%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL807-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:53:01 AM UTC 2026
% Result : Unsatisfiable 11.66s 14.11s
% Output : Refutation 12.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 266
% Syntax : Number of formulae : 533 ( 165 unt; 0 typ; 0 def)
% Number of atoms : 1079 ( 304 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 10022 ( 566 ~; 546 |; 0 &;8910 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 32 con; 0-5 aty)
% Number of variables : 1490 ( 0 ^;1490 !; 0 ?;1490 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
v_thesis____: $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Type_Otyping_decl,type,
c_Type_Otyping: $i ).
thf(c_Type_Oshift_decl,type,
c_Type_Oshift: $i > $i ).
thf(tc_Type_Otype_decl,type,
tc_Type_Otype: $i ).
thf(v_e_____decl,type,
v_e____: $i ).
thf(v_i_____decl,type,
v_i____: $i ).
thf(v_T_____decl,type,
v_T____: $i ).
thf(v_b_____decl,type,
v_b____: $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Nat_Osemiring__char__0_decl,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(c_Lambda_OdB_OVar_decl,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(c_List_Ofoldl_decl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_List_Ofoldr_decl,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(c_Lambda_OdB_OApp_decl,type,
c_Lambda_OdB_OApp: $i ).
thf(c_Lambda_OdB_OAbs_decl,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tc_Lambda_OdB_decl,type,
tc_Lambda_OdB: $i ).
thf(c_List_Olistsum_decl,type,
c_List_Olistsum: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Predicate_Oconversep_decl,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_fequal_decl,type,
c_fequal: $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Osemigroup__add_decl,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_List_Olistsp_decl,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Transitive__Closure_Ortranclp_decl,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(c_OrderedGroup_Oab__semigroup__add_decl,type,
c_OrderedGroup_Oab__semigroup__add: $i > $i > $o ).
thf(c_Lambda_Osubst_decl,type,
c_Lambda_Osubst: $i ).
thf(c_Type_Otypings_decl,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(c_Type_Otype_OFun_decl,type,
c_Type_Otype_OFun: $i ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_and_decl,type,
c_and: $i ).
thf(c_All_decl,type,
c_All: $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_implies_decl,type,
c_implies: $i ).
thf(c_InductTermi_OIT_decl,type,
c_InductTermi_OIT: $i ).
thf(c_Ex_decl,type,
c_Ex: $i > $i ).
thf(v_bs_____decl,type,
v_bs____: $i ).
thf(c_Lambda_Obeta_decl,type,
c_Lambda_Obeta: $i ).
thf(c_ListOrder_Ostep1_decl,type,
c_ListOrder_Ostep1: $i > $i > $i ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(c_Type_Osko__Type__Xlist__app__typeE__1__1_decl,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).
thf(c_Lambda_Olift_decl,type,
c_Lambda_Olift: $i ).
thf(v_u_____decl,type,
v_u____: $i ).
thf(v_T_H_H_____decl,type,
v_T_H_H____: $i ).
thf(v_Ts_____decl,type,
v_Ts____: $i ).
thf(v_T_H_____decl,type,
v_T_H____: $i ).
thf(c_Wellfounded_Oaccp_decl,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(v_ea_______decl,type,
v_ea______: $i ).
thf(v_ua_______decl,type,
v_ua______: $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(c_Type_Osko__Type__Xvar__app__typesE__1__1_decl,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).
thf(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1_decl,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xvar__app__types__1__1_decl,type,
c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xlist__app__typeD__1__1_decl,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).
thf(v_sko__local__XCons__1__1_decl,type,
v_sko__local__XCons__1__1: $i > $i > $i > $i > $i ).
thf(v_n_____decl,type,
v_n____: $i ).
thf(v_rs_____decl,type,
v_rs____: $i ).
thf(v_sko__local__XCons__Xhyps__1__1_decl,type,
v_sko__local__XCons__Xhyps__1__1: $i > $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xtyping__elims__2__1_decl,type,
c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_List_Omap_decl,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(v_as_____decl,type,
v_as____: $i ).
thf(v_ia_______decl,type,
v_ia______: $i ).
thf(v_T_Ha_______decl,type,
v_T_Ha______: $i ).
thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_decl,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(v_sko__CHAINED__1_decl,type,
v_sko__CHAINED__1: $i > $i > $i > $i > $i ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= C )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= C )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(365,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)],[47]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
thf(846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(666,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(40,axiom,
tc_nat @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(352,plain,
tc_nat @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(20,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(308,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_List_Olistsum ) )
= ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_List_Olistsum ) )
= ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olistsum ) )
= ( A @ ( C @ c_List_Olistsum ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
thf(861,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olistsum ) )
= ( A @ ( C @ c_List_Olistsum ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(55,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(384,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(89,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Otype @ ( tc_Type_Otype @ ( D @ ( E @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ c_Type_Otypings ) ) )
| ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Type_Otype @ ( tc_Type_Otype @ ( D @ ( E @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ c_Type_Otypings ) ) )
| ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(242,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( G @ ( C @ ( A @ ( E @ ( F @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( F @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( v_T____
!= ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(814,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( G @ ( C @ ( A @ ( E @ ( F @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( F @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( v_T____
!= ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(747,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(194,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(709,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(288,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_List_Olistsum ) )
= ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_0) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_List_Olistsum ) )
= ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__add ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add_Oadd__left__commute_0) ).
thf(651,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__add ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_b____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( v_b____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).
thf(570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_b____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( v_b____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(35,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(344,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(243,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( F @ c_List_Olist_OCons ) ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( F @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(817,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( F @ c_List_Olist_OCons ) ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( F @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(559,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(261,axiom,
! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(853,plain,
! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(148,axiom,
! [A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(606,plain,
! [A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(27,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).
thf(325,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(756,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(142,axiom,
! [A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(591,plain,
! [A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(156,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( G @ ( C @ ( B @ ( E @ ( F @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( F @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( v_T____
!= ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(623,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( G @ ( C @ ( B @ ( E @ ( F @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( F @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( v_T____
!= ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(646,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(834,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(41,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(353,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(38,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(348,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(687,plain,
! [B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(280,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(634,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(205,axiom,
v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(734,plain,
v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(225,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(774,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(312,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(678,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(172,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
thf(661,plain,
v_n____ = v_i____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(31,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(334,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(302,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(129,axiom,
! [B: $i,A: $i] :
~ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(561,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_Lambda_OdB_OAbs ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( C @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(435,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_Lambda_OdB_OAbs ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( C @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(174,axiom,
v_T_H____ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nT_0) ).
thf(665,plain,
v_T_H____ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(461,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
| ~ ( A @ class_Nat_Osemiring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
| ~ ( A @ class_Nat_Osemiring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
thf(697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(317,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(167,axiom,
v_i____ @ ( v_e____ @ ( v_b____ @ ( v_T____ @ v_sko__local__XCons__1__1 ) ) ) @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_I1_J_1) ).
thf(650,plain,
v_i____ @ ( v_e____ @ ( v_b____ @ ( v_T____ @ v_sko__local__XCons__1__1 ) ) ) @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__add ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add_Oadd__commute_0) ).
thf(615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__add ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(200,axiom,
tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_bs____ @ ( v_i____ @ ( v_u____ @ ( c_Lambda_Osubst @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Lambda_Olift @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(725,plain,
tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_bs____ @ ( v_i____ @ ( v_u____ @ ( c_Lambda_Osubst @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Lambda_Olift @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(403,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Predicate_Oconversep ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Predicate_Oconversep ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(593,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(150,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ c_Type_Otypings ) ) )
| ~ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_1) ).
thf(610,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( A @ c_Type_Otypings ) ) )
| ~ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ c_Transitive__Closure_Ortranclp ) )
= ( B @ ( A @ c_Transitive__Closure_Ortranclp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(420,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ c_Transitive__Closure_Ortranclp ) )
= ( B @ ( A @ c_Transitive__Closure_Ortranclp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olistsum ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
thf(339,plain,
! [A: $i] :
( ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olistsum ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(91,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(476,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)],[91]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(637,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ c_List_Olistsp ) ) )
| ( C @ ( B @ tc_List_Olist @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists__accD_0) ).
thf(547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ c_List_Olistsp ) ) )
| ( C @ ( B @ tc_List_Olist @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(554,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(214,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(753,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(254,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(837,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ c_Lambda_OdB_OVar )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(393,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OVar )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(169,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( C @ c_Type_Otypings ) ) )
| ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Type_Otype @ ( tc_Type_Otype @ ( B @ ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_0) ).
thf(654,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( C @ c_Type_Otypings ) ) )
| ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_Type_Otype @ ( tc_Type_Otype @ ( B @ ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_b____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( v_b____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_b____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( v_b____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(170,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(765,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(61,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(398,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)],[61]) ).
thf(179,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(674,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)],[179]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(718,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(15,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(298,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(212,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( C @ ( D @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(750,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( C @ ( D @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(425,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(824,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(7,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(279,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(107,axiom,
v_T____ @ ( v_u____ @ ( v_e____ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
thf(513,plain,
v_T____ @ ( v_u____ @ ( v_e____ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(73,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(430,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(244,axiom,
v_T_Ha______ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( v_T____ @ ( v_ia______ @ ( v_ea______ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).
thf(819,plain,
v_T_Ha______ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( v_T____ @ ( v_ia______ @ ( v_ea______ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(66,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(413,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(248,axiom,
! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(826,plain,
! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
thf(577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(445,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(382,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(134,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(572,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= B )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(466,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= B )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(704,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(39,axiom,
! [A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
= ( A @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(350,plain,
! [A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
= ( A @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(672,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(681,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
thf(784,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
= ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
= ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(155,axiom,
( v_T____
= ( tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( v_Ts____ @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_T_H_H____ @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_0) ).
thf(621,plain,
( v_T____
= ( tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( v_Ts____ @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_T_H_H____ @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(483,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(157,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( A @ c_List_Olist_OCons ) ) @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(626,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( A @ c_List_Olist_OCons ) ) @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ tc_List_Olist @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__acc__step1I_0) ).
thf(769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ tc_List_Olist @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(176,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(668,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(330,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(36,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(345,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(695,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(455,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(19,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(306,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(130,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(563,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(299,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)],[16]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(267,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(260,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(851,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
= ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(505,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
= ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(438,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(115,axiom,
tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( v_Ts____ @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_T_H_H____ @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( v_u____ @ ( v_e____ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_H_0) ).
thf(531,plain,
tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( v_Ts____ @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_T_H_H____ @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( v_u____ @ ( v_e____ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(241,axiom,
! [A: $i] :
( ~ ( A @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
thf(812,plain,
! [A: $i] :
( ~ ( A @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(516,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(342,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)],[34]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(355,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(125,axiom,
v_T____ @ ( v_ua______ @ ( v_ea______ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
thf(553,plain,
v_T____ @ ( v_ua______ @ ( v_ea______ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(253,axiom,
v_T_H_H____ @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argT_0) ).
thf(836,plain,
v_T_H_H____ @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(166,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(648,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__add ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( D @ ( D @ ( B @ ( C @ ( A @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add_Ofoldr__conv__foldl_0) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__add ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( D @ ( D @ ( B @ ( C @ ( A @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(246,axiom,
v_i____ @ ( v_e____ @ ( v_b____ @ ( v_T____ @ v_sko__CHAINED__1 ) ) ) @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
thf(823,plain,
v_i____ @ ( v_e____ @ ( v_b____ @ ( v_T____ @ v_sko__CHAINED__1 ) ) ) @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(282,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( A @ ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) )
= ( A @ ( A @ ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(64,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(409,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(310,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(78,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(441,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(463,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(45,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(359,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)],[45]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(544,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( A
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( B @ ( A @ c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 ) ) ) @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( A
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( B @ ( A @ c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 ) ) ) @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) )
| ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(370,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(146,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( F @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( F @ ( E @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = D )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(600,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( F @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( F @ ( E @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(612,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(127,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(556,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(177,axiom,
v_i____ @ ( v_e____ @ ( v_b____ @ ( v_T____ @ v_sko__local__XCons__Xhyps__1__1 ) ) ) @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_Ohyps_I1_J_1) ).
thf(671,plain,
v_i____ @ ( v_e____ @ ( v_b____ @ ( v_T____ @ v_sko__local__XCons__Xhyps__1__1 ) ) ) @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(495,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ tc_List_Olist @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists__accI_0) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ tc_List_Olist @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(771,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(48,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(368,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(632,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(230,axiom,
v_Ts____ @ ( v_as____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ c_Type_Otypings ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argsT_0) ).
thf(786,plain,
v_Ts____ @ ( v_as____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ c_Type_Otypings ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(228,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( F @ c_List_Olist_OCons ) ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = C )
| ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(781,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( F @ c_List_Olist_OCons ) ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = C )
| ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
= ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
= ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(190,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__add ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add_Oadd__ac_I1_J_0) ).
thf(699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__add ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(75,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(433,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(37,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(346,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(154,axiom,
v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(620,plain,
v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(213,axiom,
tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( v_Ts____ @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_a____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_headT_0) ).
thf(752,plain,
tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( v_Ts____ @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_a____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(410,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)],[65]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(735,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OVar )
= B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OVar )
= B )
| ( ( A @ c_Lambda_OdB_OVar )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(232,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(790,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( C @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
| ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( C @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(603,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)],[147]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( C @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(801,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( C @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( A @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(268,plain,
! [A: $i] :
( ~ ( A @ ( v_b____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(532,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(358,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(807,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_b____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( v_b____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_I_0) ).
thf(767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_b____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( v_b____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(332,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)],[30]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
thf(427,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(199,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(723,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_ListOrder_Ostep1 ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs )
= B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Lambda_OdB_OAbs )
= B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(102,axiom,
! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(501,plain,
! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(49,axiom,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(369,plain,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(255,axiom,
! [A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(839,plain,
! [A: $i] :
( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
| ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(202,axiom,
tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( v_Ts____ @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_T_H_H____ @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( v_n____ @ c_Lambda_OdB_OVar @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_varT_0) ).
thf(728,plain,
tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( v_Ts____ @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_T_H_H____ @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( v_n____ @ c_Lambda_OdB_OVar @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( C @ c_Lambda_OdB_OVar ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( C @ c_Lambda_OdB_OVar ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(95,axiom,
tc_Lambda_OdB @ ( v_bs____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ ( tc_Type_Otype @ c_Ex @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ ( c_InductTermi_OIT @ ( tc_nat @ ( tc_bool @ ( tc_Lambda_OdB @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( v_T____ @ ( c_Type_Otyping @ ( tc_bool @ ( tc_Type_Otype @ ( tc_Lambda_OdB @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_implies @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ ( c_implies @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( v_T____ @ ( tc_Type_Otype @ c_Type_Oshift @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ ( tc_nat @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_implies @ ( tc_nat @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_nat @ c_COMBS ) ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBS ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ c_All @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ c_All @ ( tc_Type_Otype @ ( tc_bool @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ c_All @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_All @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_and @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_List_Olistsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(486,plain,
tc_Lambda_OdB @ ( v_bs____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ ( tc_Type_Otype @ c_Ex @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ ( c_InductTermi_OIT @ ( tc_nat @ ( tc_bool @ ( tc_Lambda_OdB @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( v_T____ @ ( c_Type_Otyping @ ( tc_bool @ ( tc_Type_Otype @ ( tc_Lambda_OdB @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_implies @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ ( c_implies @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( v_T____ @ ( tc_Type_Otype @ c_Type_Oshift @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ ( tc_nat @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_implies @ ( tc_nat @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_nat @ c_COMBS ) ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBS ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ c_All @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ c_All @ ( tc_Type_Otype @ ( tc_bool @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ c_All @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_All @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_and @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_List_Olistsp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_fequal @ c_Predicate_Oconversep ) ) )
= ( A @ c_fequal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(337,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_fequal @ c_Predicate_Oconversep ) ) )
= ( A @ c_fequal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(42,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(354,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(659,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(639,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(676,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
| ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(46,axiom,
tc_nat @ class_OrderedGroup_Osemigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(364,plain,
tc_nat @ class_OrderedGroup_Osemigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(867,plain,
$false,
inference(e,[status(thm)],[809,629,365,846,666,352,523,308,379,511,861,385,384,550,797,715,472,814,747,709,288,320,651,841,417,570,702,344,542,817,559,853,606,325,492,756,591,376,623,646,834,514,353,480,348,574,687,280,634,734,774,312,452,678,661,761,534,334,302,598,820,561,693,275,729,566,435,665,461,285,583,830,519,697,317,650,615,725,403,388,593,610,420,499,339,476,637,547,554,753,837,393,738,654,721,779,792,508,657,765,398,674,794,718,298,750,618,425,824,856,745,279,689,513,430,819,732,743,579,413,826,577,641,445,382,572,787,466,804,704,350,672,406,681,784,303,271,758,323,621,483,848,626,769,668,330,345,858,799,726,521,827,695,455,608,306,563,299,431,267,851,505,438,490,531,663,812,516,342,355,754,553,836,648,487,458,823,776,525,712,295,282,707,414,327,409,310,441,502,463,359,643,544,585,370,600,864,314,612,497,556,539,671,581,495,759,771,368,844,390,632,786,781,588,699,568,290,433,478,763,346,549,536,832,684,620,752,447,410,854,273,735,422,790,373,603,801,268,532,283,358,807,474,767,332,427,596,528,723,442,501,369,395,839,728,740,277,691,486,337,469,354,659,639,676,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL807-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/10.41 % Computer : n016.cluster.edu
% 0.12/10.41 % Model : x86_64 x86_64
% 0.12/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.41 % Memory : 8046.5625MB
% 0.12/10.41 % OS : Linux 6.8.0-71-generic
% 0.12/10.41 % CPULimit : 300
% 0.12/10.41 % WCLimit : 300
% 0.12/10.41 % DateTime : Fri Sep 25 23:41:41 UTC 2026
% 0.12/10.42 % CPUTime :
% 0.12/10.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.17/10.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.87/11.33 % [INFO] Parsing done (336ms).
% 1.87/11.35 % [INFO] Running in sequential loop mode.
% 2.82/11.77 % [INFO] eprover registered as external prover.
% 2.82/11.78 % [INFO] Scanning for conjecture ...
% 3.34/11.96 % [INFO] Found a conjecture (or negated_conjecture) and 271 axioms. Running axiom selection ...
% 4.21/12.14 % [INFO] Axiom selection finished. Selected 264 axioms (removed 7 axioms).
% 4.97/12.37 % [INFO] Problem is propositional (TPTP CNF).
% 4.97/12.39 % [INFO] Type checking passed.
% 5.36/12.40 % [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 ...
% 11.66/14.10 % External prover 'e' found a proof!
% 11.66/14.10 % [INFO] Killing All external provers ...
% 11.66/14.10 % Time passed: 3540ms (effective reasoning time: 2747ms)
% 11.66/14.10 % Axioms used in derivation (264): cls_add__0__left_0, cls_xt1_I9_J_0, cls_MI1_0, cls_subst__lt_0, cls_dB_Osimps_I6_J_0, cls_apps__eq__Abs__conv_0, cls_length__0__conv_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_add__less__cancel__left_1, cls_subst__App_0, cls_Cons__step1__Cons_0, cls_Var__eq__apps__conv_1, cls_lists__accI_0, cls_of__nat__0_0, cls_subst__eq_0, cls_class__ringb_Oadd__r0__iff_1, cls_lift_Osimps_I2_J_0, cls_dB_Osimps_I8_J_0, cls_subject__reduction_0, cls_termi__implies__IT_0, cls_ab__semigroup__add_Oadd__commute_0, cls_list_Oinject_0, cls_Cons_I1_J_1, cls_Cons_Ohyps_I1_J_1, cls_conversepD_0, cls_CHAINED_0, cls_var__app__typesE_0, clsarity_fun__Orderings_Oorder, cls_class__semiring_Osemiring__rules_I20_J_0, cls_pos__add__strict_0, cls_accp__downwards_0, cls_listsum_Osimps_I1_J_0, cls_add__strict__right__mono_0, cls_uT_H_0, cls_of__nat__less__iff_0, cls_MI2_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_rtrancl__beta__Abs_0, cls_uIT_0, cls_not__Cons__self2_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_not__step1__Nil_0, cls_appR_0, cls_listsp_ONil_0, cls_comm__monoid__add_Omult__1__right_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_of__nat__0__less__iff_0, cls_add__cancel__21_1, cls_add__left__cancel_0, cls_head__Var__reduction_1, cls_rtranclp__trans_0, cls_Cons__step1__Cons_5, cls_beta_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_Abs_0, cls_foldl__foldr1_0, clsarity_nat__Ring__and__Field_Oordered__semidom, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_gr0I_0, cls_lift__type_0, cls_foldr_Osimps_I1_J_0, cls_nat__less__cases_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_Var__apps__eq__Var__apps__conv_0, cls_gr__implies__not0_0, cls_order__less__asym_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_headT_0, cls_listsum_Osimps_I2_J_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_shift__eq_0, cls_length__greater__0__conv_1, cls_Var_I2_J_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_dB_Osimps_I3_J_0, cls_foldl__absorb0_0, cls_linorder__neqE__nat_0, clsarity_bool__Orderings_Oorder, cls_subst__Var_2, cls_xt1_I10_J_0, cls_add__less__cancel__right_1, cls_Var__apps__eq__Var__apps__conv_1, cls_class__semiring_Osemiring__rules_I6_J_0, cls_CHAINED_1, cls_Var__eq__apps__conv_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_typing__elims_I2_J_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_CHAINED_0_01, cls_add__strict__left__mono_0, cls_length__0__conv_0, cls_App__eq__foldl__conv_0, cls_type_Osimps_I2_J_1, cls_dB_Osimps_I4_J_0, cls_Cons__step1__Cons_1, cls_typing__elims_I1_J_0, cls_class__semiring_Oadd__a_0, cls_var__app__types_0, cls_Var__IT_0, cls_Cons__step1__Cons_3, cls_subject__reduction_H_0, cls_var__app__typesE_1, cls_Var_I3_J_0, cls_converse__rtranclp__into__rtranclp_0, cls_list__app__typeD_1, cls_apps__preserves__betas_0, cls_of__nat__eq__iff_0, cls_argT_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_comm__monoid__add_Omult__commute_0, cls_foldl__Cons_0, cls_add__right__cancel_0, cls_App_0, cls_class__semiring_Oadd__0_0, clsarity_nat__Nat_Osemiring__char__0, cls_nT_0, cls_True_0, cls_head__Var__reduction_0, cls_add__strict__mono_0, cls_Cons_I1_J_0, cls_of__nat__0__less__iff_1, cls_IT__implies__termi_0, cls_apps__eq__Abs__conv_2, cls_add__cancel__21_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_uT_0, cls_not__Cons__self_0, cls_conversep__conversep_0, cls_dB_Osimps_I1_J_0, cls_Abs__App__neq__Var__apps_0, cls_rtrancl__beta__App_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_length__greater__0__conv_0, cls_subst__Var_1, clsarity_bool__Orderings_Opreorder, cls_Cons__step1__Cons_2, cls_rtrancl__beta__AppL_0, cls_neq__Nil__conv_1, cls_type_Osimps_I2_J_0, cls_Nitpick_Ortranclp__def_1, cls_varT_0, cls_neq0__conv_1, cls_not__Nil__step1_0, cls_foldr_Osimps_I2_J_0, cls_apps__eq__Abs__conv_1, cls_add__less__cancel__right_0, cls_listsum_0, cls_lift__preserves__beta_0, clsarity_nat__Orderings_Opreorder, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_Var__apps__neq__Abs__apps_0, cls_subst__lemma_0, cls_foldl__assoc_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_less__not__refl_0, cls_conversep_Ointros_0, cls_linorder__neqE__ordered__idom_0, cls_class__ringb_Oadd__cancel_0, cls_dB_Osimps_I2_J_1, cls_accp__downwards__aux_0, cls_foldl__foldr1__lemma_0, cls_Cons__step1__Cons_4, cls_var__app__types_1, cls_class__ringb_Oadd__r0__iff_0, cls_even__less__0__iff_1, cls_lift__preserves__beta_H_0, cls_list__app__typeD_0, cls_CHAINED_0_02, cls_rtranclp_Ortrancl__refl_0, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_ab__semigroup__add_Oadd__left__commute_0, cls_App__eq__foldl__conv_2, cls_Cons__acc__step1I_0, cls_add__neg__neg_0, cls_double__eq__0__iff_0, cls_accp__downward_0, cls_Abs__eq__apps__conv_2, cls_rtranclp__idemp_0, cls_list__app__typeE_1, cls_typing_OVar_0, cls_lift__IT_0, cls_IT_OVar_0, cls_listsum__foldr_0, cls_abs_0, cls_Var_I4_J_0, cls_comm__monoid__add_Omult__left__commute_0, cls_apps__eq__tail__conv_0, cls_typing__elims_I2_J_1, cls_lists__accD_0, cls_apps__preserves__beta2_0, cls_comm__monoid__add_Omult__1_0, cls_list__app__typeI_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_accp_Ocases_0, cls_apps__preserves__beta_0, cls_order__less__irrefl_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_class__semiring_Oadd__c_0, cls_Abs__eq__apps__conv_0, cls_list_Oinject_1, cls_foldr__conv__foldl_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_App__eq__foldl__conv_4, clsarity_fun__Orderings_Opreorder, cls_add__pos__pos_0, cls_not__less0_0, cls_dB_Osimps_I5_J_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_conversep__eq_0, cls_add__less__cancel__left_0, cls_subst__Var__IT_0, cls_shift__gt_0, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_foldl__Nil_0, cls_Lambda_0, cls_list__app__typeE_0, cls_lift_Osimps_I1_J_0, cls_ab__semigroup__add_Oadd__ac_I1_J_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_rtranclp_Ortrancl__into__rtrancl_0, cls_that_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_I_0, cls_subst__lift_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Abs__eq__apps__conv_1, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_subst__preserves__beta2_0, cls_ab__semigroup__add_Ofoldr__conv__foldl_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_T_0, cls_conversep__iff_1, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_subst__preserves__beta2_H_0, cls_dB_Osimps_I9_J_0, cls_list_Osimps_I2_J_0, cls_rtranclp__converseD_0, clsarity_nat__OrderedGroup_Osemigroup__add, cls_conversep_Ocases_0, cls_even__less__0__iff_0, cls_rtranclp__converseI_0, cls_double__induction__lemma_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_argsT_0, cls_rtrancl__beta__AppR_0, cls_of__nat__less__0__iff_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_r__into__rtranclp_0, cls_subst__preserves__beta_H_0
% 11.66/14.10 % No. of inferences in proof: 533
% 11.66/14.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3540 ms resp. 2747 ms w/o parsing
% 12.70/14.38 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.70/14.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------