%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV854-1 : 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:48 AM UTC 2026
% Result : Unsatisfiable 33.65s 8.27s
% Output : Refutation 34.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 761
% Syntax : Number of formulae : 1548 ( 467 unt; 0 typ; 0 def)
% Number of atoms : 3320 (1032 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 20282 (1788 ~;1756 |; 0 &;16738 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 103 ( 100 usr; 18 con; 0-10 aty)
% Number of variables : 5346 ( 0 ^;5346 !; 0 ?;5346 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_Procs_decl,type,
v_Procs: $i ).
thf(tc_Com_Opname_decl,type,
tc_Com_Opname: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_decl,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i ).
thf(v_na_decl,type,
v_na: $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i > $i > $i > $i ).
thf(v_P_decl,type,
v_P: $i ).
thf(c_Com_Ocom_OBODY_decl,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(v_Q_decl,type,
v_Q: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_G_decl,type,
v_G: $i ).
thf(tc_Hoare__Mirabelle_Otriple_decl,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(c_Option_Othe_decl,type,
c_Option_Othe: $i > $i > $i ).
thf(c_Com_Obody_decl,type,
c_Com_Obody: $i > $i ).
thf(tc_Com_Ocom_decl,type,
tc_Com_Ocom: $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Com_Ocom_OLocal_decl,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(c_Com_Ocom_OAss_decl,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Com_Ocom_OCall_decl,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Com_Ocom_OWhile_decl,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Orderings_Oord__class_Omin_decl,type,
c_Orderings_Oord__class_Omin: $i > $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $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_Option_Ooption_OSome_decl,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(c_Option_Ooption_ONone_decl,type,
c_Option_Ooption_ONone: $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $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(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_Natural_Oevalc_decl,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(c_Orderings_Oord__class_Omax_decl,type,
c_Orderings_Oord__class_Omax: $i > $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Power_Opower_Opower_decl,type,
c_Power_Opower_Opower: $i > $i > $i > $i > $i > $i ).
thf(c_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Com_Ocom_OCond_decl,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Com_Ocom_Ocom__rec_decl,type,
c_Com_Ocom_Ocom__rec: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_Com_Ocom_Ocom__case_decl,type,
c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Com_OWT_decl,type,
c_Com_OWT: $i > $o ).
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(c_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Fun_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_decl,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(c_Nat_Onat_Onat__rec_decl,type,
c_Nat_Onat_Onat__rec: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(c_Hoare__Mirabelle_Ohoare__derivs_decl,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $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(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Groebner__Basis_Ogb__semiring_decl,type,
c_Groebner__Basis_Ogb__semiring: $i > $i > $i > $i > $i > $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xhoare__valids__def__1_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__1: $i > $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__valids_decl,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__case_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(c_Orderings_Oorder__class_Omono_decl,type,
c_Orderings_Oorder__class_Omono: $i > $i > $i > $o ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i > $i > $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1_decl,type,
v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__2: $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2_decl,type,
v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3_decl,type,
v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1_decl,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: $i > $i > $i > $i > $i ).
thf(v_R_decl,type,
v_R: $i ).
thf(t_c_decl,type,
t_c: $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1_decl,type,
v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1: $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(1337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(263,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1411,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(1633,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(502,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(1993,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(1994,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(polarity_switch,[status(thm)],[1993]) ).
thf(1995,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[1994]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1559,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(396,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OLocal ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( L @ ( K @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( J @ ( I @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I3_J_0) ).
thf(1729,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OLocal ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( L @ ( K @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( J @ ( I @ ( C @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(38,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(846,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)],[38]) ).
thf(64,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
thf(909,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(710,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
thf(2480,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(9,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(777,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(433,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OAss ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I2_J_0) ).
thf(1818,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OAss ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(572,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(2163,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(892,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(2199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(371,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(1665,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(435,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ c_Com_Ocom_OBODY @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I70_J_0) ).
thf(1823,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ c_Com_Ocom_OBODY @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(1190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(163,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(1168,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(629,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(2295,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)],[629]) ).
thf(559,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(2131,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)],[559]) ).
thf(284,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1454,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(761,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( C @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
thf(2595,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( C @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(448,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(1850,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(169,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(1179,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(646,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(2331,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)],[646]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1554,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
thf(1110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(548,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).
thf(2104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(602,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( B @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
thf(2231,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( B @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(718,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
thf(2495,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(732,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(2527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(1073,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(546,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(2099,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(1142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(492,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
thf(1971,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(275,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1437,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(861,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(449,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(1855,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).
thf(1200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(405,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
thf(1750,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(5,negated_conjecture,
! [A: $i] :
( ~ ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(762,plain,
! [A: $i] :
( ~ ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
thf(1005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(593,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(2210,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)],[593]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(1422,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff_0) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(150,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(1137,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)],[150]) ).
thf(407,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) ) )
= ( C @ ( B @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(1756,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) ) )
= ( C @ ( B @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( B @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( 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_Opower__Suc2_0) ).
thf(1735,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( B @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(453,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(1867,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(695,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(2448,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)],[695]) ).
thf(688,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( B @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).
thf(2434,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( B @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(24,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(814,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(700,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( 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 @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(2459,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( 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 @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(485,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( B @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
thf(1954,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( B @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(522,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(2042,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)],[522]) ).
thf(421,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(1788,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)],[421]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
thf(1426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(1275,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(563,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
thf(2141,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(708,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(2476,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(1,negated_conjecture,
tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(763,plain,
tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ~ ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( A @ c_Com_Ocom_OBODY @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(766,plain,
! [A: $i] :
( ~ ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( A @ c_Com_Ocom_OBODY @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(768,plain,
! [A: $i] :
( ~ ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( A @ c_Com_Ocom_OBODY @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(cnf,[status(esa)],[766]) ).
thf(2625,plain,
! [A: $i] :
( ( ( tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) @ hBOOL )
!= ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL ) )
| ~ $true
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( A @ c_Com_Ocom_OBODY @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(paramod_ordered,[status(thm)],[763,768]) ).
thf(2626,plain,
! [A: $i] :
( ( ( tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) @ hBOOL )
!= ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL ) )
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( A @ c_Com_Ocom_OBODY @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(simp,[status(thm)],[2625]) ).
thf(2627,plain,
t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ),
inference(pattern_uni,[status(thm)],[2626:[bind(A,$thf( v_x ))]]) ).
thf(204,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(1260,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(409,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(1761,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)],[409]) ).
thf(239,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(1342,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(1640,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(754,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(2580,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)],[754]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1354,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
thf(2146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(1222,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
thf(930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(657,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) ) )
= ( C @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(2360,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) ) )
= ( C @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(1746,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(1835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(524,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(2046,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)],[524]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(2227,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(539,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
thf(2082,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(292,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(1475,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(727,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(2516,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)],[727]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(741,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
thf(2548,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(716,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(2491,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)],[716]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(365,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(1650,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)],[365]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(533,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ ( F @ ( A @ ( E @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
thf(2067,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ ( F @ ( A @ ( E @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(490,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCall ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I8_J_0) ).
thf(1967,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCall ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(310,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(1518,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)],[310]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I9_J_0) ).
thf(1265,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(734,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCall ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I71_J_0) ).
thf(2531,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCall ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(677,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(2405,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)],[677]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(353,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(1623,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)],[353]) ).
thf(294,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(1482,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)],[294]) ).
thf(215,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(1287,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ c_in ) ) @ hBOOL )
| ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triples__valid__Suc_0) ).
thf(1985,plain,
! [C: $i,B: $i,A: $i] :
( ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ c_in ) ) @ hBOOL )
| ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(2039,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(14,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(785,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)],[14]) ).
thf(455,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(1871,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)],[455]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I24_J_0) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(334,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(1577,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)],[334]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
thf(2126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(148,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(1132,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)],[148]) ).
thf(767,plain,
! [A: $i] :
( ~ ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(cnf,[status(esa)],[762]) ).
thf(2601,plain,
! [A: $i] :
( ( ( tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) @ hBOOL )
!= ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL ) )
| ~ $true
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(paramod_ordered,[status(thm)],[763,767]) ).
thf(2602,plain,
! [A: $i] :
( ( ( tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) @ hBOOL )
!= ( tc_Com_Opname @ ( v_Procs @ ( A @ c_in ) ) @ hBOOL ) )
| ( t_a @ ( t_a @ ( A @ ( v_Q @ hAPP ) @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ ( A @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(simp,[status(thm)],[2601]) ).
thf(2603,plain,
t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( tc_Com_Ocom @ ( v_x @ c_Com_Obody @ c_Option_Othe ) @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ),
inference(pattern_uni,[status(thm)],[2602:[bind(A,$thf( v_x ))]]) ).
thf(644,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCall ) ) @ c_Com_OWT )
| ( A @ c_Com_Ocom_OBODY @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).
thf(2328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCall ) ) @ c_Com_OWT )
| ( A @ c_Com_Ocom_OBODY @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ( t_a @ ( C @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__valids__def_2) ).
thf(1792,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ( t_a @ ( C @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(1430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(693,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(2444,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)],[693]) ).
thf(450,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( 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 @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(1860,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( 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 @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1511,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(66,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).
thf(917,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(747,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(2562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(714,axiom,
tc_nat @ ( tc_nat @ ( c_Suc @ c_Orderings_Oorder__class_Omono ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mono__Suc_0) ).
thf(2488,plain,
tc_nat @ ( tc_nat @ ( c_Suc @ c_Orderings_Oorder__class_Omono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(439,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
thf(1832,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(949,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(750,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 @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(2571,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 @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(463,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(1892,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(576,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
thf(2169,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(346,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(1609,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(570,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( F @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( B @ ( E @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_0) ).
thf(2158,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( F @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( B @ ( E @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
thf(1362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(735,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(2533,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(1232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(1545,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(683,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(2420,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)],[683]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(1922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) )
!= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(902,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) )
!= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
thf(1247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(743,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( B @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
thf(2552,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( B @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(229,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(1319,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(387,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(1704,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)],[387]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3 ) ) ) @ ( A @ ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2 ) ) ) @ ( C @ c_Natural_Oevaln ) ) ) )
| ( t_a @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_2) ).
thf(1890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3 ) ) ) @ ( A @ ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2 ) ) ) @ ( C @ c_Natural_Oevaln ) ) ) )
| ( t_a @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(663,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ ( C @ c_Natural_Oevaln ) ) ) )
| ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OIfFalse_0) ).
thf(2373,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ ( C @ c_Natural_Oevaln ) ) ) )
| ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( A @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(1347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( A @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
thf(1013,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(2,negated_conjecture,
~ ( t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(764,plain,
~ ( t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(770,plain,
~ ( t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) ),
inference(polarity_switch,[status(thm)],[764]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(1741,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
thf(881,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(632,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( c_Suc @ hAPP ) @ ( 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(2301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( c_Suc @ hAPP ) @ ( 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)],[632]) ).
thf(432,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(1815,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)],[432]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
thf(1494,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(580,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( c_Suc @ hAPP ) )
= B )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(2178,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( c_Suc @ hAPP ) )
= B )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(482,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(1946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(1373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(704,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(2469,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(604,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).
thf(2236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(378,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(1682,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)],[378]) ).
thf(437,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(1828,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)],[437]) ).
thf(519,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(2034,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(62,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).
thf(905,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(642,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(2324,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)],[642]) ).
thf(515,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(2027,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( D @ ( C @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( D @ ( D @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(2291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( D @ ( C @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( D @ ( D @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(612,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B = C )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(2254,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B = C )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(744,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
thf(2555,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(1183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(535,axiom,
( ( t_c @ ( t_b @ ( t_a @ ( v_R @ ( v_Q @ ( v_P @ c_COMBC ) ) ) ) ) )
= ( v_Q @ ( v_R @ ( v_P @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def__raw_0) ).
thf(2073,plain,
( ( t_c @ ( t_b @ ( t_a @ ( v_R @ ( v_Q @ ( v_P @ c_COMBC ) ) ) ) ) )
= ( v_Q @ ( v_R @ ( v_P @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1843,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(689,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(2437,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)],[689]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( 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_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(2281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( 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_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(585,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(2190,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)],[585]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
thf(866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(662,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(2371,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)],[662]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(591,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(2205,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)],[591]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
thf(1564,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(1447,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(711,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(2483,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(2523,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(1796,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(607,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(2242,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).
thf(1345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(93,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( B @ ( E @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_2) ).
thf(988,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( B @ ( E @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(625,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(2286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(137,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(1104,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)],[137]) ).
thf(384,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(1697,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)],[384]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(672,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(2392,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)],[672]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1521,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(451,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCond ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I68_J_0) ).
thf(1863,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCond ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(509,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(2011,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( tc_nat @ ( C @ ( E @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__nonstrict_0) ).
thf(1206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( tc_nat @ ( C @ ( E @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_0) ).
thf(942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(382,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(1691,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)],[382]) ).
thf(68,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(925,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(419,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( C @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( c_Suc @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I27_J_0) ).
thf(1783,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( C @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( c_Suc @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
thf(1067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(752,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Orderings_Oorder__class_Omono ) ) )
| ( ( B @ ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( E @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( C @ hAPP ) ) )
| ~ ( B @ class_Orderings_Olinorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__of__mono_0) ).
thf(2574,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Orderings_Oorder__class_Omono ) ) )
| ( ( B @ ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( E @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( C @ hAPP ) ) )
| ~ ( B @ class_Orderings_Olinorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
thf(1438,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(659,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_Orderings_Oord__class_Omax ) ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omax ) ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
thf(2364,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_Orderings_Oord__class_Omax ) ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omax ) ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(573,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(2164,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1470,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( E @ ( D @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
thf(1708,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( E @ ( D @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(543,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OWhileFalse_0) ).
thf(2093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(226,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I26_J_0) ).
thf(1311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(634,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(2307,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(412,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(1768,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(2382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(530,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(2061,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)],[530]) ).
thf(505,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(2000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(358,axiom,
tc_nat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(1636,plain,
tc_nat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I28_J_0) ).
thf(798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(118,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1057,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(691,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( 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(2441,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(758,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( E @ ( E @ ( D @ ( tc_Com_Ocom @ ( C @ c_Com_Obody @ c_Option_Othe ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_1) ).
thf(2589,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( E @ ( E @ ( D @ ( tc_Com_Ocom @ ( C @ c_Com_Obody @ c_Option_Othe ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(616,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(2264,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(1091,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(746,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OAss ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I65_J_0) ).
thf(2560,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OAss ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(1255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( 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__nonpos__neg_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( 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)],[144]) ).
thf(185,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omax ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
thf(1217,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omax ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(27,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(820,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)],[27]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(1487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I20_J_0) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(459,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(1883,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)],[459]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(466,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(1900,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(957,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(610,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(2249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
thf(1021,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(10,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(778,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(113,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(1042,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
thf(952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(738,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ c_Com_Ocom_OBODY @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I7_J_0) ).
thf(2541,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( I @ c_Com_Ocom_OBODY @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(376,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(1676,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)],[376]) ).
thf(560,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mod_0) ).
thf(2133,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(351,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(1619,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(567,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
thf(2150,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(518,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(2032,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(441,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(1837,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)],[441]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1365,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(1920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(41,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_lessequals ) ) )
| ( 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__nonneg_0) ).
thf(852,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_lessequals ) ) )
| ( 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)],[41]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( B @ c_Orderings_Oorder__class_Omono ) ) )
| ( A @ ( C @ ( c_Suc @ hAPP ) @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mono__iff__le__Suc_0) ).
thf(1888,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( B @ c_Orderings_Oorder__class_Omono ) ) )
| ( A @ ( C @ ( c_Suc @ hAPP ) @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(889,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(581,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Orderings_Oorder__class_Omono ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ( B @ ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ c_lessequals ) ) )
| ~ ( B @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoD_0) ).
thf(2181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Orderings_Oorder__class_Omono ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ( B @ ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ c_lessequals ) ) )
| ~ ( B @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).
thf(1656,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(108,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omax ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
thf(1027,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omax ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(651,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Nat_Onat_Onat__rec ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_Nat_Onat_Onat__rec ) ) ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__rec__Suc_0) ).
thf(2345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Nat_Onat_Onat__rec ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_Nat_Onat_Onat__rec ) ) ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(177,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(1195,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)],[177]) ).
thf(637,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OLocal ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I66_J_0) ).
thf(2313,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OLocal ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
thf(1392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(138,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(1106,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(702,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(2464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(479,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( 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_Opower__mult__distrib_0) ).
thf(1938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(847,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(polarity_switch,[status(thm)],[846]) ).
thf(748,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(2565,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)],[748]) ).
thf(52,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(879,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)],[52]) ).
thf(380,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(1687,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)],[380]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1457,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
thf(1573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(88,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I27_J_0) ).
thf(974,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(340,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(1592,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)],[340]) ).
thf(719,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(2498,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)],[719]) ).
thf(497,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(1983,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)],[497]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(2377,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_Com_Ocom_OBODY @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OCall_0) ).
thf(1794,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ c_Com_Ocom_OBODY @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(428,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(1804,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)],[428]) ).
thf(753,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(2577,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)],[753]) ).
thf(189,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1227,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(269,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(1425,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(1540,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(393,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(1719,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)],[393]) ).
thf(618,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(2268,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)],[618]) ).
thf(258,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).
thf(1397,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(243,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(1350,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)],[243]) ).
thf(478,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OWhile ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( F @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I69_J_0) ).
thf(1936,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OWhile ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( F @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__rec ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__rec__0_0) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__rec ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(414,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(1772,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)],[414]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(302,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(1498,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)],[302]) ).
thf(338,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1587,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(724,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( tc_Com_Ocom @ ( C @ c_Com_Obody @ c_Option_Othe ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( E @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_0) ).
thf(2509,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( tc_Com_Ocom @ ( C @ c_Com_Obody @ c_Option_Othe ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( E @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(374,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Ocases_0) ).
thf(1672,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(13,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(783,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)],[13]) ).
thf(2635,plain,
( ( ( t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
!= ( t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2627,770]) ).
thf(2636,plain,
( ( t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
!= ( t_a @ ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(simp,[status(thm)],[2635]) ).
thf(2637,plain,
( ( t_a != t_a )
| ( ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( t_a @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ c_Com_Ocom_OBODY @ ( v_x @ ( v_P @ hAPP ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) )
| ( ( v_na @ ( c_Suc @ hAPP ) )
!= v_na ) ),
inference(simp,[status(thm)],[2636]) ).
thf(2638,plain,
( ( v_na @ ( c_Suc @ hAPP ) )
!= v_na ),
inference(simp,[status(thm)],[2637]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OWhile ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
thf(1118,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OWhile ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(1082,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(369,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(1659,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)],[369]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_0) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( 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 ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(1461,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( 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 ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omax ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omax ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(698,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(2455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( 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_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(2080,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( 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_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( C @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(1584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( C @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(577,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(2172,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)],[577]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(1329,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ 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__mono_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ 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)],[265]) ).
thf(443,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(1842,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(550,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(2108,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)],[550]) ).
thf(280,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
thf(1446,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(742,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(2551,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(1016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(540,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(2085,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1612,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(706,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( 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__le__less__mono_0) ).
thf(2472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( 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)],[706]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
thf(1039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
thf(970,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ 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(2317,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ 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)],[639]) ).
thf(157,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).
thf(1155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(34,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I61_J_0) ).
thf(837,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ 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_less__diff__iff_1) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ 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)],[206]) ).
thf(696,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(2450,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(633,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( 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_Opower__add_0) ).
thf(2304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(314,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(1530,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)],[314]) ).
thf(713,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( 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(2487,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(493,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(1974,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)],[493]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(426,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(1799,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)],[426]) ).
thf(98,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1002,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).
thf(1874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(436,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
thf(1825,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(722,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3 ) ) ) @ ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_3) ).
thf(2504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3 ) ) ) @ ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(155,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(1150,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)],[155]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(728,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(2519,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(736,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ~ ( t_a @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__valids__def_1) ).
thf(2536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ~ ( t_a @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(568,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(2153,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)],[568]) ).
thf(670,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(2387,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(438,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(1831,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(655,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(2355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(476,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(1930,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1931,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(polarity_switch,[status(thm)],[1930]) ).
thf(1932,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[1931]) ).
thf(495,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( G @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ ( F @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( D @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( F @ ( F @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( D @ ( C @ c_Com_Ocom_OSemi ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(1979,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( G @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ ( F @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( D @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( F @ ( F @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( F @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( D @ ( C @ c_Com_Ocom_OSemi ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(11,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(779,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)],[11]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
thf(1333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(501,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(1991,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)],[501]) ).
thf(196,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(1241,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( A @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triples__valid__Suc_1) ).
thf(1779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( A @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( v_G @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(765,plain,
! [A: $i] :
( ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( v_G @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(164,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(1170,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(678,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(2408,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)],[678]) ).
thf(172,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(1185,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)],[172]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
thf(926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(124,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(1071,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)],[124]) ).
thf(676,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
thf(2402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(464,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
thf(1895,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(162,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(1167,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
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_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(773,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)],[7]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(1996,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(684,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
thf(2423,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(733,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Orecs_0) ).
thf(2529,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(364,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( D @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
thf(1648,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( D @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(395,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(1727,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)],[395]) ).
thf(680,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( 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(2413,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(579,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 @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(2176,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 @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(487,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(1959,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)],[487]) ).
thf(756,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(2585,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)],[756]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
thf(1631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(614,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(2260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(555,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) )
= B )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(2121,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) )
= B )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(564,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mod_5) ).
thf(2144,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(212,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I57_J_0) ).
thf(1278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(468,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
thf(1906,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(186,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(1219,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)],[186]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(1548,plain,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(475,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 @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(1927,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 @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(516,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_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(2028,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_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(222,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(1301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(1007,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(2048,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(599,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(2225,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)],[599]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(1389,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(366,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_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(1652,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_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(30,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(826,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)],[30]) ).
thf(316,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0L_0) ).
thf(1535,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(386,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Orderings_Oorder__class_Omono ) ) )
| ( ( B @ ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( E @ ( D @ c_Orderings_Oord__class_Omax ) ) @ ( C @ hAPP ) ) )
| ~ ( B @ class_Orderings_Olinorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__of__mono_0) ).
thf(1701,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Orderings_Oorder__class_Omono ) ) )
| ( ( B @ ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( E @ ( D @ c_Orderings_Oord__class_Omax ) ) @ ( C @ hAPP ) ) )
| ~ ( B @ class_Orderings_Olinorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ c_Nat_Onat_Onat__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osplit_1) ).
thf(1965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ c_Nat_Onat_Onat__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(843,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(1125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(584,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( F @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_1) ).
thf(2188,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( F @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(6,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(771,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(772,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(cnf,[status(esa)],[771]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(715,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(2489,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(511,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( C @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
thf(2016,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( C @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(749,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( C @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
thf(2568,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( C @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1428,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_Natural_Oevalc ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
thf(1786,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_Natural_Oevalc ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(936,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(597,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(2220,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)],[597]) ).
thf(643,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(2326,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(628,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
thf(2293,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(635,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(2308,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)],[635]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I23_J_0) ).
thf(787,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(452,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(1865,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)],[452]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( tc_Com_Ocom @ ( C @ c_Com_Obody @ c_Option_Othe ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( E @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weak__Body_0) ).
thf(1733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( tc_Com_Ocom @ ( C @ c_Com_Obody @ c_Option_Othe ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( E @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(119,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(1058,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)],[119]) ).
thf(692,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2 ) ) ) @ ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_1) ).
thf(2442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2 ) ) ) @ ( A @ ( C @ ( D @ ( B @ v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(699,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(2457,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)],[699]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(1503,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(574,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(2166,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( 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_Opower__commutes_0) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(288,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(1464,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)],[288]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
thf(2474,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(77,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(947,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)],[77]) ).
thf(360,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(1638,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)],[360]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(1224,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(640,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(2319,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(751,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_Suc @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__Suc_0) ).
thf(2573,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( c_Suc @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(566,axiom,
( ( v_P @ ( t_a @ c_COMBI @ hAPP ) )
= v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(2148,plain,
( ( v_P @ ( t_a @ c_COMBI @ hAPP ) )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(554,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(2119,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)],[554]) ).
thf(709,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(2478,plain,
! [B: $i,A: $i] :
( ( B @ ( c_Suc @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(2229,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(1806,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(312,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(1524,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)],[312]) ).
thf(545,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(2097,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(319,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(1542,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)],[319]) ).
thf(394,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(1722,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(553,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( B @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
thf(2116,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( B @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(666,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).
thf(2378,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__one_0) ).
thf(863,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(737,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).
thf(2538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
thf(1408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(681,axiom,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(2415,plain,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(717,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(2493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(613,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
thf(2257,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I8_J_0) ).
thf(990,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(96,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).
thf(996,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(477,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(1933,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(609,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 @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(2246,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 @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(1603,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(588,axiom,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(2197,plain,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(491,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ ( B @ c_Natural_Oevaln ) ) ) )
| ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OIfTrue_0) ).
thf(1969,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ ( B @ c_Natural_Oevaln ) ) ) )
| ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(224,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(1307,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)],[224]) ).
thf(372,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__Suc_0) ).
thf(1667,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(23,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(811,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)],[23]) ).
thf(457,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(238,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I51_J_0) ).
thf(1339,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(1731,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(469,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
thf(1909,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(694,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ 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(2446,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(679,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(2410,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)],[679]) ).
thf(240,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(1344,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(611,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(2252,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)],[611]) ).
thf(701,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(2461,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)],[701]) ).
thf(434,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
thf(1820,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(514,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(2025,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower_Opower ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power_Opower_Opower__0_0) ).
thf(1080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_Power_Opower_Opower ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(858,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(558,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(2343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(760,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( tc_Com_Ocom @ ( C @ c_Com_Obody @ c_Option_Othe ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( A @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( E @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).
thf(2593,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( tc_Com_Ocom @ ( C @ c_Com_Obody @ c_Option_Othe ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( A @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( E @ ( E @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( E @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( C @ c_Com_Ocom_OBODY @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(1029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(324,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(1556,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(769,plain,
! [A: $i] :
( ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( v_G @ ( A @ c_in ) ) @ hBOOL )
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(cnf,[status(esa)],[765]) ).
thf(626,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(2289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(484,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(1952,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)],[484]) ).
thf(690,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(2439,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(653,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower_Opower ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ c_Power_Opower_Opower ) ) ) ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power_Opower_Opower__Suc_0) ).
thf(2350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ ( A @ c_Power_Opower_Opower ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ c_Power_Opower_Opower ) ) ) ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(48,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I43_J_0) ).
thf(868,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(167,axiom,
! [B: $i,A: $i] : ( B @ ( A @ c_Com_Ocom_OAss ) @ c_Com_OWT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OAssign_0) ).
thf(1176,plain,
! [B: $i,A: $i] : ( B @ ( A @ c_Com_Ocom_OAss ) @ c_Com_OWT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(92,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(986,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)],[92]) ).
thf(141,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
thf(1113,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).
thf(2022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(1496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(592,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(2207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(723,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
thf(2506,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(91,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(983,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)],[91]) ).
thf(536,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(2075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(2418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(341,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(1594,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(594,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(2212,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)],[594]) ).
thf(82,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( c_Com_Ocom_OSKIP @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I64_J_0) ).
thf(959,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( c_Com_Ocom_OSKIP @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(526,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I30_J_0) ).
thf(2051,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(531,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( t_b @ ( t_b @ ( E @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Osplit_0) ).
thf(2064,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( t_b @ ( t_b @ ( E @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(661,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(2369,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(415,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OWhile ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( J @ ( I @ ( F @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I6_J_0) ).
thf(1775,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OWhile ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( J @ ( I @ ( F @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(608,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(2244,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)],[608]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(383,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__WHILE__case_0) ).
thf(1694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(922,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(507,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(2005,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)],[507]) ).
thf(354,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(1626,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)],[354]) ).
thf(527,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
thf(2054,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(430,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
thf(1809,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(370,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(1662,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)],[370]) ).
thf(223,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).
thf(1304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
thf(1467,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(379,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
thf(1684,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(556,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Option_Ooption_OSome ) @ c_Option_Othe ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Option_Ooption_OSome ) @ c_Option_Othe ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(1509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(590,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(2202,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)],[590]) ).
thf(75,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(939,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)],[75]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
thf(1472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
thf(1551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(755,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( E @ ( G @ ( F @ ( B @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
thf(2582,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( E @ ( G @ ( F @ ( B @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1034,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
thf(2239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(408,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
thf(1758,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(161,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(1166,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(1203,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(795,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(619,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(2271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I25_J_0) ).
thf(1145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(104,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I32_J_0) ).
thf(1018,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(28,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(823,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(404,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( A @ ( D @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( F @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( E @ ( B @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_0) ).
thf(1748,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( A @ ( D @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( F @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( E @ ( B @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(631,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(2298,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)],[631]) ).
thf(413,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1770,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(1516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(664,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(2375,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(586,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(2192,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(757,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(2588,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(249,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(1368,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(406,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(1753,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)],[406]) ).
thf(135,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(1098,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)],[135]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(993,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Oord__class_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(726,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
thf(2513,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(1845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(2397,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(107,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(1025,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)],[107]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(1400,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(1941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
thf(954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(1252,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(1230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(295,axiom,
c_Com_Ocom_OSKIP @ c_Com_OWT,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(1484,plain,
c_Com_Ocom_OSKIP @ c_Com_OWT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(571,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(2160,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)],[571]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(454,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(1869,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)],[454]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).
thf(840,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(686,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(2429,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(648,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 @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(2337,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 @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(621,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(2276,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)],[621]) ).
thf(130,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).
thf(1085,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(740,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(2545,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)],[740]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(523,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(2044,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I29_J_0) ).
thf(1579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(400,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1738,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
thf(1790,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(499,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(1987,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(392,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( E @ ( G @ ( F @ ( C @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
thf(1716,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( E @ ( G @ ( F @ ( C @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(359,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1637,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(205,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1262,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(193,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
thf(1235,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(1317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(410,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(1763,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)],[410]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(2056,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(720,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(2500,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)],[720]) ).
thf(465,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( 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(1898,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(667,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I31_J_0) ).
thf(2379,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(739,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
thf(2543,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( D @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ c_in ) ) @ hBOOL )
| ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__valids__def_0) ).
thf(1670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( D @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ c_in ) ) @ hBOOL )
| ~ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(2030,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(1272,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(745,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(2558,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(552,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(2113,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)],[552]) ).
thf(685,axiom,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(2426,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(1981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(427,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( C @ ( B @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OWhileTrue_0) ).
thf(1802,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( C @ ( B @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(1023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(622,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ( D @ ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
thf(2279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ( D @ ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(656,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(2357,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(1485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(117,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
thf(1052,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OLocal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(305,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( 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_le__eqI_1) ).
thf(1506,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( 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)],[305]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
thf(1094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omin ) ) @ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(725,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(2511,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(617,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= ( C @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__case__Suc_0) ).
thf(2266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= ( C @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( 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_le__add__diff__inverse_0) ).
thf(876,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( 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)],[51]) ).
thf(37,axiom,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(845,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(510,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( F @ ( E @ ( C @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
thf(2013,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( F @ ( E @ ( C @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(442,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(1839,plain,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(654,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I35_J_0) ).
thf(2352,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( F @ ( A @ ( D @ ( E @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(541,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
thf(2088,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(286,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(1459,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)],[286]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(1180,plain,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(483,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(1949,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)],[483]) ).
thf(537,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(2078,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(587,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(2194,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)],[587]) ).
thf(595,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(2215,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)],[595]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ c_Nat_Onat_Onat__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osplit__asm_1) ).
thf(1781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( B @ c_Nat_Onat_Onat__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(174,axiom,
tc_nat @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(1189,plain,
tc_nat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( 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__le__less__trans_0) ).
thf(1108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( 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)],[139]) ).
thf(504,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(1998,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(636,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
thf(2310,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( B @ ( E @ ( D @ ( A @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(445,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( 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(1844,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(652,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(2347,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(1654,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(264,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(1412,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)],[264]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(2110,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(1010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(333,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_lessequals ) ) )
| ( 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__nonpos_0) ).
thf(1575,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_lessequals ) ) )
| ( 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)],[333]) ).
thf(232,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(1326,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)],[232]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
thf(961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(561,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(2135,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_1) ).
thf(1062,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1101,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
thf(1629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(687,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(2431,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)],[687]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(731,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(2526,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(615,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(2262,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)],[615]) ).
thf(673,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(2394,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(759,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(2591,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(1590,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(84,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(963,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(575,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(2167,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)],[575]) ).
thf(620,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(2273,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)],[620]) ).
thf(578,axiom,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(2174,plain,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(624,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(2283,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)],[624]) ).
thf(671,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(2389,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
thf(1491,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(381,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
thf(914,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(675,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(2399,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(416,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OSemi ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( D @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I67_J_0) ).
thf(1777,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OSemi ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( D @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(219,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(1294,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)],[219]) ).
thf(532,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(2066,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(388,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_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(1706,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_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(582,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(2183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(308,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(1513,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(60,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(899,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)],[60]) ).
thf(544,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCond ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( L @ ( K @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( L @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( J @ ( I @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I5_J_0) ).
thf(2095,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( L @ ( K @ ( J @ ( I @ c_Com_Ocom_OCond ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( L @ ( K @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( L @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( J @ ( I @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(638,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OSemi ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( J @ ( I @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I4_J_0) ).
thf(2315,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ c_Com_Ocom_OSemi ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( K @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( J @ ( I @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(512,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(2019,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)],[512]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(1440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(2330,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(658,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
thf(2362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(520,axiom,
! [A: $i] :
( ( ( A @ c_Com_Obody )
= ( tc_Com_Ocom @ c_Option_Ooption_ONone ) )
| ( A @ c_Com_Ocom_OBODY @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(2036,plain,
! [A: $i] :
( ( ( A @ c_Com_Obody )
= ( tc_Com_Ocom @ c_Option_Ooption_ONone ) )
| ( A @ c_Com_Ocom_OBODY @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(279,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0R_0) ).
thf(1444,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omin ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_Com_OWT )
| ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_Com_OWT )
| ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(159,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).
thf(1161,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(349,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).
thf(1614,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(506,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( 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__less__le__mono_0) ).
thf(2003,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( 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)],[506]) ).
thf(596,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ c_Nat_Onat_Onat__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osplit_0) ).
thf(2218,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ c_Nat_Onat_Onat__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(97,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(999,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(486,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ 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(1957,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(669,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(2385,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(569,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(2155,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) )
!= ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(835,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(2233,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(257,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(1395,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)],[257]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( 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_I8_J_0) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( 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)],[26]) ).
thf(729,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(2522,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).
thf(790,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(293,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(1480,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)],[293]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(1642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(547,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(2102,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)],[547]) ).
thf(42,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(854,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)],[42]) ).
thf(508,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( 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(2008,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
thf(1527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
= ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(227,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(1314,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)],[227]) ).
thf(647,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( B @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
thf(2334,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( B @ c_Groebner__Basis_Ogb__semiring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(583,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
thf(2186,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__0_0) ).
thf(1561,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(660,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(2366,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)],[660]) ).
thf(542,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(2091,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)],[542]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(828,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(598,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( D @ ( B @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
thf(2223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
| ( D @ ( B @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(2598,plain,
! [A: $i] :
( ( ( tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) @ hBOOL )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( v_G @ ( A @ c_in ) ) @ hBOOL ) )
| ~ $true
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(paramod_ordered,[status(thm)],[763,769]) ).
thf(2599,plain,
! [A: $i] :
( ( ( tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) @ hBOOL )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( v_G @ ( A @ c_in ) ) @ hBOOL ) )
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(simp,[status(thm)],[2598]) ).
thf(2600,plain,
! [A: $i] :
( ( ( tc_Com_Opname @ ( v_Procs @ ( v_x @ c_in ) ) )
!= ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( v_G @ ( A @ c_in ) ) ) )
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(simp,[status(thm)],[2599]) ).
thf(2613,plain,
! [A: $i] :
( ( ( t_a @ tc_Hoare__Mirabelle_Otriple )
!= tc_Com_Opname )
| ( v_G != v_Procs )
| ( v_x != A )
| ( t_a @ ( A @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(simp,[status(thm)],[2600]) ).
thf(2619,plain,
( ( ( t_a @ tc_Hoare__Mirabelle_Otriple )
!= tc_Com_Opname )
| ( v_G != v_Procs )
| ( t_a @ ( v_x @ ( v_na @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(simp,[status(thm)],[2613]) ).
thf(649,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(2340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1610,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
thf(801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(500,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_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(1989,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_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
thf(1335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(534,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ ( B @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ( A
= ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
thf(2070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ ( B @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ( A
= ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1172,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(262,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(1410,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(1288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(390,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(1710,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)],[390]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(886,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(70,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( c_Com_Ocom_OSKIP @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I1_J_0) ).
thf(928,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( c_Com_Ocom_OSKIP @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(1352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(147,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(1129,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)],[147]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( 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__nonneg__pos_0) ).
thf(1268,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( 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)],[208]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_Orderings_Oord__class_Omax ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(1532,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
thf(1582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(703,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(2467,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( c_Suc @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(494,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(1976,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(246,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).
thf(1357,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(63,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(908,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(303,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I22_J_0) ).
thf(1500,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(474,axiom,
( ( v_Q @ ( t_b @ ( t_a @ ( v_P @ c_COMBK ) ) @ hAPP ) )
= v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def__raw_0) ).
thf(1925,plain,
( ( v_Q @ ( t_b @ ( t_a @ ( v_P @ c_COMBK ) ) @ hAPP ) )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(1299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(467,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 @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1902,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 @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(460,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(1885,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)],[460]) ).
thf(49,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( 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_le__eqI_0) ).
thf(871,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( 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)],[49]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
!= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
thf(1120,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
!= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(2138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( 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_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(1236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( 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_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(721,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ 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(2502,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( B @ c_Com_Ocom_OBODY @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Hoare__Mirabelle_Otriple__valid ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__0_0) ).
thf(2241,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( B @ c_Com_Ocom_OBODY @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Hoare__Mirabelle_Otriple__valid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(712,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(2485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(317,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(1537,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)],[317]) ).
thf(40,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(850,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)],[40]) ).
thf(391,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(1713,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)],[391]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(458,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1880,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(230,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I33_J_0) ).
thf(1320,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( E @ ( D @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(488,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( 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(1962,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ ( 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)],[488]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
thf(1917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(697,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(2453,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)],[697]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(1088,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(431,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(1812,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)],[431]) ).
thf(549,axiom,
( ( t_c @ ( t_b @ ( t_a @ ( v_R @ ( v_Q @ ( v_P @ c_COMBB ) ) ) ) ) )
= ( v_R @ ( v_Q @ hAPP ) @ ( v_P @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def__raw_0) ).
thf(2106,plain,
( ( t_c @ ( t_b @ ( t_a @ ( v_R @ ( v_Q @ ( v_P @ c_COMBB ) ) ) ) ) )
= ( v_R @ ( v_Q @ hAPP ) @ ( v_P @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(705,axiom,
( ( t_c @ ( t_b @ ( t_a @ ( v_R @ ( v_Q @ ( v_P @ c_COMBS ) ) ) ) ) )
= ( v_R @ ( v_Q @ hAPP ) @ ( v_R @ ( v_P @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def__raw_0) ).
thf(2470,plain,
( ( t_c @ ( t_b @ ( t_a @ ( v_R @ ( v_Q @ ( v_P @ c_COMBS ) ) ) ) ) )
= ( v_R @ ( v_Q @ hAPP ) @ ( v_R @ ( v_P @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(1069,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omax ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(470,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(1912,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_While_0) ).
thf(972,plain,
! [B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(234,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(1331,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(1606,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_nat @ ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( 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_Opower__Suc_0) ).
thf(2321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( c_Suc @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower_Opower ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( 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_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(1944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( 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_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( 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(1848,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(529,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( t_b @ ( t_b @ ( E @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Osplit__asm_0) ).
thf(2059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( t_b @ ( t_b @ ( E @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(298,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(1490,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__case__0_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Nat_Onat_Onat__case ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(630,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(2297,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(775,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3038,plain,
$false,
inference(e,[status(thm)],[809,1337,1411,1633,1995,1559,1729,846,909,2480,777,1818,2163,892,2199,1665,1823,1190,1168,2295,2131,1454,2595,1850,1179,2331,1554,1110,1211,2104,1290,2231,2495,2527,1073,2099,1142,1971,1437,861,1855,1200,1750,977,1158,762,1005,2210,1422,1569,1137,1756,1735,1867,1164,2448,2434,814,2459,1954,2042,1788,1426,1275,2141,2476,2627,1260,1761,1342,1640,2580,1354,2146,1222,930,2360,1746,1835,2046,2227,2082,1475,2516,1127,2548,2491,1243,1650,1645,2067,1967,1518,1265,2531,2405,1228,1623,1482,1287,1985,2039,785,1871,1323,1577,2126,1132,2603,2328,1792,1430,2444,1860,1511,917,2562,2488,1832,934,949,2571,1892,2169,1609,2158,1362,2533,1232,1545,2420,1922,902,1247,2552,1319,1704,1890,2373,1347,1013,770,1741,881,2301,1815,1494,2178,1946,1450,1373,2469,2236,1682,1828,2034,905,2324,2027,2291,2254,2555,806,1183,2073,766,1843,2437,2281,2190,866,2371,1600,2205,1564,1447,2483,2523,1796,2242,1345,988,2286,1104,1697,1242,2392,1521,1863,2011,1206,942,1691,925,1783,1067,2574,1438,2364,2164,1470,1708,2093,1311,2307,1768,2382,2061,2000,1636,1047,798,1057,2441,2589,2264,1091,2560,1255,1123,1217,820,1487,1238,1883,1387,1900,957,894,2249,1021,778,1042,952,2541,1174,1676,2133,1619,2150,2032,815,1837,1365,1920,852,1888,830,889,2181,1656,1027,2345,1195,2313,1281,1392,1106,2464,1938,847,2565,879,1687,1457,1573,974,1592,2498,1983,874,2377,1794,1804,2577,1227,1425,1540,1719,2268,1397,1350,1936,1270,1772,980,1498,1587,1096,2509,1672,783,2638,1118,1567,1082,1659,1292,1461,1075,2455,2080,1584,2172,1214,1419,884,1329,1414,1842,2108,1446,2551,1016,2085,1612,2472,1039,970,2317,1155,837,1263,2450,2304,1530,2487,1974,1060,1799,1002,1874,1825,2504,1150,1249,2519,2536,1297,2153,2387,1831,2355,1192,1932,1979,779,1333,1991,1241,1779,765,1170,1187,2408,1185,926,1071,2402,1895,1167,773,1996,2423,2529,1648,1727,2413,2176,1959,2585,856,1631,2260,2121,2144,1278,1906,1219,824,1548,1927,2028,1301,1007,2048,2225,1389,1652,826,1535,1403,1701,1965,843,1125,2188,772,1620,2489,2016,2568,1428,1786,936,2220,2326,2293,2308,787,1865,1733,1058,2442,2457,1139,1503,2166,1765,1464,2474,947,1638,1224,2319,2573,2148,764,2119,2478,2229,1806,1524,2097,1542,1722,2116,2378,863,2538,1408,2415,2493,2257,990,996,1933,2246,1603,1571,1376,2197,1969,1307,1667,811,1877,1339,1993,1731,1909,2446,848,2410,1344,2252,2461,1820,2025,1080,858,1557,2129,2343,2593,1029,1556,769,2289,1177,1381,932,1952,2439,2350,768,868,1176,986,1113,2022,1496,2207,2506,983,2075,2418,1594,1699,2212,959,2051,1245,2064,2369,1775,2244,1435,1694,922,2005,1626,2054,1809,1662,1304,1467,1684,2124,1134,1509,2202,939,1472,1551,2582,1049,1034,2239,1758,1166,1203,1208,795,2271,1145,1018,968,823,1748,2298,1770,1516,2375,2192,2588,1368,1753,1098,993,2513,1845,2397,1025,1743,1400,1941,954,1252,1230,1484,2160,1432,1869,840,2429,2337,2276,1085,2545,1679,2044,1579,1738,1790,1987,1716,1452,1637,1262,1235,1317,1763,2056,2500,1898,2379,2543,1284,1670,2030,1272,1617,2558,2113,2426,1981,1802,1023,2279,2357,1485,1052,1506,1094,2511,2266,876,845,2013,1839,2352,2088,1459,1180,1949,2078,2194,2215,1781,1189,771,1108,1998,2310,1844,2347,1654,1412,2110,1010,1575,1326,961,896,1674,2135,1062,1101,1629,2431,781,2526,2262,2394,2591,1590,963,2167,2273,2174,2283,2389,1491,1689,914,2399,1777,1294,2066,1706,2183,763,1513,899,2095,2315,2019,1045,1440,2330,1077,2362,2036,1309,1444,1442,1161,1614,2003,2218,999,1957,2385,2155,835,2233,1395,818,2522,790,1480,1642,2102,854,2008,1527,1148,1314,2334,2186,1561,2366,2091,828,2223,2619,2340,1610,801,1989,1335,2070,1172,1410,767,1288,1710,1197,886,928,1930,1352,1129,1268,1152,1532,1582,2467,1976,1357,908,1500,1925,1299,1902,1885,871,1120,2138,1236,2502,2241,2600,1384,2485,1537,850,1713,1597,1880,803,1320,1962,1416,1917,2453,1088,1812,2106,2470,1069,1912,972,1331,1606,2321,1944,1848,2059,1490,1037,2297,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV854-1 : 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
% 0.16/0.41 % Computer : n004.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 15:04:06 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.06/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.52/1.35 % [INFO] Parsing done (446ms).
% 2.52/1.37 % [INFO] Running in sequential loop mode.
% 4.01/1.72 % [INFO] eprover registered as external prover.
% 4.01/1.72 % [INFO] Scanning for conjecture ...
% 4.74/1.95 % [INFO] Found a conjecture (or negated_conjecture) and 758 axioms. Running axiom selection ...
% 6.20/2.26 % [INFO] Axiom selection finished. Selected 756 axioms (removed 2 axioms).
% 7.86/2.69 % [INFO] Problem is propositional (TPTP CNF).
% 8.27/2.73 % [INFO] Type checking passed.
% 8.27/2.74 % [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 ...
% 33.65/8.26 % External prover 'e' found a proof!
% 33.65/8.26 % [INFO] Killing All external provers ...
% 33.65/8.26 % Time passed: 7712ms (effective reasoning time: 6888ms)
% 33.65/8.27 % Axioms used in derivation (756): cls_com_Osimps_I1_J_0, cls_com_Osimps_I55_J_0, cls_less__iff__diff__less__0_0, cls_min__max_Oinf__commute_0, cls_add__0__left_0, cls_linorder__antisym__conv2_1, cls_add__pos__nonneg_0, cls_com_Osimps_I18_J_0, cls_evaln_OWhileFalse_0, cls_min__max_Ole__infE_0, cls_comm__monoid__add_Opower__mult__distrib_0, cls_bot__fun__eq_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_option_Oinject_0, cls_Suc__pred_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_order__le__less__trans_0, cls_min__max_Oless__infI1_0, cls_add__is__1_1, cls_less__diff__iff_1, cls_WTs__elim__cases_I6_J_0, cls_class__ringb_Oadd__r0__iff_1, cls_Suc__inject_0, cls_order__less__le__trans_0, cls_Suc__mono_0, cls_min__add__distrib__left_0, cls_le__diff__iff_0, cls_gb__semiring_Osemiring__rules_I12_J_0, cls_gb__semiring_Osemiring__rules_I7_J_0, cls_min__max_Osup__inf__distrib1_0, cls_le__diff__conv_1, cls_add__less__cancel__left_1, cls_insertE_0, cls_gb__semiring_Omul__0_0, cls_com_Osimps_I3_J_0, cls_com_Osimps_I32_J_0, cls_eq__imp__le_0, cls_order__eq__iff_0, cls_com_Osimps_I5_J_0, cls_le__add__diff__inverse2_0, cls_Nat_Odiff__diff__eq_0, cls_COMBC__def_0, cls_min__max_Oinf__sup__distrib1_0, cls_one__is__add_4, cls_Suc__n__not__n_0, cls_min__max_Ole__sup__iff_2, cls_min__max_Oinf__le1_0, cls_com_Osimps_I44_J_0, cls_com_Osimps_I14_J_0, cls_min__less__iff__conj_0, cls_insert__code_1, cls_nat_Osplit_1, cls_hoare__valids__def_2, cls_id__o_0, cls_xt1_I12_J_0, cls_weak__Body_0, cls_nat__add__left__cancel__less_1, cls_termination__basic__simps_I5_J_0, cls_WT_OSemi_0, cls_add__increasing2_0, cls_eq__diff__iff_0, cls_min__0R_0, cls_less__antisym_0, cls_WTs__elim__cases_I4_J_1, cls_less__add__Suc2_0, clsarity_fun__Orderings_Oorder, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_mod__by__0_0, cls_add__is__1_2, cls_linorder__neqE_0, cls_add__strict__right__mono_0, cls_COMBK__def_0, cls_min__max_Osup__inf__absorb_0, cls_nat__rec__Suc_0, cls_insert__absorb_0, cls_evaln__WHILE__case_0, cls_triple_Oinject_1, cls_empty__iff_0, cls_gb__semiring_Osemiring__rules_I3_J_0, cls_min__less__iff__disj_2, cls_o__eq__id__dest_0, cls_not__less__eq_1, cls_option_Osimps_I2_J_0, cls_com_Osimps_I31_J_0, clsarity_nat__Orderings_Olinorder, cls_mod__add__eq_0, cls_termination__basic__simps_I1_J_0, cls_com_Osimps_I56_J_0, cls_add__le__cancel__left_1, cls_WT_OSkip_0, cls_gb__semiring_Opwr__Suc_0, cls_evalc_OSemi_0, cls_add__is__0_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_mod__add__left__eq_0, cls_less__Suc__eq_2, cls_nat__add__left__cancel__less_0, cls_of__nat__aux_Osimps_I2_J_0, cls_min__less__iff__disj_0, cls_one__is__add_1, cls_mem__def_1, cls_add__le__cancel__right_1, cls_gb__semiring_Osemiring__rules_I28_J_0, cls_nat_Osplit__asm_1, cls_derivs__insertD_1, cls_com_Osimps_I5_J_1, cls_comm__monoid__add_Omult__1__right_0, cls_add__leE_0, cls_COMBI__def__raw_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_triples__valid__Suc_1, cls_mod__diff__eq_0, cls_K__record__comp_0, cls_add__cancel__21_1, cls_com_Osimps_I4_J_2, cls_gb__semiring_Osemiring__rules_I13_J_0, cls_min__max_Oinf__sup__distrib2_0, cls_com_Osimps_I7_J_1, cls_com_Osimps_I43_J_0, cls_insert__iff_1, cls_add__diff__assoc2_0, cls_add__nonpos__neg_0, cls_le__maxI2_0, cls_evalc__WHILE__case_0, cls_com_Osimps_I66_J_0, cls_add__left__cancel_0, cls_COMBB__def_0, cls_le__0__eq_0, cls_triple__valid__def2_3, cls_add__gr__0_0, cls_less__max__iff__disj_2, cls_Comp_0, cls_com_Osimps_I54_J_0, cls_evalc__elim__cases_I1_J_0, cls_add__nonneg__pos_0, cls_evaln_OSkip_0, cls_com_Orecs_I6_J_0, cls_gr0I_0, cls_com_Osimps_I47_J_0, cls_WTs__elim__cases_I5_J_0, cls_mod__add__self2_0, cls_add__is__0_1, cls_less__max__iff__disj_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_hoare__derivs_OSkip_0, cls_gb__semiring_Oadd__c_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_nat__less__cases_0, cls_BodyN_0, cls_diff__diff__left_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_min__max_Oless__infI2_0, clsarity_nat__Divides_Osemiring__div, cls_com_Osimps_I45_J_0, cls_gr__implies__not0_0, cls_add__le__mono_0, cls_diff__diff__cancel_0, cls_nat__minus__add__max_0, cls_power_Opower_Opower__0_0, cls_COMBC__def__raw_0, cls_add__less__mono_0, cls_gb__semiring_Omul__c_0, cls_diff__diff__right_0, cls_COMBS__def_0, cls_diff__le__mono2_0, cls_Suc__le__mono_0, cls_order__less__asym_0, cls_min__max_Ole__inf__iff_1, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_le__antisym_0, cls_evalc__elim__cases_I6_J_0, cls_add__right__mono_0, cls_triple_Ocases_0, cls_evaln__elim__cases_I5_J_1, cls_mod__if_1, cls_less__iff__diff__less__0_1, cls_order__eq__refl_0, cls_order__le__less_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_inj__on__insert_0, clsarity_fun__Orderings_Obot, cls_gb__semiring_Omul__d_0, cls_triple_Oinject_2, cls_com_Osimps_I26_J_0, cls_linorder__antisym__conv2_0, cls_WTs__elim__cases_I4_J_0, cls_linorder__antisym__conv1_0, cls_right__minus__eq_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_min__max_Ole__infE_1, cls_insert__ident_0, cls_gb__semiring_Osemiring__rules_I16_J_0, cls_le__imp__diff__is__add_1, cls_gb__semiring_Osemiring__rules_I14_J_0, cls_triple__valid__Suc_0, cls_Suc__leI_0, cls_add__Suc_0, cls_id__apply_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_max__0R_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_diff__add__inverse2_0, cls_min__max_Odistrib__inf__le_0, cls_add__nonneg__eq__0__iff_0, cls_com_Osimps_I10_J_0, cls_nat__add__left__commute_0, cls_trans__le__add2_0, cls_comm__monoid__add_Opower__commutes_0, cls_min__max_Osup__least_0, cls_com_Osimps_I38_J_0, cls_one__is__add_5, cls_class__semiring_Osemiring__rules_I6_J_0, cls_comm__monoid__add_Opower__Suc_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_com_Osimps_I61_J_0, cls_com_Orecs_I7_J_0, cls_xt1_I10_J_0, cls_mod__add__cong_0, cls_not__None__eq_1, cls_com_Osimps_I48_J_0, cls_add__left__mono_0, cls_le__maxI1_0, cls_com_Osimps_I37_J_0, cls_com_Osimps_I60_J_0, cls_evalc_OWhileFalse_0, cls_add__less__cancel__right_1, cls_nat_Osplit_0, cls_com_Osimps_I6_J_0, cls_com_Orecs_I1_J_0, cls_triple_Orecs_0, cls_com_Osimps_I23_J_0, cls_not__less__iff__gr__or__eq_0, cls_diff__Suc__Suc_0, cls_com_Osimps_I65_J_0, cls_min__max_Ole__supE_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_min__max_Ole__sup__iff_1, cls_singleton__iff_1, cls_min__max_Osup__left__idem_0, cls_com_Osimps_I20_J_0, cls_max__diff__distrib__left_0, cls_gb__semiring_Osemiring__rules_I9_J_0, cls_insert__code_2, cls_gb__semiring_Omul__1_0, cls_add__strict__left__mono_0, cls_mod__le__divisor_0, cls_com_Osimps_I58_J_0, cls_evalc_OSkip_0, cls_not__less__eq__eq_1, cls_com_Osimps_I40_J_0, cls_le__iff__diff__le__0_0, cls_com_Osimps_I21_J_0, cls_WTs__elim__cases_I8_J_0, cls_mod__Suc_0, cls_add__le__less__mono_0, cls_add__less__mono1_0, cls_nat__diff__split_0, cls_com_Osimps_I57_J_0, cls_com_Osimps_I64_J_0, cls_com_Osimps_I51_J_0, cls_gb__semiring_Osemiring__rules_I25_J_0, cls_add__is__1_0, cls_evaln_OBody_0, cls_one__is__add_0, cls_WT_OCall_0, cls_com_Osimps_I7_J_0, cls_less__add__Suc1_0, cls_gb__semiring_Osemiring__rules_I21_J_0, cls_com_Osimps_I59_J_0, cls_evalc__elim__cases_I5_J_0, cls_min__max_Ole__infI2_0, cls_Suc__neq__Zero_0, cls_diff__add__0_0, cls_COMBB__def__raw_0, cls_le__max__iff__disj_1, cls_class__semiring_Oadd__a_0, cls_min__max_Ole__iff__inf_1, cls_trans__le__add1_0, cls_the_Osimps_0, cls_evaln__elim__cases_I6_J_0, cls_less__Suc__eq__le_1, cls_le__mod__geq_0, cls_doubleton__eq__iff_2, cls_termination__basic__simps_I4_J_0, cls_min__max_Oless__supI1_0, clsarity_nat__Orderings_Obot, cls_gb__semiring_Osemiring__rules_I5_J_0, cls_xt1_I8_J_0, cls_ex__in__conv_0, cls_termination__basic__simps_I3_J_0, cls_id__fcomp_0, cls_min__max_Oinf__assoc_0, cls_gb__semiring_Osemiring__rules_I17_J_0, cls_evaln__nonstrict_0, cls_min__max_Oinf__idem_0, cls_monoD_0, cls_comm__monoid__add_Omult__commute_0, cls_min__max_Ole__inf__iff_0, cls_evaln_OSemi_0, cls_add__right__cancel_0, cls_com__det_0, cls_class__semiring_Oadd__0_0, cls_com_Osimps_I50_J_0, cls_evalc_OBody_0, cls_min__max_Odistrib__sup__le_0, cls_min__max_Oinf__left__idem_0, cls_com_Osimps_I30_J_0, cls_add__strict__mono_0, cls_comm__monoid__add_Opower__one_0, cls_lessI_0, cls_le__SucE_0, cls_Suc__le__mono_1, cls_com_Osimps_I69_J_0, cls_COMBK__def__raw_0, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_comm__monoid__add_Opower__0_0, cls_mono__Suc_0, cls_min__max_Osup__idem_0, cls_not__leE_0, cls_evaln__elim__cases_I5_J_0, cls_min__max_Ole__supI_0, cls_min__le__iff__disj_0, cls_com_Orecs_I5_J_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_order__antisym_0, cls_add__cancel__21_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_less__Suc__eq__0__disj_3, cls_com_Osimps_I2_J_0, cls_less__add__eq__less_0, cls_max__less__iff__conj_2, cls_com_Osimps_I68_J_0, cls_diff__Suc__diff__eq1_0, cls_evaln_OIfFalse_0, cls_com_Osimps_I46_J_0, cls_split__mod_0, cls_com_Osimps_I19_J_0, cls_order__trans_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_comm__monoid__add_Opower__add_0, cls_com_Osimps_I3_J_1, cls_power_Opower_Opower__Suc_0, cls_com_Osimps_I27_J_0, cls_com_Osimps_I8_J_0, cls_linorder__antisym__conv1_1, cls_evaln_OWhileTrue_0, cls_com_Osimps_I29_J_0, cls_com_Osimps_I9_J_0, clsarity_bool__Orderings_Opreorder, cls_empty__not__insert_0, cls_diff__Suc__diff__eq2_0, cls_com_Osimps_I67_J_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_gb__semiring_Osemiring__rules_I8_J_0, cls_insertI1_0, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_diff__self_0, cls_less__imp__diff__less_0, cls_hoare__derivs_Oinsert_0, cls_diff__is__0__eq_0, cls_natgb_Oadd__cancel_0, cls_diff__less_0, cls_Nitpick_Onat__case__def_0, cls_mod__diff__cong_0, cls_mod__Suc_1, cls_com_Osimps_I70_J_0, cls_neq0__conv_1, cls_linorder__not__le_1, cls_doubleton__eq__iff_0, cls_min__max_Ole__sup__iff_0, cls_gb__semiring_Osemiring__rules_I35_J_0, cls_add__less__cancel__right_0, cls_gb__semiring_Osemiring__rules_I27_J_0, cls_WTs__elim__cases_I5_J_1, cls_com_Orecs_I8_J_0, cls_not__less__less__Suc__eq_0, cls_add__diff__cancel_0, cls_le__trans_0, cls_com_Osimps_I17_J_0, cls_one__is__add_2, cls_WTs__elim__cases_I3_J_0, cls_add__Suc__right_0, cls_singletonE_0, cls_not__less__iff__gr__or__eq_1, cls_not__Some__eq_1, cls_inj__on__empty_0, cls_add__diff__assoc_0, cls_diff__add__assoc_0, cls_insertCI_0, cls_order__le__neq__trans_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_Suc__le__eq_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_nat__diff__split__asm_1, cls_com_Osimps_I25_J_0, cls_mono__iff__le__Suc_0, cls_add__increasing_0, cls_mod__1_0, cls_max__0L_0, cls_le__imp__diff__is__add_0, cls_gb__semiring_Osemiring__rules_I10_J_0, cls_COMBS__def__raw_0, cls_com_Osimps_I34_J_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_order__eq__iff_2, cls_less__not__refl_0, cls_min__max_Oinf__greatest_0, cls_gb__semiring_Osemiring__rules_I2_J_0, cls_gr0__conv__Suc_1, cls_class__ringb_Oadd__cancel_0, cls_add__nonpos__nonpos_0, cls_less__le__not__le_1, cls_add__nonneg__eq__0__iff_1, cls_mod__0_0, cls_bex__empty_0, cls_diff__less__Suc_0, cls_right__minus__eq_1, cls_bot1E_0, cls_linorder__antisym__conv3_0, cls_nat__diff__split_1, cls_linorder__neqE__ordered__idom_0, cls_evalc_OWhileTrue_0, cls_WT_OBody_0, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_mod__diff__right__eq_0, cls_eval__eq_1, cls_mod__add__self1_0, cls_o__eq__dest_0, cls_Suc__diff__diff_0, cls_diff__cancel2_0, cls_add__nonneg__nonneg_0, cls_fcomp__id_0, cls_com_Osimps_I28_J_0, cls_less__diff__conv_1, cls_o__eq__dest__lhs_0, cls_le__diff__conv_0, cls_le__diff__conv2_0, cls_com_Osimps_I42_J_0, cls_order__antisym__conv_0, cls_add__lessD1_0, cls_gb__semiring_Osemiring__rules_I6_J_0, cls_diff__less__mono_0, cls_less__SucE_0, cls_order__neq__le__trans_0, cls_id__def_0, cls_doubleton__eq__iff_3, cls_mod__mod__trivial_0, cls_min__max_Osup__absorb1_0, cls_class__ringb_Oadd__r0__iff_0, cls_less__diff__conv_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_com_Osimps_I13_J_0, cls_inj__on__def_0, cls_gb__semiring_Omul__pwr_0, cls_gb__semiring_Osemiring__rules_I22_J_0, cls_nat_Oinject_0, cls_com_Osimps_I2_J_1, cls_even__less__0__iff_1, cls_add__strict__increasing_0, cls_min__max_Ole__infI1_0, cls_max__less__iff__conj_1, cls_not__less__less__Suc__eq_1, cls_nat__add__left__cancel__le_1, cls_le__add__diff__inverse_0, cls_Nat_Oadd__0__right_0, cls_evaln__Suc_0, cls_min__max_Oinf__sup__absorb_0, cls_linorder__less__linear_0, cls_hoare__valids__def_1, cls_com_Osimps_I49_J_0, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_less__eq__Suc__le_0, cls_gb__semiring_Osemiring__rules_I18_J_0, cls_Suc__lessD_0, cls_order__less__le_2, cls_nat__neq__iff_0, cls_le__less__Suc__eq_0, cls_le0_0, cls_com_Osimps_I12_J_0, cls_gb__semiring_Oadd__0_0, cls_min__max_Osup__inf__distrib2_0, cls_natgb_Oadd__r0__iff_0, cls_com_Osimps_I35_J_0, cls_less__eq__Suc__le_1, cls_com_Osimps_I36_J_0, cls_WT_OIf_0, cls_add__is__1_5, cls_o__id_0, cls_diff__self__eq__0_0, cls_le__add2_0, cls_insert__not__empty_0, cls_xt1_I11_J_0, cls_add__neg__neg_0, cls_mod__less__eq__dividend_0, cls_double__eq__0__iff_0, cls_o__def_0, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_evaln__elim__cases_I6_J_1, cls_add__is__1_4, cls_le__eqI_0, cls_triple__valid__def2_1, cls_min__Suc__Suc_0, cls_min__max_Ole__supI1_0, cls_less__Suc__eq__le_0, cls_Body__triple__valid__Suc_0, cls_nat__add__left__cancel__le_0, cls_insert__absorb2_0, cls_zmod__simps_I2_J_0, cls_inj__on__id_0, cls_min__max_Ole__inf__iff_2, cls_min__less__iff__conj_2, cls_com_Osimps_I52_J_0, cls_diff__Suc__less_0, cls_le__max__iff__disj_2, cls_less__Suc0_0, cls_min__max_Osup__left__commute_0, cls_mod__add__right__eq_0, cls_comm__monoid__add_Omult__left__commute_0, cls_diff__0__right_0, cls_xt1_I6_J_0, cls_empty_0, cls_le__add__right__mono_0, cls_min__max_Ole__iff__sup_1, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_gb__semiring_Oadd__a_0, cls_diff__le__self_0, cls_min__max_Oinf__le2_0, cls_doubleton__eq__iff_1, cls_nat__less__le_0, cls_diff__add__assoc2_0, cls_le__diff__conv2_1, cls_nat_Osimps_I3_J_0, cls_less__trans__Suc_0, cls_le__Suc__eq_2, cls_com_Osimps_I1_J_1, cls_plus__nat_Oadd__0_0, cls_min__max_Osup__assoc_0, cls_min__max_Oinf__absorb2_0, cls_linorder__not__le_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_diff__less__mono2_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_trans__less__add1_0, cls_nat__rec__0_0, cls_comm__monoid__add_Omult__1_0, cls_nat__less__le_2, cls_mod__diff__left__eq_0, cls_evaln__evalc_0, cls_min__max_Oinf__left__commute_0, cls_comp__cong_0, cls_emptyE_0, cls_add__nonneg__eq__0__iff_2, cls_add__is__0_2, cls_less__diff__iff_0, cls_zero__less__diff_1, cls_add__le__mono1_0, cls_minus__nat_Odiff__0_0, cls_add__is__1_3, cls_triple_Oinject_0, cls_order__less__irrefl_0, cls_evalc__elim__cases_I5_J_2, cls_le__iff__add_1, cls_evaln_OIfTrue_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_diff__is__0__eq_1, cls_diff__0__eq__0_0, cls_eq__eqI_1, cls_com_Osimps_I4_J_1, cls_evaln__elim__cases_I1_J_0, cls_Suc__n__not__le__n_0, cls_comm__monoid__add_Ononempty__iff_2, cls_class__semiring_Oadd__c_0, cls_singleton__inject_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_min__max_Oless__supI2_0, cls_of__nat__aux_Osimps_I1_J_0, cls_Suc__leD_0, cls_add__eq__self__zero_0, cls_le__diff__iff_1, cls_add__pos__pos_0, cls_split__mod_5, cls_add__mono_0, cls_mod__less__divisor_0, cls_le__max__iff__disj_0, cls_option_Osimps_I3_J_0, cls_min__le__iff__disj_1, cls_gb__semiring_Osemiring__rules_I24_J_0, cls_min__diff__distrib__left_0, cls_less__SucI_0, cls_add__neg__nonpos_0, clsarity_fun__Orderings_Opreorder, cls_min__le__iff__disj_2, cls_triple_Osplit_0, cls_n__not__Suc__n_0, cls_min__max_Ole__infI_0, cls_inj__on__contraD_0, cls_inj__onD_0, cls_zmod__simps_I1_J_0, cls_com_Osimps_I41_J_0, cls_com_Orecs_I2_J_0, cls_diff__add__inverse_0, cls_diffs0__imp__equal_0, cls_gb__semiring_Osemiring__rules_I19_J_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_fcomp__apply_0, cls_eq__iff__diff__eq__0_1, cls_max__of__mono_0, cls_add__less__cancel__left_0, cls_gb__semiring_Omul__a_0, cls_one__is__add_3, cls_com_Osimps_I22_J_0, cls_not__less0_0, cls_inj__Suc_0, cls_insertCI_1, cls_min__max_Ole__iff__inf_0, cls_class__ringb_Osubr0__iff_1, cls_doubleton__eq__iff_4, cls_Body__triple__valid__0_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_min__max_Ole__iff__sup_0, cls_gb__semiring_Opwr__0_0, cls_less__max__iff__disj_1, cls_insert__code_0, cls_Suc__less__eq_0, cls_min__max_Ole__supI2_0, cls_gb__semiring_Osemiring__rules_I20_J_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_add__leE_1, cls_max__add__distrib__left_0, cls_min__of__mono_0, cls_le__eqI_1, cls_Suc__diff__le_0, cls_gb__semiring_Osemiring__rules_I4_J_0, cls_nat__case__0_0, cls_le__iff__diff__le__0_1, cls_inj__on__id2_0, cls_add__gr__0_2, cls_diff__le__mono_0, cls_add__less__le__mono_0, cls_max__less__iff__conj_0, cls_triple_Osplit__asm_0, cls_evalc_OIfFalse_0, cls_nat__case__Suc_0, cls_WT_OAssign_0, cls_order__less__imp__le_0, cls_fcomp__def_0, cls_add__gr__0_1, cls_min__max_Ole__supE_1, cls_diff__commute_0, cls_hoare__valids__def_0, cls_comm__monoid__add_Opower__Suc2_0, cls_mod__if_0, cls_le__less__Suc__eq_1, cls_less__Suc0_1, cls_le__eq__less__or__eq_0, cls_eq__iff__diff__eq__0_0, cls_insert__commute_0, cls_insert__iff_2, cls_gb__semiring_Opwr__mul_0, cls_monoid__add__class_Oadd__0__right_0, cls_le__add1_0, cls_evaln__elim__cases_I5_J_2, cls_com_Orecs_I3_J_0, cls_add__strict__increasing2_0, cls_le__add__diff_0, cls_evalc__elim__cases_I5_J_1, cls_com_Osimps_I16_J_0, cls_fcomp__assoc_0, cls_termination__basic__simps_I2_J_0, cls_com_Osimps_I15_J_0, cls_class__ringb_Osubr0__iff_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_COMBI__def_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_le__neq__implies__less_0, cls_nat__less__le_1, cls_min__diff_0, cls_com_Osimps_I2_J_2, cls_com_Osimps_I24_J_0, cls_com_Osimps_I63_J_0, cls_com_Osimps_I11_J_0, cls_WT_OLocal_0, cls_add__le__cancel__left_0, cls_com_Osimps_I53_J_0, cls_com_Osimps_I39_J_0, cls_gb__semiring_Osemiring__rules_I11_J_0, cls_min__less__iff__conj_1, cls_xt1_I7_J_0, cls_triple__valid__def2_2, cls_linorder__not__less_1, cls_zero__less__Suc_0, cls_com_Osimps_I33_J_0, cls_cut_0, cls_min__max_Osup__commute_0, cls_com_Osimps_I4_J_0, cls_evalc_OIfTrue_0, cls_max__Suc__Suc_0, cls_o__apply_0, cls_triple__valid__def2_0, cls_mod__self_0, cls_gb__semiring_Osemiring__rules_I23_J_0, cls_less__eqI_1, cls_min__0L_0, cls_Body__triple__valid__Suc_1, cls_not__less__eq__eq_0, cls_gb__semiring_Osemiring__rules_I15_J_0, cls_ball__empty_0, cls_mod__Suc__eq__Suc__mod_0, cls_add__le__cancel__right_0, cls_gb__semiring_Osemiring__rules_I1_J_0, cls_com_Orecs_I4_J_0, cls_derivs__insertD_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_add__diff__inverse_0, cls_com_Osimps_I7_J_2, cls_o__assoc_0, cls_com_Osimps_I71_J_0, cls_le__refl_0, cls_min__less__iff__disj_1, cls_triples__valid__Suc_0, cls_even__less__0__iff_0, cls_le__SucI_0, cls_nat__add__commute_0, cls_com_Osimps_I62_J_0, cls_While_0
% 33.65/8.27 % No. of inferences in proof: 1548
% 33.65/8.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7712 ms resp. 6888 ms w/o parsing
% 33.94/8.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.39/8.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------