%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV925-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 09:01:02 AM UTC 2026
% Result : Unsatisfiable 16.49s 5.17s
% Output : Refutation 18.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 612
% Syntax : Number of formulae : 1225 ( 675 unt; 0 typ; 0 def)
% Number of atoms : 2015 (1118 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 19958 (1124 ~; 790 |; 0 &;18044 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 82 usr; 12 con; 0-8 aty)
% Number of variables : 5406 ( 0 ^;5406 !; 0 ?;5406 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(tc_String_Ochar_decl,type,
tc_String_Ochar: $i ).
thf(tc_Type_Oty_decl,type,
tc_Type_Oty: $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(v_aj_decl,type,
v_aj: $i ).
thf(v_ak_decl,type,
v_ak: $i ).
thf(tc_Value_Oval_decl,type,
tc_Value_Oval: $i ).
thf(c_DefAss_O_092_060D_062_decl,type,
c_DefAss_O_092_060D_062: $i > $i > $i > $o ).
thf(v_al_decl,type,
v_al: $i ).
thf(c_DefAss_OhyperUn_decl,type,
c_DefAss_OhyperUn: $i > $i > $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Option_Ooption_OSome_decl,type,
c_Option_Ooption_OSome: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i ).
thf(c_SmallStep_Oblocks_decl,type,
c_SmallStep_Oblocks: $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tc_Expr_Oexp_decl,type,
tc_Expr_Oexp: $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Expr_Oexp_OBlock_decl,type,
c_Expr_Oexp_OBlock: $i > $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_Olinorder__class_Oinsort__key_decl,type,
c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_OTryCatch_decl,type,
c_Expr_Oexp_OTryCatch: $i > $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_Onew_decl,type,
c_Expr_Oexp_Onew: $i > $i > $i ).
thf(c_Expr_Oexp_Othrow_decl,type,
c_Expr_Oexp_Othrow: $i > $i > $i ).
thf(c_Expr_Oexp_OFAcc_decl,type,
c_Expr_Oexp_OFAcc: $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_OCond_decl,type,
c_Expr_Oexp_OCond: $i > $i > $i > $i > $i ).
thf(c_List_Olinorder__class_Osorted_decl,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(c_List_OtakeWhile_decl,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(c_Expr_Oexp_OLAss_decl,type,
c_Expr_Oexp_OLAss: $i > $i > $i > $i ).
thf(c_Expr_Oexp_OVal_decl,type,
c_Expr_Oexp_OVal: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Expr_Oexp_OFAss_decl,type,
c_Expr_Oexp_OFAss: $i > $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_OBinOp_decl,type,
c_Expr_Oexp_OBinOp: $i > $i > $i > $i > $i ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i > $i ).
thf(c_Expr_Oexp_OCall_decl,type,
c_Expr_Oexp_OCall: $i > $i > $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_Expr_Oexp_OSeq_decl,type,
c_Expr_Oexp_OSeq: $i > $i > $i > $i ).
thf(c_Expr_Oexp_OWhile_decl,type,
c_Expr_Oexp_OWhile: $i > $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_Expr_Oexp_OCast_decl,type,
c_Expr_Oexp_OCast: $i > $i > $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_BigStep_Ofinal_decl,type,
c_BigStep_Ofinal: $i > $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $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_DefAss_O_092_060A_062_decl,type,
c_DefAss_O_092_060A_062: $i > $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
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_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(c_Map_Omap__upds_decl,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_List_Oconcat_decl,type,
c_List_Oconcat: $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_Fun_Ooverride__on_decl,type,
c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).
thf(c_SmallStep_Ored_decl,type,
c_SmallStep_Ored: $i > $i ).
thf(c_List_Osplice_decl,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(c_Map_Omap__comp_decl,type,
c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_DefAss_Ohyper__subset_decl,type,
c_DefAss_Ohyper__subset: $i > $i > $i > $o ).
thf(c_BigStep_Oeval_decl,type,
c_BigStep_Oeval: $i > $i > $i > $i > $i > $o ).
thf(c_Equivalence_Osko__Equivalence__XblocksEval__1__1_decl,type,
c_Equivalence_Osko__Equivalence__XblocksEval__1__1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(645,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).
thf(1337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(266,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).
thf(1411,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(186,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I168_J_0) ).
thf(1168,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(527,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(2031,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(395,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__None__iff_3) ).
thf(1729,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)],[395]) ).
thf(7,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I43_J_0) ).
thf(628,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(189,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I138_J_0) ).
thf(1179,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(55,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).
thf(777,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(1554,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_1) ).
thf(1686,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)],[376]) ).
thf(601,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( C @ ( C @ ( C @ ( A @ c_DefAss_O_092_060A_062 ) @ ( D @ c_DefAss_OhyperUn ) ) @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I11_J_2) ).
thf(2199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( C @ ( C @ ( C @ ( A @ c_DefAss_O_092_060A_062 ) @ ( D @ c_DefAss_OhyperUn ) ) @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(237,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__upds ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upds_0) ).
thf(1322,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__upds ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( F @ ( E @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(367,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ c_in ) ) )
| ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) )
| ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1665,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ c_in ) ) )
| ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) )
| ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_List_Olist @ ( B @ ( A @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oconcat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__eq__concat__conv_0) ).
thf(1586,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_List_Olist @ ( B @ ( A @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oconcat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(66,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I106_J_0) ).
thf(809,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(254,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I97_J_0) ).
thf(1369,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(1823,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(492,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1950,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)],[492]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( A @ c_DefAss_OhyperUn ) ) )
= ( B @ ( A @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ c_DefAss_OhyperUn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hyper__insert__comm_0) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( A @ c_DefAss_OhyperUn ) ) )
= ( B @ ( A @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ c_DefAss_OhyperUn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060A_062 ) )
= ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( D @ ( A @ c_DefAss_O_092_060A_062 ) @ c_DefAss_OhyperUn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I4_J_0) ).
thf(2117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060A_062 ) )
= ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( D @ ( A @ c_DefAss_O_092_060A_062 ) @ c_DefAss_OhyperUn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(38,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).
thf(730,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(540,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(2062,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(277,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I182_J_0) ).
thf(1443,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(347,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).
thf(1618,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(132,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).
thf(994,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(741,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)],[42]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1544,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)],[314]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1591,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)],[333]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(878,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I38_J_0) ).
thf(1305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I221_J_0) ).
thf(861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_2) ).
thf(1855,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)],[451]) ).
thf(196,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(1200,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(480,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( F @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( E @ ( E @ ( E @ ( A @ c_DefAss_O_092_060A_062 ) @ ( F @ c_DefAss_OhyperUn ) ) @ ( D @ c_DefAss_O_092_060D_062 ) ) )
| ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I8_J_2) ).
thf(1924,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( F @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( E @ ( E @ ( E @ ( A @ c_DefAss_O_092_060A_062 ) @ ( F @ c_DefAss_OhyperUn ) ) @ ( D @ c_DefAss_O_092_060D_062 ) ) )
| ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(606,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(2210,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(270,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I217_J_0) ).
thf(1422,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(324,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_0) ).
thf(1569,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)],[324]) ).
thf(500,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(1971,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)],[500]) ).
thf(424,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ c_in ) ) )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1793,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ c_in ) ) )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(2,negated_conjecture,
( ( tc_Value_Oval @ tc_List_Olist @ ( tc_Value_Oval @ ( v_ak @ ( v_aj @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_Type_Oty @ tc_List_Olist @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(614,plain,
( ( tc_Value_Oval @ tc_List_Olist @ ( tc_Value_Oval @ ( v_ak @ ( v_aj @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_Type_Oty @ tc_List_Olist @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( B @ c_List_Odistinct ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oset @ hAPP ) )
!= ( C @ ( A @ c_List_Oset @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__distinct__set__unique_0) ).
thf(1692,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( B @ c_List_Odistinct ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oset @ hAPP ) )
!= ( C @ ( A @ c_List_Oset @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(677,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(384,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( E @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).
thf(1705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( E @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).
thf(2035,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(33,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I47_J_0) ).
thf(715,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(221,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I198_J_0) ).
thf(1275,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(457,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_OVal ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedBlock_0) ).
thf(1872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_OVal ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).
thf(1327,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(112,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I191_J_0) ).
thf(945,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(532,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(2042,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(578,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_1) ).
thf(2146,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)],[578]) ).
thf(184,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I153_J_0) ).
thf(1164,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(62,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I113_J_0) ).
thf(797,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(587,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(2168,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)],[587]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(698,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)],[28]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1761,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)],[408]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060A_062 ) )
= ( C @ ( B @ c_DefAss_O_092_060A_062 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I2_J_0) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060A_062 ) )
= ( C @ ( B @ c_DefAss_O_092_060A_062 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(106,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I203_J_0) ).
thf(930,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(608,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(2216,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)],[608]) ).
thf(522,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(2020,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)],[522]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ ( A @ c_List_Oset @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oset @ hAPP ) )
= ( A @ ( C @ ( A @ c_List_Oset @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(259,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).
thf(1386,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(549,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Expr_Oexp_Onew ) @ c_DefAss_O_092_060A_062 ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I1_J_0) ).
thf(2082,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Expr_Oexp_Onew ) @ c_DefAss_O_092_060A_062 ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(1724,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(1529,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_0) ).
thf(1482,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(1243,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)],[209]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( A @ c_List_OtakeWhile ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).
thf(1782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( A @ c_List_OtakeWhile ) ) @ ( C @ c_List_Oset @ hAPP ) @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(260,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I205_J_0) ).
thf(1391,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(1576,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)],[327]) ).
thf(123,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).
thf(973,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(91,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).
thf(885,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(518,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).
thf(2010,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)],[518]) ).
thf(485,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1935,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)],[485]) ).
thf(589,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(2173,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(253,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I199_J_0) ).
thf(1366,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(471,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1904,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)],[471]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ ( D @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I6_J_0) ).
thf(1703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ ( D @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).
thf(1430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(365,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).
thf(1660,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(217,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I148_J_0) ).
thf(1264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(234,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I172_J_0) ).
thf(1313,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(2126,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)],[569]) ).
thf(174,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I114_J_0) ).
thf(1132,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(152,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I70_J_0) ).
thf(1055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(36,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).
thf(724,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I64_J_0) ).
thf(917,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(46,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I46_J_0) ).
thf(751,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(2185,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__None_0) ).
thf(1455,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)],[281]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I66_J_0) ).
thf(934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(193,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I188_J_0) ).
thf(1191,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(479,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(1922,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(1800,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(853,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(1892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(302,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I207_J_0) ).
thf(1514,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(534,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(2049,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)],[534]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( B @ ( B @ ( D @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( B @ ( B @ ( D @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( A @ c_List_Oset @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( A @ tc_List_Olist @ ( A @ c_List_Oset @ ( B @ ( A @ tc_List_Olist @ c_List_Oset @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__concat_0) ).
thf(1741,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_List_Oconcat ) @ ( A @ c_List_Oset @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( A @ tc_List_Olist @ ( A @ c_List_Oset @ ( B @ ( A @ tc_List_Olist @ c_List_Oset @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(169,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I108_J_0) ).
thf(1115,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(483,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Oset @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty_1) ).
thf(1931,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Oset @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(357,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_in ) ) )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1641,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_in ) ) )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(434,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ ( D @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I15_J_1) ).
thf(1815,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ ( D @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(1100,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1847,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)],[446]) ).
thf(236,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).
thf(1319,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(87,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I190_J_0) ).
thf(870,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(464,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/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1890,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)],[464]) ).
thf(121,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).
thf(969,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(246,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I109_J_0) ).
thf(1347,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I9_J_0) ).
thf(1572,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(459,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( J @ ( I @ c_Pair ) ) ) @ ( H @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( D @ c_BigStep_Oeval ) ) ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( B @ ( A @ ( G @ ( I @ ( F @ ( H @ ( E @ ( D @ c_Equivalence_Osko__Equivalence__XblocksEval__1__1 ) ) ) ) ) ) ) @ ( I @ c_Pair ) ) ) @ ( H @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ ( G @ c_Map_Omap__upds ) ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ ( D @ c_BigStep_Oeval ) ) ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_Value_Oval @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_blocksEval_0) ).
thf(1875,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( J @ ( I @ c_Pair ) ) ) @ ( H @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( D @ c_BigStep_Oeval ) ) ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( B @ ( A @ ( G @ ( I @ ( F @ ( H @ ( E @ ( D @ c_Equivalence_Osko__Equivalence__XblocksEval__1__1 ) ) ) ) ) ) ) @ ( I @ c_Pair ) ) ) @ ( H @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ ( G @ c_Map_Omap__upds ) ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ ( D @ c_BigStep_Oeval ) ) ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_Value_Oval @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(1778,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(924,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)],[104]) ).
thf(231,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I92_J_0) ).
thf(1302,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I220_J_0) ).
thf(789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(554,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(2090,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) )
| ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_2) ).
thf(1911,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(503,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1978,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)],[503]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(372,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I7_J_1) ).
thf(1677,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).
thf(806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(224,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I200_J_0) ).
thf(1283,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(70,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I101_J_0) ).
thf(821,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).
thf(2017,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(1946,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(285,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I42_J_0) ).
thf(1465,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(560,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(2105,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)],[560]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( B @ ( B @ ( D @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).
thf(1811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( B @ ( B @ ( D @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(1858,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(454,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(1864,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(567,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( E @ ( C @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I12_J_2) ).
thf(2122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( E @ ( C @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(258,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I149_J_0) ).
thf(1383,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(140,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).
thf(1020,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(329,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I15_J_0) ).
thf(1581,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(120,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I219_J_0) ).
thf(966,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(51,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I142_J_0) ).
thf(766,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(538,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( C @ ( C @ ( C @ ( A @ c_DefAss_O_092_060A_062 ) @ ( D @ c_DefAss_OhyperUn ) ) @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I13_J_2) ).
thf(2058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( C @ ( C @ ( C @ ( A @ c_DefAss_O_092_060A_062 ) @ ( D @ c_DefAss_OhyperUn ) ) @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(482,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__simps_I2_J_0) ).
thf(1928,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)],[482]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I89_J_0) ).
thf(1377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I162_J_0) ).
thf(634,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(597,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(2190,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(157,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).
thf(1072,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(349,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/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(1622,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)],[349]) ).
thf(261,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I103_J_0) ).
thf(1394,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(988,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1433,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)],[274]) ).
thf(559,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_DefAss_O_092_060A_062 ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I3_J_0) ).
thf(2103,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_DefAss_O_092_060A_062 ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( C @ c_Expr_Oexp_Onew ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I1_J_0) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( C @ c_Expr_Oexp_Onew ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(604,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/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(2205,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)],[604]) ).
thf(198,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).
thf(1206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I4_J_0) ).
thf(920,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)],[102]) ).
thf(111,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(942,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(2204,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).
thf(1438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(585,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( D @ c_List_OtakeWhile ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).
thf(2164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( D @ c_List_OtakeWhile ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(50,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).
thf(761,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I6_J_1) ).
thf(2047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(385,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(1708,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(1736,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oset @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty_0) ).
thf(1768,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oset @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(149,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I164_J_0) ).
thf(1047,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(513,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(2000,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)],[513]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(1900,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1255,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)],[213]) ).
thf(572,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( C @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I13_J_1) ).
thf(2133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( C @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(1217,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)],[201]) ).
thf(292,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).
thf(1487,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(27,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = G )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_1) ).
thf(693,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = G )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(815,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_DefAss_Ohyper__subset ) ) )
| ~ ( C @ ( D @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_D__mono_0) ).
thf(2015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_DefAss_Ohyper__subset ) ) )
| ~ ( C @ ( D @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I209_J_0) ).
thf(957,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).
thf(1223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(94,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I215_J_0) ).
thf(894,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(162,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I115_J_0) ).
thf(1091,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(148,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).
thf(1042,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(403,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ c_in ) ) )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1751,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ c_in ) ) )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(462,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(1883,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(320,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ~ ( E @ ( D @ c_List_Odistinct ) )
| ( E @ ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__insort_2) ).
thf(1560,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ~ ( E @ ( D @ c_List_Odistinct ) )
| ( E @ ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(486,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/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1938,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)],[486]) ).
thf(144,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).
thf(1032,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(478,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/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1920,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)],[478]) ).
thf(499,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(463,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ c_in ) ) )
| ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) )
| ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1888,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ c_in ) ) )
| ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) )
| ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(282,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).
thf(1457,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(73,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).
thf(830,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(592,axiom,
! [B: $i,A: $i] : ( A @ tc_Option_Ooption @ ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__Some_0) ).
thf(2179,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)],[592]) ).
thf(607,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( D @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( D @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insort__key_Osimps_I1_J_0) ).
thf(2213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( D @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( D @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(48,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(757,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(24,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).
thf(682,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(1281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(354,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/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1634,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)],[354]) ).
thf(77,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_BigStep_Ofinal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_final__def_1) ).
thf(842,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_BigStep_Ofinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(543,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(2068,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)],[543]) ).
thf(350,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__Some__iff_2) ).
thf(1624,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)],[350]) ).
thf(442,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).
thf(1836,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)],[442]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(1787,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).
thf(2112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(227,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).
thf(1291,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(247,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I32_J_0) ).
thf(1350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(206,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(1234,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(505,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1983,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(171,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_0) ).
thf(1121,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(271,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).
thf(1425,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( E @ c_in ) ) )
| ( E @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__append1_0) ).
thf(1672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( E @ c_in ) ) )
| ( E @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(1878,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_DefAss_Ohyper__subset ) ) )
| ( C @ ( C @ ( B @ ( D @ c_DefAss_OhyperUn ) ) @ ( C @ ( B @ ( A @ c_DefAss_OhyperUn ) ) @ c_DefAss_Ohyper__subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sqUn__lem_0) ).
thf(1755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_DefAss_Ohyper__subset ) ) )
| ( C @ ( C @ ( B @ ( D @ c_DefAss_OhyperUn ) ) @ ( C @ ( B @ ( A @ c_DefAss_OhyperUn ) ) @ c_DefAss_Ohyper__subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(262,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I165_J_0) ).
thf(1397,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(582,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/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(2157,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)],[582]) ).
thf(177,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I29_J_0) ).
thf(1143,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(564,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/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(2115,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)],[564]) ).
thf(409,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1762,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)],[409]) ).
thf(558,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).
thf(2100,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)],[558]) ).
thf(220,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).
thf(1270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(449,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1851,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)],[449]) ).
thf(15,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).
thf(650,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(113,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I58_J_0) ).
thf(948,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(1017,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ ( D @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I2_J_0) ).
thf(1953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ ( D @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060A_062 ) )
= ( C @ ( C @ ( B @ c_DefAss_O_092_060A_062 ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ c_DefAss_OhyperUn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I6_J_0) ).
thf(1804,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060A_062 ) )
= ( C @ ( C @ ( B @ c_DefAss_O_092_060A_062 ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ c_DefAss_OhyperUn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(3,negated_conjecture,
( ~ ( tc_String_Ochar @ tc_List_Olist @ ( v_A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( v_al @ ( tc_Value_Oval @ ( v_ak @ ( v_aj @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( v_A @ c_DefAss_OhyperUn ) ) @ ( v_al @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(615,plain,
( ~ ( tc_String_Ochar @ tc_List_Olist @ ( v_A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( v_al @ ( tc_Value_Oval @ ( v_ak @ ( v_aj @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( v_A @ c_DefAss_OhyperUn ) ) @ ( v_al @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(136,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = H )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).
thf(1006,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = H )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(176,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_2) ).
thf(1138,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(390,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1719,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(57,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I194_J_0) ).
thf(783,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(170,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I21_J_0) ).
thf(1118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1567,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(524,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( A @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(2023,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)],[524]) ).
thf(251,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).
thf(1361,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(933,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)],[107]) ).
thf(190,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I31_J_0) ).
thf(1182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).
thf(669,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I83_J_0) ).
thf(642,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).
thf(637,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I2_J_1) ).
thf(1791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(1644,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(497,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1964,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)],[497]) ).
thf(488,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(1942,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(600,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(2196,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(444,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(1842,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(561,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( E @ ( C @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I4_J_1) ).
thf(2108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( E @ ( C @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(278,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(1446,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(1612,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(23,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I105_J_0) ).
thf(679,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1039,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1297,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)],[229]) ).
thf(580,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ c_List_Olist_ONil @ ( A @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty2_1) ).
thf(2153,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ c_List_Olist_ONil @ ( A @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1974,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)],[501]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).
thf(1050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(1984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(2052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(1715,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_Onew ) @ c_DefAss_O_092_060D_062 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I1_J_0) ).
thf(1720,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_Onew ) @ c_DefAss_O_092_060D_062 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(407,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1759,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)],[407]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ c_Expr_Oexp_Othrow ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I14_J_0) ).
thf(1825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( A @ c_Expr_Oexp_Othrow ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(238,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I102_J_0) ).
thf(1324,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(14,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).
thf(647,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( B @ ( B @ ( D @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).
thf(1776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( B @ ( B @ ( D @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Oappend ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(216,axiom,
! [A: $i] : ( A @ ( A @ c_Option_Ooption_ONone @ c_Option_Ois__none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__none__def_1) ).
thf(1263,plain,
! [A: $i] : ( A @ ( A @ c_Option_Ooption_ONone @ c_Option_Ois__none ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(133,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I163_J_0) ).
thf(997,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(128,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I28_J_0) ).
thf(984,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).
thf(911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(516,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ~ ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_0) ).
thf(2006,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ~ ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(35,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I98_J_0) ).
thf(721,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( B @ ( B @ ( D @ ( C @ c_List_Oappend ) ) @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_0) ).
thf(1627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( B @ ( B @ ( D @ ( C @ c_List_Oappend ) ) @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_Othrow ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I14_J_1) ).
thf(1525,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_Othrow ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(509,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( E @ ( D @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ ( B @ c_List_Oset @ hAPP ) )
= ( B @ ( E @ ( B @ c_List_Oset @ hAPP ) @ ( D @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__insort_0) ).
thf(1991,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( E @ ( D @ ( C @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ ( B @ c_List_Oset @ hAPP ) )
= ( B @ ( E @ ( B @ c_List_Oset @ hAPP ) @ ( D @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(792,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(605,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(2208,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(380,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1695,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)],[380]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__takeWhile__le_0) ).
thf(2057,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(546,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).
thf(2076,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)],[546]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_DefAss_OhyperUn ) ) @ c_DefAss_OhyperUn ) ) )
= ( C @ ( C @ ( D @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_OhyperUn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hyperUn__assoc_0) ).
thf(1663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_DefAss_OhyperUn ) ) @ c_DefAss_OhyperUn ) ) )
= ( C @ ( C @ ( D @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_OhyperUn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060A_062 ) )
= ( C @ ( C @ ( B @ c_DefAss_O_092_060A_062 ) @ ( C @ ( A @ c_DefAss_O_092_060A_062 ) @ c_DefAss_OhyperUn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I11_J_0) ).
thf(1616,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060A_062 ) )
= ( C @ ( C @ ( B @ c_DefAss_O_092_060A_062 ) @ ( C @ ( A @ c_DefAss_O_092_060A_062 ) @ c_DefAss_OhyperUn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I20_J_0) ).
thf(1185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(1286,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(145,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(1035,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(142,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I197_J_0) ).
thf(1026,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1895,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1167,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)],[185]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I210_J_0) ).
thf(794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(511,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1996,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(718,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(92,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I111_J_0) ).
thf(888,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(98,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_2) ).
thf(906,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1764,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)],[410]) ).
thf(591,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).
thf(2176,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)],[591]) ).
thf(178,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).
thf(1146,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( C @ ( B @ ( D @ c_DefAss_Ohyper__subset ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_D__mono_H_0) ).
thf(1698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( C @ ( B @ ( D @ c_DefAss_Ohyper__subset ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(528,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060A_062 ) )
= ( E @ ( E @ ( D @ c_DefAss_O_092_060A_062 ) @ ( E @ ( A @ c_DefAss_O_092_060A_062 ) @ c_DefAss_OhyperUn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I8_J_0) ).
thf(2033,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060A_062 ) )
= ( E @ ( E @ ( D @ c_DefAss_O_092_060A_062 ) @ ( E @ ( A @ c_DefAss_O_092_060A_062 ) @ c_DefAss_OhyperUn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(71,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I65_J_0) ).
thf(824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(335,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/sandbox2/benchmark/theBenchmark.p',cls_ospec_1) ).
thf(1595,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)],[335]) ).
thf(222,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).
thf(1278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(472,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( E @ ( A @ ( C @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I12_J_1) ).
thf(1906,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( E @ ( A @ ( C @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(175,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).
thf(1135,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(1648,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)],[360]) ).
thf(353,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).
thf(1631,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)],[353]) ).
thf(39,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I178_J_0) ).
thf(733,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(441,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( I @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( D @ ( H @ c_Fun_Ooverride__on ) ) ) ) @ ( G @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( B @ ( F @ c_Pair ) ) ) @ ( J @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( J @ c_Nat_Osize__class_Osize ) ) )
| ( ( tc_Value_Oval @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( J @ c_Nat_Osize__class_Osize ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_List_Odistinct ) )
| ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( I @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( H @ ( G @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Map_Omap__upds ) ) ) ) @ ( C @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_BigStep_Ofinal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_blocksRedsFinal_0) ).
thf(1833,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( I @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( D @ ( H @ c_Fun_Ooverride__on ) ) ) ) @ ( G @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( B @ ( F @ c_Pair ) ) ) @ ( J @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( J @ c_Nat_Osize__class_Osize ) ) )
| ( ( tc_Value_Oval @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( J @ c_Nat_Osize__class_Osize ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_List_Odistinct ) )
| ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( I @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( H @ ( G @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Map_Omap__upds ) ) ) ) @ ( C @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_BigStep_Ofinal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(476,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I12_J_0) ).
thf(1916,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(612,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(2225,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(419,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1784,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(843,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(348,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(1620,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(362,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( E @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( E @ ( A @ c_List_Oset @ hAPP ) @ ( B @ c_in ) ) )
| ~ ( A @ ( D @ ( A @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_2) ).
thf(1652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( E @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( E @ ( A @ c_List_Oset @ hAPP ) @ ( B @ c_in ) ) )
| ~ ( A @ ( D @ ( A @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(43,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I192_J_0) ).
thf(743,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(1535,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)],[310]) ).
thf(264,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_1) ).
thf(1403,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(1795,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(304,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I146_J_0) ).
thf(1520,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(204,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).
thf(1226,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( D @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( B @ ( B @ ( D @ ( C @ c_List_Oappend ) ) @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_1) ).
thf(2188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( D @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( B @ ( B @ ( B @ ( D @ ( C @ c_List_Oappend ) ) @ c_List_Obutlast ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I30_J_0) ).
thf(772,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(610,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( F @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__apply__nontin_0) ).
thf(2220,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( D @ c_List_Oset @ hAPP ) @ ( F @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(526,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I5_J_0) ).
thf(2029,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)],[526]) ).
thf(240,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I158_J_0) ).
thf(1332,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(536,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/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_0) ).
thf(2055,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)],[536]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1258,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)],[214]) ).
thf(356,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(1638,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( D @ ( A @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_1) ).
thf(1675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( D @ ( A @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(21,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_2) ).
thf(672,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(1428,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(584,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(2161,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(153,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I177_J_0) ).
thf(1058,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(167,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).
thf(1107,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(586,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( F @ ( E @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I8_J_1) ).
thf(2166,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( F @ ( E @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(411,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).
thf(1765,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)],[411]) ).
thf(579,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(2148,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(126,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).
thf(979,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(194,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).
thf(1194,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(548,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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(2079,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)],[548]) ).
thf(96,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I137_J_0) ).
thf(900,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(550,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(2084,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(466,axiom,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1894,plain,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(40,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I184_J_0) ).
thf(736,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1542,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)],[313]) ).
thf(413,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_0) ).
thf(1771,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(90,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).
thf(880,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(4,negated_conjecture,
( ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( v_A @ c_DefAss_OhyperUn ) ) @ ( v_al @ c_DefAss_O_092_060D_062 ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ ( v_A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( v_al @ ( tc_Value_Oval @ ( v_ak @ ( v_aj @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(616,plain,
( ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( v_A @ c_DefAss_OhyperUn ) ) @ ( v_al @ c_DefAss_O_092_060D_062 ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ ( v_A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( v_al @ ( tc_Value_Oval @ ( v_ak @ ( v_aj @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(1690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(199,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I99_J_0) ).
thf(1209,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( A @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(2119,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)],[566]) ).
thf(450,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( C @ ( D @ ( B @ ( E @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ~ ( C @ ( D @ ( C @ c_List_Oset @ hAPP ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__insort_0) ).
thf(1853,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( C @ ( D @ ( B @ ( E @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ~ ( C @ ( D @ ( C @ c_List_Oset @ hAPP ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(265,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I145_J_0) ).
thf(1408,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(326,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(1574,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(1806,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I34_J_0) ).
thf(1011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(332,axiom,
! [A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( A @ ( tc_Value_Oval @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Pair ) ) ) @ c_SmallStep_Oblocks )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_blocks_Osimps_I2_J_0) ).
thf(1589,plain,
! [A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( A @ ( tc_Value_Oval @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Pair ) ) ) @ c_SmallStep_Oblocks )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(484,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(1933,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(1492,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(339,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( D @ ( D @ ( D @ ( A @ c_DefAss_O_092_060A_062 ) @ ( E @ c_DefAss_OhyperUn ) ) @ ( C @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I4_J_2) ).
thf(1603,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( D @ ( D @ ( D @ ( A @ c_DefAss_O_092_060A_062 ) @ ( E @ c_DefAss_OhyperUn ) ) @ ( C @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(287,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I59_J_0) ).
thf(1471,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(159,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).
thf(1080,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I40_J_0) ).
thf(631,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).
thf(758,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1162,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)],[183]) ).
thf(5,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_0) ).
thf(621,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).
thf(1029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I24_J_0) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( C @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ( C @ ( B @ c_List_Odistinct ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__insort_1) ).
thf(626,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( C @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ( C @ ( B @ c_List_Odistinct ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I19_J_0) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(154,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).
thf(1061,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(436,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/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1820,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)],[436]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( D @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( A = D )
| ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).
thf(1667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( D @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) )
| ( A = D )
| ( B @ ( C @ ( B @ c_List_Oset @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(593,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_override__on__apply__in_0) ).
thf(2180,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(83,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I100_J_0) ).
thf(858,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(52,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).
thf(769,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I41_J_0) ).
thf(1460,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I87_J_0) ).
thf(1112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1688,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)],[377]) ).
thf(481,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I4_J_0) ).
thf(1926,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(288,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).
thf(1474,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(72,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I159_J_0) ).
thf(827,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(210,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).
thf(1245,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__is__None_0) ).
thf(1066,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)],[155]) ).
thf(551,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_OVal ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedInitBlock_0) ).
thf(2086,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_OVal ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(56,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(780,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(2139,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(541,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( D @ ( D @ ( D @ ( A @ c_DefAss_O_092_060A_062 ) @ ( E @ c_DefAss_OhyperUn ) ) @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( D @ ( D @ ( D @ ( A @ c_DefAss_O_092_060A_062 ) @ ( E @ c_DefAss_OhyperUn ) ) @ ( C @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I12_J_3) ).
thf(2064,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( D @ ( D @ ( D @ ( A @ c_DefAss_O_092_060A_062 ) @ ( E @ c_DefAss_OhyperUn ) ) @ ( B @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( D @ ( D @ ( D @ ( A @ c_DefAss_O_092_060A_062 ) @ ( E @ c_DefAss_OhyperUn ) ) @ ( C @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(188,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).
thf(1176,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedSeq_0) ).
thf(2022,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(289,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).
thf(1477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(295,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I181_J_0) ).
thf(1496,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(166,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = I )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).
thf(1102,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = I )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I96_J_0) ).
thf(653,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060A_062 ) )
= ( D @ ( A @ c_DefAss_O_092_060A_062 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I7_J_0) ).
thf(922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060A_062 ) )
= ( D @ ( A @ c_DefAss_O_092_060A_062 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( B @ ( A @ c_List_Oset @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty2_0) ).
thf(1562,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( B @ ( A @ c_List_Oset @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(134,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).
thf(1000,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(275,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).
thf(1435,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(394,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_BigStep_Ofinal ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) )
| ( ( tc_Value_Oval @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_blocksFinal_0) ).
thf(1726,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_BigStep_Ofinal ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( G @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) )
| ( ( tc_Value_Oval @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060A_062 ) )
= ( C @ ( A @ c_DefAss_O_092_060A_062 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I13_J_0) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060A_062 ) )
= ( C @ ( A @ c_DefAss_O_092_060A_062 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(212,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_1) ).
thf(1250,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(2005,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(491,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(1948,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(1583,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)],[330]) ).
thf(431,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SeqReds_0) ).
thf(1809,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(458,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( F @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( E @ ( E @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( F @ c_DefAss_OhyperUn ) ) @ ( D @ c_DefAss_O_092_060D_062 ) ) )
| ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I15_J_2) ).
thf(1873,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( F @ ( A @ c_DefAss_O_092_060D_062 ) ) )
| ~ ( E @ ( E @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ ( F @ c_DefAss_OhyperUn ) ) @ ( D @ c_DefAss_O_092_060D_062 ) ) )
| ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).
thf(1684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(568,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/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(2124,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)],[568]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__takeWhile_0) ).
thf(749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(495,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__None__iff_2) ).
thf(1958,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)],[495]) ).
thf(47,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).
thf(754,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(105,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).
thf(927,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(530,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(2037,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I39_J_0) ).
thf(812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Option_Ois__none ) )
| ( A
= ( B @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__none__def_0) ).
thf(1509,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)],[300]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I27_J_0) ).
thf(939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).
thf(1340,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)],[243]) ).
thf(75,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I50_J_0) ).
thf(836,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ c_in ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).
thf(1551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ c_List_Oset @ hAPP ) @ ( D @ c_in ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(82,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).
thf(855,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1961,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)],[496]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(577,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(2143,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)],[577]) ).
thf(340,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_Option_Ooption @ ( F @ ( C @ ( B @ hAPP ) @ ( C @ ( D @ tc_Option_Ooption @ ( F @ ( G @ ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ tc_Option_Ooption @ ( F @ ( F @ ( G @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_override__on__upd__lemma_0) ).
thf(1605,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_Option_Ooption @ ( F @ ( C @ ( B @ hAPP ) @ ( C @ ( D @ tc_Option_Ooption @ ( F @ ( G @ ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ tc_Option_Ooption @ ( F @ ( F @ ( G @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I25_J_0) ).
thf(954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(739,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(2175,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(1780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( D @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_OhyperUn ) ) )
= ( B @ ( B @ ( D @ ( A @ c_DefAss_OhyperUn ) ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ c_DefAss_OhyperUn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hyper__insert__comm_1) ).
thf(1547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( D @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_OhyperUn ) ) )
= ( B @ ( B @ ( D @ ( A @ c_DefAss_OhyperUn ) ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) @ c_DefAss_OhyperUn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(1748,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I196_J_0) ).
thf(712,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(135,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I112_J_0) ).
thf(1003,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(26,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I208_J_0) ).
thf(690,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(1598,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(539,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( tc_Value_Oval @ ( F @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks )
= ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( F @ c_Pair ) ) ) @ ( D @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_OVal ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( A @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_blocks_Osimps_I1_J_0) ).
thf(2060,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( tc_Value_Oval @ ( F @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks )
= ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( F @ c_Pair ) ) ) @ ( D @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_OVal ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( A @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(401,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1743,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(263,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).
thf(1400,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(31,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).
thf(707,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(1753,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(218,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1267,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(555,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(2092,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)],[555]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I35_J_0) ).
thf(1188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(1869,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1785,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)],[420]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).
thf(1235,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(440,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).
thf(1830,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)],[440]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1085,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(399,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).
thf(1738,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)],[399]) ).
thf(202,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).
thf(1220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(151,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(1053,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)],[151]) ).
thf(296,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I179_J_0) ).
thf(1499,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1813,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(280,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I107_J_0) ).
thf(1452,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1538,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)],[311]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(951,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)],[114]) ).
thf(250,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I225_J_0) ).
thf(1358,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(504,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1981,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1,negated_conjecture,
( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_Type_Oty @ tc_List_Olist @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(613,plain,
( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
= ( tc_Type_Oty @ tc_List_Olist @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(85,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I62_J_0) ).
thf(864,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(1717,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(255,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).
thf(1372,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(461,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( C @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I11_J_1) ).
thf(1881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( C @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( D @ ( D @ ( D @ ( C @ c_DefAss_O_092_060A_062 ) @ ( B @ c_DefAss_OhyperUn ) ) @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(468,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( F @ ( E @ ( G @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Seq_0) ).
thf(1898,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( F @ ( E @ ( G @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( D @ ( C @ ( B @ c_BigStep_Oeval ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_BigStep_Ofinal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__final_0) ).
thf(1849,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( D @ ( C @ ( B @ c_BigStep_Oeval ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_BigStep_Ofinal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I18_J_0) ).
thf(656,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(428,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(1802,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(141,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I201_J_0) ).
thf(1023,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(248,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).
thf(1353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(494,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1955,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)],[494]) ).
thf(298,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).
thf(1504,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(37,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I33_J_0) ).
thf(727,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(163,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I143_J_0) ).
thf(1094,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(125,axiom,
tc_nat @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(978,plain,
tc_nat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(1670,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(426,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1797,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)],[426]) ).
thf(208,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I213_J_0) ).
thf(1240,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(131,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).
thf(991,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1940,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(845,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(1839,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(553,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_override__on__emptyset_0) ).
thf(2088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(498,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SeqReds2_0) ).
thf(1966,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(435,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).
thf(1817,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(599,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(2194,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(1654,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(303,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).
thf(1517,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(172,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I141_J_0) ).
thf(1126,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(562,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(2110,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)],[562]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(1734,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)],[397]) ).
thf(512,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1998,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)],[512]) ).
thf(269,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(1421,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(2013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(477,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1918,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)],[477]) ).
thf(235,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I104_J_0) ).
thf(1316,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(1157,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(547,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(2078,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(475,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ tc_List_Olist @ ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( E @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_Suc ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__insert_0) ).
thf(1913,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ tc_List_Olist @ ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( E @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_Suc ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(976,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(445,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_1) ).
thf(1844,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)],[445]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I16_J_0) ).
thf(903,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1866,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)],[455]) ).
thf(544,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
| ( A
= ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_0) ).
thf(2071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
| ( A
= ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( D @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I11_J_0) ).
thf(1646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( D @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).
thf(1721,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)],[392]) ).
thf(119,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).
thf(963,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_BigStep_Ofinal ) )
| ( C @ ( B @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__finalId_0) ).
thf(2098,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_BigStep_Ofinal ) )
| ( C @ ( B @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(573,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(2135,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(352,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).
thf(1629,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(525,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_1) ).
thf(2026,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(58,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I214_J_0) ).
thf(786,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(305,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/sandbox2/benchmark/theBenchmark.p',cls_option__map__Some_0) ).
thf(1523,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)],[305]) ).
thf(571,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(2130,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)],[571]) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).
thf(1861,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)],[453]) ).
thf(100,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).
thf(914,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(228,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I167_J_0) ).
thf(1294,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(233,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = H )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).
thf(1308,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = H )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(542,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).
thf(2066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I151_J_0) ).
thf(1077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
= ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
thf(1607,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
= ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ tc_List_Olist @ ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ( C
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oconcat ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat__eq__Nil__conv_0) ).
thf(2095,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ tc_List_Olist @ ( A @ ( B @ tc_List_Olist @ c_List_Oset @ hAPP ) @ ( C @ c_in ) ) )
| ( C
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oconcat ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(1994,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(594,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I7_J_0) ).
thf(2183,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(200,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_1) ).
thf(1212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(345,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1614,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)],[345]) ).
thf(63,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I202_J_0) ).
thf(800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(609,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(2218,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)],[609]) ).
thf(328,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/sandbox2/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).
thf(1578,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)],[328]) ).
thf(581,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( D @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I13_J_0) ).
thf(2155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( D @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(74,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I204_J_0) ).
thf(833,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(164,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).
thf(1097,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(205,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = I )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).
thf(1229,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = I )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(69,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I222_J_0) ).
thf(818,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(1527,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(1480,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1908,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(514,axiom,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_Option_Ois__none ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__none__code_I2_J_0) ).
thf(2003,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)],[514]) ).
thf(576,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oset @ hAPP ) @ ( B @ ( A @ c_List_Oset @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).
thf(2142,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oset @ hAPP ) @ ( B @ ( A @ c_List_Oset @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(1512,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oconcat ) )
= ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat_Osimps_I2_J_0) ).
thf(1774,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oconcat ) )
= ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(334,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I8_J_0) ).
thf(1593,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
| ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(257,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).
thf(1380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
thf(2008,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(507,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/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(1986,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)],[507]) ).
thf(86,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).
thf(867,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(1757,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(294,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(1495,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(364,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( F @ ( A @ ( F @ ( E @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_1) ).
thf(1657,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( F @ ( A @ ( F @ ( E @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(241,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(1335,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I150_J_0) ).
thf(897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(531,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(2040,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(343,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LAssReds_0) ).
thf(1610,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( F @ c_SmallStep_Ored @ c_Transitive__Closure_Ortrancl ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(2201,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(508,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/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd_0) ).
thf(1989,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)],[508]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(19,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).
thf(664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(226,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).
thf(1288,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(195,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I185_J_0) ).
thf(1197,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(611,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Map_Omap__upds ) ) ) ) )
= ( G @ ( D @ ( F @ ( C @ ( G @ tc_Option_Ooption @ ( D @ ( E @ ( G @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Cons_0) ).
thf(2223,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Map_Omap__upds ) ) ) ) )
= ( G @ ( D @ ( F @ ( C @ ( G @ tc_Option_Ooption @ ( D @ ( E @ ( G @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).
thf(960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(76,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I37_J_0) ).
thf(839,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
thf(2159,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(173,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I110_J_0) ).
thf(1129,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1268,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I88_J_0) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(309,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ c_List_Oset @ hAPP ) @ ( B @ c_in ) ) )
| ( ( C @ ( E @ ( G @ ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__upds ) ) ) ) )
= ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( C @ ( E @ ( G @ ( F @ ( A @ c_Map_Omap__upds ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__twist_0) ).
thf(1532,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ c_List_Oset @ hAPP ) @ ( B @ c_in ) ) )
| ( ( C @ ( E @ ( G @ ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__upds ) ) ) ) )
= ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( C @ ( E @ ( G @ ( F @ ( A @ c_Map_Omap__upds ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(502,axiom,
! [A: $i] :
( ( A @ ( A @ tc_List_Olist @ c_List_Olist_ONil @ c_List_Oconcat ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat_Osimps_I1_J_0) ).
thf(1976,plain,
! [A: $i] :
( ( A @ ( A @ tc_List_Olist @ c_List_Olist_ONil @ c_List_Oconcat ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(230,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OWhile ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I223_J_0) ).
thf(1299,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
!= ( E @ ( G @ ( F @ c_Expr_Oexp_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).
thf(1902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(129,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(987,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(570,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( F @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_override__on__apply__notin_0) ).
thf(2127,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( F @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(1827,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1261,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)],[215]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I36_J_0) ).
thf(850,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1713,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_DefAss_O_092_060D_062 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I3_J_0) ).
thf(1597,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_DefAss_O_092_060D_062 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(982,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(64,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).
thf(803,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(489,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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1944,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)],[489]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1848,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)],[447]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(775,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(267,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).
thf(1416,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).
thf(639,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
!= ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(552,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( A @ c_BigStep_Oeval ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Val_0) ).
thf(2087,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( A @ c_BigStep_Oeval ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(286,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I26_J_0) ).
thf(1468,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Onew ) )
!= ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I71_J_0) ).
thf(1069,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
!= ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( B @ ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ ( A @ c_List_Olast ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__in__set_0) ).
thf(1681,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( B @ ( A @ ( B @ c_List_Oset @ hAPP ) @ ( B @ ( A @ c_List_Olast ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(545,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).
thf(2074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(1463,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(18,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = G )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).
thf(659,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = G )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
!= ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ c_List_Orev ) @ ( A @ c_List_Oset @ hAPP ) )
= ( B @ ( A @ c_List_Oset @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev_0) ).
thf(1565,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_List_Orev ) @ ( A @ c_List_Oset @ hAPP ) )
= ( B @ ( A @ c_List_Oset @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(588,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/sandbox2/benchmark/theBenchmark.p',cls_map__comp__simps_I1_J_0) ).
thf(2170,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)],[588]) ).
thf(161,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I68_J_0) ).
thf(1088,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(598,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/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(2191,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)],[598]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I17_J_0) ).
thf(1449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
!= ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(138,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I173_J_0) ).
thf(1014,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(122,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(972,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(2234,plain,
$false,
inference(e,[status(thm)],[645,1036,1337,1411,1168,2031,1729,628,1179,777,1554,1686,2199,1322,1665,1586,809,1369,1823,1950,1549,2117,730,2062,1443,1618,994,741,1544,873,1591,878,1305,861,1855,1200,1924,2210,1422,1569,1971,1793,614,1692,677,1705,2035,715,1275,1872,1327,945,2042,2146,1164,797,2168,698,1761,1342,1507,930,2216,2020,1650,1386,2082,1724,1529,1482,1243,1782,1391,1576,973,885,2010,1935,2173,1366,2136,1904,1703,1430,1660,1264,1313,2126,1132,1055,724,917,751,2185,1455,934,1191,1922,1800,853,1892,1514,2049,1609,1741,1115,1931,1641,1815,1100,1847,1319,870,1890,969,1347,1572,1875,1778,924,1302,789,2090,1911,1978,937,1677,806,1283,821,2017,1946,1465,2105,1811,1858,1864,2122,1383,1020,1581,966,766,2058,1928,1377,634,2190,1072,1622,1394,988,1433,2103,1201,1600,2205,1206,920,942,2204,1438,2164,761,2047,1708,1736,1768,1047,2000,1636,1900,1255,2133,1217,1487,693,815,2015,957,1223,894,746,1091,1042,952,1502,1751,1883,1560,1938,1032,1920,1968,1888,1457,830,2179,2213,757,682,1281,1634,842,2068,1624,1836,1787,2112,1291,1350,1234,1983,1121,1425,1672,1878,1755,1397,2157,1143,2115,1762,2100,1270,1851,650,948,1017,1953,1804,615,1540,1006,1138,1719,783,1118,1567,2023,1361,933,1182,669,642,637,1700,1791,1644,1155,1419,1964,1942,2196,1842,2108,1446,1612,679,1039,1297,2153,1974,1050,1984,2052,1715,1720,1759,1825,1324,647,1776,1263,997,984,911,2006,721,1627,1525,1991,792,2208,1695,2057,2076,1663,1616,1185,1732,1286,1035,1026,1895,1167,794,1996,718,888,906,1764,2176,1146,1698,2033,824,1595,1278,1906,1135,1648,1631,733,1833,1916,2225,1784,843,1620,1652,743,1535,1403,1795,1520,1226,2188,772,2220,2029,1332,2055,1258,1638,1675,672,1428,2161,1058,1107,2166,1765,2148,1356,979,1194,2079,900,2084,1894,736,1542,1771,880,616,1690,1209,2119,1853,1408,1574,1806,1011,1589,1933,1492,1603,1471,1080,631,758,1162,621,700,1029,1149,626,1344,1061,1820,1667,2180,858,1557,769,1460,1112,1688,1926,1474,827,1245,1066,2086,780,2139,2064,1176,2022,1477,1496,1102,653,922,1562,685,1171,1000,1435,1726,1364,1250,2005,1948,1583,1809,1873,1684,2124,749,1958,754,927,2037,812,1509,939,1340,836,1551,855,1961,705,2143,1605,954,739,2175,1780,1547,1748,712,1003,690,1598,2060,1743,1400,707,1753,1267,2092,1188,1869,1785,1235,1830,1085,1679,1738,1220,1711,1053,1499,1813,1452,1538,951,1358,1981,613,864,1717,1372,1881,1898,1849,656,1802,1023,1353,1955,1504,727,1094,978,1670,1797,1240,991,1940,845,1839,2088,1966,1817,2194,1654,1517,891,1126,2110,1734,1998,1421,2013,1918,1316,1157,2078,1913,976,1844,903,1866,2071,1646,1721,963,2098,2135,1629,2026,786,1523,2130,1861,914,1294,1308,2066,1077,1607,2095,1994,2183,1212,1614,800,2218,1578,2155,833,1097,1229,818,1527,1248,1480,1908,2003,2142,1512,1774,1593,1380,2008,1986,867,1757,1495,1657,1335,897,2040,1610,2201,1989,1789,664,1288,1197,2223,960,839,2159,1129,1268,1152,1532,1976,1299,1902,987,2127,1827,1261,850,1713,1597,982,803,1944,1848,775,1416,639,2087,1468,1069,1681,2074,1463,659,1565,2170,1088,2191,1449,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV925-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.42 % Computer : n010.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Sat Sep 26 15:10:45 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.82/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.24/1.41 % [INFO] Parsing done (393ms).
% 2.24/1.42 % [INFO] Running in sequential loop mode.
% 3.18/1.80 % [INFO] eprover registered as external prover.
% 3.18/1.81 % [INFO] Scanning for conjecture ...
% 3.97/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 610 axioms. Running axiom selection ...
% 4.70/2.28 % [INFO] Axiom selection finished. Selected 608 axioms (removed 2 axioms).
% 5.76/2.54 % [INFO] Problem is propositional (TPTP CNF).
% 5.76/2.56 % [INFO] Type checking passed.
% 5.76/2.57 % [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 ...
% 16.49/5.16 % External prover 'e' found a proof!
% 16.49/5.16 % [INFO] Killing All external provers ...
% 16.49/5.16 % Time passed: 4593ms (effective reasoning time: 3734ms)
% 16.49/5.17 % Axioms used in derivation (608): cls_Nil__is__rev__conv_1, cls_last_Osimps_0, cls_exp_Osimps_I56_J_0, cls_inj__Some_0, cls_exp_Osimps_I9_J_1, cls_sorted__append_2, cls_subset__insert_1, cls_le__0__eq_1, cls_length__0__conv_1, cls__092_060D_062___092_060D_062s_Osimps_I12_J_1, cls__092_060D_062___092_060D_062s_Osimps_I8_J_1, cls_set__subset__Cons_0, clsarity_nat__HOL_Oord, cls_red__reds_ORedInitBlock_0, cls_butlast__snoc_0, cls_option_Oinject_0, cls__092_060D_062___092_060D_062s_Osimps_I15_J_1, cls_map__upd__eqD1_0, cls_exp_Osimps_I156_J_0, cls_rtrancl__idemp_0, cls_exp_Osimps_I92_J_0, cls_exp_Osimps_I195_J_0, cls_exp_Osimps_I103_J_0, cls_rev__swap_1, cls_last_Osimps_1, cls_exp_Osimps_I184_J_0, cls_insertE_0, cls_eq__imp__le_0, cls_order__eq__iff_0, cls_Cons__eq__append__conv_5, cls_equalityI_0, cls_exp_Osimps_I218_J_0, cls_exp_Osimps_I213_J_0, cls_map__add__None_2, cls_Suc__inject_0, cls_Nil__eq__concat__conv_0, cls_blocks_Osimps_I2_J_0, cls_exp_Osimps_I193_J_0, cls_append__self__conv_0, cls_Suc__n__not__n_0, cls_ospec_1, cls_exp_Osimps_I137_J_0, cls_in__set__butlast__appendI_1, cls_fun__upd__apply_1, cls_le__funD_0, cls_subset__empty_1, cls_eval__cases_I1_J_1, cls_map__add__assoc_0, cls_set__ConsD_0, cls_exp_Osimps_I10_J_1, cls_insort__key_Osimps_I2_J_1, cls_exp_Osimps_I225_J_0, cls_exp_Osimps_I138_J_0, cls_set__empty2_1, cls_exp_Osimps_I81_J_0, cls_butlast_Osimps_I1_J_0, cls__092_060D_062___092_060D_062s_Osimps_I7_J_1, cls_exp_Osimps_I165_J_0, cls_exp_Osimps_I7_J_2, cls_insert__code_1, cls_map__upd__Some__unfold_4, cls_splice__Cons__Cons_0, cls_list_Oinject_0, cls__092_060D_062___092_060D_062s_Osimps_I11_J_1, cls_map__upd__Some__unfold_3, cls_exp_Osimps_I219_J_0, cls_eval__final_0, cls_in__set__conv__decomp_1, cls_exp_Osimps_I42_J_0, cls_exp_Osimps_I190_J_0, clsarity_fun__Orderings_Oorder, cls_exp_Osimps_I221_J_0, cls_exp_Osimps_I15_J_1, cls_set__empty_1, cls_exp_Osimps_I204_J_0, cls_exp_Osimps_I149_J_0, cls_le__SUPI_0, cls_exp_Osimps_I20_J_0, cls_map__upds__apply__nontin_0, cls_rev__singleton__conv_1, cls_exp_Osimps_I11_J_0, cls_map__comp__simps_I2_J_0, cls_insert__absorb_0, cls_exp_Osimps_I28_J_0, cls_exp_Osimps_I115_J_0, cls_exp_Osimps_I25_J_0, cls_exp_Osimps_I211_J_0, cls__092_060D_062___092_060D_062s_Osimps_I15_J_0, cls_exp_Osimps_I36_J_0, cls_rtrancl__trans_0, cls_mem__def_1, cls_distinct__rev_1, clsarity_nat__Orderings_Olinorder, cls_exp_Osimps_I19_J_0, cls_empty__iff_0, cls_not__Cons__self2_0, cls__092_060D_062___092_060D_062s_Osimps_I6_J_1, cls_rev__is__rev__conv_0, cls_option_Osimps_I2_J_0, cls_exp_Osimps_I13_J_0, cls_exp_Osimps_I154_J_0, cls_insert__subset_0, cls_exp_Osimps_I185_J_0, cls_self__append__conv_0, cls_same__append__eq_0, cls_exp_Osimps_I141_J_0, cls_distinct__insort_2, cls_exp_Osimps_I97_J_0, cls_exp_Osimps_I170_J_0, cls_exp_Osimps_I199_J_0, cls_insert__iff_1, cls_LAssReds_0, cls_append__eq__Cons__conv_4, cls_eq__Nil__appendI_0, cls_SeqReds2_0, cls_exp_Osimps_I208_J_0, cls_exp_Osimps_I188_J_0, cls_set__rev__mp_0, cls_exp_Osimps_I109_J_0, cls_append__Cons_0, cls_map__add__Some__iff_3, cls_subset__insert__iff_2, cls_exp_Osimps_I178_J_0, cls__092_060A_062___092_060A_062s_Osimps_I7_J_0, cls_exp_Osimps_I2_J_1, cls_exp_Osimps_I8_J_3, cls__092_060D_062___092_060D_062s_Osimps_I13_J_1, cls_distinct_Osimps_I2_J_0, cls_butlast_Osimps_I2_J_1, cls_le__0__eq_0, cls_takeWhile__append1_0, cls_exp_Osimps_I212_J_0, cls_exp_Osimps_I79_J_0, cls_exp_Osimps_I206_J_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_exp_Osimps_I194_J_0, cls_append__eq__append__conv2_4, cls_exp_Osimps_I113_J_0, cls_exp_Osimps_I11_J_1, cls_exp_Osimps_I40_J_0, cls_Suc__le__mono_0, cls_sorted_Osimps_I3_J_1, cls_exp_Osimps_I4_J_1, cls_sorted__takeWhile_0, cls_le__antisym_0, cls_UN__extend__simps_I1_J_0, cls_exp_Osimps_I171_J_0, cls_exp_Osimps_I223_J_0, cls_in__set__conv__decomp__first_2, cls_exp_Osimps_I136_J_0, cls_exp_Osimps_I175_J_0, cls_red__reds_OLAssRed_0, cls__092_060D_062___092_060D_062s_Osimps_I4_J_0, cls_append1__eq__conv_1, cls_exp_Osimps_I157_J_0, cls_D__mono_H_0, cls_order__eq__refl_0, cls_exp_Osimps_I67_J_0, cls_converse__rtrancl__into__rtrancl_0, cls_exp_Osimps_I4_J_0, cls_splice_Osimps_I2_J_0, cls_exp_Osimps_I17_J_0, cls_inj__on__insert_0, cls_distinct_Osimps_I2_J_1, clsarity_fun__Orderings_Obot, cls_exp_Osimps_I160_J_0, cls_UN__iff_2, cls_distinct_Osimps_I1_J_0, cls_is__none__code_I2_J_0, cls_override__on__upd__lemma_0, cls_SUP1__I_0, cls_map__upd__Some__unfold_0, cls__092_060D_062___092_060D_062s_Osimps_I2_J_0, cls_fun__upd__other_0, cls_exp_Osimps_I84_J_0, cls_exp_Osimps_I209_J_0, cls_takeWhile_Osimps_I1_J_0, cls__092_060D_062___092_060D_062s_Osimps_I12_J_0, cls_exp_Osimps_I21_J_0, cls_exp_Osimps_I142_J_0, cls_exp_Osimps_I74_J_0, cls_exp_Osimps_I110_J_0, cls__092_060D_062___092_060D_062s_Osimps_I11_J_2, cls_hyper__insert__comm_1, cls_exp_Osimps_I205_J_0, cls_rev__singleton__conv_0, cls__092_060A_062___092_060A_062s_Osimps_I13_J_0, cls_insert__ident_0, cls__092_060A_062___092_060A_062s_Osimps_I2_J_0, cls_in__set__conv__decomp__last_2, cls_exp_Osimps_I29_J_0, cls_map__comp__simps_I1_J_0, cls_exp_Osimps_I24_J_0, cls_rev_Osimps_I2_J_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_exp_Osimps_I9_J_0, cls_exp_Osimps_I85_J_0, cls_override__on__apply__notin_0, cls_exp_Osimps_I176_J_0, cls_exp_Osimps_I143_J_0, cls__092_060D_062___092_060D_062s_Osimps_I7_J_0, cls_append__Nil2_0, cls_exp_Osimps_I146_J_0, cls_exp_Osimps_I174_J_0, cls_exp_Osimps_I148_J_0, cls_append__self__conv2_0, cls_exp_Osimps_I172_J_0, cls_exp_Osimps_I139_J_0, cls_exp_Osimps_I10_J_2, cls_Nil__is__append__conv_0, cls_not__None__eq_1, cls_exp_Osimps_I43_J_0, cls__092_060D_062___092_060D_062s_Osimps_I4_J_2, cls_in__set__butlast__appendI_0, cls_singleton__iff_1, cls_subset__iff_0, cls_distinct__append_0, clsarity_fun__HOL_Oord, cls_exp_Osimps_I99_J_0, cls_subset__empty_0, cls_map__upds__Cons_0, cls_sorted_Osimps_I3_J_2, cls__092_060D_062___092_060D_062s_Osimps_I1_J_0, cls_self__append__conv2_0, cls_insort__key_Osimps_I2_J_0, cls_insert__code_2, cls_exp_Osimps_I46_J_0, cls_takeWhile__tail_0, cls_length__0__conv_0, cls_not__less__eq__eq_1, cls_self__append__conv2_1, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_UN__subset__iff_0, cls_Suc__neq__Zero_0, cls_SUP1__iff_2, cls_last__append_1, cls_exp_Osimps_I180_J_0, cls_append__eq__append__conv2_5, cls__092_060A_062___092_060A_062s_Osimps_I11_J_0, cls_doubleton__eq__iff_2, cls_exp_Osimps_I77_J_0, cls_set__empty2_0, cls_append__is__Nil__conv_2, cls_exp_Osimps_I69_J_0, cls_last__in__set_0, cls_append__Nil_0, cls_exp_Osimps_I98_J_0, cls_exp_Osimps_I61_J_0, cls_exp_Osimps_I15_J_0, cls_exp_Osimps_I183_J_0, cls_exp_Osimps_I26_J_0, cls_append__butlast__last__id_0, cls_singleton__rev__conv_0, cls_append__eq__Cons__conv_5, cls_red__reds_ORedBlock_0, cls_fun__upd__triv_0, cls_exp_Osimps_I2_J_0, cls_exp_Osimps_I12_J_2, cls_exp_Osimps_I8_J_2, cls_rev__is__Nil__conv_0, cls_distinct__rev_0, cls_set__eq__subset_2, cls__092_060D_062___092_060D_062s_Osimps_I8_J_2, cls_exp_Osimps_I207_J_0, cls_map__upds__twist_0, clsarity_nat__Orderings_Obot, cls_exp_Osimps_I83_J_0, cls_ex__in__conv_0, cls_exp_Osimps_I76_J_0, cls_exp_Osimps_I70_J_0, cls_option__map__None_0, cls_exp_Osimps_I177_J_0, cls__092_060D_062___092_060D_062s_Osimps_I12_J_3, cls_insert__subset_1, cls_map__upds__Nil2_0, cls_Seq_0, cls_exp_Osimps_I27_J_0, cls_linorder__linear_0, cls_distinct__insort_1, cls_is__none__def_0, cls_exp_Osimps_I89_J_0, cls_exp_Osimps_I159_J_0, cls_map__comp__Some__iff_2, cls_le__SucE_0, cls_Suc__le__mono_1, cls_set__rev_0, cls__092_060A_062___092_060A_062s_Osimps_I3_J_0, cls_exp_Osimps_I186_J_0, cls_exp_Osimps_I210_J_0, cls_exp_Osimps_I105_J_0, cls_exp_Osimps_I220_J_0, cls_map__add__None_0, cls_exp_Osimps_I62_J_0, cls_self__append__conv_1, cls_splice__Nil2_0, cls_fun__upds__append2__drop_0, cls_order__antisym_0, cls_order__trans_0, cls_butlast__append_0, cls_exp_Osimps_I112_J_0, cls_exp_Osimps_I60_J_0, cls_exp_Osimps_I162_J_0, cls__092_060D_062___092_060D_062s_Osimps_I13_J_2, cls_not__Cons__self_0, cls__092_060D_062___092_060D_062s_Osimps_I2_J_1, cls_exp_Osimps_I158_J_0, cls__092_060A_062___092_060A_062s_Osimps_I4_J_0, cls_in__set__butlastD_0, cls_subset__trans_0, cls_exp_Osimps_I201_J_0, cls_map__upd__Some__unfold_1, clsarity_bool__Orderings_Opreorder, cls_exp_Osimps_I47_J_0, cls_map__add__upds_0, cls_exp_Osimps_I7_J_1, cls_empty__not__insert_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_last__append_0, cls_exp_Osimps_I224_J_0, cls_sqUn__lem_0, cls_exp_Osimps_I15_J_3, cls_insertI1_0, cls_exp_Osimps_I169_J_0, cls_map__upd__triv_0, cls_exp_Osimps_I166_J_0, cls_append__same__eq_0, cls_last__snoc_0, cls_blocksFinal_0, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_rtrancl__eq__or__trancl_1, cls_concat__eq__Nil__conv_0, cls_exp_Osimps_I55_J_0, cls_fun__upds__append__drop_0, cls_splice_Osimps_I1_J_0, cls_option_Osimps_I4_J_0, cls_exp_Osimps_I189_J_0, cls_sorted__Cons_0, cls_exp_Osimps_I101_J_0, cls_exp_Osimps_I102_J_0, cls_exp_Osimps_I30_J_0, cls_length__rev_0, cls_exp_Osimps_I75_J_0, cls_empty__subsetI_0, cls_fun__upd__twist_0, cls_exp_Osimps_I16_J_0, cls_set__insort_0, cls_subset__refl_0, cls_exp_Osimps_I1_J_0, cls_exp_Osimps_I145_J_0, cls_butlast__append_1, cls_Pair__eq_0, cls_append__assoc_0, cls_red__reds_OSeqRed_0, cls_doubleton__eq__iff_0, cls_override__on__apply__in_0, cls_exp_Osimps_I80_J_0, cls_distinct__takeWhile_0, cls_exp_Osimps_I59_J_0, cls_le__trans_0, cls_map__upds__Nil1_0, cls_singletonE_0, cls_hyper__insert__comm_0, cls_not__Some__eq_1, cls_exp_Osimps_I35_J_0, cls_exp_Osimps_I39_J_0, cls_fun__upd__apply_0, cls__092_060D_062___092_060D_062s_Osimps_I14_J_1, cls_blocksRedsFinal_0, cls_exp_Osimps_I68_J_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_final__def_1, cls_inj__on__empty_0, cls_insertCI_0, cls_exp_Osimps_I182_J_0, cls_exp_Osimps_I4_J_2, cls_exp_Osimps_I114_J_0, cls_order__eq__iff_2, cls_bot1E_0, cls_option_Osplit_1, cls_exp_Osimps_I216_J_0, cls__092_060D_062___092_060D_062s_Osimps_I4_J_1, cls_insert__mono_0, cls_exp_Osimps_I203_J_0, cls_exp_Osimps_I41_J_0, cls_exp_Osimps_I57_J_0, cls_exp_Osimps_I191_J_0, cls_bex__empty_0, cls_distinct__append_1, cls_subset__insertI2_0, cls__092_060D_062___092_060D_062s_Osimps_I12_J_2, cls_map__comp__None__iff_3, cls_exp_Osimps_I93_J_0, cls_SeqReds_0, cls_exp_Osimps_I53_J_0, cls_sorted_Osimps_I1_J_0, cls_inj__on__def_0, cls_nat_Oinject_0, cls_order__antisym__conv_0, cls_exp_Osimps_I152_J_0, cls_exp_Osimps_I50_J_0, cls_doubleton__eq__iff_3, cls_exp_Osimps_I215_J_0, cls_map__add__SomeD_0, cls_override__on__emptyset_0, cls_sorted__distinct__set__unique_0, cls_sorted__append_0, cls_exp_Osimps_I86_J_0, cls_rev__eq__Cons__iff_1, cls_distinct_Osimps_I2_J_2, cls_hyperUn__assoc_0, cls_exp_Osimps_I179_J_0, cls_exp_Osimps_I144_J_0, cls_exp_Osimps_I150_J_0, cls_exp_Osimps_I54_J_0, cls_takeWhile_Osimps_I2_J_1, cls_nat_Osimps_I2_J_0, cls_map__add__upd_0, cls_Zero__neq__Suc_0, cls_exp_Osimps_I37_J_0, cls_list_Osimps_I3_J_0, cls_exp_Osimps_I8_J_1, cls_le0_0, cls_exp_Osimps_I58_J_0, cls_rev__is__Nil__conv_1, cls_insert__subset_2, cls_exp_Osimps_I66_J_0, cls_subsetD_0, cls_exp_Osimps_I108_J_0, cls_exp_Osimps_I222_J_0, cls_insert__not__empty_0, cls_exp_Osimps_I90_J_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_exp_Osimps_I106_J_0, cls_Suc__length__conv_2, cls_option__map__is__None_0, cls_exp_Osimps_I34_J_0, cls_distinct__insort_0, cls_exp_Osimps_I6_J_0, cls_insert__absorb2_0, cls_UNION__empty__conv_I1_J_0, cls_fun__upd__idem_0, cls_concat_Osimps_I2_J_0, cls_xt1_I6_J_0, cls_exp_Osimps_I155_J_0, cls_subset__singletonD_0, cls_doubleton__eq__iff_1, cls_exp_Osimps_I12_J_1, cls_fun__upd__idem__iff_0, cls_append__is__Nil__conv_1, cls_takeWhile__eq__all__conv_0, cls_eval__cases_I1_J_0, cls_UN__I_0, cls_rtrancl_Ortrancl__refl_0, cls_exp_Osimps_I71_J_0, cls_option_Osplit__asm_1, cls_blocksEval_0, cls_nat_Osimps_I3_J_0, cls_Nil__is__rev__conv_0, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_exp_Osimps_I14_J_0, cls_exp_Osimps_I107_J_0, cls_exp_Osimps_I167_J_0, cls__092_060D_062___092_060D_062s_Osimps_I11_J_0, cls__092_060A_062___092_060A_062s_Osimps_I8_J_0, cls_exp_Osimps_I9_J_2, cls_Cons__eq__appendI_0, cls_exp_Osimps_I161_J_0, cls_exp_Osimps_I82_J_0, cls_nat__le__linear_0, cls_le__Suc__eq_2, cls__092_060D_062___092_060D_062s_Osimps_I8_J_0, cls_set__concat_0, cls_fun__upd__same_0, cls_exp_Osimps_I217_J_0, cls_singleton__rev__conv_1, cls_append__eq__appendI_0, cls_exp_Osimps_I45_J_0, cls_set__takeWhileD_1, cls_map__upd__Some__unfold_2, cls_exp_Osimps_I8_J_0, cls_exp_Osimps_I192_J_0, cls_subset__insert_0, cls_Cons__eq__append__conv_4, cls_exp_Osimps_I7_J_0, cls_emptyE_0, cls_exp_Osimps_I151_J_0, cls_length__Suc__conv_2, cls__092_060D_062___092_060D_062s_Osimps_I14_J_0, cls_is__none__def_1, cls_append__is__Nil__conv_0, cls_Suc__n__not__le__n_0, cls_comm__monoid__add_Ononempty__iff_2, cls_list_Oinject_1, cls_blocks_Osimps_I1_J_0, cls_subset__inj__on_0, cls_exp_Osimps_I153_J_0, cls_singleton__inject_0, cls_butlast_Osimps_I2_J_0, cls_exp_Osimps_I44_J_0, cls_exp_Osimps_I18_J_0, cls_Suc__leD_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_exp_Osimps_I32_J_0, cls_exp_Osimps_I6_J_1, cls_exp_Osimps_I65_J_0, cls_UN__upper_0, cls_rev__append_0, cls_option_Osimps_I3_J_0, cls_set__empty_0, cls_inj__on__contraD_0, cls__092_060D_062___092_060D_062s_Osimps_I3_J_0, cls_inj__onD_0, clsarity_fun__Orderings_Opreorder, cls_exp_Osimps_I164_J_0, cls_n__not__Suc__n_0, cls_exp_Osimps_I51_J_0, cls_exp_Osimps_I52_J_0, cls_exp_Osimps_I31_J_0, cls_set__takeWhileD_0, cls_Val_0, cls_exp_Osimps_I187_J_0, cls_exp_Osimps_I15_J_2, cls__092_060D_062___092_060D_062s_Osimps_I15_J_2, cls_insertCI_1, cls_sorted_Osimps_I2_J_0, cls_exp_Osimps_I111_J_0, cls_Nil__is__append__conv_2, cls_exp_Osimps_I64_J_0, cls_exp_Osimps_I88_J_0, cls_rev__swap_0, cls_r__into__rtrancl_0, cls_exp_Osimps_I10_J_0, cls_option_Osplit_0, cls_doubleton__eq__iff_4, cls_exp_Osimps_I96_J_0, cls_length__takeWhile__le_0, cls_subset__insertI_0, cls_impossible__Cons_0, cls_exp_Osimps_I196_J_0, cls_exp_Osimps_I91_J_0, cls_exp_Osimps_I181_J_0, cls_exp_Osimps_I200_J_0, cls_exp_Osimps_I63_J_0, cls_map__add__Some__iff_2, cls_sorted__Cons_1, cls_insert__code_0, cls_takeWhile_Osimps_I2_J_0, cls_map__add__find__right_0, cls_exp_Osimps_I214_J_0, cls_exp_Osimps_I168_J_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_UNION__empty__conv_I2_J_0, cls_length__insert_0, cls_insort__key_Osimps_I1_J_0, cls_fun__upd__upd_0, cls_concat_Osimps_I1_J_0, cls_map__add__SomeD_1, cls__092_060A_062___092_060A_062s_Osimps_I6_J_0, cls_exp_Osimps_I140_J_0, cls_exp_Osimps_I87_J_0, cls__092_060D_062___092_060D_062s_Osimps_I9_J_0, cls_insert__commute_0, cls_insert__iff_2, cls_exp_Osimps_I198_J_0, cls_option__map__Some_0, cls_exp_Osimps_I12_J_0, cls_Pair__eq_1, cls_exp_Osimps_I33_J_0, cls__092_060D_062___092_060D_062s_Osimps_I13_J_0, cls_list_Osimps_I2_J_0, cls_exp_Osimps_I104_J_0, cls_exp_Osimps_I78_J_0, clsarity_nat__Orderings_Oorder, cls_append1__eq__conv_0, cls_exp_Osimps_I202_J_0, cls_exp_Osimps_I100_J_0, cls_option_Osimps_I5_J_0, cls_equalityE_0, cls_exp_Osimps_I163_J_0, cls_red__reds_ORedSeq_0, cls_exp_Osimps_I173_J_0, cls_rev__rev__ident_0, cls__092_060A_062___092_060A_062s_Osimps_I1_J_0, cls_map__comp__None__iff_2, cls_sorted_Osimps_I3_J_0, cls_eval__finalId_0, cls_le__refl_0, cls_le__SucI_0, cls_not__less__eq__eq_0, cls_ball__empty_0, cls_exp_Osimps_I38_J_0, cls_exp_Osimps_I147_J_0, cls_map__add__None_1, cls_predicate1D_0, cls_exp_Osimps_I197_J_0, cls__092_060D_062___092_060D_062s_Osimps_I6_J_0, cls_subset__insert__iff_1, cls_D__mono_0, cls_exp_Osimps_I3_J_0, cls_exp_Osimps_I13_J_1, cls_fun__upd__idem__iff_1
% 16.49/5.17 % No. of inferences in proof: 1225
% 16.49/5.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4593 ms resp. 3734 ms w/o parsing
% 18.03/5.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.03/5.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------