%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV926-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:01:03 AM UTC 2026
% Result : Unsatisfiable 22.81s 7.84s
% Output : Refutation 25.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 494
% Syntax : Number of formulae : 989 ( 509 unt; 0 typ; 0 def)
% Number of atoms : 1633 ( 724 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52248 ( 942 ~; 644 |; 0 &;50662 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 77 usr; 22 con; 0-5 aty)
% Number of variables : 4944 ( 0 ^;4944 !; 0 ?;4944 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_ad_decl,type,
v_ad: $i ).
thf(v_ab_decl,type,
v_ab: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $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_bool_decl,type,
tc_bool: $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_Expr_Oexp_decl,type,
tc_Expr_Oexp: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(tc_Value_Oval_decl,type,
tc_Value_Oval: $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_ea_decl,type,
v_ea: $i ).
thf(v_a_decl,type,
v_a: $i ).
thf(v_b_decl,type,
v_b: $i ).
thf(v_e_Ha_decl,type,
v_e_Ha: $i ).
thf(v_aa_decl,type,
v_aa: $i ).
thf(v_ba_decl,type,
v_ba: $i ).
thf(c_SmallStep_Ored_decl,type,
c_SmallStep_Ored: $i > $i ).
thf(v_P_decl,type,
v_P: $i ).
thf(c_DefAss_O_092_060A_062_decl,type,
c_DefAss_O_092_060A_062: $i > $i > $i ).
thf(c_Option_Ooption_OSome_decl,type,
c_Option_Ooption_OSome: $i > $i ).
thf(v_ac_decl,type,
v_ac: $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(c_Map_Odom_decl,type,
c_Map_Odom: $i > $i > $i > $i ).
thf(v_ae_decl,type,
v_ae: $i ).
thf(v_e_092_060_094isub_0622_decl,type,
v_e_092_060_094isub_0622: $i ).
thf(v_x_decl,type,
v_x: $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_Expr_Oexp_OBlock_decl,type,
c_Expr_Oexp_OBlock: $i > $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_OTryCatch_decl,type,
c_Expr_Oexp_OTryCatch: $i > $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_OBinOp_decl,type,
c_Expr_Oexp_OBinOp: $i > $i > $i > $i > $i ).
thf(c_Expr_Oexp_Othrow_decl,type,
c_Expr_Oexp_Othrow: $i > $i > $i ).
thf(c_Expr_Oexp_OCall_decl,type,
c_Expr_Oexp_OCall: $i > $i > $i > $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(c_Expr_Oexp_OCast_decl,type,
c_Expr_Oexp_OCast: $i > $i > $i > $i ).
thf(c_Value_Oval_OAddr_decl,type,
c_Value_Oval_OAddr: $i > $i ).
thf(c_Value_Oval_ONull_decl,type,
c_Value_Oval_ONull: $i ).
thf(c_BigStep_Ofinal_decl,type,
c_BigStep_Ofinal: $i > $i > $o ).
thf(c_Objects_Ohext_decl,type,
c_Objects_Ohext: $i > $i > $o ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_decl,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Map_Omap__add_decl,type,
c_Map_Omap__add: $i > $i > $i > $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_BigStep_Oeval_decl,type,
c_BigStep_Oeval: $i > $i > $i > $i > $i > $o ).
thf(c_Map_Orestrict__map_decl,type,
c_Map_Orestrict__map: $i > $i > $i > $i > $i ).
thf(c_Expr_Ofv_decl,type,
c_Expr_Ofv: $i > $i ).
thf(c_WellForm_Owf__prog_decl,type,
c_WellForm_Owf__prog: $i > $i > $i > $o ).
thf(c_WWellForm_Owwf__J__mdecl_decl,type,
c_WWellForm_Owwf__J__mdecl: $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_BigStep_Oevals_decl,type,
c_BigStep_Oevals: $i > $i > $i > $i > $i > $o ).
thf(t_a_decl,type,
t_a: $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(c_Option_Ooption_Ooption__case_decl,type,
c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_Recdef_Osame__fst_decl,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Relation_Orefl__on_decl,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Expr_Ofvs_decl,type,
c_Expr_Ofvs: $i > $i ).
thf(c_Wellfounded_Olex__prod_decl,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Map_Osko__Map__XdomD__1__1_decl,type,
c_Map_Osko__Map__XdomD__1__1: $i > $i > $i > $i > $i ).
thf(280,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1322,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Expr_Ofvs )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofvs @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I17_J_0) ).
thf(1586,plain,
! [B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Expr_Ofvs )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofvs @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(322,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 ) @ ( H @ 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 @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssReds1_0) ).
thf(1411,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 ) @ ( H @ 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 @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).
thf(760,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)],[88]) ).
thf(430,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OLAssThrow_0) ).
thf(1633,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).
thf(846,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)],[114]) ).
thf(277,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 ) @ ( H @ 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 @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( F @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_TryRedsVal_0) ).
thf(1315,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 ) @ ( H @ 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 @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( F @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I149_J_0) ).
thf(1083,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)],[183]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).
thf(941,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)],[141]) ).
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_OBlock ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I204_J_0) ).
thf(666,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)],[57]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1549,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)],[390]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).
thf(645,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)],[50]) ).
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_OLAss ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I141_J_0) ).
thf(892,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)],[126]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I172_J_0) ).
thf(1024,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)],[165]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( D @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I8_J_0) ).
thf(1469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( D @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(301,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OInitBlockThrow_0) ).
thf(1369,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(217,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCondRed_0) ).
thf(1190,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(222,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 ) @ ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssRedsThrow_0) ).
thf(1200,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 ) @ ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(1211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
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/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(523,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(375,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 ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqReds_0) ).
thf(1522,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 ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(423,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Option_Ooption_Ooption__case ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I5_J_0) ).
thf(1618,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)],[423]) ).
thf(317,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( E @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(1401,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( E @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(474,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 ) @ ( H @ 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 ) @ ( G @ ( F @ c_Pair ) ) ) @ ( E @ 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 @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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_String_Ochar @ tc_List_Olist @ ( G @ ( C @ c_Map_Omap__add ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ 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 @ ( D @ ( C @ c_Map_Omap__add ) ) ) @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__lcl__add_0) ).
thf(1728,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 ) @ ( H @ 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 ) @ ( G @ ( F @ c_Pair ) ) ) @ ( E @ 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 @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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_String_Ochar @ tc_List_Olist @ ( G @ ( C @ c_Map_Omap__add ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ 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 @ ( D @ ( C @ c_Map_Omap__add ) ) ) @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(224,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCallObj_0) ).
thf(1205,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).
thf(1142,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)],[200]) ).
thf(458,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/sandbox/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I13_J_0) ).
thf(1692,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)],[458]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).
thf(1041,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)],[170]) ).
thf(209,axiom,
! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__refl_0) ).
thf(1173,plain,
! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(417,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( I @ c_Expr_Oexp_OVal ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( H @ ( D @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OBinOp ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OBinOpThrow2_0) ).
thf(1608,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( I @ c_Expr_Oexp_OVal ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( H @ ( D @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OBinOp ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(440,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1655,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).
thf(550,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)],[21]) ).
thf(477,axiom,
! [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 ) @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( 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 ) @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oeval ) ) ) ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__hext_0) ).
thf(1735,plain,
! [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 ) @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( 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 ) @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oeval ) ) ) ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(3,negated_conjecture,
( ( tc_String_Ochar @ tc_List_Olist @ ( v_e_Ha @ c_DefAss_O_092_060A_062 ) )
= ( v_ac @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(500,plain,
( ( tc_String_Ochar @ tc_List_Olist @ ( v_e_Ha @ c_DefAss_O_092_060A_062 ) )
= ( v_ac @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I181_J_0) ).
thf(1164,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)],[206]) ).
thf(491,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).
thf(1761,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).
thf(1063,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)],[177]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1354,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Expr_Ofv )
= ( B @ c_Expr_Ofv ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I2_J_0) ).
thf(1458,plain,
! [B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Expr_Ofv )
= ( B @ c_Expr_Ofv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ 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_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OSeqThrow_0) ).
thf(1756,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ 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_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1507,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)],[368]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I4_J_0) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I114_J_0) ).
thf(898,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)],[128]) ).
thf(312,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1391,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)],[312]) ).
thf(336,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OBinOp ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed1_0) ).
thf(1441,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OBinOp ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I137_J_0) ).
thf(709,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)],[72]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I158_J_0) ).
thf(1046,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)],[171]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Expr_Ofv )
= ( A @ c_Expr_Ofv ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I7_J_0) ).
thf(1613,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Expr_Ofv )
= ( A @ c_Expr_Ofv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(472,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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_Othrow ) @ 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_Othrow ) @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow2_0) ).
thf(1724,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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_Othrow ) @ 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_Othrow ) @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(1529,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(252,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1265,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I101_J_0) ).
thf(651,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)],[52]) ).
thf(414,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( G @ ( F @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ ( E @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_3) ).
thf(1601,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( B @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( G @ ( F @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ ( E @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(1386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(247,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 ) @ ( E @ 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 @ ( D @ ( C @ 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 @ ( B @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ThrowReds_0) ).
thf(1254,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 ) @ ( E @ 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 @ ( D @ ( C @ 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 @ ( B @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(321,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Try_0) ).
thf(1409,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_in @ c_COMBC ) ) ) ) )
!= ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_in @ c_COMBC ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(1330,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_in @ c_COMBC ) ) ) ) )
!= ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_in @ c_COMBC ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).
thf(838,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)],[112]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).
thf(802,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)],[102]) ).
thf(347,axiom,
! [A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Ofv )
= ( A @ c_Expr_Ofv ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I14_J_0) ).
thf(1462,plain,
! [A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Ofv )
= ( A @ c_Expr_Ofv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(1511,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I215_J_0) ).
thf(702,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)],[69]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).
thf(751,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)],[85]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ ( C @ ( E @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(1313,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ ( C @ ( E @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(259,axiom,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1279,plain,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1577,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(343,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1455,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(388,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1545,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)],[388]) ).
thf(306,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1379,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)],[306]) ).
thf(371,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1514,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(1319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(356,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 ) @ ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ c_Expr_Oexp_Othrow ) @ 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_OWhile ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WhileRedsThrow_0) ).
thf(1479,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 ) @ ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ c_Expr_Oexp_Othrow ) @ 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_OWhile ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(434,axiom,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccReds_0) ).
thf(1641,plain,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(298,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).
thf(1362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).
thf(1100,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)],[188]) ).
thf(236,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 ) @ ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqRedsThrow_0) ).
thf(1232,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 ) @ ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I213_J_0) ).
thf(969,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)],[149]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I13_J_0) ).
thf(1347,plain,
! [B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1572,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)],[400]) ).
thf(481,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1741,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I87_J_0) ).
thf(881,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)],[123]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1415,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(349,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_Relation_Orefl__on ) ) )
| ~ ( E @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(1465,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_Relation_Orefl__on ) ) )
| ~ ( E @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(340,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OLAssThrow_0) ).
thf(1450,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(303,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAccThrow_0) ).
thf(1373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(326,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = D )
| ~ ( 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 ) ) ) @ ( E @ ( 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 ) ) ) @ ( A @ ( B @ c_BigStep_Oeval ) ) ) ) )
| ( ( A @ c_Expr_Ofv )
!= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__closed__lcl__unchanged_0) ).
thf(1418,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G = D )
| ~ ( 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 ) ) ) @ ( E @ ( 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 ) ) ) @ ( A @ ( B @ c_BigStep_Oeval ) ) ) ) )
| ( ( A @ c_Expr_Ofv )
!= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(286,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ tc_Option_Ooption @ ( F @ ( A @ ( E @ c_Option_Ooption_OSome @ hAPP ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( B @ ( E @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).
thf(1334,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)],[286]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I182_J_0) ).
thf(1136,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)],[198]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).
thf(1151,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)],[203]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I47_J_0) ).
thf(574,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)],[27]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
!= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(1581,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)],[404]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).
thf(821,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)],[107]) ).
thf(270,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCallThrowObj_0) ).
thf(1302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( v_x @ ( C @ ( t_a @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( C @ ( C @ tc_Option_Ooption @ ( v_x @ ( B @ hAPP ) @ ( C @ c_Option_Ooption_OSome @ ( v_x @ ( A @ hAPP ) @ c_Option_Ooption_Ooption__case ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__def_0) ).
thf(1664,plain,
! [C: $i,B: $i,A: $i] :
( ( v_x @ ( C @ ( t_a @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( C @ ( C @ tc_Option_Ooption @ ( v_x @ ( B @ hAPP ) @ ( C @ c_Option_Ooption_OSome @ ( v_x @ ( A @ hAPP ) @ c_Option_Ooption_Ooption__case ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).
thf(766,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)],[90]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(1377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(229,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAccRed_0) ).
thf(1215,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I203_J_0) ).
thf(734,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)],[79]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).
thf(1072,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)],[180]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I217_J_0) ).
thf(1119,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)],[193]) ).
thf(314,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).
thf(1394,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)],[314]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1526,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I159_J_0) ).
thf(660,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)],[55]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).
thf(998,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)],[157]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(397,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1564,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)],[397]) ).
thf(461,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1697,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(1242,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(438,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OCondThrow_0) ).
thf(1651,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_0) ).
thf(512,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)],[10]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(1438,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I197_J_0) ).
thf(793,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)],[99]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).
thf(810,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)],[104]) ).
thf(466,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_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( G @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) @ ( A @ ( F @ c_Pair ) ) ) @ ( E @ 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 ) @ ( B @ ( D @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofv @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Reds__dom__lcl_0) ).
thf(1708,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_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( G @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) @ ( A @ ( F @ c_Pair ) ) ) @ ( E @ 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 ) @ ( B @ ( D @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofv @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).
thf(534,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)],[17]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedSeq_0) ).
thf(1768,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).
thf(1057,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)],[175]) ).
thf(257,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_List_Olist_OCons ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_BigStep_Oevals ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ConsThrow_0) ).
thf(1274,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ c_List_Olist_OCons ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_BigStep_Oevals ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_2) ).
thf(910,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)],[132]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I205_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_OBlock ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(290,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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_Othrow ) @ 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 @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow2_0) ).
thf(1343,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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_Othrow ) @ 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 @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(144,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(952,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)],[144]) ).
thf(485,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAcc ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OFAccThrow_0) ).
thf(1751,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAcc ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(360,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = G )
| ( ( F @ ( A @ hAPP ) )
= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).
thf(1487,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)],[360]) ).
thf(302,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).
thf(1370,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I164_J_0) ).
thf(815,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)],[105]) ).
thf(239,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_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) @ ( A @ 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 @ ( F @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( G @ ( F @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extend__eval_0) ).
thf(1238,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_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) @ ( A @ 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 @ ( F @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( G @ ( F @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1560,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I92_J_0) ).
thf(1021,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)],[164]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).
thf(778,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)],[94]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I207_J_0) ).
thf(1174,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)],[210]) ).
thf(451,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/sandbox/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I2_J_0) ).
thf(1676,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)],[451]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(1217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).
thf(598,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)],[35]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).
thf(561,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)],[24]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1666,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).
thf(693,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)],[66]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I220_J_0) ).
thf(630,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)],[45]) ).
thf(328,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( E @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(1423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( E @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I196_J_0) ).
thf(566,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)],[25]) ).
thf(299,axiom,
! [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 ) @ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOpRedsThrow1_0) ).
thf(1365,plain,
! [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 ) @ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(267,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( I @ ( E @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow2_0) ).
thf(1296,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( I @ ( E @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(456,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
= ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1687,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
= ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).
thf(1159,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)],[205]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1656,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)],[441]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I104_J_0) ).
thf(1027,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)],[166]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I219_J_0) ).
thf(757,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)],[87]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).
thf(1128,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)],[196]) ).
thf(260,axiom,
! [B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I11_J_0) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1392,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).
thf(974,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)],[151]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).
thf(1012,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)],[161]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).
thf(583,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)],[30]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I71_J_0) ).
thf(830,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)],[110]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).
thf(682,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)],[63]) ).
thf(320,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(297,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(1360,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)],[297]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I191_J_0) ).
thf(742,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)],[82]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCondThrow_0) ).
thf(1534,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I142_J_0) ).
thf(615,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)],[40]) ).
thf(283,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_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( G @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( G @ 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 @ ( 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 ) ) ) @ ( 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 ) ) ) @ ( B @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__fv_0) ).
thf(1328,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_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( G @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( G @ 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 @ ( 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 ) ) ) @ ( 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 ) ) ) @ ( B @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).
thf(1111,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)],[191]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).
thf(725,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)],[76]) ).
thf(364,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 ) @ ( H @ 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 @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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 ) @ ( H @ 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 @ ( F @ c_Expr_Oexp_Othrow ) @ 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 @ ( I @ ( D @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( F @ c_Expr_Oexp_Othrow ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsThrow2_0) ).
thf(1498,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 ) @ ( H @ 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 @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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 ) @ ( H @ 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 @ ( F @ c_Expr_Oexp_Othrow ) @ 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 @ ( I @ ( D @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( F @ c_Expr_Oexp_Othrow ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(329,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ hAPP ) @ hBOOL )
| ~ ( C @ ( G @ hAPP ) @ ( B @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( G @ ( F @ c_Recdef_Osame__fst ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ ( E @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__fstI_0) ).
thf(1425,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ hAPP ) @ hBOOL )
| ~ ( C @ ( G @ hAPP ) @ ( B @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( G @ ( F @ c_Recdef_Osame__fst ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ ( E @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).
thf(1006,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)],[159]) ).
thf(470,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( H @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( G @ ( B @ c_Pair ) ) ) @ ( E @ ( C @ ( F @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_0) ).
thf(1719,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( H @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( G @ ( B @ c_Pair ) ) ) @ ( E @ ( C @ ( F @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).
thf(610,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)],[39]) ).
thf(7,negated_conjecture,
( ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622 @ c_DefAss_O_092_060A_062 ) )
= ( v_x @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(499,plain,
( ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622 @ c_DefAss_O_092_060A_062 ) )
= ( v_x @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(237,axiom,
! [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 ) @ ( 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 @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( I @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( H @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOpRedsThrow2_0) ).
thf(1234,plain,
! [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 ) @ ( 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 @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( I @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( H @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(386,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).
thf(1541,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(255,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 ) @ ( H @ 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 @ ( F @ 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 @ ( D @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( F @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssReds2_0) ).
thf(1270,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 ) @ ( H @ 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 @ ( F @ 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 @ ( D @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( F @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1259,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I143_J_0) ).
thf(857,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)],[117]) ).
thf(315,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1397,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(398,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 ) @ ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ c_Expr_Oexp_Othrow ) @ 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_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastRedsThrow_0) ).
thf(1567,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 ) @ ( 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 @ c_Expr_Oexp_Othrow ) @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ c_Expr_Oexp_Othrow ) @ 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_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(454,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ 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 @ ( G @ ( F @ 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 @ ( D @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ 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 @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssRed2_0) ).
thf(1683,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ 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 @ ( G @ ( F @ 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 @ ( D @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ 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 @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I108_J_0) ).
thf(884,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)],[124]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(265,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OThrowThrow_0) ).
thf(1292,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I50_J_0) ).
thf(669,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)],[58]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).
thf(901,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)],[129]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).
thf(642,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)],[49]) ).
thf(405,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( D @ ( F @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upd_0) ).
thf(1584,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)],[405]) ).
thf(338,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 ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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_OCast ) ) @ 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_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastReds_0) ).
thf(1446,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 ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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_OCast ) ) @ 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_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(1207,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I105_J_0) ).
thf(547,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)],[20]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I150_J_0) ).
thf(706,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)],[71]) ).
thf(419,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1612,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I62_J_0) ).
thf(679,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)],[62]) ).
thf(281,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( E @ ( A @ ( D @ ( C @ ( B @ c_BigStep_Oeval ) ) ) ) )
| ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_BigStep_Ofinal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_big__iff__small_1) ).
thf(1324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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)],[281]) ).
thf(407,axiom,
! [A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I3_J_0) ).
thf(1588,plain,
! [A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(355,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedInitBlock_0) ).
thf(1478,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1451,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)],[341]) ).
thf(253,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OWhile ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WhileCondThrow_0) ).
thf(1266,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OWhile ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1668,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(218,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) ) ) @ ( F @ ( 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 ) ) ) @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( E @ ( B @ c_Expr_Ofv @ c_lessequals ) ) )
| ( 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 @ ( E @ ( H @ c_Map_Orestrict__map ) ) ) @ ( G @ c_Pair ) ) ) @ ( F @ ( 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 @ ( E @ ( D @ c_Map_Orestrict__map ) ) ) @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__restrict__lcl_0) ).
thf(1192,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) ) ) @ ( F @ ( 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 ) ) ) @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( E @ ( B @ c_Expr_Ofv @ c_lessequals ) ) )
| ( 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 @ ( E @ ( H @ c_Map_Orestrict__map ) ) ) @ ( G @ c_Pair ) ) ) @ ( F @ ( 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 @ ( E @ ( D @ c_Map_Orestrict__map ) ) ) @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I225_J_0) ).
thf(1060,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)],[176]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_2) ).
thf(569,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)],[26]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(427,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 ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqReds2_0) ).
thf(1627,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 ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(379,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1530,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(385,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_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( A @ 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 @ ( G @ ( F @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( G @ ( F @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extend__1__eval_0) ).
thf(1539,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_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( A @ 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 @ ( G @ ( F @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( G @ ( F @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(344,axiom,
! [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 ) @ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccRedsThrow_0) ).
thf(1456,plain,
! [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 ) @ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(1382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).
thf(1131,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)],[197]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I106_J_0) ).
thf(654,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)],[53]) ).
thf(413,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( A @ ( A @ ( E @ ( C @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( H @ ( G @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ ( F @ ( E @ c_Pair ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_2) ).
thf(1599,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( A @ ( A @ ( E @ ( C @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( H @ ( G @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ ( F @ ( E @ c_Pair ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ ( B @ ( A @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(243,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ 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 @ ( G @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ 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 @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OTryRed_0) ).
thf(1246,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ 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 @ ( G @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ 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 @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(285,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1333,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(223,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domI_0) ).
thf(1202,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I210_J_0) ).
thf(633,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)],[46]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
!= ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).
thf(921,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)],[135]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I65_J_0) ).
thf(657,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)],[54]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).
thf(1170,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)],[208]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(1286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(215,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow1_0) ).
thf(1187,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(444,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/sandbox/benchmark/theBenchmark.p',cls_Val_0) ).
thf(1663,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)],[444]) ).
thf(207,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I179_J_0) ).
thf(1167,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)],[207]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1616,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( C @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( C @ c_in @ c_COMBC ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
thf(1185,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( C @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( C @ c_in @ c_COMBC ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I178_J_0) ).
thf(586,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)],[31]) ).
thf(476,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ tc_Option_Ooption @ ( G @ ( F @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( B = E )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).
thf(1732,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)],[476]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).
thf(926,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)],[136]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).
thf(1086,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)],[184]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I185_J_0) ).
thf(938,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)],[140]) ).
thf(468,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/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(1712,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)],[468]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I109_J_0) ).
thf(1054,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)],[174]) ).
thf(369,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ 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 @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedTry_0) ).
thf(1510,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ 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 @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).
thf(618,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)],[41]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_1) ).
thf(1103,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)],[189]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I70_J_0) ).
thf(824,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)],[108]) ).
thf(358,axiom,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CondReds_0) ).
thf(1483,plain,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I58_J_0) ).
thf(745,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)],[83]) ).
thf(411,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( A @ ( E @ tc_prod ) @ ( A @ ( E @ tc_prod ) @ ( A @ ( E @ ( C @ ( G @ c_Pair ) ) ) @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ ( A @ ( E @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( E @ ( G @ ( F @ c_Pair ) ) ) @ ( E @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_1) ).
thf(1595,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( A @ ( E @ tc_prod ) @ ( A @ ( E @ tc_prod ) @ ( A @ ( E @ ( C @ ( G @ c_Pair ) ) ) @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ ( A @ ( E @ tc_prod ) @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( E @ ( G @ ( F @ c_Pair ) ) ) @ ( E @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(304,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/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1374,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)],[304]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofvs @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I9_J_0) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofvs @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I46_J_0) ).
thf(601,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)],[36]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_0) ).
thf(1154,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)],[204]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).
thf(904,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)],[130]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).
thf(772,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)],[92]) ).
thf(424,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/sandbox/benchmark/theBenchmark.p',cls_eval__cases_I1_J_1) ).
thf(1620,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)],[424]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I98_J_0) ).
thf(577,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)],[28]) ).
thf(382,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1535,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)],[382]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(1520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(421,axiom,
tc_nat @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(1615,plain,
tc_nat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I7_J_0) ).
thf(1389,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)],[311]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I151_J_0) ).
thf(843,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)],[113]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).
thf(1125,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)],[195]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).
thf(958,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)],[146]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Odom ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dom__map__add_0) ).
thf(1403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Odom ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(248,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( F @ c_Map_Odom ) ) @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( E @ ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__add ) ) ) )
= ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( C @ ( E @ ( F @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__upd__left_0) ).
thf(1256,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( F @ c_Map_Odom ) ) @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( E @ ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__add ) ) ) )
= ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( C @ ( E @ ( F @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(234,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = G )
| ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= ( C @ tc_Option_Ooption @ ( E @ ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).
thf(1226,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)],[234]) ).
thf(331,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1428,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)],[331]) ).
thf(465,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1707,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).
thf(787,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)],[97]) ).
thf(2,negated_conjecture,
v_P @ 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 @ ( 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 ) @ ( v_ba @ ( v_aa @ c_Pair ) ) ) @ ( v_e_Ha @ 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 ) @ ( v_b @ ( v_a @ c_Pair ) ) ) @ ( v_ea @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(498,plain,
v_P @ 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 @ ( 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 ) @ ( v_ba @ ( v_aa @ c_Pair ) ) ) @ ( v_e_Ha @ 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 ) @ ( v_b @ ( v_a @ c_Pair ) ) ) @ ( v_ea @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1635,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(59,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_BigStep_Ofinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_final__def_1) ).
thf(672,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_BigStep_Ofinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I107_J_0) ).
thf(1139,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)],[199]) ).
thf(366,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 ) @ ( H @ 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 @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_TryReds_0) ).
thf(1503,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 ) @ ( H @ 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 @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(348,axiom,
tc_nat @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(1464,plain,
tc_nat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_1) ).
thf(947,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)],[143]) ).
thf(432,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow1_0) ).
thf(1638,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(233,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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ 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 @ ( B @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastRedsNull_0) ).
thf(1224,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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ 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 @ ( B @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(226,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ 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 @ ( G @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ 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 @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssRed1_0) ).
thf(1209,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ 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 @ ( G @ ( F @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ 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 @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I173_J_0) ).
thf(784,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)],[96]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1574,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(1524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(293,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/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1349,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)],[293]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(990,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)],[155]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1722,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)],[471]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Objects_Ohext ) )
| ~ ( B @ ( C @ c_Objects_Ohext ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__trans_0) ).
thf(737,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Objects_Ohext ) )
| ~ ( B @ ( C @ c_Objects_Ohext ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I162_J_0) ).
thf(509,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(194,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).
thf(1122,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)],[194]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).
thf(979,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)],[152]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).
thf(604,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)],[37]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(1492,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1603,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)],[415]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1471,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)],[352]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).
thf(1080,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)],[182]) ).
thf(288,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) @ ( A @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_BigStep_Ofinal ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_big__iff__small_2) ).
thf(1339,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) @ ( A @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_BigStep_Ofinal ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(799,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).
thf(621,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)],[42]) ).
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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I83_J_0) ).
thf(520,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(127,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I110_J_0) ).
thf(895,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)],[127]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).
thf(964,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)],[148]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I153_J_0) ).
thf(915,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)],[133]) ).
thf(291,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).
thf(1344,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)],[291]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).
thf(1177,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)],[211]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I188_J_0) ).
thf(932,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)],[138]) ).
thf(393,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( 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 @ ( B @ c_Pair ) ) ) @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__hext__incr_0) ).
thf(1556,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( 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 @ ( B @ c_Pair ) ) ) @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).
thf(769,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)],[91]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofv @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I12_J_0) ).
thf(1460,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Expr_Ofv )
= ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofv @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( B @ c_Expr_Ofv @ ( A @ c_Expr_Ofv @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I190_J_0) ).
thf(685,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)],[64]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1198,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)],[221]) ).
thf(353,axiom,
! [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 ) @ ( B @ ( G @ c_Pair ) ) ) @ ( F @ ( 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 ) @ ( A @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oeval ) ) ) ) )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__lcl__incr_0) ).
thf(1474,plain,
! [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 ) @ ( B @ ( G @ c_Pair ) ) ) @ ( F @ ( 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 ) @ ( A @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oeval ) ) ) ) )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I113_J_0) ).
thf(636,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)],[47]) ).
thf(435,axiom,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1643,plain,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I167_J_0) ).
thf(1015,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)],[162]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I68_J_0) ).
thf(851,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)],[115]) ).
thf(459,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1694,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1562,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(1213,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I177_J_0) ).
thf(827,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)],[109]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I199_J_0) ).
thf(1066,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)],[178]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).
thf(868,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)],[120]) ).
thf(323,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCall ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallObjThrow_0) ).
thf(1413,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCall ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).
thf(722,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)],[75]) ).
thf(272,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Throw_0) ).
thf(1304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(489,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(1758,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I184_J_0) ).
thf(589,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)],[32]) ).
thf(350,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( 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 ) @ ( A @ ( F @ c_Pair ) ) ) @ ( E @ 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 ) @ ( B @ ( D @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofv @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__dom__lcl_0) ).
thf(1467,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( 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 ) @ ( A @ ( F @ c_Pair ) ) ) @ ( E @ 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 ) @ ( B @ ( D @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( C @ c_Expr_Ofv @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).
thf(663,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)],[56]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I222_J_0) ).
thf(648,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)],[51]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).
thf(754,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)],[86]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I208_J_0) ).
thf(553,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)],[22]) ).
thf(391,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) @ ( A @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_BigStep_Ofinal ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_small__by__big_0) ).
thf(1551,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( 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 ) @ ( A @ 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_BigStep_Ofinal ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).
thf(1049,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)],[172]) ).
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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I96_J_0) ).
thf(531,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(142,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I99_J_0) ).
thf(944,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)],[142]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I59_J_0) ).
thf(1145,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)],[201]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I223_J_0) ).
thf(1018,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)],[163]) ).
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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).
thf(525,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(29,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).
thf(580,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)],[29]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] : ( C @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ c_Expr_Oexp_OVal ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedCastNull_0) ).
thf(1516,plain,
! [C: $i,B: $i,A: $i] : ( C @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ c_Expr_Oexp_OVal ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(70,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ c_BigStep_Ofinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_final__def_2) ).
thf(705,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ c_BigStep_Ofinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_in @ c_COMBC ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
thf(1743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_in @ c_COMBC ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_0) ).
thf(887,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)],[125]) ).
thf(416,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ hAPP ) )
= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( E @ ( A @ hAPP ) )
= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
!= ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).
thf(1605,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)],[416]) ).
thf(246,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OSeqThrow_0) ).
thf(1252,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( 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)],[246]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I66_J_0) ).
thf(739,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)],[81]) ).
thf(486,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).
thf(1753,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(389,axiom,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OBinOp ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOp1Reds_0) ).
thf(1547,plain,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OBinOp ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(484,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= ( C @ ( D @ ( A @ ( B @ c_Map_Osko__Map__XdomD__1__1 ) ) ) @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domD_0) ).
thf(1748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= ( C @ ( D @ ( A @ ( B @ c_Map_Osko__Map__XdomD__1__1 ) ) ) @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_2) ).
thf(712,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)],[73]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I198_J_0) ).
thf(1003,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)],[158]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I100_J_0) ).
thf(673,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)],[60]) ).
thf(269,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_OVal ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( G @ ( F @ ( H @ ( C @ ( A @ c_BigStep_Oevals ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_OVal ) @ c_List_Olist_OCons ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_BigStep_Oevals ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OCons_0) ).
thf(1300,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_OVal ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ~ ( G @ ( F @ ( H @ ( C @ ( A @ c_BigStep_Oevals ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_OVal ) @ c_List_Olist_OCons ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_BigStep_Oevals ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(1188,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
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_OCall ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I102_J_0) ).
thf(1038,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)],[169]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Value_Oval_OAddr )
!= ( B @ c_Value_Oval_OAddr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I3_J_0) ).
thf(717,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Value_Oval_OAddr )
!= ( B @ c_Value_Oval_OAddr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(4,negated_conjecture,
( ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_ac @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_ba @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= v_ab ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(502,plain,
( ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_ac @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_ba @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= v_ab ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(251,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A )
| ( ( B @ ( A @ hAPP ) )
!= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).
thf(1262,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)],[251]) ).
thf(384,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBlockThrow_0) ).
thf(1538,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Value_Oval_OAddr @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_Othrow ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(403,axiom,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallRedsObj_0) ).
thf(1579,plain,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(1220,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)],[231]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit_1) ).
thf(1317,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)],[278]) ).
thf(492,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ ( E @ 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 ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ 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 @ ( D @ ( C @ 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 @ ( B @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_big__by__small_0) ).
thf(1763,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( c_WWellForm_Owwf__J__mdecl @ c_WellForm_Owf__prog ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ ( E @ 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 ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( E @ 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 @ ( D @ ( C @ 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 @ ( B @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(479,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedBlock_0) ).
thf(1738,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Expr_Oexp_OVal ) )
!= ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).
thf(544,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)],[19]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I88_J_0) ).
thf(907,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)],[131]) ).
thf(296,axiom,
! [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 ) @ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallRedsThrowObj_0) ).
thf(1358,plain,
! [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 ) @ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(387,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 ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssReds_0) ).
thf(1543,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 ) @ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1702,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(330,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1427,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I103_J_0) ).
thf(1094,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)],[186]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).
thf(1670,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( B @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( A @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( B @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( A @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ c_Value_Oval_OAddr )
!= c_Value_Oval_ONull ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I17_J_0) ).
thf(595,plain,
! [A: $i] :
( ( A @ c_Value_Oval_OAddr )
!= c_Value_Oval_ONull ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(1272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(240,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( 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 @ ( F @ c_Pair ) ) ) @ ( E @ 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 ) @ ( A @ ( D @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__lcl__incr_0) ).
thf(1240,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( 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 @ ( F @ c_Pair ) ) ) @ ( E @ 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 ) @ ( A @ ( D @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(173,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
= ( E @ ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__add ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).
thf(1052,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)],[173]) ).
thf(6,negated_conjecture,
( ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_ae @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_b @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= v_ad ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(497,plain,
( ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_ae @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_b @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= v_ad ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).
thf(876,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)],[122]) ).
thf(327,axiom,
! [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 ) @ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CondRedsThrow_0) ).
thf(1421,plain,
! [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 ) @ ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ 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 @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I214_J_0) ).
thf(627,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)],[44]) ).
thf(437,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OCastThrow_0) ).
thf(1649,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I146_J_0) ).
thf(1180,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)],[212]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_1) ).
thf(556,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)],[23]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).
thf(688,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)],[65]) ).
thf(5,negated_conjecture,
( ( tc_String_Ochar @ tc_List_Olist @ ( v_ea @ c_DefAss_O_092_060A_062 ) )
= ( v_ae @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(495,plain,
( ( tc_String_Ochar @ tc_List_Olist @ ( v_ea @ c_DefAss_O_092_060A_062 ) )
= ( v_ae @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1517,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)],[373]) ).
thf(339,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow1_0) ).
thf(1448,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I145_J_0) ).
thf(1108,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)],[190]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).
thf(539,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)],[18]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__in_0) ).
thf(1289,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(342,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 ) @ ( H @ 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 @ ( F @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( F @ c_Expr_Oexp_Othrow ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsThrow1_0) ).
thf(1453,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 ) @ ( H @ 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 @ ( F @ c_Expr_Oexp_Othrow ) @ 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 @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( H @ 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 @ ( F @ c_Expr_Oexp_Othrow ) @ 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 @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(436,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/sandbox/benchmark/theBenchmark.p',cls_eval__cases_I1_J_0) ).
thf(1646,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)],[436]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I111_J_0) ).
thf(699,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)],[68]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).
thf(961,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)],[147]) ).
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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).
thf(517,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(354,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ c_Expr_Oexp_OVal ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ c_Expr_Oexp_OVal ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastNull_0) ).
thf(1476,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ c_Expr_Oexp_OVal ) @ ( D @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ c_Expr_Oexp_OVal ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',cls_eval__final_0) ).
thf(1481,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)],[357]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(483,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(1745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(242,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed2_0) ).
thf(1244,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ 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 @ ( F @ ( E @ 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 @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).
thf(731,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)],[78]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I112_J_0) ).
thf(781,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)],[95]) ).
thf(258,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 ) @ ( A @ ( H @ c_Pair ) ) ) @ ( G @ ( 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 ) @ ( C @ ( F @ c_Pair ) ) ) @ ( D @ ( E @ c_BigStep_Oeval ) ) ) ) )
| ( D @ c_Expr_Ofv @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__notfree__unchanged_0) ).
thf(1276,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 ) @ ( A @ ( H @ c_Pair ) ) ) @ ( G @ ( 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 ) @ ( C @ ( F @ c_Pair ) ) ) @ ( D @ ( E @ c_BigStep_Oeval ) ) ) ) )
| ( D @ c_Expr_Ofv @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(408,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1590,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(289,axiom,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOp2Reds_0) ).
thf(1341,plain,
! [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 ) @ ( 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 @ ( F @ ( E @ 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 @ ( C @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ 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 @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OBinOp ) ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I209_J_0) ).
thf(748,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)],[84]) ).
thf(450,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/sandbox/benchmark/theBenchmark.p',cls_eval__finalId_0) ).
thf(1674,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)],[450]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1639,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)],[433]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I200_J_0) ).
thf(995,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)],[156]) ).
thf(394,axiom,
! [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 ) @ ( B @ ( G @ c_Pair ) ) ) @ ( F @ ( 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 ) @ ( A @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oevals ) ) ) ) )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evals__lcl__incr_0) ).
thf(1558,plain,
! [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 ) @ ( B @ ( G @ c_Pair ) ) ) @ ( F @ ( 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 ) @ ( A @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oevals ) ) ) ) )
| ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Map_Odom ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Map_Odom ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).
thf(1030,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)],[167]) ).
thf(457,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(1689,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)],[457]) ).
thf(266,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1294,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I138_J_0) ).
thf(929,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)],[137]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I89_J_0) ).
thf(1077,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)],[181]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).
thf(763,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)],[89]) ).
thf(443,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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_OCast ) ) @ 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_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCastRed_0) ).
thf(1661,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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 ) ) ) @ ( 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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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_OCast ) ) @ 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_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).
thf(1116,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)],[192]) ).
thf(473,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( A @ c_Expr_Ofv @ ( B @ c_lessequals ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_DefAss_O_092_060A_062 ) )
!= ( B @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A__fv_0) ).
thf(1725,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( A @ c_Expr_Ofv @ ( B @ c_lessequals ) ) )
| ( ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_DefAss_O_092_060A_062 ) )
!= ( B @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(452,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( A @ hAPP ) )
= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
!= ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).
thf(1678,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)],[452]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).
thf(833,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)],[111]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I165_J_0) ).
thf(1097,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)],[187]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(818,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(488,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1757,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(119,axiom,
! [A: $i] :
( c_Value_Oval_ONull
!= ( A @ c_Value_Oval_OAddr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I16_J_0) ).
thf(865,plain,
! [A: $i] :
( c_Value_Oval_ONull
!= ( A @ c_Value_Oval_OAddr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I115_J_0) ).
thf(854,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)],[116]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCastThrow_0) ).
thf(1303,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ 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 @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).
thf(1148,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)],[202]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] : ( C @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OThrowThrow_0) ).
thf(1673,plain,
! [C: $i,B: $i,A: $i] : ( C @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(244,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ 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 @ ( 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 ) ) ) @ ( E @ 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 @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ 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 @ ( 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 @ ( G @ ( C @ c_Map_Omap__add ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ 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 @ ( D @ ( C @ c_Map_Omap__add ) ) ) @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__lcl__add_0) ).
thf(1248,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ 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 @ ( 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 ) ) ) @ ( E @ 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 @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ 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 @ ( 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 @ ( G @ ( C @ c_Map_Omap__add ) ) ) @ ( F @ c_Pair ) ) ) @ ( E @ 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 @ ( D @ ( C @ c_Map_Omap__add ) ) ) @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I201_J_0) ).
thf(790,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)],[98]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I168_J_0) ).
thf(918,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)],[134]) ).
thf(363,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/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1495,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)],[363]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).
thf(807,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)],[103]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).
thf(696,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)],[67]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).
thf(955,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)],[145]) ).
thf(418,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_Relation_Orefl__on ) ) )
| ~ ( E @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(1610,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_Relation_Orefl__on ) ) )
| ~ ( E @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).
thf(796,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)],[100]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).
thf(1033,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)],[168]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osplit__asm_1) ).
thf(1710,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)],[467]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I194_J_0) ).
thf(624,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)],[43]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I64_J_0) ).
thf(728,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)],[77]) ).
thf(250,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1261,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(254,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1268,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).
thf(528,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(365,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).
thf(871,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)],[121]) ).
thf(367,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1505,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(8,negated_conjecture,
( ~ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_x @ ( v_ac @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_ba @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_b @ c_Map_Odom ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_x @ ( v_ac @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_ba @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_ae @ c_lessequals ) ) )
| ~ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_x @ ( v_ac @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_ba @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_x @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(501,plain,
( ~ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_x @ ( v_ac @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_ba @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_b @ c_Map_Odom ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_x @ ( v_ac @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_ba @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_ae @ c_lessequals ) ) )
| ~ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_x @ ( v_ac @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Value_Oval @ ( tc_String_Ochar @ tc_List_Olist @ ( v_ba @ c_Map_Odom ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_x @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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_OFAcc ) ) ) )
!= ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).
thf(607,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)],[38]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(1236,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)],[238]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I148_J_0) ).
thf(987,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)],[154]) ).
thf(380,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/sandbox/benchmark/theBenchmark.p',cls_Seq_0) ).
thf(1532,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)],[380]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(860,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)],[118]) ).
thf(309,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1384,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)],[309]) ).
thf(383,axiom,
tc_nat @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(1537,plain,
tc_nat @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(412,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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 @ ( C @ 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 @ ( B @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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_Othrow ) @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OThrowRed_0) ).
thf(1597,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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 @ ( C @ 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 @ ( B @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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_Othrow ) @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_1) ).
thf(982,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)],[153]) ).
thf(332,axiom,
! [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 ) @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( 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 ) @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oevals ) ) ) ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evals__hext_0) ).
thf(1431,plain,
! [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 ) @ ( G @ ( B @ c_Pair ) ) ) @ ( F @ ( 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 ) @ ( E @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ c_BigStep_Oevals ) ) ) ) )
| ( B @ ( A @ c_Objects_Ohext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1737,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(453,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/sandbox/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I3_J_0) ).
thf(1681,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)],[453]) ).
thf(325,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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ 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 @ ( B @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ThrowRedsThrow_0) ).
thf(1416,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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ 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 @ ( B @ ( A @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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 ) @ ( E @ 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 @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ 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 @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ 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_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 ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I202_J_0) ).
thf(639,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)],[48]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I221_J_0) ).
thf(676,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)],[61]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I192_J_0) ).
thf(592,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)],[33]) ).
thf(150,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(972,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)],[150]) ).
thf(439,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).
thf(1653,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)],[439]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(1367,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).
thf(935,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)],[139]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).
thf(1009,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)],[160]) ).
thf(361,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OBinOp ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__evals_OBinOpThrow1_0) ).
thf(1490,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
| ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OBinOp ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I163_J_0) ).
thf(775,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)],[93]) ).
thf(1,negated_conjecture,
tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_ab @ ( v_ad @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(496,plain,
tc_bool @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( v_ab @ ( v_ad @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I97_J_0) ).
thf(1069,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)],[179]) ).
thf(1772,plain,
$false,
inference(e,[status(thm)],[1322,1586,1337,1411,760,1633,846,1315,1083,941,666,1549,645,892,1024,1469,1369,1190,1200,1211,523,1522,1443,1618,1401,1569,1728,1205,1591,1142,1692,1041,1173,1705,1608,1655,550,1735,500,1164,1761,1063,1354,1458,1756,1310,1507,1222,1196,898,1391,1441,709,1046,1613,1724,1529,1265,651,1601,1386,1623,1254,1409,1298,1330,838,802,1462,1511,702,751,1313,1279,1577,1455,1545,1379,1514,1319,1479,1641,1362,1100,1232,969,1347,1572,1741,1398,881,1415,1465,1450,1373,1418,1334,1136,1151,574,1581,821,1302,1664,1183,1283,766,1377,1215,734,1072,1119,1394,1526,660,998,1433,1405,1564,1697,1242,1651,512,1438,793,1306,810,1708,534,1768,1730,1057,1274,910,1091,1343,952,1751,1487,1370,815,1238,1560,1021,778,1174,1676,1217,598,561,1666,693,630,1423,566,1365,1296,1687,1159,1656,1027,757,1128,1281,1392,974,1012,583,830,682,1407,1360,742,1534,615,1328,1111,725,1498,1425,1006,1719,610,499,1234,1541,1270,1259,857,1397,1567,1683,884,1659,1292,1739,669,901,642,1584,1446,1207,547,706,1612,679,1324,1588,1478,1451,1266,1668,1192,1060,569,1759,1627,1530,1539,1456,1382,1131,654,1599,1246,1333,1202,633,1695,921,657,1170,1286,1187,1663,1167,1616,1185,586,1732,926,1086,938,1712,1054,1510,618,1103,824,1483,745,1595,1374,1631,601,1154,904,772,1620,577,1535,1520,1615,1389,843,1125,958,1403,1256,1226,1428,1707,787,498,1635,1765,1356,672,1139,1503,1464,947,1638,1224,1194,1209,784,1574,1524,1349,990,1722,737,509,1122,979,604,1492,1603,1471,1080,1339,799,621,520,895,964,915,1344,1177,932,1556,769,1460,685,1198,1474,1699,636,1643,1015,1250,851,1694,1562,1213,827,1066,868,1413,722,1304,1758,589,1467,663,648,754,553,1551,1049,531,944,1145,1018,525,580,1516,705,1743,887,1605,1252,739,1753,1547,1748,712,1003,673,1300,1188,1038,717,502,1262,1538,1579,1220,1317,1763,1285,1738,544,907,1358,1543,1702,1427,1094,1670,1717,595,1272,1240,1485,1052,497,876,1421,627,1649,1180,556,1553,688,495,1517,1448,1108,1685,539,1289,1453,1646,1326,699,961,517,1476,1481,1629,1745,1244,731,781,1276,1590,1341,748,1674,1639,995,1558,1030,1689,1294,929,1308,1077,763,1661,1116,1725,1678,833,1097,1229,1625,818,1757,865,1593,1380,854,1303,1148,1673,1248,790,1436,918,1495,807,696,955,1610,796,1033,1710,624,728,1261,1268,528,1500,871,1505,501,607,1236,987,1532,860,1384,1537,1597,982,1431,1737,1681,1416,639,676,592,972,1653,1367,935,1009,1490,775,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV926-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n016.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 15:15:00 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.24/1.45 % [INFO] Parsing done (471ms).
% 2.24/1.46 % [INFO] Running in sequential loop mode.
% 3.45/1.84 % [INFO] eprover registered as external prover.
% 3.45/1.85 % [INFO] Scanning for conjecture ...
% 4.83/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 488 axioms. Running axiom selection ...
% 6.08/2.55 % [INFO] Axiom selection finished. Selected 486 axioms (removed 2 axioms).
% 7.49/2.98 % [INFO] Problem is propositional (TPTP CNF).
% 7.49/3.01 % [INFO] Type checking passed.
% 7.49/3.02 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 22.81/7.83 % External prover 'e' found a proof!
% 22.81/7.83 % [INFO] Killing All external provers ...
% 22.81/7.83 % Time passed: 7287ms (effective reasoning time: 6357ms)
% 22.81/7.84 % Axioms used in derivation (486): cls_option_Oinject_0, cls_red__lcl__add_0, cls_exp_Osimps_I56_J_0, cls_red__reds_OInitBlockThrow_0, cls_CallObjThrow_0, cls_red__reds_OLAssThrow_0, cls_bot__fun__eq_0, cls_exp_Osimps_I184_J_0, clsarity_nat__HOL_Oord, cls_red__reds_ORedInitBlock_0, cls_map__upd__eqD1_0, cls_exp_Osimps_I156_J_0, cls_val_Osimps_I3_J_0, cls_exp_Osimps_I9_J_1, cls_rtrancl__idemp_0, cls_exp_Osimps_I92_J_0, cls_exp_Osimps_I195_J_0, cls_exp_Osimps_I103_J_0, cls_sup__ge1_0, cls_red__reds_OFAssRed2_0, cls_Un__subset__iff_0, cls_CallRedsThrowObj_0, cls_order__eq__iff_0, cls_equalityI_0, cls_exp_Osimps_I218_J_0, cls_exp_Osimps_I213_J_0, cls_fv__fvs_Osimps_I3_J_0, cls_red__reds_OFAssRed1_0, cls_COMBC__def_0, cls_map__add__assoc_0, cls_eval__evals_OFAssThrow2_0, cls_Un__empty__left_0, cls_fun__upd__apply_1, cls_map__upd__Some__unfold_4, cls_le__funD_0, cls_subset__empty_1, cls_eval__cases_I1_J_1, cls_exp_Osimps_I193_J_0, cls_CastReds_0, cls_exp_Osimps_I10_J_1, cls_exp_Osimps_I225_J_0, cls_exp_Osimps_I138_J_0, cls_exp_Osimps_I81_J_0, cls_exp_Osimps_I137_J_0, cls_BinOpRedsThrow2_0, cls_sup__bot__right_0, cls_exp_Osimps_I165_J_0, cls_exp_Osimps_I7_J_2, cls_fv__fvs_Osimps_I11_J_0, cls_list_Oinject_0, cls_exp_Osimps_I204_J_0, cls_CallRedsObj_0, cls_exp_Osimps_I219_J_0, cls_exp_Osimps_I149_J_0, cls_eval__final_0, cls_extend__eval_0, cls_fv__fvs_Osimps_I17_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_exp_Osimps_I190_J_0, clsarity_fun__Orderings_Oorder, cls_exp_Osimps_I221_J_0, cls_big__iff__small_2, cls_exp_Osimps_I11_J_0, cls_UnCI_1, cls_exp_Osimps_I15_J_1, cls_BinOpRedsThrow1_0, cls_map__upd__Some__unfold_3, cls_inf__sup__aci_I6_J_0, cls_eval__evals_OCondThrow_0, cls_exp_Osimps_I115_J_0, cls_exp_Osimps_I211_J_0, cls_rtrancl__trans_0, cls_mem__def_1, cls_BinOp2Reds_0, clsarity_nat__Orderings_Olinorder, cls_empty__iff_0, cls_not__Cons__self2_0, cls_FAssReds2_0, cls_exp_Osimps_I13_J_0, cls_exp_Osimps_I154_J_0, cls_exp_Osimps_I199_J_0, cls_LAssReds_0, cls_exp_Osimps_I185_J_0, cls_SeqReds2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_exp_Osimps_I141_J_0, cls_le__sup__iff_0, cls_exp_Osimps_I97_J_0, cls_exp_Osimps_I170_J_0, cls_exp_Osimps_I208_J_0, cls_red__reds_OFAssThrow2_0, cls_exp_Osimps_I188_J_0, cls_set__rev__mp_0, cls_exp_Osimps_I109_J_0, cls_pred__equals__eq_0, cls_exp_Osimps_I212_J_0, cls_exp_Osimps_I178_J_0, cls__092_060A_062___092_060A_062s_Osimps_I7_J_0, cls_exp_Osimps_I2_J_1, cls_Un__left__commute_0, cls_exp_Osimps_I8_J_3, cls_in__lex__prod_1, 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_exp_Osimps_I113_J_0, cls_exp_Osimps_I223_J_0, cls_exp_Osimps_I11_J_1, cls_exp_Osimps_I4_J_1, cls_le__supI_0, cls_Un__subset__iff_1, cls_exp_Osimps_I171_J_0, cls_red__reds_OCallThrowObj_0, cls_red__reds_OLAssRed_0, cls_exp_Osimps_I157_J_0, cls_exp_Osimps_I136_J_0, cls_exp_Osimps_I175_J_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_order__eq__refl_0, cls_eval__evals_OSeqThrow_0, cls_exp_Osimps_I67_J_0, cls_converse__rtrancl__into__rtrancl_0, cls_exp_Osimps_I4_J_0, cls_CondReds_0, cls_map__upd__Some__unfold_0, cls_exp_Osimps_I160_J_0, cls_le__iff__sup_0, clsarity_fun__Orderings_Obot, cls_hext__trans_0, cls_le__supE_1, cls_fun__upd__other_0, cls_exp_Osimps_I84_J_0, cls_exp_Osimps_I209_J_0, cls_hext__refl_0, cls_big__iff__small_1, cls_Red__dom__lcl_0, cls_exp_Osimps_I142_J_0, cls_exp_Osimps_I74_J_0, cls_Un__absorb2_0, cls_exp_Osimps_I205_J_0, cls_inf__sup__aci_I8_J_0, cls_red__reds_OCallObj_0, cls_Un__empty__right_0, cls__092_060A_062___092_060A_062s_Osimps_I13_J_0, cls__092_060A_062___092_060A_062s_Osimps_I2_J_0, cls_WhileRedsThrow_0, cls_map__add__upd__left_0, cls_exp_Osimps_I110_J_0, clsarity_bool__Orderings_Oorder, cls_red__reds_OThrowThrow_0, cls_bot__least_0, cls_exp_Osimps_I9_J_0, cls_exp_Osimps_I85_J_0, cls_eval__evals_OBinOpThrow2_0, cls_eval__evals_OFAccThrow_0, cls_exp_Osimps_I143_J_0, cls_sup__eq__bot__eq2_0, cls_refl__on__def_1, cls_exp_Osimps_I146_J_0, cls_exp_Osimps_I174_J_0, cls_UnCI_0, cls_Un__upper2_0, cls_exp_Osimps_I148_J_0, cls_map__add__dom__app__simps_I2_J_0, cls_red__reds_OBinOpThrow1_0, cls_WhileCondThrow_0, cls_exp_Osimps_I172_J_0, cls_exp_Osimps_I139_J_0, cls_exp_Osimps_I10_J_2, cls_exp_Osimps_I176_J_0, cls_eval__notfree__unchanged_0, cls_fv__fvs_Osimps_I7_J_0, cls_ThrowReds_0, cls_ConsThrow_0, cls_exp_Osimps_I46_J_0, cls_Reds__dom__lcl_0, clsarity_fun__HOL_Oord, cls_exp_Osimps_I99_J_0, cls_subset__empty_0, cls_fv__fvs_Osimps_I12_J_0, cls_subset__iff_0, cls_eval__evals_OFAssThrow1_0, cls_rev__predicate1D_0, cls_red__reds_OTryRed_0, cls_exp_Osimps_I69_J_0, cls_in__lex__prod_2, cls_fv__fvs_Osimps_I8_J_0, clsarity_bool__Lattices_Oupper__semilattice, cls_exp_Osimps_I180_J_0, cls_red__reds_ORedBlock_0, cls_FAccReds_0, cls_exp_Osimps_I77_J_0, cls_map__add__dom__app__simps_I3_J_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_I207_J_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_set__eq__subset_2, cls_Un__mono_0, cls_Seq_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_sup__commute_0, cls_exp_Osimps_I177_J_0, cls_FAssRedsThrow2_0, cls__092_060A_062___092_060A_062s_Osimps_I3_J_0, cls_CastRedsNull_0, cls_exp_Osimps_I89_J_0, cls_exp_Osimps_I159_J_0, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_exp_Osimps_I62_J_0, cls_red__reds_OBinOpRed2_0, cls_linorder__linear_0, cls_Un__empty_0, cls_TryReds_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_order__antisym_0, cls_exp_Osimps_I158_J_0, cls_dom__map__add_0, cls_fv__fvs_Osimps_I13_J_0, cls_exp_Osimps_I112_J_0, cls_exp_Osimps_I60_J_0, cls_sup__Un__eq_0, cls_exp_Osimps_I162_J_0, cls_CondRedsThrow_0, cls_subset__trans_0, cls_not__Cons__self_0, cls_refl__onD2_0, cls_val_Osimps_I16_J_0, cls_order__trans_0, cls_exp_Osimps_I15_J_3, cls_exp_Osimps_I201_J_0, cls_exp_Osimps_I166_J_0, cls_map__upd__Some__unfold_1, cls_red__reds_OFAssThrow1_0, cls_le__supE_0, cls_exp_Osimps_I47_J_0, cls_exp_Osimps_I7_J_1, cls_red__reds_OBlockThrow_0, cls_sup__assoc_0, cls_exp_Osimps_I189_J_0, cls_exp_Osimps_I224_J_0, cls_eval__evals_OThrowThrow_0, cls_red__reds_OBinOpRed1_0, cls_exp_Osimps_I169_J_0, cls_map__upd__triv_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, clsarity_bool__Orderings_Opreorder, cls_TryRedsVal_0, cls_rtrancl__eq__or__trancl_1, cls_exp_Osimps_I55_J_0, cls_exp_Osimps_I101_J_0, cls_exp_Osimps_I102_J_0, cls_CastRedsThrow_0, cls_exp_Osimps_I75_J_0, cls_empty__subsetI_0, cls_red__reds_OSeqRed_0, cls_sup1E_0, cls_refl__onD_0, cls_sup__least_0, cls_subset__refl_0, cls_CastNull_0, cls_exp_Osimps_I145_J_0, cls_Pair__eq_0, cls_fun__upd__twist_0, cls_SeqRedsThrow_0, cls_Un__absorb1_0, cls_exp_Osimps_I80_J_0, cls_in__lex__prod_3, cls_exp_Osimps_I59_J_0, clsarity_nat__Orderings_Opreorder, clsarity_nat__Lattices_Olattice, cls_final__def_1, cls_sup1CI_1, cls_exp_Osimps_I182_J_0, cls_fun__upd__apply_0, cls_LAssRedsThrow_0, cls_pred__subset__eq_1, cls_exp_Osimps_I68_J_0, cls_restrict__in_0, cls_exp_Osimps_I4_J_2, cls_exp_Osimps_I114_J_0, cls_order__eq__iff_2, cls_bot1E_0, cls_exp_Osimps_I216_J_0, cls_exp_Osimps_I203_J_0, cls_Un__assoc_0, cls_red__reds_OCastThrow_0, cls_exp_Osimps_I191_J_0, cls_option_Osplit_1, cls_evals__hext_0, cls_domI_0, cls_le__supI2_0, cls_fv__fvs_Osimps_I2_J_0, cls_extend__1__eval_0, cls_exp_Osimps_I57_J_0, cls_bex__empty_0, cls_eval__evals_OCons_0, cls_UnE_0, cls_exp_Osimps_I215_J_0, cls_inf__sup__ord_I4_J_0, cls_eval__evals_OCastThrow_0, cls_exp_Osimps_I93_J_0, cls_SeqReds_0, cls_exp_Osimps_I53_J_0, cls_Un__absorb_0, cls_exp_Osimps_I152_J_0, cls_eval__evals_OLAssThrow_0, cls_exp_Osimps_I50_J_0, cls_eval__restrict__lcl_0, cls_order__antisym__conv_0, cls_red__reds_OThrowRed_0, cls_val_Osimps_I17_J_0, cls_red__reds_OFAccRed_0, cls_exp_Osimps_I54_J_0, cls_exp_Osimps_I86_J_0, cls_bot__empty__eq_0, cls_map__add__upd_0, cls_fv__fvs_Osimps_I9_J_0, cls_refl__onD1_0, cls_exp_Osimps_I179_J_0, clsarity_bool__Lattices_Olattice, cls_exp_Osimps_I144_J_0, cls_exp_Osimps_I150_J_0, clsarity_bool__Lattices_Obounded__lattice, cls_exp_Osimps_I8_J_1, cls_exp_Osimps_I58_J_0, cls_exp_Osimps_I106_J_0, cls_le__supI1_0, cls_sup__left__idem_0, cls_exp_Osimps_I66_J_0, cls_exp_Osimps_I6_J_0, cls_exp_Osimps_I108_J_0, cls_exp_Osimps_I222_J_0, cls_final__def_2, cls_red__reds_OBinOpThrow2_0, cls_le__sup__iff_2, cls_subsetD_0, cls_fv__fvs_Osimps_I14_J_0, cls_exp_Osimps_I90_J_0, clsarity_fun__Lattices_Obounded__lattice, cls_fun__upd__idem_0, cls_FAssRedsThrow1_0, cls_xt1_I6_J_0, cls_eval__cases_I1_J_0, cls_red__reds_OCondThrow_0, cls_exp_Osimps_I12_J_1, cls_eval__evals_OBinOpThrow1_0, cls_fun__upd__idem__iff_0, cls_sup__fun__eq_0, cls_FAccRedsThrow_0, cls_exp_Osimps_I155_J_0, cls_domD_0, cls_rtrancl_Ortrancl__refl_0, cls_exp_Osimps_I71_J_0, cls_option_Osplit__asm_1, cls_exp_Osimps_I82_J_0, cls_exp_Osimps_I14_J_0, cls_exp_Osimps_I107_J_0, cls_exp_Osimps_I167_J_0, cls_exp_Osimps_I161_J_0, cls_Un__left__absorb_0, cls_exp_Osimps_I9_J_2, cls_red__reds_ORedCastNull_0, cls_sup__idem_0, cls_exp_Osimps_I217_J_0, cls_inf__sup__aci_I5_J_0, cls_sup__eq__bot__eq1_0, cls_A__fv_0, cls_list_Oinject_1, cls_exp_Osimps_I45_J_0, cls_Red__fv_0, cls_exp_Osimps_I8_J_0, cls_exp_Osimps_I44_J_0, cls_ThrowRedsThrow_0, cls_exp_Osimps_I192_J_0, cls_Un__empty_1, clsarity_nat__Lattices_Oupper__semilattice, cls_exp_Osimps_I7_J_0, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_fun__upd__same_0, cls_exp_Osimps_I151_J_0, cls_same__fstI_0, cls_map__add__dom__app__simps_I1_J_0, cls_exp_Osimps_I153_J_0, cls_red__lcl__incr_0, cls_map__upd__Some__unfold_2, cls_eval__lcl__incr_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_sup__ge2_0, cls_exp_Osimps_I6_J_1, cls_red__reds_OSeqThrow_0, cls_exp_Osimps_I65_J_0, cls_Try_0, cls_exp_Osimps_I51_J_0, cls_Un__least_0, cls_BinOp1Reds_0, cls_red__hext__incr_0, cls_sup1CI_0, cls_restrict__fun__upd_1, clsarity_fun__Orderings_Opreorder, cls_exp_Osimps_I164_J_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_exp_Osimps_I111_J_0, cls_exp_Osimps_I52_J_0, cls_red__reds_OCastRed_0, cls_Val_0, cls_exp_Osimps_I187_J_0, cls_exp_Osimps_I15_J_2, cls_r__into__rtrancl_0, cls_small__by__big_0, cls_red__reds_OFAccThrow_0, cls_exp_Osimps_I10_J_0, cls_eval__hext_0, cls_exp_Osimps_I64_J_0, cls_exp_Osimps_I88_J_0, cls_FAssReds1_0, cls_pred__subset__eq_0, cls_exp_Osimps_I96_J_0, cls_map__add__find__right_0, cls_exp_Osimps_I196_J_0, cls_fv__fvs_Osimps_I4_J_0, cls_exp_Osimps_I91_J_0, cls_exp_Osimps_I200_J_0, cls_exp_Osimps_I63_J_0, cls_map__add__Some__iff_2, cls_exp_Osimps_I214_J_0, cls_exp_Osimps_I168_J_0, cls_Throw_0, cls_exp_Osimps_I181_J_0, cls_sup__bot__left_0, cls_red__reds_OCondRed_0, cls_fun__upd__upd_0, cls_map__add__SomeD_1, cls_exp_Osimps_I140_J_0, cls_eval__closed__lcl__unchanged_0, cls_Red__lcl__add_0, cls_exp_Osimps_I87_J_0, cls_exp_Osimps_I198_J_0, cls_exp_Osimps_I202_J_0, cls_exp_Osimps_I12_J_0, cls_Pair__eq_1, cls_exp_Osimps_I173_J_0, cls_big__by__small_0, cls_sup__absorb1_0, cls_exp_Osimps_I104_J_0, cls_eval__finalId_0, cls_exp_Osimps_I78_J_0, clsarity_nat__Orderings_Oorder, 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_ball__empty_0, cls_in__lex__prod_0, cls_exp_Osimps_I147_J_0, cls_exp_Osimps_I3_J_0, cls_map__add__def_0, cls_red__reds_ORedTry_0, cls_predicate1D_0, cls_exp_Osimps_I197_J_0, cls_evals__lcl__incr_0, cls_exp_Osimps_I13_J_1, cls_fun__upd__idem__iff_1
% 22.81/7.84 % No. of inferences in proof: 989
% 22.81/7.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 7287 ms resp. 6357 ms w/o parsing
% 25.00/8.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.00/8.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------