ( D @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(171,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( H @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__idemp_0) ).
thf(959,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( H @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(868,plain,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(179,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_0) ).
thf(986,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(362,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I10_J_1) ).
thf(1477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
thf(1496,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(134,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).
thf(851,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I30_J_0) ).
thf(653,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(59,axiom,
c_Type_Oty_ONT @ c_Type_Ois__refT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__refT__def_1) ).
thf(658,plain,
c_Type_Oty_ONT @ c_Type_Ois__refT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(1562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).
thf(1594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( A @ c_Decl_Ois__class ) ) )
| ( C @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Onew ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTNew_0) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( A @ c_Decl_Ois__class ) ) )
| ( C @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Onew ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(74,axiom,
c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I2_J_0) ).
thf(695,plain,
c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(273,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_18) ).
thf(1245,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( C @ ( B @ c_Expr_Oexp_OVal @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I18_J_0) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( C @ ( B @ c_Expr_Oexp_OVal @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(39,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).
thf(608,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(224,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( K @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_5) ).
thf(1113,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( K @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(24,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_25) ).
thf(563,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(185,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( F @ ( E @ c_Expr_Oexp_OVal @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).
thf(1000,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( F @ ( E @ c_Expr_Oexp_OVal @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__trans_0) ).
thf(1435,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(197,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(1034,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(408,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( I @ ( E @ ( H @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OInteger ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_26) ).
thf(1583,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( I @ ( E @ ( H @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OInteger ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__refl_0) ).
thf(1758,plain,
! [C: $i,B: $i,A: $i] : ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(261,axiom,
c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I3_J_0) ).
thf(1208,plain,
c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(358,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).
thf(1467,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(68,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I24_J_0) ).
thf(680,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( ( C @ ( B @ ( A @ c_List_Oremove1 ) ) )
= ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1__removeAll_0) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( ( C @ ( B @ ( A @ c_List_Oremove1 ) ) )
= ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(55,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I25_J_0) ).
thf(648,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(377,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).
thf(1509,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(94,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_24) ).
thf(749,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(516,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1340,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(1472,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(754,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(122,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( E @ ( D @ tc_Option_Ooption @ ( D @ c_Option_Ooption_ONone @ c_COMBK ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__nonempty_0) ).
thf(823,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( E @ ( D @ tc_Option_Ooption @ ( D @ c_Option_Ooption_ONone @ c_COMBK ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(203,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_19) ).
thf(1049,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(501,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__upds ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upds_0) ).
thf(1798,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__upds ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(72,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_21) ).
thf(690,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(176,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).
thf(971,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(276,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).
thf(1252,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(479,axiom,
tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RedCall_I5_J_0) ).
thf(1753,plain,
tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(365,axiom,
v_T_H_H____ @ ( v_body____ @ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_Type_Oty @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__upds ) ) ) ) @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1484,plain,
v_T_H_H____ @ ( v_body____ @ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_Type_Oty @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__upds ) ) ) ) @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(182,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).
thf(993,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(393,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(1547,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(103,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(776,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(22,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_20) ).
thf(557,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(186,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( F @ ( E @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) )
| ( ( B @ ( E @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).
thf(1003,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( F @ ( E @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) )
| ( ( B @ ( E @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(488,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtFAssNT_0) ).
thf(1770,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(1225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(331,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).
thf(1400,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(79,axiom,
c_Type_Oty_OVoid != c_Type_Oty_OInteger,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I4_J_0) ).
thf(707,plain,
c_Type_Oty_OVoid != c_Type_Oty_OInteger,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(1499,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(343,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append_0) ).
thf(1432,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(253,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_20) ).
thf(1186,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1,negated_conjecture,
~ ( v_T_H_H____ @ ( v_body____ @ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ ( v_E____ @ c_Map_Omap__upds ) ) ) ) @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(502,plain,
~ ( v_T_H_H____ @ ( v_body____ @ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ ( v_E____ @ c_Map_Omap__upds ) ) ) ) @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Olist__all ) ) )
| ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_2) ).
thf(840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Olist__all ) ) )
| ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(279,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = c_Type_Oty_OInteger )
| ( A = c_Type_Oty_ONT )
| ( A
= ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( K @ ( J @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_8) ).
thf(1262,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = c_Type_Oty_OInteger )
| ( A = c_Type_Oty_ONT )
| ( A
= ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( K @ ( J @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(115,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( J @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_13) ).
thf(808,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( J @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(447,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_0) ).
thf(1679,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(17,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).
thf(544,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(291,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( A @ hAPP ) )
= ( D @ ( G @ c_Option_Ooption_OSome ) ) )
| ( ( F @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( D @ ( G @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).
thf(1300,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( A @ hAPP ) )
= ( D @ ( G @ c_Option_Ooption_OSome ) ) )
| ( ( F @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( D @ ( G @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( C @ c_Expr_Oexp_Onew ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I1_J_0) ).
thf(1085,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( C @ c_Expr_Oexp_Onew ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(29,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__trans_0) ).
thf(576,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(278,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).
thf(1257,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(77,axiom,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).
thf(703,plain,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(58,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Orecs_I1_J_0) ).
thf(656,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(477,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( F @ c_Map_Omap__le ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__env__mono_0) ).
thf(1749,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( F @ c_Map_Omap__le ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(234,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).
thf(1140,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(188,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_16) ).
thf(1008,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_List_Omember ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_0) ).
thf(1717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_List_Omember ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(571,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(319,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_17) ).
thf(1372,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(876,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(421,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= ( F @ ( E @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Orecs_I5_J_0) ).
thf(1617,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= ( F @ ( E @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(391,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(1543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).
thf(1766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( A @ c_List_OdropWhile ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).
thf(1485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( A @ c_List_OdropWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(204,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( J @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_21) ).
thf(1052,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( J @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(339,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = c_Type_Oty_ONT )
| ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( I @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_12) ).
thf(1421,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = c_Type_Oty_ONT )
| ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( I @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(1316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll__filter__not_0) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_OremoveAll ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(65,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( B @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__fun_3) ).
thf(671,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( B @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(381,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append_2) ).
thf(1517,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OremoveAll ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I1_J_0) ).
thf(759,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OremoveAll ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( C @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I19_J_0) ).
thf(1126,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( C @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(254,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_5) ).
thf(1189,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(240,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Orecs_I4_J_0) ).
thf(1157,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(299,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I23_J_0) ).
thf(1321,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(177,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).
thf(976,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
= ( C @ c_List_Olist_ONil ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Ohd ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
= ( C @ c_List_Olist_ONil ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Ohd ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(11,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = G )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).
thf(524,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = G )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
| ( A
= ( B @ c_Type_Oty_OClass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I10_J_0) ).
thf(1781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
| ( A
= ( B @ c_Type_Oty_OClass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I34_J_0) ).
thf(891,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(288,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_25) ).
thf(1289,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wts_H__wts_0) ).
thf(844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(470,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( C @ ( A @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__append2_5) ).
thf(1734,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( C @ ( A @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(101,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).
thf(771,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(432,axiom,
! [B: $i,A: $i] :
( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
| ~ ( A @ v_sko__Value__Xdefault__val__Xinduct__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_default__val_Oinduct_0) ).
thf(1646,plain,
! [B: $i,A: $i] :
( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
| ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
| ~ ( A @ v_sko__Value__Xdefault__val__Xinduct__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(301,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I26_J_0) ).
thf(1326,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(33,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).
thf(588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(429,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ c_Expr_Oexp_OCast ) ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( A
= ( B @ c_Type_Oty_OClass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_0) ).
thf(1639,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ c_Expr_Oexp_OCast ) ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( A
= ( B @ c_Type_Oty_OClass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(364,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = c_Type_Oty_ONT )
| ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( I @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OBoolean ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_20) ).
thf(1481,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = c_Type_Oty_ONT )
| ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( I @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OBoolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(426,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(1629,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__filter_0) ).
thf(731,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(105,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_26) ).
thf(781,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OBoolean )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(172,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrts__hext__mono_0) ).
thf(961,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__refl_0) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(324,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1385,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(5,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_14) ).
thf(510,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).
thf(1777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(294,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).
thf(1308,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(213,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_33) ).
thf(1077,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(417,axiom,
! [A: $i] :
( c_Type_Oty_ONT
!= ( A @ c_Type_Oty_OClass ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I20_J_0) ).
thf(1607,plain,
! [A: $i] :
( c_Type_Oty_ONT
!= ( A @ c_Type_Oty_OClass ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(439,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).
thf(1661,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(832,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(684,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(242,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Orecs_I2_J_0) ).
thf(1161,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(1614,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(225,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(1116,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(232,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).
thf(1133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(44,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_8) ).
thf(620,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(1578,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(168,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( F @ ( A @ hAPP ) )
= ( D @ ( G @ c_Option_Ooption_OSome ) ) )
| ( ( F @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( D @ ( G @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).
thf(950,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( F @ ( A @ hAPP ) )
= ( D @ ( G @ c_Option_Ooption_OSome ) ) )
| ( ( F @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( D @ ( G @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(329,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( I @ ( E @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OBoolean ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_22) ).
thf(1395,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( I @ ( E @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OBoolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(139,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).
thf(865,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(90,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OBoolean )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_7) ).
thf(735,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OBoolean )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_OListMem ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OListMem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert_0) ).
thf(1642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_OListMem ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OListMem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(752,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(378,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_1) ).
thf(1512,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(490,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).
thf(1774,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( B @ ( F @ c_Objects_Ohext ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(466,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I12_J_0) ).
thf(1725,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(285,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).
thf(1280,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(135,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I28_J_0) ).
thf(854,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(292,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_19) ).
thf(1303,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(385,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( E @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OInteger ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_10) ).
thf(1527,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( A @ ( J @ ( E @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OInteger ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(444,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).
thf(1673,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(274,axiom,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__ex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I1_J_0) ).
thf(1248,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__ex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Onull ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_1) ).
thf(790,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Onull ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(157,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).
thf(918,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(437,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( F @ c_Type_Ois__refT )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
| ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCast_0) ).
thf(1657,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
| ~ ( F @ c_Type_Ois__refT )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
| ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).
thf(1693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(50,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).
thf(635,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__map__add_0) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(315,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wts__wts_H_0) ).
thf(1363,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_1) ).
thf(1314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(247,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).
thf(1172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(150,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_14) ).
thf(897,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ( G = c_Type_Oty_ONT )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(497,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I8_J_0) ).
thf(1789,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(62,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( H @ ( G @ ( F @ ( E @ ( D @ ( B @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( C @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__is__class_0) ).
thf(664,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( H @ ( G @ ( F @ ( E @ ( D @ ( B @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
| ( C @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(461,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(1710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(257,axiom,
! [A: $i] :
( ( A @ c_Type_Ois__refT )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__refTE_0) ).
thf(1197,plain,
! [A: $i] :
( ( A @ c_Type_Ois__refT )
| ( A = c_Type_Oty_OVoid )
| ( A = c_Type_Oty_OBoolean )
| ( A = c_Type_Oty_OInteger ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(13,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).
thf(532,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I31_J_0) ).
thf(1065,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(84,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).
thf(720,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
!= ( A @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(244,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).
thf(1165,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(308,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).
thf(1346,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(418,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I9_J_0) ).
thf(1610,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(147,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = H )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).
thf(886,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = H )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(474,axiom,
( ( tc_Value_Oval @ tc_List_Olist @ ( v_vs____ @ c_Nat_Osize__class_Osize ) )
= ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__vs_0) ).
thf(1742,plain,
( ( tc_Value_Oval @ tc_List_Olist @ ( v_vs____ @ c_Nat_Osize__class_Osize ) )
= ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_1) ).
thf(928,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(217,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).
thf(1093,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(310,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Map_Omap__le ) ) ) )
| ( E @ ( D @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__upd_0) ).
thf(1352,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Map_Omap__le ) ) ) )
| ( E @ ( D @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(230,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_15) ).
thf(1129,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(281,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_15) ).
thf(1268,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(238,axiom,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omember ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I1_J_0) ).
thf(1152,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omember ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).
thf(1537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(35,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_31) ).
thf(596,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1019,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(85,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( D @ ( F @ c_Option_Ooption_OSome ) ) )
| ( ( E @ ( A @ hAPP ) )
= ( D @ ( F @ c_Option_Ooption_OSome ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ ( F @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).
thf(723,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( D @ ( F @ c_Option_Ooption_OSome ) ) )
| ( ( E @ ( A @ hAPP ) )
= ( D @ ( F @ c_Option_Ooption_OSome ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ ( F @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(270,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit__asm_35) ).
thf(1236,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(180,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_17) ).
thf(987,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( G = c_Type_Oty_ONT )
| ( G
= ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Type_Oty_OClass )
!= ( B @ c_Type_Oty_OClass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Oinject_0) ).
thf(1532,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Type_Oty_OClass )
!= ( B @ c_Type_Oty_OClass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(137,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).
thf(860,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( A @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__None__map__le_0) ).
thf(644,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( A @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(394,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( D @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_3) ).
thf(1550,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( D @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
| ( tc_Type_Oty @ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Omember ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_2) ).
thf(1505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Omember ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(423,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__def_0) ).
thf(1621,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(303,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).
thf(1331,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
| ~ ( D @ ( C @ ( E @ ( B @ c_Map_Omap__le ) ) ) )
| ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
| ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__le__mapI_0) ).
thf(1184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
| ~ ( D @ ( C @ ( E @ ( B @ c_Map_Omap__le ) ) ) )
| ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
| ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(60,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).
thf(659,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(337,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = c_Type_Oty_ONT )
| ( F
= ( G @ ( I @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( I @ ( H @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_28) ).
thf(1416,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = c_Type_Oty_ONT )
| ( F
= ( G @ ( I @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( G @ ( F @ ( I @ ( H @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(1449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(435,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_4) ).
thf(1653,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(317,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( L @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_OInteger )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Ocase__cong_1) ).
thf(1367,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
= ( D @ ( B @ ( C @ ( L @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
| ( B = c_Type_Oty_OVoid )
| ( B = c_Type_Oty_OBoolean )
| ( B = c_Type_Oty_OInteger )
| ( B = c_Type_Oty_ONT )
| ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(164,axiom,
c_Type_Oty_ONT != c_Type_Oty_OInteger,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I17_J_0) ).
thf(940,plain,
c_Type_Oty_ONT != c_Type_Oty_OInteger,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(158,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_36) ).
thf(923,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).
thf(1737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
| ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtNew_0) ).
thf(1490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
| ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(23,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osplit_8) ).
thf(560,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = c_Type_Oty_OVoid )
| ( G = c_Type_Oty_OBoolean )
| ( G = c_Type_Oty_OInteger )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1887,plain,
$false,
inference(e,[status(thm)],[645,1665,1036,1337,1411,1024,1168,1454,1559,846,518,1179,1110,1686,1586,1501,909,628,1031,666,1295,1200,1211,1596,1068,1522,1443,994,741,1591,878,1437,873,1205,614,677,1705,1426,1671,1655,550,797,715,814,698,1761,945,1063,1458,538,1354,1507,1222,1746,1441,1228,1391,1576,1601,1386,1265,1703,1055,504,1323,802,1455,934,1462,1132,1545,638,1379,1514,1479,969,1572,1741,1398,881,756,1109,623,1334,937,1677,966,1283,821,1682,834,687,956,774,1351,1405,507,1564,602,981,766,1104,1697,1242,849,1651,529,793,925,1306,761,1311,1768,1636,1074,1604,1470,1708,1047,1730,1163,1274,894,1343,1042,1255,1570,1217,1751,729,1021,778,1355,1580,693,630,1619,1370,566,1365,1555,1624,1159,1787,1027,682,1634,710,522,830,1740,842,1402,1360,578,1234,1143,1772,650,1794,1096,1006,1138,593,1755,1118,857,1375,1121,1567,1493,1659,1292,554,1182,1424,1414,1791,1214,1446,1016,1644,1419,884,1329,1612,1039,547,1744,837,701,738,1231,1668,1552,1192,1599,1715,1720,1627,1776,997,1588,1099,1530,1539,1382,569,1429,605,1759,1393,1318,1202,805,508,1695,541,1170,1286,1071,674,1663,1515,953,586,1732,633,1779,662,718,906,1648,1727,573,733,618,1764,513,1146,1754,1154,819,1784,1388,826,1520,1124,1488,1795,1701,641,1503,1271,713,1239,1090,704,1675,611,787,1058,1107,1464,947,1194,900,1408,784,1524,990,1492,1542,1722,616,1690,1574,1011,599,1376,1439,863,1175,811,1080,535,816,520,1029,1149,1460,943,668,1061,1688,1557,552,799,726,626,915,912,1474,959,868,986,1477,1250,1496,851,653,658,1562,1594,1699,695,1245,1176,608,1113,563,1000,1435,1034,1583,1758,1208,1467,680,1684,1277,648,1509,749,516,1340,1472,754,823,1049,1798,690,971,1252,1753,1484,993,1547,776,557,1003,1770,1225,1400,707,1499,1432,1186,502,840,1262,808,1679,544,1300,1452,1085,576,1358,744,1257,703,656,1749,1140,1008,1717,571,1372,876,1617,1543,1766,1485,1052,1421,1316,931,671,1517,759,1126,1189,1157,1321,976,903,524,581,1781,891,1289,844,1734,771,1646,1326,588,963,1639,1481,1629,731,781,961,813,1385,510,1777,1308,1077,1607,1661,1045,832,684,1161,1614,1116,1133,620,1578,950,1395,865,735,1642,752,1512,1774,1725,1280,854,1303,1527,1673,1248,790,918,1657,1693,828,635,796,1363,1314,1172,897,1789,664,1710,1197,532,1065,720,1165,1346,1610,886,1742,928,1093,1352,1129,1268,1152,1537,596,1019,723,871,1236,987,1532,860,644,1550,1505,1621,1331,1184,659,1416,1449,1653,1367,940,923,1737,1490,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV938-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 15:12:15 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.95/1.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.04/1.72 % [INFO] Parsing done (509ms).
% 2.04/1.74 % [INFO] Running in sequential loop mode.
% 3.32/2.34 % [INFO] eprover registered as external prover.
% 3.32/2.35 % [INFO] Scanning for conjecture ...
% 3.59/2.58 % [INFO] Found a conjecture (or negated_conjecture) and 500 axioms. Running axiom selection ...
% 4.47/2.80 % [INFO] Axiom selection finished. Selected 500 axioms (removed 0 axioms).
% 5.54/3.32 % [INFO] Problem is propositional (TPTP CNF).
% 5.54/3.36 % [INFO] Type checking passed.
% 5.54/3.37 % [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 ...
% 18.02/7.91 % External prover 'e' found a proof!
% 18.02/7.91 % [INFO] Killing All external provers ...
% 18.02/7.91 % Time passed: 7311ms (effective reasoning time: 6158ms)
% 18.02/7.92 % Axioms used in derivation (500): cls_ty_Osplit__asm_29, cls_Nil__is__map__conv_1, cls_exp_Osimps_I56_J_0, cls_sees__method__fun_1, cls_WTSeq_0, cls_ty_Osplit__asm_23, cls_ty_Osplit__asm_12, cls_ty_Osplit_9, cls_option_Oinject_0, cls_map__le__upd_0, cls_map__upd__eqD1_0, cls_exp_Osimps_I156_J_0, cls_exp_Osimps_I9_J_1, cls_list_Orecs_I1_J_0, cls_ty_Osplit_4, cls_ty_Osplit__asm_30, cls_dropWhile_Osimps_I1_J_0, cls_default__val_Oinduct_0, cls_Cons__eq__append__conv_5, cls_remove1_Osimps_I2_J_0, cls_listrelp_OCons_0, cls_list__all__append_1, cls_ty_Osplit_24, cls_list__all2__Cons_2, cls_map__add__None_2, cls_list__all_Osimps_I2_J_1, cls_splice_Osimps_I2_J_1, cls_map__add__assoc_0, cls_append__self__conv_0, cls_ty_Osimps_I22_J_0, cls_exp_Osimps_I81_J_0, cls_ty_Ocase__cong_14, cls_distinct__remove1__removeAll_0, cls_ty_Ocase__cong_4, cls_exp_Osimps_I7_J_2, cls_dropWhile__eq__Cons__conv_0, cls_WTrtCallNT_0, cls_ty_Ocase__cong_5, cls_list__all2__eq_1, cls_map__le__trans_0, cls_fun__upd__apply_1, cls_map__upd__Some__unfold_4, cls_ty_Osplit_5, cls_splice__Cons__Cons_0, cls_ty_Osimps_I17_J_0, cls_ty_Osimps_I25_J_0, cls_WTrt__elim__cases_I10_J_0, cls_list_Oinject_0, cls_ty_Osplit_0, cls_tl_Osimps_I1_J_0, cls_map__filter_Osimps_I2_J_1, cls_CHAINED_0, cls_Cons__eq__map__conv_3, cls_exp_Osimps_I11_J_0, cls_WT__elim__cases_I10_J_1, cls_ty_Ocase__cong_25, cls_ty_Osplit__asm_34, cls_map__upd__Some__unfold_3, cls_ty_Osplit_11, cls_ty_Ocase__cong_28, cls_COMBK__def_0, cls_WT__elim__cases_I8_J_0, cls_distinct__filter_0, cls_ty_Ocase__cong_20, cls_ty_Osplit_27, cls_not__Cons__self2_0, cls_exp_Osimps_I28_J_0, cls_ty_Osplit__asm_28, cls_WTs__implies__WTrts_0, cls_ty_Osimps_I5_J_0, cls_option_Osimps_I2_J_0, cls_map__le__iff__map__add__commute_0, clsarity_nat__Orderings_Olinorder, cls_exp_Osimps_I19_J_0, cls_ty_Osimps_I8_J_0, cls_WTrt_H__WTrts_H_Ointros_I13_J_0, cls_not__refTE_0, cls_widen__Class_2, cls_ty_Ocase__cong_8, cls_ty_Osplit_32, cls_removeAll_Osimps_I2_J_0, cls_ty_Ocase__cong_18, cls_remove1__filter__not_0, cls_wts__wts_H_0, cls_ty_Osimps_I13_J_0, cls_exp_Osimps_I170_J_0, cls_exp_Osimps_I154_J_0, cls_WTrt__elim__cases_I6_J_0, cls_append__eq__Cons__conv_4, cls_COMBI__def__raw_0, cls_filter__eq__ConsD_2, cls_eq__Nil__appendI_0, cls_self__append__conv_0, cls_WTrt__elim__cases_I10_J_1, cls_ty_Osplit_16, cls_ty_Osplit__asm_5, cls_ty_Osplit_21, cls_list_Osimps_I5_J_0, cls_List_Omember_Osimps_I2_J_0, cls_ty_Osimps_I20_J_0, cls_same__append__eq_0, cls_append__Cons_0, cls_list__all_Osimps_I2_J_0, cls_map__add__Some__iff_3, cls_map__le__empty_0, cls_Nil__is__map__conv_0, cls_exp_Osimps_I79_J_0, cls_T_H_HsubT_0, cls_hd__append_0, cls_ty_Osplit_36, cls_exp_Osimps_I2_J_1, cls_ty_Ocase__cong_31, cls_exp_Osimps_I8_J_3, cls_length__map_0, cls_filter_Osimps_I2_J_0, cls_sees__method__fun_2, cls_ty_Osplit_14, cls_ty_Osimps_I24_J_0, cls_append__eq__append__conv2_4, cls_exp_Osimps_I11_J_1, cls_widens__trans_0, cls_exp_Osimps_I175_J_0, cls_sorted_Osimps_I3_J_1, cls_WTrt_H__WTrts_H_Ointros_I9_J_0, cls_sorted__takeWhile_0, cls_WTrt__elim__cases_I6_J_3, cls_ty_Osplit__asm_17, cls_list__all2__append2_5, cls_foldr_Osimps_I1_J_0, cls_ty_Osplit_10, cls_ty_Onchotomy_0, cls_ty_Osplit__asm_9, cls_exp_Osimps_I171_J_0, cls_ty_Osplit_25, cls_append1__eq__conv_1, cls_exp_Osimps_I157_J_0, cls_ty_Osplit__asm_26, cls_exp_Osimps_I17_J_0, cls_distinct_Osimps_I2_J_1, cls_hext__trans_0, cls_map__upd__Some__unfold_0, cls_exp_Osimps_I160_J_0, cls_list__all2__Cons_1, cls_distinct_Osimps_I1_J_0, cls_filter__append_0, cls_ty_Ocase__cong_13, cls_splice_Osimps_I2_J_0, cls_widen__refl_0, cls_fun__upd__other_0, cls_exp_Osimps_I84_J_0, cls_RedCall_I3_J_0, cls_ty_Ocase__cong_29, cls_ty_Osplit__asm_15, cls_hext__refl_0, cls_exp_Osimps_I29_J_0, cls_hd__append_1, cls_filter_Osimps_I1_J_0, cls_ty_Osimps_I11_J_0, cls_empty__null_0, cls_takeWhile_Osimps_I1_J_0, cls_distinct__remove1_0, cls_list_Osimps_I4_J_0, cls_exp_Osimps_I9_J_0, cls_exp_Osimps_I85_J_0, cls_ty_Osplit_12, cls_ty_Osplit_6, cls_ty_Osimps_I3_J_0, cls_ty_Ocase__cong_26, cls_append__self__conv2_0, cls_WTrtFAssNT_0, cls_removeAll__filter__not_0, cls_ty_Osplit__asm_19, cls_Nil__is__append__conv_0, cls_not__None__eq_1, cls_list__all__append_2, cls_dropWhile__eq__Cons__conv_1, cls_append__Nil2_0, cls_exp_Osimps_I174_J_0, cls_listrelp_ONil_0, cls_widens__refl_0, cls_ty_Osimps_I9_J_0, cls_ty_Ocase__cong_3, cls_self__append__conv2_0, cls_distinct__map_0, cls_distinct__append_0, cls_map__eq__Cons__conv_3, cls_WTrtFAccNT_0, cls_self__append__conv2_1, cls_map__upds__Cons_0, cls_sees__method__fun_0, cls_WTrt__hext__mono_0, cls_WTrtFAss_0, cls_takeWhile__tail_0, cls_removeAll__append_0, cls_map__le__refl_0, cls_subs_0, cls_WTrt_H__WTrts_H_Ointros_I11_J_0, cls_WTrt_H__WTrts_H_Ointros_I15_J_0, cls_ty_Osimps_I12_J_0, cls_List_Omember_Osimps_I2_J_1, cls_append__is__Nil__conv_2, cls_list_Osplit_0, cls_ty_Osplit__asm_18, cls_exp_Osimps_I61_J_0, cls_map__is__Nil__conv_0, cls_map__le__upds_0, cls_WTrt__env__mono_0, cls_append__eq__append__conv2_5, cls_ty_Osplit_1, cls_WT__elim__cases_I6_J_0, cls_ty_Osplit__asm_33, cls_append__eq__Cons__conv_5, cls_map__upd__nonempty_0, cls_exp_Osimps_I77_J_0, cls_ty_Osplit_13, cls_append__Nil_0, cls_wts_H__wts_0, cls_exp_Osimps_I26_J_0, cls_ty_Ocase__cong_7, cls_fun__upd__triv_0, cls_ty_Osimps_I19_J_0, cls_exp_Osimps_I76_J_0, cls_List_Omember_Osimps_I1_J_0, cls_exp_Osimps_I8_J_2, cls_list__all2__Cons_0, cls_WTrtNew_0, cls_dropWhile__eq__Cons__conv_2, cls_map__upds__Nil2_0, cls_ty_Osimps_I15_J_0, cls_foldl__Cons_0, cls_exp_Osimps_I2_J_0, cls_ty_Osplit__asm_6, cls_map__filter_Osimps_I1_J_0, cls_ty_Osimps_I18_J_0, cls_list__ex_Osimps_I1_J_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_ty_Ocase__cong_17, cls_ty_Osplit_22, cls_exp_Osimps_I186_J_0, cls_rotate__simps_0, cls_RedCall_I4_J_0, cls_map__filter_Osimps_I2_J_0, cls_map__add__None_0, cls_hd__dropWhile_0, cls_ty_Osplit_33, cls_exp_Osimps_I27_J_0, cls_WTrt_H__WTrts_H_Ointros_I2_J_0, cls_ty_Osplit__asm_22, cls_self__append__conv_1, cls_splice__Nil2_0, cls_is__refT__def_1, cls_ty_Osplit__asm_11, cls_map__eq__imp__length__eq_0, cls_ty_Osplit_35, cls_exp_Osimps_I60_J_0, cls_list__all2__appendI_0, cls_list__all2__Nil_1, cls_not__Cons__self_0, cls_map__add__le__mapE_0, cls_fun__upds__append2__drop_0, cls_ty_Osimps_I7_J_0, cls_ty_Ocase__cong_30, cls_rotate1__is__Nil__conv_0, cls_ty_Orecs_I1_J_0, cls_ty_Osplit_19, cls_ty_Osimps_I16_J_0, cls_map__upd__triv_0, cls_ty_Osplit_2, cls_append__same__eq_0, cls_map__upd__Some__unfold_1, cls_ty_Ocase__cong_9, cls_splice_Osimps_I1_J_0, cls_map__add__upds_0, cls_exp_Osimps_I7_J_1, cls_neq__Nil__conv_1, cls_exp_Osimps_I30_J_0, cls_list__all2__def_0, cls_WTrtCall_0, cls_ty_Osimps_I26_J_0, cls_exp_Osimps_I55_J_0, cls_fun__upds__append__drop_0, cls_Nil__is__append__conv_1, cls_WTrtSeq_0, cls_empty__map__add_0, cls_wtabody_0, cls_sorted__Cons_0, cls_distinct1__rotate_0, cls_fun__upd__twist_0, cls_foldr_Osimps_I2_J_0, cls_exp_Osimps_I16_J_0, cls_ty_Osplit__asm_25, cls_ty_Osplit__asm_10, cls_Pair__eq_0, cls_ty_Osplit_29, cls_append__assoc_0, cls_exp_Osimps_I80_J_0, cls_distinct__takeWhile_0, cls_ty_Osplit_30, cls_ty_Ocase__cong_12, cls_ty_Osplit_7, cls_exp_Osimps_I1_J_0, cls_map__upds__Nil1_0, cls_list__all2__Nil2_0, cls_remove1_Osimps_I1_J_0, cls_not__Some__eq_1, cls_exp_Osimps_I35_J_0, cls_ty_Osplit__asm_36, cls_fun__upd__apply_0, cls_WT__implies__WTrt_0, cls_ty_Oinject_0, cls_takeWhile__dropWhile__id_0, cls_map__le__antisym_0, cls_map__append_0, cls_ty_Osplit_18, cls_removeAll_Osimps_I1_J_0, cls_exp_Osimps_I57_J_0, cls_ty_Ocase__cong_10, cls_distinct__append_1, cls_WTrt_H__WTrts_H_Ointros_I18_J_0, cls_ty_Osplit__asm_14, cls_WTCons_0, cls_ty_Osplit__asm_32, cls_ty_Ocase__cong_2, cls_WTrt_H__WTrts_H_Ointros_I8_J_0, cls_ty_Orecs_I2_J_0, cls_exp_Osimps_I53_J_0, cls_ty_Orecs_I3_J_0, cls_tl__append2_0, cls_list__all2__Nil_0, cls_List_Onull_Osimps_I2_J_0, cls_foldr__append_0, cls_sorted_Osimps_I1_J_0, cls_sorted__remove1_0, cls_rotate__simps_1, cls_ty_Ocase__cong_22, cls_distinct__dropWhile_0, cls_WTrtFAcc_0, cls_map__le__imp__upd__le_0, cls_list_Orecs_I2_J_0, cls_sorted__append_0, cls_ty_Oinduct_0, cls_map__add__upd_0, cls_map__is__Nil__conv_1, cls_map__add__SomeD_0, cls_list_Osplit__asm_1, cls_exp_Osimps_I54_J_0, cls_takeWhile_Osimps_I2_J_1, cls_list_Osimps_I3_J_0, cls_exp_Osimps_I8_J_1, cls_ty_Orecs_I4_J_0, cls_WTNew_0, cls_list__all2__Cons1_3, cls_wt_H__wt_0, cls_map__add__empty_0, cls_length__rotate1_0, cls_map_Osimps_I2_J_0, cls_ty_Osimps_I21_J_0, cls_list__ex_Osimps_I2_J_1, cls_exp_Osimps_I34_J_0, cls_rotate1__hd__tl_0, cls_ty_Osplit__asm_7, cls_ty_Osplit_8, cls_ty_Osplit_23, cls_ty_Osimps_I23_J_0, cls_fun__upd__idem_0, cls_widen__trans_0, cls_WTrt__elim__cases_I7_J_1, cls_is__refT__def_2, cls_ty_Osimps_I6_J_0, cls_exp_Osimps_I155_J_0, cls_append__is__Nil__conv_1, cls_ty_Ocase__cong_16, cls_list__all2__append_0, cls_dropWhile_Osimps_I2_J_1, cls_ty_Osplit__asm_21, cls_ty_Osplit_34, cls_fun__upd__idem__iff_0, cls_list__all2__append1_5, cls_concat_Osimps_I2_J_0, cls_ty_Osplit__asm_8, cls_ty_Osplit__asm_13, cls_WTrts__hext__mono_0, cls_WTrtCons_0, cls_list__all2__append_2, cls_exp_Osimps_I9_J_2, cls_Cons__eq__appendI_0, cls_exp_Osimps_I161_J_0, cls_WTrt_H__WTrts_H_Ointros_I12_J_0, cls_ty_Osplit__asm_24, cls_Cons__eq__append__conv_4, cls_exp_Osimps_I7_J_0, cls_fun__upd__same_0, cls_append__is__Nil__conv_0, cls_list_Oinject_1, cls_ty_Orecs_I5_J_0, cls_ty_Ocase__cong_24, cls_exp_Osimps_I45_J_0, cls_exp_Osimps_I8_J_0, cls_sees__method__fun_3, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_append__eq__appendI_0, cls_list__all_Osimps_I2_J_2, cls_wtes_0, cls_ty_Osplit__asm_35, cls_map__upd__Some__unfold_2, cls_exp_Osimps_I44_J_0, cls_ty_Ocase__cong_0, cls_exp_Osimps_I18_J_0, cls_foldl__append_0, cls_ty_Ocase__cong_27, cls_remove1_Osimps_I2_J_1, cls_list__all_Osimps_I1_J_0, cls_ty_Ocase__cong_11, cls_WTrt_H__WTrts_H_Ointros_I1_J_0, cls_option_Osimps_I3_J_0, cls_ty_Osplit_17, cls_WTCall_0, cls_hd_Osimps_0, cls_sees__method__idemp_0, cls_exp_Osimps_I52_J_0, cls_list_Osplit_1, cls_exp_Osimps_I31_J_0, cls_ty_Ocase__cong_15, cls_length__vs_0, cls_WTrt__elim__cases_I8_J_0, cls_List_Omember_Osimps_I2_J_2, cls_exp_Osimps_I187_J_0, cls_ty_Oexhaust_0, cls_ty_Osplit__asm_20, cls_ty_Ocase__cong_6, cls_list__all2__eq_0, cls_RedCall_I5_J_0, cls_WT__elim__cases_I10_J_0, cls_ty_Osplit_28, cls_wt__env__mono_0, cls_sorted_Osimps_I2_J_0, cls_ty_Osimps_I2_J_0, cls_Nil__is__append__conv_2, cls_method_0, cls_tl_Osimps_I2_J_0, cls_foldl__Nil_0, cls_ty_Osplit_26, cls_sorted__append_1, cls_ty_Osimps_I14_J_0, cls_map__add__Some__iff_2, cls_ty_Osimps_I10_J_0, cls_elem_0, cls_ty_Osplit__asm_4, cls_wt__wt_H_0, cls_takeWhile_Osimps_I2_J_0, cls_map__add__find__right_0, cls_list__ex_Osimps_I2_J_0, cls_ty_Ocase__cong_19, cls_ty_Osimps_I4_J_0, cls_map__le__iff__map__add__commute_1, cls_map__le__map__add_0, cls_sees__method__is__class_0, cls_ty_Ocase__cong_1, cls_map__add__SomeD_1, cls_COMBI__def_0, cls_ty_Osplit__asm_27, cls_ty_Osplit_31, cls_list__ex_Osimps_I2_J_2, cls_ty_Osplit_15, cls_fun__upd__upd_0, cls_exp_Osimps_I78_J_0, cls_filter_Osimps_I2_J_1, cls_Pair__eq_1, cls_map__filter__conv_0, cls_sorted__dropWhile_0, cls_distinct1__rotate_1, cls_Cons__eq__filterD_2, cls_upd__None__map__le_0, cls_insert_0, cls_widens__Cons_3, cls_removeAll_Osimps_I2_J_1, cls_list__all2__Cons2_3, cls_append1__eq__conv_0, cls_list_Osimps_I2_J_0, cls_ty_Oinducts_0, cls_WTrt__elim__cases_I7_J_0, cls_WTrtCast_0, cls_map__add__le__mapI_0, cls_list__all2__append_1, cls_dropWhile_Osimps_I2_J_0, cls_WTrt_H__WTrts_H_Ointros_I10_J_0, cls_exp_Osimps_I3_J_0, cls_map__add__None_1, cls_ty_Ocase__cong_21, cls_WT__elim__cases_I6_J_2, cls_ty_Osplit_3, cls_fun__upd__idem__iff_1, cls_WTrt__elim__cases_I8_J_1, cls_ty_Osplit_20, cls_list__all__append_0, cls_ty_Osplit__asm_16, cls_ty_Osplit__asm_31, cls_empty__null_1, cls_ty_Ocase__cong_23, cls_length__pns_0
% 18.02/7.92 % No. of inferences in proof: 1003
% 18.02/7.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 7311 ms resp. 6158 ms w/o parsing
% 19.36/8.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.36/8.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------