%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV908-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:01:00 AM UTC 2026
% Result : Unsatisfiable 22.46s 6.57s
% Output : Refutation 24.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 468
% Syntax : Number of formulae : 937 ( 375 unt; 0 typ; 0 def)
% Number of atoms : 1763 ( 688 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 13252 ( 884 ~; 826 |; 0 &;11542 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 79 usr; 17 con; 0-10 aty)
% Number of variables : 3678 ( 0 ^;3678 !; 0 ?;3678 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Hoare__Mirabelle_Ostate__not__singleton_decl,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
thf(c_Com_OWT__bodies_decl,type,
c_Com_OWT__bodies: $o ).
thf(c_Com_OWT_decl,type,
c_Com_OWT: $i > $o ).
thf(v_c_decl,type,
v_c: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Com_Obody_decl,type,
c_Com_Obody: $i ).
thf(v_pn_decl,type,
v_pn: $i ).
thf(c_Option_Ooption_OSome_decl,type,
c_Option_Ooption_OSome: $i > $i ).
thf(tc_Com_Ocom_decl,type,
tc_Com_Ocom: $i ).
thf(v_y_decl,type,
v_y: $i ).
thf(c_Hoare__Mirabelle_Ohoare__derivs_decl,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_OMGT_decl,type,
c_Hoare__Mirabelle_OMGT: $i ).
thf(c_Com_Ocom_OBODY_decl,type,
c_Com_Ocom_OBODY: $i ).
thf(tc_Hoare__Mirabelle_Otriple_decl,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(tc_Com_Ostate_decl,type,
tc_Com_Ostate: $i ).
thf(tc_Com_Opname_decl,type,
tc_Com_Opname: $i ).
thf(c_Map_Odom_decl,type,
c_Map_Odom: $i > $i > $i > $i ).
thf(c_Option_Othe_decl,type,
c_Option_Othe: $i > $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
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(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_Finite__Set_Ofinite_Ofinite_decl,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Com_Ocom_OWhile_decl,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_decl,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Com_Ocom_OCond_decl,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
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(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_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(class_Orderings_Otop_decl,type,
class_Orderings_Otop: $i > $o ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(c_Option_Ooption_Ooption__case_decl,type,
c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).
thf(c_Option_Ooption_ONone_decl,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_Option_Omap_decl,type,
c_Option_Omap: $i > $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_decl,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Option_Ooption_Ooption__rec_decl,type,
c_Option_Ooption_Ooption__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Oid_decl,type,
c_Fun_Oid: $i > $i ).
thf(c_Option_Ois__none_decl,type,
c_Option_Ois__none: $i > $i > $o ).
thf(c_Map_Omap__add_decl,type,
c_Map_Omap__add: $i > $i > $i > $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Natural_Oevalc_decl,type,
c_Natural_Oevalc: $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Option__Xospec__1__1_decl,type,
c_ATP__Linkup_Osko__Option__Xospec__1__1: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(c_Map_Omap__comp_decl,type,
c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i > $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xfinite__pointwise__1_decl,type,
v_sko__Hoare__Mirabelle__Xfinite__pointwise__1: $i > $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xsingle__stateE__1_decl,type,
v_sko__Hoare__Mirabelle__Xsingle__stateE__1: $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__valids_decl,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(c_fequal_decl,type,
c_fequal: $i > $i ).
thf(v_sko__Hoare__Mirabelle__XMGF__lemma1__1_decl,type,
v_sko__Hoare__Mirabelle__XMGF__lemma1__1: $i > $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(c_Map_Osko__Map__XdomD__1__1_decl,type,
c_Map_Osko__Map__XdomD__1__1: $i > $i > $i > $i > $i ).
thf(c_Com_Osko__Com__XWTs__elim__cases__7__1_decl,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).
thf(c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1_decl,type,
c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1: $i > $i > $i > $i > $i ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(362,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__Body_0) ).
thf(1337,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(227,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1024,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(299,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).
thf(1190,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__add ) ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__map__add_0) ).
thf(1237,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__add ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(666,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I8_J_0) ).
thf(645,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
thf(892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(459,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( B @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_0) ).
thf(1559,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( B @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
thf(1083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(197,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(962,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(1554,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(262,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1110,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(307,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(1211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(84,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(683,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(730,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_0) ).
thf(1068,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)],[245]) ).
thf(408,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
thf(1443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(994,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(398,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( F @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( F @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Com_Opname @ ( F @ ( D @ c_in ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( E @ hAPP ) @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( D @ ( C @ hAPP ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body1_0) ).
thf(1422,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( F @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( F @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Com_Opname @ ( F @ ( D @ c_in ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( E @ hAPP ) @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( D @ ( C @ hAPP ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(453,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( C @ ( B @ ( A @ ( D @ c_Map_Omap__comp ) ) ) ) ) )
= ( E @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__simps_I1_J_0) ).
thf(1544,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( C @ ( B @ ( A @ ( D @ c_Map_Omap__comp ) ) ) ) ) )
= ( E @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_0) ).
thf(614,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)],[60]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_Option_Ooption_OSome @ hAPP ) @ ( A @ c_Option_Omap ) ) ) )
= ( C @ ( A @ hAPP ) @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__Some_0) ).
thf(1041,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_Option_Ooption_OSome @ hAPP ) @ ( A @ c_Option_Omap ) ) ) )
= ( C @ ( A @ hAPP ) @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(164,axiom,
tc_bool @ class_Orderings_Otop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(878,plain,
tc_bool @ class_Orderings_Otop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(655,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)],[75]) ).
thf(22,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(511,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(292,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ tc_Option_Ooption @ ( F @ ( A @ ( E @ c_Option_Ooption_OSome @ hAPP ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( B @ ( E @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).
thf(1173,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ tc_Option_Ooption @ ( F @ ( A @ ( E @ c_Option_Ooption_OSome @ hAPP ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( B @ ( E @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(428,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OBody_0) ).
thf(1486,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(433,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
thf(1497,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I3_J_0) ).
thf(1078,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)],[249]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ ( A @ c_Option_Othe @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ ( A @ c_Option_Othe @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(31,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(533,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(337,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( E @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).
thf(1275,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( E @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(3,negated_conjecture,
v_c @ c_Com_OWT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(472,plain,
v_c @ c_Com_OWT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(139,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(814,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).
thf(747,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)],[112]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(416,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
thf(1458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(33,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_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(538,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_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_in ) ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_in ) ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(1507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).
thf(930,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)],[185]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( C @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I30_J_0) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( C @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(215,axiom,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1001,plain,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(466,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domI_0) ).
thf(1576,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit__asm_1) ).
thf(1529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',cls_evaln_OWhileFalse_0) ).
thf(1243,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)],[322]) ).
thf(271,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( C @ ( G @ ( F @ ( E @ ( A @ c_Map_Omap__comp ) ) ) ) ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( F @ ( E @ hAPP ) )
!= ( B @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__Some__iff_2) ).
thf(1127,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( C @ ( G @ ( F @ ( E @ ( A @ c_Map_Omap__comp ) ) ) ) ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( F @ ( E @ hAPP ) )
!= ( B @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(126,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(782,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
thf(1441,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)],[407]) ).
thf(202,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( E @ ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__add ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).
thf(973,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( E @ ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__add ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(236,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(1046,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(426,axiom,
! [A: $i] :
( ( A @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) )
= ( A @ c_Natural_Oevalc @ ( A @ ( tc_Com_Ostate @ c_fequal @ ( tc_Com_Ostate @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGT__def_0) ).
thf(1482,plain,
! [A: $i] :
( ( A @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) )
= ( A @ c_Natural_Oevalc @ ( A @ ( tc_Com_Ostate @ c_fequal @ ( tc_Com_Ostate @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(328,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( B @ c_in ) ) )
| ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(1254,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( B @ c_in ) ) )
| ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OCall_0) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
thf(570,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ( A = B )
| c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_state__not__singleton__def_1) ).
thf(1298,plain,
! [B: $i,A: $i] :
( ( A = B )
| c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(414,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Option_Ooption_Ooption__case ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I5_J_0) ).
thf(1455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Option_Ooption_Ooption__case ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I22_J_0) ).
thf(949,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)],[192]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(587,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I1_J_0) ).
thf(619,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)],[61]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(114,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(751,plain,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ c_Option_Ooption_ONone @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_0) ).
thf(1462,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ c_Option_Ooption_ONone @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(273,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).
thf(1132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(638,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)],[68]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( A @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(1514,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( A @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( A @ v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ c_in ) ) )
| ~ ( B @ c_Com_OWT )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF__lemma1_0) ).
thf(1247,plain,
! [B: $i,A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( A @ v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ c_in ) ) )
| ~ ( B @ c_Com_OWT )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(870,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(425,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 ) ) )
| ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1479,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 ) ) )
| ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(770,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I6_J_0) ).
thf(1115,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)],[264]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(924,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(361,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I33_J_0) ).
thf(834,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)],[147]) ).
thf(381,axiom,
! [A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_Com_Ostate @ ( A @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( c_Com_Ocom_OBODY @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF__lemma2__simult_0) ).
thf(1383,plain,
! [A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_Com_Ostate @ ( A @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( c_Com_Ocom_OBODY @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).
thf(821,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)],[142]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(1465,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(396,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Option_Ooption_Ooption__rec ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Orecs_I2_J_0) ).
thf(1418,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Option_Ooption_Ooption__rec ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(623,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(296,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(1183,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(340,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
= ( C @ ( D @ ( A @ ( B @ c_Map_Osko__Map__XdomD__1__1 ) ) ) @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domD_0) ).
thf(1283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
= ( C @ ( D @ ( A @ ( B @ c_Map_Osko__Map__XdomD__1__1 ) ) ) @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I29_J_0) ).
thf(981,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)],[206]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(379,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 ) ) )
| ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1377,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 ) ) )
| ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(309,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).
thf(1215,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(1447,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).
thf(1119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1351,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(660,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)],[77]) ).
thf(303,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( D @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) )
!= ( D @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domIff_0) ).
thf(1521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(19,axiom,
tc_nat @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(507,plain,
tc_nat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(527,plain,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(180,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
thf(920,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(23,axiom,
tc_nat @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(512,plain,
tc_nat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
thf(678,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)],[83]) ).
thf(29,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(529,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(406,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
thf(1438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(793,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)],[131]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body__sound__lemma_0) ).
thf(1199,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( E @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_Com_Opname @ ( D @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Ocom_OBODY @ ( tc_Com_Opname @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( B @ tc_fun ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(351,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(1311,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(714,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I57_J_0) ).
thf(798,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)],[133]) ).
thf(241,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 ) ) )
| ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1057,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 ) ) )
| ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(287,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 @ hAPP ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I7_J_0) ).
thf(1163,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 @ hAPP ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(383,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1387,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(225,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(1021,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(952,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)],[193]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(157,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(862,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(464,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ c_Set_Oinsert ) ) )
= ( C @ ( E @ ( A @ c_Map_Odom ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__dom_0) ).
thf(1570,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ c_Set_Oinsert ) ) )
= ( C @ ( E @ ( A @ c_Map_Odom ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(435,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(1502,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(561,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(630,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(957,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)],[195]) ).
thf(312,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Odom ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__map__add_0) ).
thf(1223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Odom ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(894,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)],[169]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(788,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)],[130]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Option_Ooption_Ooption__rec ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Orecs_I1_J_0) ).
thf(916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Option_Ooption_Ooption__rec ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ tc_Option_Ooption @ ( B @ ( C @ ( B @ ( D @ ( A @ c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1 ) ) ) @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( D @ ( B @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Fun_Ofun__upd ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_Map_Odom ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_0) ).
thf(1365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ tc_Option_Ooption @ ( B @ ( C @ ( B @ ( D @ ( A @ c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1 ) ) ) @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( D @ ( B @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Fun_Ofun__upd ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_Map_Odom ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(625,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)],[64]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(879,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)],[165]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(852,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(294,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Map_Omap__comp ) ) ) ) ) )
= ( C @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ hAPP ) )
!= ( B @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__None__iff_3) ).
thf(1178,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Map_Omap__comp ) ) ) ) ) )
= ( C @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ hAPP ) )
!= ( B @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(345,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/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_0) ).
thf(1296,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)],[345]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
thf(1457,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)],[415]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(583,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(889,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)],[167]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_1) ).
thf(1159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(757,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)],[117]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(1407,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_Option_Ooption @ ( B @ ( C @ ( B @ ( A @ c_Map_Odom ) ) @ ( C @ ( B @ ( A @ ( D @ c_Map_Omap__add ) ) ) @ c_Fun_Oinj__on ) ) ) )
| ( C @ tc_Option_Ooption @ ( B @ ( C @ ( B @ ( A @ c_Map_Odom ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__map__add__dom_0) ).
thf(1281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_Option_Ooption @ ( B @ ( C @ ( B @ ( A @ c_Map_Odom ) ) @ ( C @ ( B @ ( A @ ( D @ c_Map_Omap__add ) ) ) @ c_Fun_Oinj__on ) ) ) )
| ( C @ tc_Option_Ooption @ ( B @ ( C @ ( B @ ( A @ c_Map_Odom ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).
thf(1573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1402,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(372,axiom,
! [A: $i] :
( ~ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Com_OWT )
| ( ( A @ ( c_Com_Obody @ hAPP ) )
= ( A @ c_Com_Osko__Com__XWTs__elim__cases__7__1 @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).
thf(1360,plain,
! [A: $i] :
( ~ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Com_OWT )
| ( ( A @ ( c_Com_Obody @ hAPP ) )
= ( A @ c_Com_Osko__Com__XWTs__elim__cases__7__1 @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).
thf(519,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)],[26]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).
thf(650,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)],[73]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(1534,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(1227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCall ) ) @ c_Com_OWT )
| ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).
thf(1425,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCall ) ) @ c_Com_OWT )
| ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(451,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Odom ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__empty_0) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Odom ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
thf(593,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)],[53]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(783,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)],[127]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(499,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).
thf(857,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)],[156]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).
thf(1089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ ( B @ ( A @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
thf(1270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ ( B @ ( A @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(330,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(431,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( B @ ( E @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_1) ).
thf(1493,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( B @ ( E @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Option_Ois__none ) )
| ( A
= ( B @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__none__def_0) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Option_Ois__none ) )
| ( A
= ( B @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1424,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(394,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/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I4_J_0) ).
thf(1414,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)],[394]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1039,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)],[233]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
thf(706,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)],[94]) ).
thf(463,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_in ) ) )
| ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1567,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_in ) ) )
| ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(2,negated_conjecture,
c_Com_OWT__bodies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(471,plain,
c_Com_OWT__bodies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(884,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)],[166]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( D @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).
thf(1329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= ( D @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_1) ).
thf(1292,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)],[343]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(933,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)],[186]) ).
thf(248,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( E @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__nonempty_0) ).
thf(1075,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( E @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).
thf(590,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)],[52]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I24_J_0) ).
thf(837,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)],[148]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Option_Ooption @ ( B @ ( D @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_1) ).
thf(1324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Option_Ooption @ ( B @ ( D @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(91,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(701,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Option_Ooption_Ooption__case ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I4_J_0) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Option_Ooption_Ooption__case ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).
thf(1002,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)],[216]) ).
thf(402,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( E @ ( A @ hAPP ) )
= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).
thf(1429,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( E @ ( A @ hAPP ) )
= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I20_J_0) ).
thf(779,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)],[125]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( A @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGT__BodyN_0) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( A @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(985,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I68_J_0) ).
thf(1150,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)],[281]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1249,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(1266,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(316,axiom,
( ( v_c @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) )
= ( v_c @ c_Natural_Oevalc @ ( v_c @ ( tc_Com_Ostate @ c_fequal @ ( tc_Com_Ostate @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGT__def__raw_0) ).
thf(1231,plain,
( ( v_c @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) )
= ( v_c @ c_Natural_Oevalc @ ( v_c @ ( tc_Com_Ostate @ c_fequal @ ( tc_Com_Ostate @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(238,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).
thf(1050,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(911,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(385,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/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(1393,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)],[385]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).
thf(605,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)],[57]) ).
thf(354,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/sandbox/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
thf(1318,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)],[354]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ tc_Option_Ooption @ ( B @ c_Option_Ooption_ONone @ c_COMBK ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__empty_0) ).
thf(1241,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ tc_Option_Ooption @ ( B @ c_Option_Ooption_ONone @ c_COMBK ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(508,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(461,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(1563,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(765,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)],[120]) ).
thf(341,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).
thf(1286,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(246,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
thf(1071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I28_J_0) ).
thf(530,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)],[30]) ).
thf(297,axiom,
! [A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ( ( A @ v_sko__Hoare__Mirabelle__Xsingle__stateE__1 )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__stateE_0) ).
thf(1185,plain,
! [A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ( ( A @ v_sko__Hoare__Mirabelle__Xsingle__stateE__1 )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(718,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(1086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_thin_0) ).
thf(1167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(174,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(906,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(338,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( F @ ( E @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( E @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).
thf(1278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( F @ ( E @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( E @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( B @ c_Option_Ooption_OSome @ hAPP ) @ c_ATP__Linkup_Osko__Option__Xospec__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ospec_1) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( B @ c_Option_Ooption_OSome @ hAPP ) @ c_ATP__Linkup_Osko__Option__Xospec__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(347,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( E @ ( D @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( D @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_2) ).
thf(1301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( E @ ( D @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( D @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(378,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( E @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
= ( D @ ( E @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__fun__upd_1) ).
thf(1374,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( E @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
= ( D @ ( E @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
thf(1146,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)],[279]) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(1154,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)],[283]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(743,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)],[110]) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',cls_evaln_OWhileTrue_0) ).
thf(1124,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)],[269]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1007,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
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_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(694,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)],[88]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I51_J_0) ).
thf(875,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)],[163]) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I26_J_0) ).
thf(826,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)],[144]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(577,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(95,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_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(711,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_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I61_J_0) ).
thf(545,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)],[35]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( B @ ( c_Com_Ocom_OBODY @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(1488,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( B @ ( c_Com_Ocom_OBODY @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(276,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(187,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(936,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(96,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(713,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(261,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(1107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1239,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)],[320]) ).
thf(360,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( E @ c_Finite__Set_Ofinite ) )
| ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( D @ hAPP ) @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( B @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( E @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( G @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( C @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( F @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( E @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( D @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( C @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( B @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__pointwise_1) ).
thf(1332,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( E @ c_Finite__Set_Ofinite ) )
| ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( D @ hAPP ) @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( B @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( E @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( G @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( C @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( F @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( E @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( D @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( C @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( B @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(1092,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I9_J_0) ).
thf(804,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(704,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)],[93]) ).
thf(419,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1464,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(540,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)],[34]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(979,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(306,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1209,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)],[306]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).
thf(900,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)],[171]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(831,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(1524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(237,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1048,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(990,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)],[210]) ).
thf(452,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1542,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I43_J_0) ).
thf(567,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)],[43]) ).
thf(278,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(1144,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(108,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(737,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(235,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1043,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(349,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( G @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( G @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(1307,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( G @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( G @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I67_J_0) ).
thf(1117,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)],[265]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(1471,plain,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(250,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = G )
| ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( C @ tc_Option_Ooption @ ( E @ ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).
thf(1080,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = G )
| ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( C @ tc_Option_Ooption @ ( E @ ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(363,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1339,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(816,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I64_J_0) ).
thf(621,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)],[62]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(483,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( B @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( B @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( c_Com_Ocom_OBODY @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Com_Opname @ ( B @ c_Finite__Set_Ofinite ) )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( B @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( c_Com_Ocom_OBODY @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGT__Body_0) ).
thf(1344,plain,
! [B: $i,A: $i] :
( ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( B @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( B @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( c_Com_Ocom_OBODY @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Com_Opname @ ( B @ c_Finite__Set_Ofinite ) )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( B @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( c_Com_Ocom_OBODY @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(668,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)],[80]) ).
thf(263,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ ( F @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
| ( ( C @ ( E @ ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__add ) ) ) )
= ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( C @ ( E @ ( F @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upd__left_0) ).
thf(1112,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ ( F @ c_Map_Odom ) ) @ ( B @ c_in ) ) )
| ( ( C @ ( E @ ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__add ) ) ) )
= ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( C @ ( E @ ( F @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(458,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(1557,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)],[458]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(552,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)],[38]) ).
thf(190,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(943,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I69_J_0) ).
thf(1171,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)],[291]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(1474,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(323,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/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I5_J_0) ).
thf(1245,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)],[323]) ).
thf(293,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( E @ c_Finite__Set_Ofinite ) )
| ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( G @ hAPP ) @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( E @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( G @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( C @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( F @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( E @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( D @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( C @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( B @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__pointwise_0) ).
thf(1176,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( E @ c_Finite__Set_Ofinite ) )
| ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( G @ hAPP ) @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( C @ ( G @ ( D @ ( F @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xfinite__pointwise__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( E @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( G @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( C @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( F @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( E @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( D @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( C @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( B @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(404,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1435,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(424,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1477,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(658,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OWhile ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
thf(1213,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)],[308]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(409,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/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
thf(1445,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)],[409]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(868,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(4,negated_conjecture,
( ( v_pn @ ( c_Com_Obody @ hAPP ) )
= ( v_y @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(473,plain,
( ( v_pn @ ( c_Com_Obody @ hAPP ) )
= ( v_y @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).
thf(1034,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)],[231]) ).
thf(348,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = G )
| ( ( F @ ( A @ hAPP ) )
= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).
thf(1304,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = G )
| ( ( F @ ( A @ hAPP ) )
= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(944,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)],[191]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_Option_Ooption_ONone ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Option_Omap ) ) ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__is__None_0) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_Option_Ooption_ONone ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Option_Omap ) ) ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(397,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(1420,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(927,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)],[183]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(648,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(1509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I23_J_0) ).
thf(516,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)],[25]) ).
thf(224,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 ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1018,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 ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I32_J_0) ).
thf(663,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)],[78]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(548,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(968,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I8_J_0) ).
thf(1181,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)],[295]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(580,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(872,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)],[162]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(447,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ( A
= ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
thf(1531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ( A
= ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(427,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).
thf(1484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(211,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(993,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(454,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ tc_Option_Ooption @ ( G @ ( F @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( B = E )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).
thf(1547,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ tc_Option_Ooption @ ( G @ ( F @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( B = E )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(776,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_Com_OWT )
| ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
thf(1225,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)],[313]) ).
thf(388,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 @ hAPP ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I70_J_0) ).
thf(1400,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 @ hAPP ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( I @ ( G @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(326,axiom,
tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ c_Finite__Set_Ofinite ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).
thf(1252,plain,
tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ c_Finite__Set_Ofinite ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(673,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)],[82]) ).
thf(403,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(1432,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(412,axiom,
c_Com_Ocom_OSKIP @ c_Com_OWT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(1452,plain,
c_Com_Ocom_OSKIP @ c_Com_OWT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',cls_evaln_OIfTrue_0) ).
thf(1188,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)],[298]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(585,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(840,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(318,axiom,
! [A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ ( A @ c_Com_OWT )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF_0) ).
thf(1235,plain,
! [A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ ( A @ c_Com_OWT )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(1,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(470,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(450,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I71_J_0) ).
thf(1538,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)],[450]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( A @ tc_Option_Ooption @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_COMBK ) ) @ c_Map_Odom ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__const_0) ).
thf(1218,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( A @ tc_Option_Ooption @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_COMBK ) ) @ c_Map_Odom ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_2) ).
thf(643,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)],[70]) ).
thf(311,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).
thf(1220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( E @ c_in ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(434,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( A @ hAPP ) )
= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).
thf(1499,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( A @ hAPP ) )
= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',cls_com_Orecs_I2_J_0) ).
thf(1130,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)],[272]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( C @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I31_J_0) ).
thf(1579,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( C @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) ) )
| ( ( C @ ( B @ ( A @ c_Map_Odom ) ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__eq__empty__conv_0) ).
thf(1404,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) ) )
| ( ( C @ ( B @ ( A @ c_Map_Odom ) ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(1257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
thf(600,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)],[55]) ).
thf(401,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/sandbox/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(1427,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)],[401]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_0) ).
thf(1094,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_Option_Ooption_ONone @ ( A @ c_Option_Omap ) ) ) )
= ( C @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option__map__None_0) ).
thf(1008,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_Option_Ooption_ONone @ ( A @ c_Option_Omap ) ) ) )
= ( C @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
thf(1372,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)],[377]) ).
thf(277,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(1141,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(449,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
thf(1536,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(336,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(1272,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
thf(1316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(556,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(8,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(482,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(671,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(172,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(903,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(524,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)],[27]) ).
thf(441,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) )
| ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
thf(1517,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) )
| ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(270,axiom,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(1126,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(13,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(495,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I66_J_0) ).
thf(1412,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)],[393]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(384,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( C @ ( B @ ( A @ ( D @ c_Map_Omap__comp ) ) ) ) ) )
= ( E @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__None__iff_2) ).
thf(1390,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( C @ ( B @ ( A @ ( D @ c_Map_Omap__comp ) ) ) ) ) )
= ( E @ c_Option_Ooption_ONone ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(342,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__None_1) ).
thf(1289,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( D @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(413,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/sandbox/benchmark/theBenchmark.p',cls_evaln_OIfFalse_0) ).
thf(1453,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)],[413]) ).
thf(358,axiom,
! [A: $i] :
( ( ( A @ ( c_Com_Obody @ hAPP ) )
= ( tc_Com_Ocom @ c_Option_Ooption_ONone ) )
| ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(1326,plain,
! [A: $i] :
( ( ( A @ ( c_Com_Obody @ hAPP ) )
= ( tc_Com_Ocom @ c_Option_Ooption_ONone ) )
| ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(382,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
thf(1385,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(963,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(258,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(1101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(327,axiom,
! [B: $i,A: $i] : ( B @ ( A @ c_Com_Ocom_OAss ) @ c_Com_OWT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OAssign_0) ).
thf(1253,plain,
! [B: $i,A: $i] : ( B @ ( A @ c_Com_Ocom_OAss ) @ c_Com_OWT ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(90,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_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(699,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_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I25_J_0) ).
thf(731,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)],[105]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(1491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(21,axiom,
tc_nat @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(510,plain,
tc_nat @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( A @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BodyN_0) ).
thf(1294,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( A @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(184,axiom,
! [A: $i] : ( A @ ( A @ c_Option_Ooption_ONone @ c_Option_Ois__none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__none__def_1) ).
thf(929,plain,
! [A: $i] : ( A @ ( A @ c_Option_Ooption_ONone @ c_Option_Ois__none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ( B @ c_Com_OWT )
| ~ c_Com_OWT__bodies
| ( ( A @ ( c_Com_Obody @ hAPP ) )
!= ( B @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ( B @ c_Com_OWT )
| ~ c_Com_OWT__bodies
| ( ( A @ ( c_Com_Obody @ hAPP ) )
!= ( B @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Otop )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(763,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Otop )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_1) ).
thf(684,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)],[85]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Com_Ocom_OCond ) ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
thf(1161,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)],[286]) ).
thf(367,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/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1348,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)],[367]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).
thf(752,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)],[115]) ).
thf(439,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(1512,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(1097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(1395,plain,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(818,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)],[141]) ).
thf(380,axiom,
! [A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(1380,plain,
! [A: $i] :
( ( A @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(854,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(56,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(603,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Oimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(1527,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Oimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OWhile ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_While_0) ).
thf(1148,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)],[280]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(405,axiom,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_Option_Ois__none ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_is__none__code_I2_J_0) ).
thf(1436,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_Option_Ois__none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(432,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
thf(1495,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(18,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(506,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(136,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(807,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(460,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( E @ ( D @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
thf(1561,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( E @ ( D @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domIff_1) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
| ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(1165,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)],[288]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__sound_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(179,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(918,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(801,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(352,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(1314,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(897,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)],[170]) ).
thf(392,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( D @ ( F @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upd_0) ).
thf(1410,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( D @ ( F @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(196,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I27_J_0) ).
thf(635,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)],[67]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(987,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ ( tc_Com_Ostate @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ ( tc_Com_Ostate @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF__complete_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ ( tc_Com_Ostate @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ ( tc_Com_Ostate @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(331,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1261,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(282,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1152,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(468,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( A @ ( D @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_triple__valid__def2_0) ).
thf(1582,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( A @ ( D @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( 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)],[468]) ).
thf(455,axiom,
! [B: $i,A: $i] : ( A @ tc_Option_Ooption @ ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__Some_0) ).
thf(1550,plain,
! [B: $i,A: $i] : ( A @ tc_Option_Ooption @ ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(371,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ ( C @ ( B @ ( A @ ( E @ c_Map_Omap__comp ) ) ) ) ) )
= ( D @ ( E @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__comp__simps_I2_J_0) ).
thf(1357,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ ( C @ ( B @ ( A @ ( E @ c_Map_Omap__comp ) ) ) ) ) )
= ( D @ ( E @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).
thf(691,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)],[87]) ).
thf(436,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(1505,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(501,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(103,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(728,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).
thf(740,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)],[109]) ).
thf(334,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/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
thf(1268,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)],[334]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(575,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)],[46]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(462,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I65_J_0) ).
thf(1565,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)],[462]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1037,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ c_Com_OWT )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF__lemma1_1) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ c_Com_OWT )
| ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( c_Hoare__Mirabelle_OMGT @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(1468,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(496,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(5,negated_conjecture,
~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( c_Com_Ocom_OBODY @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(469,plain,
~ ( tc_Com_Ostate @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Ocom @ tc_Option_Ooption @ ( c_Com_Obody @ ( tc_Com_Ocom @ c_Option_Othe @ c_COMBB ) ) ) ) @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ ( tc_Com_Opname @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ ( tc_Com_Ocom @ ( c_Com_Ocom_OBODY @ ( c_Hoare__Mirabelle_OMGT @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
thf(940,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)],[189]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ tc_Option_Ooption @ ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( D @ tc_Option_Ooption @ ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__map__add__dom_1) ).
thf(1204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ tc_Option_Ooption @ ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( D @ tc_Option_Ooption @ ( C @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( A @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(1449,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( A @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1599,plain,
$false,
inference(e,[status(thm)],[1322,809,1337,1024,1190,760,1237,666,645,892,479,1559,1105,909,1031,1083,962,1554,1110,977,1211,1005,683,730,1068,1443,994,1422,1073,1544,614,1041,878,655,511,1173,1486,1497,1078,1137,533,550,1275,472,1233,814,747,1063,1458,538,1354,1507,930,829,1196,1001,1576,1529,1243,1127,782,1441,973,1046,1482,1254,1055,570,1298,1455,949,587,619,702,751,1462,1132,638,1514,1247,870,1479,770,1398,1115,924,1334,834,1383,966,821,492,1465,1418,623,1183,1283,981,1169,1377,1215,734,1447,1119,1351,660,1201,849,1521,507,527,1206,920,512,678,529,1438,793,1199,1311,714,798,1057,1163,1387,1021,952,1519,862,1570,598,1502,561,630,957,1223,894,788,1370,916,847,1365,625,879,852,1178,1296,1457,583,889,1159,757,1407,1281,1573,1012,1402,1360,519,650,1534,1121,1227,1425,1540,593,610,783,499,857,697,1089,1270,1259,1493,1028,554,1424,1414,489,1039,706,1567,471,884,1329,1292,933,1075,476,1016,590,837,1324,701,721,1002,1429,779,1263,997,1099,985,1150,1249,1266,1231,1060,1050,984,911,1393,503,605,1318,1241,633,508,921,1563,765,1286,1071,530,1185,773,718,1086,938,1026,1167,906,1278,1135,750,1103,824,745,1301,689,1374,513,1146,1154,743,1124,904,975,1007,694,875,826,577,711,545,1488,641,1139,936,572,713,1107,1239,1332,1092,804,704,1464,540,979,1209,900,831,1524,1048,990,1542,567,1144,737,1043,1122,1307,863,784,1117,811,1471,1080,1339,816,726,621,483,1344,1460,668,1112,1557,552,943,1022,1171,1474,1245,1176,1435,1477,851,653,658,1213,768,1445,868,473,1034,1304,944,795,1420,927,648,1509,516,1018,1551,663,548,968,1181,580,872,1156,971,1368,1531,1484,993,1547,776,1225,1400,954,1252,673,1432,1452,1188,585,840,1235,470,1538,1218,643,1220,1053,1499,1130,1579,1404,1257,600,1427,1094,1008,1372,1141,1536,1272,612,845,1316,556,482,671,903,524,1517,1126,495,1412,1010,1390,1289,1453,1326,1385,963,1341,1101,1253,699,731,786,1491,914,510,1294,929,1193,763,684,1309,536,716,1161,1348,999,752,1512,1097,1229,1395,818,1380,854,865,603,735,1527,1148,564,1436,1495,506,807,1561,1065,1165,1346,918,801,1363,1314,897,1410,960,635,987,1352,1261,1152,1582,1550,1357,723,691,1505,501,728,740,1268,575,486,1320,1565,1037,1416,755,1468,496,1014,469,940,1204,1449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV908-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.70 % Computer : n015.cluster.edu
% 0.11/0.70 % Model : x86_64 x86_64
% 0.11/0.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.70 % Memory : 8046.5625MB
% 0.11/0.70 % OS : Linux 6.8.0-71-generic
% 0.11/0.70 % CPULimit : 300
% 0.11/0.70 % WCLimit : 300
% 0.11/0.70 % DateTime : Sat Sep 26 15:12:14 UTC 2026
% 0.11/0.70 % CPUTime :
% 0.11/0.70 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.14/1.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.14/1.59 % [INFO] Parsing done (383ms).
% 2.62/1.60 % [INFO] Running in sequential loop mode.
% 3.66/1.94 % [INFO] eprover registered as external prover.
% 3.66/1.95 % [INFO] Scanning for conjecture ...
% 4.07/2.14 % [INFO] Found a conjecture (or negated_conjecture) and 476 axioms. Running axiom selection ...
% 5.54/2.48 % [INFO] Axiom selection finished. Selected 463 axioms (removed 13 axioms).
% 7.18/2.89 % [INFO] Problem is propositional (TPTP CNF).
% 7.59/2.93 % [INFO] Type checking passed.
% 7.59/2.94 % [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 ...
% 22.46/6.56 % External prover 'e' found a proof!
% 22.46/6.56 % [INFO] Killing All external provers ...
% 22.46/6.56 % Time passed: 5717ms (effective reasoning time: 4957ms)
% 22.46/6.57 % Axioms used in derivation (463): cls_inj__image__mem__iff_1, cls_com_Osimps_I55_J_0, cls_option_Oinject_0, cls_map__upd__eqD1_0, cls_inj__Some_0, cls_com_Osimps_I18_J_0, cls_WTs__elim__cases_I6_J_0, clsarity_nat__HOL_Oord, cls_com_Osimps_I1_J_0, cls_asm_0, cls_subset__insert_1, cls_evaln_OWhileFalse_0, cls_sup__ge1_0, cls_insertE_0, cls_com_Osimps_I3_J_0, cls_com_Osimps_I32_J_0, cls_com_Osimps_I5_J_0, cls_equalityI_0, cls_map__add__None_2, cls_sup__top__left_0, cls_image__constant_0, clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite, cls_Un__subset__iff_0, cls_Suc__inject_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_map__add__assoc_0, cls_finite__insert_0, cls_Suc__n__not__n_0, cls_ospec_1, cls_empty__is__image_1, cls_com_Osimps_I14_J_0, cls_image__mono_0, cls_Un__empty__left_0, cls_fun__upd__apply_1, cls_map__upd__Some__unfold_4, cls_le__funD_0, cls_fun__upd__image_1, cls_weak__Body_0, cls_inj__image__eq__iff_0, cls_com_Osimps_I44_J_0, cls_sup__bot__right_0, cls_insert__code_1, cls_WT_OSemi_0, cls_map__upd__Some__unfold_3, cls_WTs__elim__cases_I4_J_1, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_finite__Un_2, cls_COMBK__def_0, cls_UnCI_1, cls_map__comp__simps_I2_J_0, cls_insert__absorb_0, cls_evaln__WHILE__case_0, cls_triple_Oinject_1, cls_evalc_OSemi_0, cls_hoare__derivs_OBody_0, cls_option_Osimps_I2_J_0, cls_com_Osimps_I31_J_0, cls_mem__def_1, clsarity_nat__Orderings_Olinorder, cls_com_Osimps_I56_J_0, cls_WT_OSkip_0, cls_WTs__elim__cases_I7_J_0, cls_empty__iff_0, cls_derivs__insertD_1, cls_com_Osimps_I7_J_1, cls_com_Osimps_I5_J_1, cls_evalc__WHILE__case_0, cls_insert__subset_0, clsarity_fun__Lattices_Oupper__semilattice, cls_inj__image__subset__iff_0, cls_com_Osimps_I4_J_2, cls_le__sup__iff_0, cls_set__rev__mp_0, cls_inj__on__Un__image__eq__iff_0, cls_com_Osimps_I66_J_0, cls_com_Osimps_I43_J_0, cls_insert__iff_1, cls_COMBB__def_0, cls_map__add__Some__iff_3, cls_com_Osimps_I47_J_0, cls_inj__image__mem__iff_0, cls_subset__insert__iff_2, cls_WTs__elim__cases_I5_J_0, clsarity_fun__Orderings_Otop, cls_Comp_0, cls_com_Osimps_I54_J_0, cls_evalc__elim__cases_I1_J_0, cls_hoare__derivs_OSkip_0, cls_finite__insert_1, cls_evaln_OSkip_0, cls_com_Orecs_I6_J_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_COMBS__def_0, cls_BodyN_0, cls_com_Osimps_I45_J_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_evalc__elim__cases_I6_J_0, cls_le__supI_0, cls_Un__subset__iff_1, cls_evaln__elim__cases_I5_J_1, cls_empty__is__image_0, cls_rangeI_0, cls_rev__image__eqI_0, clsarity_fun__Orderings_Obot, cls_map__upd__Some__unfold_0, cls_triple_Oinject_2, cls_com_Osimps_I26_J_0, cls_inj__on__insert_0, cls_finite__range__imageI_0, cls_is__none__code_I2_J_0, cls_range__composition_0, cls_le__supE_1, cls_fun__upd__other_0, cls_le__iff__sup_0, cls_WTs__elim__cases_I4_J_0, cls_image__id_0, cls_image__constant__conv_1, cls_map__comp__simps_I1_J_0, cls_Un__UNIV__right_0, cls_dom__const_0, cls_Un__absorb2_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_triple__valid__Suc_0, cls_MGF__lemma1_1, cls_id__apply_0, cls_map__add__upd__left_0, cls_com_Osimps_I61_J_0, cls_WT__bodiesD_0, cls_com_Orecs_I7_J_0, cls_sup__eq__bot__eq2_0, cls_com_Osimps_I37_J_0, cls_com_Osimps_I10_J_0, cls_Un__upper2_0, cls_com_Osimps_I65_J_0, cls_com_Osimps_I38_J_0, cls_not__None__eq_1, cls_com_Osimps_I48_J_0, cls_MGF__complete_0, cls_com_Osimps_I60_J_0, cls_evalc_OWhileFalse_0, cls_com_Osimps_I6_J_0, cls_com_Orecs_I1_J_0, cls_UnCI_0, cls_com_Osimps_I23_J_0, cls_map__add__dom__app__simps_I2_J_0, cls_MGF_0, cls_ATP__Linkup_OCOMBC__def_0, cls_singleton__iff_1, cls_com_Osimps_I20_J_0, cls_finite_0, cls_subset__iff_0, cls_insert__code_2, cls_Body__sound__lemma_0, cls_com_Osimps_I58_J_0, clsarity_fun__HOL_Oord, cls_evalc_OSkip_0, cls_subset__empty_0, cls_com_Osimps_I40_J_0, cls_rev__predicate1D_0, cls_com_Osimps_I21_J_0, cls_WTs__elim__cases_I8_J_0, cls_com_Osimps_I57_J_0, cls_image__insert_0, cls_evalc__elim__cases_I5_J_0, cls_com_Osimps_I64_J_0, cls_UNIV__not__empty_0, cls_WT_OCall_0, cls_com_Osimps_I7_J_0, cls_the_Osimps_0, cls_com_Osimps_I59_J_0, cls_map__add__dom__app__simps_I3_J_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_com_Osimps_I51_J_0, cls_evaln_OBody_0, clsarity_bool__Lattices_Oupper__semilattice, cls_evaln__elim__cases_I6_J_0, cls_Un__insert__left_0, cls_doubleton__eq__iff_2, cls_map__upd__nonempty_0, cls_fun__upd__triv_0, clsarity_nat__Orderings_Obot, cls_option_Orecs_I2_J_0, cls_com__det_0, cls_finite__surj_0, cls_finite__UnI_0, cls_Un__mono_0, cls_dom__eq__empty__conv_0, cls_insert__subset_1, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_com_Osimps_I50_J_0, cls_inj__image__subset__iff_1, cls_evaln_OSemi_0, cls_ex__in__conv_0, cls_option__map__None_0, cls_sup__commute_0, cls_finite__pointwise_0, cls_set__eq__subset_2, cls_evalc_OBody_0, cls_com_Osimps_I69_J_0, cls_is__none__def_0, cls_com_Osimps_I30_J_0, cls_map__comp__Some__iff_2, cls_evaln__elim__cases_I5_J_0, clsarity_fun__Lattices_Olattice, cls_com_Orecs_I5_J_0, cls_map__add__None_0, cls_linorder__linear_0, cls_Un__empty_0, cls_ATP__Linkup_OCOMBB__def_0, cls_Un__subset__iff_2, cls_MGT__BodyN_0, cls_com_Osimps_I19_J_0, cls_com_Osimps_I2_J_0, cls_dom__map__add_0, cls_com_Osimps_I68_J_0, cls_evaln_OIfFalse_0, cls_subset__trans_0, cls_com_Osimps_I3_J_1, cls_com_Osimps_I46_J_0, cls_insert__is__Un_0, cls_image__empty_0, cls_finite__UNIV_0, cls_dom__eq__singleton__conv_0, cls_com_Osimps_I27_J_0, cls_com_Osimps_I8_J_0, cls_map__upd__triv_0, cls_com_Osimps_I29_J_0, cls_map__upd__Some__unfold_1, cls_com_Osimps_I9_J_0, cls_le__supE_0, cls_option_Osimps_I4_J_0, cls_hoare__derivs_Oinsert_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_empty__map__add_0, cls_dom__empty_0, cls_MGT__def__raw_0, cls_com_Osimps_I67_J_0, cls_image__constant__conv_0, cls_MGF__lemma1_0, cls_insertI1_0, cls_state__not__singleton__def_1, cls_evaln_OWhileTrue_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_com_Osimps_I70_J_0, cls_fun__upd__twist_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup__top__right_0, cls_MGT__def_0, cls_Un__UNIV__left_0, cls_sup__least_0, cls_com_Orecs_I8_J_0, cls_com_Osimps_I17_J_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_sup1E_0, cls_WTs__elim__cases_I3_J_0, cls_subset__refl_0, cls_WTs__elim__cases_I5_J_1, cls_singletonE_0, cls_inj__on__iff_0, cls_com_Osimps_I25_J_0, cls_image__Un_0, clsarity_nat__Lattices_Olattice, cls_inj__on__empty_0, cls_UNIV__I_0, cls_sup1CI_1, cls_image__iff_2, cls_finite__dom__body_0, cls_insertCI_0, cls_fun__upd__apply_0, cls_dom__eq__singleton__conv_1, cls_com_Osimps_I34_J_0, cls_not__Some__eq_1, cls_insert__dom_0, cls_top1I_0, cls_bot1E_0, cls_weaken_0, cls_option_Osplit_1, cls_Body1_0, cls_evalc_OWhileTrue_0, cls_WT_OBody_0, cls_Un__assoc_0, cls_bex__empty_0, cls_insert__mono_0, cls_eval__eq_1, cls_le__supI2_0, cls_domI_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_domIff_0, cls_inj__on__fun__updI_0, cls_com_Osimps_I42_J_0, cls_nat_Oinject_0, cls_com_Osimps_I2_J_1, cls_UnE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_map__comp__None__iff_3, cls_com_Osimps_I28_J_0, cls_Un__absorb_0, cls_com_Osimps_I13_J_0, cls_inj__on__def_0, cls_map__add__SomeD_0, clsarity_bool__Lattices_Olattice, cls_MGT__Body_0, cls_injD_0, cls_com_Osimps_I49_J_0, cls_inj__on__map__add__dom_0, cls_map__add__upd_0, cls_evaln__Suc_0, clsarity_bool__Lattices_Obounded__lattice, cls_com_Osimps_I36_J_0, cls_map__add__empty_0, cls_WT_OIf_0, cls_sup__left__idem_0, cls_option__map__is__None_0, cls_thin_0, cls_subsetD_0, cls_finite__imageD_0, cls_Body__triple__valid__Suc_0, cls_insert__not__empty_0, cls_finite__Un_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_com_Osimps_I12_J_0, cls_finite__subset_0, cls_insert__subset_2, cls_com_Osimps_I35_J_0, cls_evaln__elim__cases_I6_J_1, cls_le__supI1_0, cls_insert__absorb2_0, cls_fun__upd__idem_0, cls_inj__on__id_0, cls_empty_0, cls_domD_0, cls_subset__singletonD_0, cls_com_Osimps_I52_J_0, cls_single__stateE_0, cls_doubleton__eq__iff_1, cls_finite__pointwise_1, cls_fun__upd__idem__iff_0, cls_option_Osplit__asm_1, cls_com_Osimps_I1_J_1, cls_Un__left__absorb_0, cls_evaln__evalc_0, cls_evalc__elim__cases_I5_J_2, cls_is__none__def_1, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_inf__sup__aci_I5_J_0, cls_map__upd__Some__unfold_2, cls_triple_Oinject_0, cls_Un__empty_1, cls_subset__insert_0, cls_sup__idem_0, cls_MGF__lemma2__simult_0, cls_evaln_OIfTrue_0, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_fun__upd__same_0, cls_com_Osimps_I4_J_1, cls_evaln__elim__cases_I1_J_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_subset__inj__on_0, cls_map__add__dom__app__simps_I1_J_0, cls_singleton__inject_0, cls_sup__ge2_0, cls_n__not__Suc__n_0, cls_Un__least_0, cls_option_Osimps_I3_J_0, cls_inj__on__contraD_0, cls_sup1CI_0, cls_inj__onD_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_finite__surj__inj_0, cls_com_Osimps_I41_J_0, cls_image__eqI_0, cls_subset__UNIV_0, cls_image__subset__iff_0, cls_finite__imageI_0, cls_com_Osimps_I22_J_0, cls_com_Orecs_I2_J_0, cls_finite_OemptyI_0, cls_insertCI_1, cls_option_Orecs_I1_J_0, cls_option_Osplit_0, cls_doubleton__eq__iff_4, cls_dom__fun__upd_1, cls_insert__code_0, cls_map__add__find__right_0, cls_subset__insertI_0, cls_evalc_OIfFalse_0, cls_WT_OAssign_0, cls_domIff_1, cls_map__add__Some__iff_2, cls_image__image_0, cls_sup__bot__left_0, cls_insert__image_0, cls_rev__finite__subset_0, cls_finite__Un_1, cls_fun__upd__upd_0, cls_evaln__elim__cases_I5_J_2, cls_hoare__sound_0, cls_map__add__SomeD_1, cls_com_Osimps_I15_J_0, cls_endo__inj__surj_0, cls_insert__commute_0, cls_insert__iff_2, cls_com_Orecs_I3_J_0, cls_inj__on__Un_1, cls_evalc__elim__cases_I5_J_1, cls_com_Osimps_I16_J_0, cls_option__map__Some_0, cls_image__is__empty_0, cls_com_Osimps_I33_J_0, cls_inj__on__map__add__dom_1, cls_Un__insert__right_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_cut_0, cls_sup__absorb1_0, cls_com_Osimps_I53_J_0, cls_com_Osimps_I39_J_0, cls_option_Osimps_I5_J_0, cls_equalityE_0, cls_imageI_0, cls_WT_OLocal_0, cls_com_Osimps_I4_J_0, cls_evalc_OIfTrue_0, cls_triple__valid__def2_0, cls_map__comp__None__iff_2, cls_ball__empty_0, cls_com_Orecs_I4_J_0, cls_map__add__None_1, cls_fun__upd__idem__iff_1, cls_com_Osimps_I7_J_2, cls_com_Osimps_I71_J_0, cls_subset__insert__iff_1, cls_Body__triple__valid__Suc_1, clsarity_bool__Orderings_Otop, cls_com_Osimps_I62_J_0, cls_While_0, cls_derivs__insertD_0, cls_predicate1D_0
% 22.46/6.57 % No. of inferences in proof: 937
% 22.46/6.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5717 ms resp. 4957 ms w/o parsing
% 24.27/7.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.27/7.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------