%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL826-1 : 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 : n013.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 07:53:06 AM UTC 2026
% Result : Unsatisfiable 29.43s 7.24s
% Output : Refutation 28.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 404
% Syntax : Number of formulae : 830 ( 315 unt; 0 typ; 0 def)
% Number of atoms : 1582 ( 597 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 13562 ( 758 ~; 740 |; 0 &;12064 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 107 ( 104 usr; 33 con; 0-5 aty)
% Number of variables : 2104 ( 0 ^;2104 !; 0 ?;2104 :)
% Comments :
%------------------------------------------------------------------------------
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_x_decl,type,
v_x: $i ).
thf(v_xc_decl,type,
v_xc: $i ).
thf(v_T_____decl,type,
v_T____: $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(v_xa_decl,type,
v_xa: $i ).
thf(c_InductTermi_OIT_decl,type,
c_InductTermi_OIT: $i ).
thf(v_xb_decl,type,
v_xb: $i ).
thf(c_Lambda_Osubst_decl,type,
c_Lambda_Osubst: $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(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_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
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_List_Ofoldr_decl,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $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_Omap_decl,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_Fun_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_Lambda_Osubstn_decl,type,
c_Lambda_Osubstn: $i > $i > $i > $i ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(c_Fun_Ofcomp_decl,type,
c_Fun_Ofcomp: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Oid_decl,type,
c_Fun_Oid: $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Lambda_OdB_OdB__size_decl,type,
c_Lambda_OdB_OdB__size: $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_Nat_Ocompow_decl,type,
c_Nat_Ocompow: $i > $i > $i > $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_Nat_Osemiring__char__0_decl,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_decl,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $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(c_Lambda_Oliftn_decl,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
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(v_n_____decl,type,
v_n____: $i ).
thf(v_i_____decl,type,
v_i____: $i ).
thf(c_Transitive__Closure_Ortranclp_decl,type,
c_Transitive__Closure_Ortranclp: $i > $i > $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_Type_Otype_Otype__size_decl,type,
c_Type_Otype_Otype__size: $i > $i ).
thf(v_e_____decl,type,
v_e____: $i ).
thf(v_sko__local__XCons__1__1_decl,type,
v_sko__local__XCons__1__1: $i > $i > $i > $i > $i ).
thf(c_Lambda_Obeta_decl,type,
c_Lambda_Obeta: $i ).
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(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i ).
thf(v_u_____decl,type,
v_u____: $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_List_Olistsp_decl,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_Lambda_Osko__Lambda__Xbeta__cases__2__1_decl,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(t_a_decl,type,
t_a: $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__Xtyping__elims__3__1_decl,type,
c_Type_Osko__Type__Xtyping__elims__3__1: $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xtyping__elims__3__2_decl,type,
c_Type_Osko__Type__Xtyping__elims__3__2: $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(c_ListOrder_Ostep1_decl,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
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_implies_decl,type,
c_implies: $i ).
thf(c_Ex_decl,type,
c_Ex: $i > $i ).
thf(v_as_____decl,type,
v_as____: $i ).
thf(v_rs_____decl,type,
v_rs____: $i ).
thf(v_T_H_____decl,type,
v_T_H____: $i ).
thf(v_sko__CHAINED__1_decl,type,
v_sko__CHAINED__1: $i > $i > $i > $i > $i ).
thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_decl,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(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(c_Type_Osko__Type__Xabs__typeE__1__1_decl,type,
c_Type_Osko__Type__Xabs__typeE__1__1: $i > $i > $i ).
thf(c_Type_Osko__Type__Xabs__typeE__1__2_decl,type,
c_Type_Osko__Type__Xabs__typeE__1__2: $i > $i > $i ).
thf(v_ia_______decl,type,
v_ia______: $i ).
thf(v_T_Ha_______decl,type,
v_T_Ha______: $i ).
thf(277,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(1036,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)],[277]) ).
thf(271,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(1024,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)],[271]) ).
thf(346,axiom,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(1190,plain,
! [A: $i] :
( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(35,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(479,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)],[35]) ).
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 @ ( 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(846,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)],[195]) ).
thf(215,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(893,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)],[215]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ( tc_Type_Otype @ ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Type_Otype @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_Type_Otype @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osize_I4_J_0) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( tc_Type_Otype @ ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Type_Otype @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_Type_Otype @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= C )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I1_J_0) ).
thf(555,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= C )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(666,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(481,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(1168,plain,
! [A: $i] :
( ( A @ c_Suc )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(157,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(760,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)],[157]) ).
thf(401,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Suc @ ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ ( E @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__subst_0) ).
thf(1315,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Suc @ ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( C @ ( E @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(518,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Lambda_OdB_OAbs @ ( B @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
thf(1005,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Lambda_OdB_OAbs @ ( B @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(123,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(683,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(143,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(730,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(121,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(677,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)],[121]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(1305,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(861,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(338,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(1173,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)],[338]) ).
thf(4,negated_conjecture,
~ ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(408,plain,
~ ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(251,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(977,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(54,axiom,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(523,plain,
( ( tc_nat @ c_HOL_Oone__class_Oone )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(331,axiom,
v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(1158,plain,
v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(158,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(762,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)],[158]) ).
thf(149,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(741,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)],[149]) ).
thf(295,axiom,
v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__CHAINED__1 ) ) ) @ ( 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_CHAINED_1) ).
thf(1073,plain,
v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__CHAINED__1 ) ) ) @ ( 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)],[295]) ).
thf(207,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(873,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)],[207]) ).
thf(354,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(1205,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(209,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(878,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)],[209]) ).
thf(20,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(440,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)],[20]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(655,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(50,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(511,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)],[50]) ).
thf(323,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(1137,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)],[323]) ).
thf(399,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1310,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(334,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(1164,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)],[334]) ).
thf(137,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(715,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(32,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(472,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(181,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(814,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)],[181]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
thf(945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(291,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(1063,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)],[291]) ).
thf(61,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(538,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(118,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(670,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(377,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1260,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(129,axiom,
v_n____ != v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_False_0) ).
thf(696,plain,
v_n____ != v_i____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(697,plain,
v_n____ != v_i____,
inference(polarity_switch,[status(thm)],[696]) ).
thf(698,plain,
v_i____ != v_n____,
inference(lifteq,[status(thm)],[697]) ).
thf(152,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(747,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)],[152]) ).
thf(224,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(913,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)],[224]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubstn ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubstn ) ) )
= ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(261,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(1001,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)],[261]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ c_Suc @ ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__commute_0) ).
thf(782,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ c_Suc @ ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(134,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(709,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)],[134]) ).
thf(193,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(841,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)],[193]) ).
thf(379,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(1265,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)],[379]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(829,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(305,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(1095,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)],[305]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ c_Type_Otypings ) ) )
| ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_Olift @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( C @ ( B @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ c_Type_Otypings ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__types_0) ).
thf(1243,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ c_Type_Otypings ) ) )
| ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_Olift @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( C @ ( B @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ c_Type_Otypings ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(1127,plain,
! [B: $i,A: $i] :
( ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(212,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(885,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)],[212]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OdB__size )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( B @ c_Lambda_OdB_OdB__size @ ( A @ c_Lambda_OdB_OdB__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OdB__size )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( B @ c_Lambda_OdB_OdB__size @ ( A @ c_Lambda_OdB_OdB__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(389,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(1287,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)],[389]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(570,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(3,negated_conjecture,
v_T____ @ ( v_xb @ ( v_x @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(407,plain,
v_T____ @ ( v_xb @ ( v_x @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(409,plain,
~ ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
inference(polarity_switch,[status(thm)],[408]) ).
thf(1324,plain,
( ( ( v_T____ @ ( v_xb @ ( v_x @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
!= ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[407,409]) ).
thf(1325,plain,
( ( v_T____ @ ( v_xb @ ( v_x @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
!= ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[1324]) ).
thf(1330,plain,
( ( v_T____ @ ( v_xb @ ( v_x @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) ) ),
inference(simp,[status(thm)],[1325]) ).
thf(176,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(802,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(289,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(1059,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)],[289]) ).
thf(239,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
thf(949,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(63,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(542,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(286,axiom,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(1055,plain,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(141,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
thf(724,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(587,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(404,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(1323,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(192,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(838,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)],[192]) ).
thf(182,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(817,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)],[182]) ).
thf(73,axiom,
! [A: $i] :
( ( tc_Lambda_OdB @ ( A @ c_Lambda_OdB_OVar @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
thf(559,plain,
! [A: $i] :
( ( tc_Lambda_OdB @ ( A @ c_Lambda_OdB_OVar @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(372,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(1247,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)],[372]) ).
thf(248,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(969,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)],[248]) ).
thf(8,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(416,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)],[8]) ).
thf(314,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(1115,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)],[314]) ).
thf(22,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(448,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(307,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(1100,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)],[307]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Suc @ c_Nat_Ocompow ) ) ) )
= ( C @ ( C @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Nat_Ocompow ) ) ) @ ( B @ c_Fun_Ocomp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funpow_Osimps_I2_J_0) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Suc @ c_Nat_Ocompow ) ) ) )
= ( C @ ( C @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Nat_Ocompow ) ) ) @ ( B @ c_Fun_Ocomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(198,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(853,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)],[198]) ).
thf(11,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(421,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(205,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(870,plain,
v_T____ @ ( v_ua______ @ ( v_ea______ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_0) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(41,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(492,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)],[41]) ).
thf(170,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(789,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)],[170]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(443,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(190,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(834,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)],[190]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(514,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(937,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(80,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(574,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(178,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( F @ ( C @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ c_Type_Otypings ) ) )
| ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( B @ ( 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 ) ) ) @ ( A @ c_Type_Otypings ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substs__lemma_0) ).
thf(806,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( F @ ( C @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ c_Type_Otypings ) ) )
| ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( B @ ( 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 ) ) ) @ ( A @ c_Type_Otypings ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(246,axiom,
v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(966,plain,
v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(387,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(1283,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)],[387]) ).
thf(279,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(1040,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)],[279]) ).
thf(311,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(1109,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)],[311]) ).
thf(2,negated_conjecture,
v_xb @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(406,plain,
v_xb @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1328,plain,
( ( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
!= ( v_xb @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,409]) ).
thf(1329,plain,
( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
!= ( v_xb @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1332,plain,
( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) )
!= ( v_xb @ ( c_InductTermi_OIT @ hAPP ) ) ),
inference(simp,[status(thm)],[1329]) ).
thf(1333,plain,
( ( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
!= v_xb )
| ( c_InductTermi_OIT != c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1332]) ).
thf(1334,plain,
( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
!= v_xb ),
inference(simp,[status(thm)],[1333]) ).
thf(109,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(646,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(125,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(687,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(242,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(956,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(203,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(866,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)],[203]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(660,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(5,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(410,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)],[5]) ).
thf(411,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(cnf,[status(esa)],[410]) ).
thf(352,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(1201,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)],[352]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ c_Lambda_OdB_OVar @ c_Lambda_OdB_OdB__size )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
thf(507,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OVar @ c_Lambda_OdB_OdB__size )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(602,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(766,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(1215,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(104,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(634,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( C @ ( 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 ) ) ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__map_0) ).
thf(1074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( C @ ( 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 ) ) ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
thf(452,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(1199,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ 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 ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ 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 ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(59,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(534,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(136,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(714,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(174,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(798,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)],[174]) ).
thf(287,axiom,
tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_as____ @ ( 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 ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_I3_J_0) ).
thf(1057,plain,
tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_as____ @ ( 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 ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(165,axiom,
v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__local__XCons__1__1 ) ) ) @ ( 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_Cons_I1_J_1) ).
thf(778,plain,
v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__local__XCons__1__1 ) ) ) @ ( 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)],[165]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ c_Suc @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__lift_0) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ c_Suc @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Type_Osko__Type__Xabs__typeE__1__2 ) @ ( B @ ( B @ ( A @ c_Type_Osko__Type__Xabs__typeE__1__1 ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( 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_abs__typeE_0) ).
thf(1255,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Type_Osko__Type__Xabs__typeE__1__2 ) @ ( B @ ( B @ ( A @ c_Type_Osko__Type__Xabs__typeE__1__1 ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( 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)],[375]) ).
thf(183,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__lt_0) ).
thf(820,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(74,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(561,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(13,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(424,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)],[13]) ).
thf(128,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(693,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(630,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(225,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(916,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)],[225]) ).
thf(275,axiom,
tc_Lambda_OdB @ ( v_as____ @ ( 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(1032,plain,
tc_Lambda_OdB @ ( v_as____ @ ( 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)],[275]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(435,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(393,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(1296,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)],[393]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(356,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(1210,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)],[356]) ).
thf(298,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(1079,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)],[298]) ).
thf(68,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(551,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
thf(974,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(266,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(1012,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)],[266]) ).
thf(309,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(1106,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)],[309]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_Olift @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__map_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_Olift @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(1017,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(97,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(615,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(88,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(593,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(256,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(989,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)],[256]) ).
thf(312,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(1111,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)],[312]) ).
thf(363,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1227,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(1028,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(39,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(488,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_a____ @ ( 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_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).
thf(753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_a____ @ ( 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_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(342,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(1182,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)],[342]) ).
thf(117,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(669,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(901,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(40,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(489,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)],[40]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(706,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(355,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(1207,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)],[355]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( B @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( B @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(330,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(1155,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)],[330]) ).
thf(66,axiom,
tc_nat @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(547,plain,
tc_nat @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(701,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(321,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(1131,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)],[321]) ).
thf(347,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(1192,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)],[347]) ).
thf(77,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(569,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(166,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(779,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)],[166]) ).
thf(46,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(503,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)],[46]) ).
thf(380,axiom,
! [A: $i] :
( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(1266,plain,
! [A: $i] :
( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(365,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(1231,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)],[365]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__gt_0) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(26,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(457,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(254,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(984,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)],[254]) ).
thf(223,axiom,
! [A: $i] :
( ~ ( tc_Lambda_OdB @ ( A @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( 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_lifts__IT_0) ).
thf(911,plain,
! [A: $i] :
( ~ ( tc_Lambda_OdB @ ( A @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( 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)],[223]) ).
thf(402,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(1318,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)],[402]) ).
thf(171,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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_zero__less__two_0) ).
thf(792,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[171]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(1241,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(921,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(113,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(657,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OAbs )
!= ( B @ c_Lambda_OdB_OVar ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(159,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(765,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(337,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(1170,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)],[337]) ).
thf(72,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(558,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(530,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(172,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(794,plain,
! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(138,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(718,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)],[138]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ ( A @ ( B @ c_Nat_Ocompow ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( C @ ( A @ ( B @ c_Nat_Ocompow ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funpow__swap1_0) ).
thf(926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ ( A @ ( B @ c_Nat_Ocompow ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( C @ ( A @ ( B @ c_Nat_Ocompow ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(221,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(906,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)],[221]) ).
thf(385,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(1278,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
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_0) ).
thf(412,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(153,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(750,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)],[153]) ).
thf(98,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(618,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)],[98]) ).
thf(308,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(1103,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)],[308]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(199,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(856,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)],[199]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ c_Type_Otype_Otype__size )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( B @ c_Type_Otype_Otype__size @ ( A @ c_Type_Otype_Otype__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osize_I2_J_0) ).
thf(745,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ c_Type_Otype_Otype__size )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( B @ c_Type_Otype_Otype__size @ ( A @ c_Type_Otype_Otype__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(395,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(1301,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)],[395]) ).
thf(79,axiom,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(573,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(145,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(733,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)],[145]) ).
thf(220,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(904,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)],[220]) ).
thf(1376,plain,
( ( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
!= ( v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[966,409]) ).
thf(1377,plain,
( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
!= ( v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[1376]) ).
thf(1378,plain,
( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) )
!= ( v_ua______ @ ( c_InductTermi_OIT @ hAPP ) ) ),
inference(simp,[status(thm)],[1377]) ).
thf(1388,plain,
( ( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
!= v_ua______ )
| ( c_InductTermi_OIT != c_InductTermi_OIT ) ),
inference(simp,[status(thm)],[1378]) ).
thf(1389,plain,
( ( v_xc @ ( v_xb @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
!= v_ua______ ),
inference(simp,[status(thm)],[1388]) ).
thf(318,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(1125,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)],[318]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ c_Suc )
= ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(743,plain,
! [A: $i] :
( ( A @ c_Suc )
= ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(579,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(243,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(958,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)],[243]) ).
thf(65,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(545,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(413,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(cnf,[status(esa)],[412]) ).
thf(208,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(875,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)],[208]) ).
thf(185,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(826,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)],[185]) ).
thf(382,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(1271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(400,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(1312,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)],[400]) ).
thf(169,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(787,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)],[169]) ).
thf(44,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(498,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)],[44]) ).
thf(288,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(1058,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)],[288]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(30,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(466,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)],[30]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(704,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(238,axiom,
! [A: $i] :
( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OdB__size )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Lambda_OdB_OdB__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).
thf(947,plain,
! [A: $i] :
( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OdB__size )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Lambda_OdB_OdB__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( 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_zero__less__one_0) ).
thf(540,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( 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)],[62]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(1194,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(188,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(831,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(10,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(419,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)],[10]) ).
thf(147,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(737,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(317,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(1122,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)],[317]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(599,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(339,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(1175,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)],[339]) ).
thf(252,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(979,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)],[252]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(604,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(168,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(784,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)],[168]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semiring__1__class_Oof__nat__code_0) ).
thf(1117,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(1048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(146,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(736,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(23,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(450,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)],[23]) ).
thf(451,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(polarity_switch,[status(thm)],[450]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(567,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(210,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(880,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)],[210]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(649,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(16,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(434,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(214,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(890,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)],[214]) ).
thf(180,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(811,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(494,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(156,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(758,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)],[156]) ).
thf(60,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(535,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(94,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(609,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(594,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A = C )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
= ( A @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(483,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(769,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(340,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(1177,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)],[340]) ).
thf(200,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(858,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)],[200]) ).
thf(69,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(552,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Lambda_OdB @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_Lambda_OdB @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).
thf(943,plain,
! [B: $i,A: $i] :
( ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Lambda_OdB @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_Lambda_OdB @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(232,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(290,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(1061,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(685,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(350,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(1198,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)],[350]) ).
thf(357,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(1213,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)],[357]) ).
thf(371,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(1245,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)],[371]) ).
thf(292,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(1066,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)],[292]) ).
thf(25,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(455,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)],[25]) ).
thf(267,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(1015,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)],[267]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( A @ ( B @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ c_Lambda_OdB_OAbs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).
thf(986,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( A @ ( B @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ c_Lambda_OdB_OAbs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(313,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(1113,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)],[313]) ).
thf(373,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(1250,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)],[373]) ).
thf(197,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(851,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(15,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(431,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)],[15]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(505,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(19,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(438,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(1076,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(140,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(722,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)],[140]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(675,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(396,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(1304,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)],[396]) ).
thf(353,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( D @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( D @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(322,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(1134,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)],[322]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_Lambda_OdB @ ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(516,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(326,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1145,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(553,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(184,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(823,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)],[184]) ).
thf(191,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(836,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)],[191]) ).
thf(14,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(426,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)],[14]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
thf(1166,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(173,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(795,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(680,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(115,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(663,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(548,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(776,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(107,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(640,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)],[107]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(362,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(1225,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)],[362]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_Suc @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I2_J_0) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_Suc @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(7,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(414,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)],[7]) ).
thf(241,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(954,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)],[241]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(135,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(712,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)],[135]) ).
thf(262,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(1003,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)],[262]) ).
thf(285,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(1053,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)],[285]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(673,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(378,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(1262,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)],[378]) ).
thf(359,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(1218,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)],[359]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(643,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(1220,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(345,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(1188,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)],[345]) ).
thf(344,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(1186,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)],[344]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( D @ ( C @ ( t_a @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__def_0) ).
thf(1038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( D @ ( C @ ( t_a @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(585,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(301,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 ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(1085,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 ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(82,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(576,plain,
! [B: $i,A: $i] :
( ( A @ c_Lambda_OdB_OVar )
!= ( B @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(951,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(179,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(808,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)],[179]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
= ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ofcomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
thf(613,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ofcomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(388,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(1284,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)],[388]) ).
thf(202,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(864,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(142,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(727,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)],[142]) ).
thf(324,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(1140,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)],[324]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(1008,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(95,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(612,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(101,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(627,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)],[101]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat_Ocompow ) ) ) )
= ( D @ ( D @ ( D @ ( D @ ( D @ ( C @ ( B @ c_Nat_Ocompow ) ) ) @ ( D @ ( D @ ( C @ ( A @ c_Nat_Ocompow ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funpow__add_0) ).
thf(1180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat_Ocompow ) ) ) )
= ( D @ ( D @ ( D @ ( D @ ( D @ ( C @ ( B @ c_Nat_Ocompow ) ) ) @ ( D @ ( D @ ( C @ ( A @ c_Nat_Ocompow ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(126,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(688,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)],[126]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( 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_less__add__one_0) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( 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)],[265]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(310,axiom,
v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__local__XCons__Xhyps__1__1 ) ) ) @ ( 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_Cons_Ohyps_I1_J_1) ).
thf(1108,plain,
v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__local__XCons__Xhyps__1__1 ) ) ) @ ( 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)],[310]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(1289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(194,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(844,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)],[194]) ).
thf(384,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(1276,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)],[384]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_0) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(652,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(103,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(632,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(258,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(995,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)],[258]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(130,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(699,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)],[130]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(731,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(9,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(418,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) )
| ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_a____ @ ( 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_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( v_a____ @ ( 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_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(398,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(1308,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)],[398]) ).
thf(34,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(478,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(218,axiom,
! [A: $i] :
( ( tc_Lambda_OdB @ ( A @ c_Lambda_OdB_OAbs @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Lambda_OdB @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).
thf(899,plain,
! [A: $i] :
( ( tc_Lambda_OdB @ ( A @ c_Lambda_OdB_OAbs @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Lambda_OdB @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(189,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(832,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)],[189]) ).
thf(281,axiom,
tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_as____ @ ( 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 ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1045,plain,
tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_as____ @ ( 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 ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(333,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(1161,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)],[333]) ).
thf(175,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(800,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)],[175]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_Oliftn ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OAbs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_Oliftn ) ) )
= ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OAbs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(364,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(1229,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)],[364]) ).
thf(1,negated_conjecture,
v_xa @ ( v_a____ @ ( v_T____ @ ( v_xc @ ( v_x @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(405,plain,
v_xa @ ( v_a____ @ ( v_T____ @ ( v_xc @ ( v_x @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(327,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(1148,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)],[327]) ).
thf(12,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(422,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)],[12]) ).
thf(204,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(867,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)],[204]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
thf(967,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(75,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(564,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)],[75]) ).
thf(226,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(918,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)],[226]) ).
thf(18,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(437,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(276,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(1033,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)],[276]) ).
thf(186,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(828,plain,
v_T____ @ ( v_u____ @ ( v_e____ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Ocompow ) ) ) )
= ( B @ c_Fun_Oid ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funpow_Osimps_I1_J_0) ).
thf(532,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Ocompow ) ) ) )
= ( B @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(139,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(720,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(230,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(928,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)],[230]) ).
thf(217,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(897,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)],[217]) ).
thf(473,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(polarity_switch,[status(thm)],[472]) ).
thf(474,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(lifteq,[status(thm)],[473]) ).
thf(244,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(960,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)],[244]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(1236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
!= ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(29,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Omap ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__map_0) ).
thf(464,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Omap ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(320,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(1129,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)],[320]) ).
thf(269,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(1019,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(56,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(528,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(27,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(459,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)],[27]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(982,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
= ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(394,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(1299,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)],[394]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(691,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(316,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(1120,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)],[316]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(501,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(93,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ c_Fun_Ofcomp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Fun_Ofcomp ) ) ) ) @ ( A @ c_Fun_Ofcomp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
thf(607,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ c_Fun_Ofcomp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Fun_Ofcomp ) ) ) ) @ ( A @ c_Fun_Ofcomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
thf(1093,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(100,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(624,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)],[100]) ).
thf(381,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(1268,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)],[381]) ).
thf(81,axiom,
tc_nat @ class_OrderedGroup_Osemigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(575,plain,
tc_nat @ class_OrderedGroup_Osemigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(992,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ofcomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
thf(486,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ofcomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).
thf(935,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(923,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Oliftn ) ) )
= ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(1184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Oliftn ) ) )
= ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(64,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(543,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(755,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(302,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(1088,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)],[302]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(496,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(211,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(882,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)],[211]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( 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_typing__elims_I3_J_1) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( 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)],[249]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(469,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(940,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(4331,plain,
$false,
inference(e,[status(thm)],[1036,1024,1190,479,846,893,1083,555,666,481,1168,760,1315,518,1005,683,730,1068,677,1305,861,1173,408,977,523,1158,582,762,741,1073,873,1205,878,440,655,511,1137,1310,1164,715,472,814,945,1063,538,930,670,1260,698,747,913,1196,1001,782,709,841,1265,829,1095,1243,1127,885,1046,1287,570,1330,802,1059,949,542,1055,724,587,1323,838,817,559,1247,969,416,1115,448,1100,638,853,421,870,475,492,789,443,834,514,937,574,806,966,1283,1040,1109,1334,646,687,956,866,774,660,411,1201,849,507,602,766,1215,634,1074,452,1199,1153,534,714,798,1057,1223,778,1042,1255,820,561,424,407,693,630,916,1032,435,1296,1159,1210,1079,551,974,1012,1106,1234,1143,1017,615,593,989,1111,1227,1028,488,1292,753,1182,669,901,489,706,1207,590,1155,547,997,701,1150,1131,1192,569,779,503,1266,1231,1050,457,984,911,1318,792,1241,921,657,765,1170,558,1026,530,794,718,926,906,1278,412,750,618,1103,1273,856,745,1301,573,733,904,1389,1125,743,579,958,545,413,875,826,1271,1312,787,498,1058,1239,1332,466,1090,804,704,947,540,1194,406,831,419,737,1122,599,1175,979,604,784,1117,1048,736,451,567,509,880,649,434,890,811,494,758,535,609,594,621,483,895,769,1177,858,552,943,1022,462,932,1061,685,1198,1213,1245,1066,455,1015,986,1113,1250,851,431,505,438,1076,722,675,1304,1203,1134,1081,516,1145,553,823,836,426,1166,795,680,663,548,776,525,640,1070,1225,887,414,954,739,409,1098,712,1003,1053,673,1262,1218,643,1220,1188,1186,1038,585,1085,576,951,808,1257,613,1284,864,727,1140,1008,612,627,450,1180,1321,688,1010,771,1108,1289,844,1276,963,652,632,995,1253,699,731,418,1030,1294,1308,478,899,832,1045,1161,800,999,1280,1229,405,1148,422,867,410,967,564,918,437,1033,828,532,696,720,928,897,474,960,635,1236,464,1129,1378,1019,528,459,982,1299,691,871,1120,501,607,1093,624,1268,575,908,992,486,935,923,1184,543,755,1088,496,882,972,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL826-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n013.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 23:38:51 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.90/1.35 % [INFO] Parsing done (355ms).
% 1.90/1.36 % [INFO] Running in sequential loop mode.
% 3.09/1.77 % [INFO] eprover registered as external prover.
% 3.09/1.77 % [INFO] Scanning for conjecture ...
% 3.54/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 409 axioms. Running axiom selection ...
% 4.51/2.18 % [INFO] Axiom selection finished. Selected 400 axioms (removed 9 axioms).
% 5.36/2.43 % [INFO] Problem is propositional (TPTP CNF).
% 5.36/2.46 % [INFO] Type checking passed.
% 5.36/2.46 % [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 ...
% 29.43/7.23 % External prover 'e' found a proof!
% 29.43/7.23 % [INFO] Killing All external provers ...
% 29.43/7.23 % Time passed: 6683ms (effective reasoning time: 5867ms)
% 29.43/7.24 % Axioms used in derivation (400): cls_Suc__pred_0, cls_not__one__less__zero_0, cls_less__iff__diff__less__0_0, cls_shift__commute_0, cls_add__0__left_0, cls_MI1_0, cls_subst__lt_0, cls_natgb_Oadd__r0__iff_1, cls_subst__map_0, cls_dB_Osimps_I6_J_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_apps__eq__Abs__conv_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_add__is__1_1, cls_zero__less__one_0, cls_of__nat__add_0, cls_add__less__cancel__left_1, cls_Suc__inject_0, cls_subst__App_0, cls_Suc__mono_0, cls_of__nat__0_0, cls_subst__eq_0, cls_class__ringb_Oadd__r0__iff_1, cls_lift_Osimps_I2_J_0, cls_funpow_Osimps_I1_J_0, cls_COMBC__def_0, cls_beta__cases_I2_J_1, cls_dB_Osimps_I8_J_0, cls_one__is__add_4, cls_nat__add__left__cancel__less_1, cls_diff__Suc__1_0, cls_liftn_Osimps_I1_J_1, cls_id__o_0, cls_typing__elims_I3_J_0, cls_subject__reduction_0, cls_Suc__n__not__n_0, cls_Cons_I1_J_1, cls_add__is__1_2, cls_add__strict__right__mono_0, cls_Cons_Ohyps_I1_J_1, cls_less__antisym_0, cls_liftn_Osimps_I2_J_0, cls_CHAINED_0, cls_less__add__Suc2_0, cls_of__nat__less__iff_0, cls_var__app__typesE_0, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_MI2_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_rtrancl__beta__Abs_0, cls_uIT_0, cls_add__is__0_0, cls_less__Suc__eq_2, cls_o__eq__id__dest_0, cls_not__less__eq_1, cls_one__is__add_1, cls_appR_0, cls_termination__basic__simps_I1_J_0, cls_substn__subst__0_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_nat__add__left__cancel__less_0, cls_of__nat__aux_Osimps_I2_J_0, cls_comm__monoid__add_Omult__1__right_0, cls_lift__subst__lt_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_rtranclp__trans_0, cls_K__record__comp_0, cls_add__cancel__21_1, cls_add__left__cancel_0, cls_head__Var__reduction_1, cls_substn_Osimps_I1_J_2, cls_of__nat__0__less__iff_0, cls_beta_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_add__gr__0_0, cls_Abs_0, cls_foldl__foldr1_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_gr0I_0, cls_lift__type_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_nat__less__cases_0, cls_diff__diff__left_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_add__less__mono_0, cls_less__iff__diff__less__0_1, cls_funpow_Osimps_I2_J_0, cls_subst__gt_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_type_Osize_I2_J_0, cls_substn__subst__n_0, cls_shift__eq_0, cls_right__minus__eq_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_dB_Osimps_I3_J_0, cls_foldl__absorb0_0, cls_type_Osize_I4_J_0, cls_add__Suc_0, cls_id__apply_0, cls_Var_I2_J_0, cls_liftn__0_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, clsarity_bool__Orderings_Oorder, cls_subst__Var_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_diff__add__inverse2_0, cls_xt1_I10_J_0, cls_add__less__cancel__right_1, cls_nat__add__left__commute_0, cls_Var__apps__eq__Var__apps__conv_1, cls_lift__lift_0, cls_one__is__add_5, cls_typing__elims_I3_J_1, cls_class__semiring_Osemiring__rules_I6_J_0, cls_CHAINED_1, cls_typing__elims_I2_J_0, cls_diff__Suc__Suc_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_beta__cases_I2_J_0, cls_CHAINED_0_01, cls_add__strict__left__mono_0, cls_add__less__mono1_0, cls_type_Osimps_I2_J_1, cls_dB_Osimps_I4_J_0, cls_nat__diff__split_0, cls_Suc__diff__1_0, cls_of__nat__1_0, cls_typing__elims_I1_J_0, cls_class__semiring_Oadd__a_0, cls_var__app__types_0, cls_Suc__neq__Zero_0, cls_diff__add__0_0, cls_subject__reduction_H_0, cls_add__is__1_0, cls_var__app__typesE_1, cls_dB_Osize_I5_J_0, cls_one__is__add_0, cls_less__add__Suc1_0, cls_Var__IT_0, cls_liftn_Osimps_I3_J_0, cls_Var_I3_J_0, cls_converse__rtranclp__into__rtranclp_0, cls_list__app__typeD_1, cls_apps__preserves__betas_0, cls_id__fcomp_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_of__nat__eq__iff_0, cls_comm__monoid__add_Omult__commute_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_nat__add__assoc_0, cls_head__Var__reduction_0, cls_of__nat__0__less__iff_1, cls_One__nat__def_0, cls_less__add__one_0, cls_add__strict__mono_0, cls_Cons_I1_J_0, cls_lessI_0, cls_diff__Suc__eq__diff__pred_0, cls_zero__less__two_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_less__Suc__eq__0__disj_3, cls_uT_0, cls_less__add__eq__less_0, cls_lift_Osimps_I3_J_0, cls_dB_Osimps_I1_J_0, cls_Abs__App__neq__Var__apps_0, cls_rtrancl__beta__App_0, cls_lift__map_0, cls_add__cancel__21_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_dB_Osize_I3_J_0, cls_Cons_I3_J_0, cls_subst__Var_1, clsarity_bool__Orderings_Opreorder, cls_rtrancl__beta__AppL_0, cls_natgb_Oadd__cancel_0, cls_Nitpick_Ortranclp__def_1, cls_diff__less_0, cls_diff__self_0, cls_less__imp__diff__less_0, cls_type_Osimps_I2_J_0, cls_zero__neq__one_0, cls_neq0__conv_1, cls_one__is__add_2, cls_dB_Osize_I4_J_0, cls_add__less__cancel__right_0, cls_add__diff__cancel_0, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_add__Suc__right_0, cls_lifts__IT_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_substn_Osimps_I1_J_0, cls_Var__apps__neq__Abs__apps_0, cls_subst__lemma_0, cls_foldl__assoc_0, cls_map__map_0, clsarity_nat__Orderings_Opreorder, cls_nat__diff__split__asm_1, cls_less__not__refl_0, cls_gr0__conv__Suc_1, cls_class__ringb_Oadd__cancel_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_lift__subst_0, cls_right__minus__eq_1, cls_foldl__foldr1__lemma_0, cls_diff__less__Suc_0, cls_nat__diff__split_1, cls_linorder__neqE__ordered__idom_0, cls_o__eq__dest_0, cls_Suc__diff__diff_0, cls_diff__cancel2_0, cls_dB_Osimps_I2_J_1, cls_var__app__types_1, cls_fcomp__id_0, cls_less__diff__conv_1, cls_o__eq__dest__lhs_0, cls_funpow__add_0, cls_nat_Oinject_0, cls_add__lessD1_0, cls_even__less__0__iff_1, cls_id__def_0, cls_subst__subst_0, cls_False_0, cls_class__ringb_Oadd__r0__iff_0, cls_less__diff__conv_0, cls_less__SucE_0, cls_lift__preserves__beta_H_0, cls_list__app__typeD_0, cls_CHAINED_0_02, cls_rtranclp_Ortrancl__refl_0, cls_Nat_Oadd__0__right_0, cls_nat__neq__iff_0, cls_substn_Osimps_I2_J_0, cls_not__less__less__Suc__eq_1, cls_liftn__lift_0, cls_eq__eqI_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_lift_Osimps_I1_J_1, cls_Suc__lessD_0, cls_natgb_Oadd__r0__iff_0, cls_add__is__1_4, cls_add__is__1_5, cls_o__id_0, cls_diff__self__eq__0_0, cls_add__neg__neg_0, cls_dB_Osize_I1_J_0, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_o__def_0, cls_add__eq__if_1, cls_abs_0, cls_less__Suc0_0, cls_diff__0__right_0, cls_rtranclp__idemp_0, cls_list__app__typeE_1, cls_typing_OVar_0, cls_diff__Suc__less_0, cls_lift__IT_0, cls_IT_OVar_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_nat_Osimps_I3_J_0, cls_apps__preserves__beta2_0, cls_less__trans__Suc_0, cls_plus__nat_Oadd__0_0, cls_list__app__typeI_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_diff__less__mono2_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_comm__monoid__add_Omult__1_0, cls_liftn_Osimps_I1_J_0, cls_order__less__irrefl_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_diff__0__eq__0_0, cls_add__is__0_2, cls_eq__eqI_1, cls_class__semiring_Oadd__c_0, cls_Abs__eq__apps__conv_0, cls_zero__less__diff_1, cls_of__nat__aux_Osimps_I1_J_0, cls_minus__nat_Odiff__0_0, cls_apps__preserves__beta_0, cls_comp__cong_0, cls_shift__lt_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_foldr__conv__foldl_0, cls_add__is__1_3, cls_substn_Osimps_I1_J_1, cls_add__eq__self__zero_0, clsarity_fun__Orderings_Opreorder, cls_add__pos__pos_0, cls_Suc__eq__plus1_0, cls_n__not__Suc__n_0, cls_less__SucI_0, cls_not__less0_0, cls_substn_Osimps_I3_J_0, cls_diffs0__imp__equal_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_fcomp__apply_0, cls_eq__iff__diff__eq__0_1, cls_subst__Abs_0, cls_add__less__cancel__left_0, cls_subst__Var__IT_0, cls_class__ringb_Osubr0__iff_1, cls_shift__gt_0, cls_one__is__add_3, 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_dB_Osimps_I5_J_0, cls_diff__add__inverse_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_abs__typeE_0, cls_Lambda_0, cls_Suc__less__eq_0, cls_add__gr__0_2, cls_list__app__typeE_0, cls_lift_Osimps_I1_J_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_Suc__pred_H_0, cls_subst__Var_0, cls_fcomp__def_0, cls_rtranclp_Ortrancl__into__rtrancl_0, cls_add__gr__0_1, cls_less__Suc0_1, cls_subst__lift_0, cls_substs__lemma_0, cls_subst__preserves__beta2_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_lift__types_0, cls_dB_Osize_I2_J_0, cls_diff__commute_0, cls_fcomp__assoc_0, cls_termination__basic__simps_I2_J_0, cls_of__nat__Suc_0, cls_class__ringb_Osubr0__iff_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, cls_dB_Osize_I6_J_0, cls_eq__iff__diff__eq__0_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_zero__less__Suc_0, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_subst__preserves__beta2_H_0, cls_less__eqI_1, cls_dB_Osimps_I9_J_0, clsarity_nat__OrderedGroup_Osemigroup__add, cls_o__apply_0, cls_even__less__0__iff_0, cls_funpow__swap1_0, cls_nat__add__commute_0, cls_semiring__1__class_Oof__nat__code_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_o__assoc_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, cls_add__diff__inverse_0, cls_rtrancl__beta__AppR_0
% 29.43/7.24 % No. of inferences in proof: 830
% 29.43/7.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6683 ms resp. 5867 ms w/o parsing
% 28.03/7.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 28.03/7.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------