%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP083^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:25 AM UTC 2026
% Result : Theorem 2.96s 1.68s
% Output : Refutation 2.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP083^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:45 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : ITP083^2 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.47 % Domain : Interactive Theorem Proving
% 0.28/0.47 % Problem : Sledgehammer Irreducible problem prob_641__6629180_1
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Des21]
% 0.28/0.47 % Names : Irreducible/prob_641__6629180_1 [Des21]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.28/0.47 % Syntax : Number of formulae : 367 ( 90 unt; 66 typ; 0 def)
% 0.28/0.47 % Number of atoms : 834 ( 225 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 8 ( 2 avg)
% 0.28/0.47 % Number of connectives : 4837 ( 69 ~; 6 |; 78 &;4315 @)
% 0.28/0.47 % ( 0 <=>; 369 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 29 ( 8 avg)
% 0.28/0.47 % Number of types : 6 ( 5 usr)
% 0.28/0.47 % Number of type conns : 383 ( 383 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 63 ( 61 usr; 6 con; 0-12 aty)
% 0.28/0.47 % Number of variables : 1063 ( 84 ^; 851 !; 32 ?;1063 :)
% 0.28/0.47 % ( 96 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.47 % SPC : TH1_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:28:47.811
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % Could-be-implicit typings (9)
% 0.28/0.47 thf(ty_t_Product__Type_Oprod,type,
% 0.28/0.47 product_prod: $tType > $tType > $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Option_Ooption,type,
% 0.28/0.47 option: $tType > $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_List_Olist,type,
% 0.28/0.47 list: $tType > $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_t_Set_Oset,type,
% 0.28/0.47 set: $tType > $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_tf_edgeD,type,
% 0.28/0.47 edgeD: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_tf_node,type,
% 0.28/0.47 node: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_tf_var,type,
% 0.28/0.47 var: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_tf_val,type,
% 0.28/0.47 val: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(ty_tf_g,type,
% 0.28/0.47 g: $tType ).
% 0.28/0.47
% 0.28/0.47 % Explicit typings (57)
% 0.28/0.47 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.28/0.47 bounded_lattice_top:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.28/0.47 bounded_lattice:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_HOL_Otype,type,
% 0.28/0.47 type:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Lattices_Osup,type,
% 0.28/0.47 sup:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.28/0.47 order:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Lattices_Olattice,type,
% 0.28/0.47 lattice:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Finite__Set_Ofinite,type,
% 0.28/0.47 finite_finite:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.28/0.47 linorder:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.28/0.47 preorder:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.28/0.47 semilattice_sup:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.28/0.47 bounde1808546759up_bot:
% 0.28/0.47 !>[A: $tType] : $o ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Finite__Set_Ofinite,type,
% 0.28/0.47 finite_finite2:
% 0.28/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors,type,
% 0.28/0.47 graph_1201503639essors:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Graph__path_Ograph__path__base_Osuccessors,type,
% 0.28/0.47 graph_449533722essors:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Ocondensation__edges,type,
% 0.28/0.47 irredu280805948_edges:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) > ( set @ ( product_prod @ ( set @ Val ) @ ( set @ Val ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Ocondensation__nodes,type,
% 0.28/0.47 irredu1918690039_nodes:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) > ( set @ ( set @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Oredundant__scc,type,
% 0.28/0.47 irredu2110774547nt_scc:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) > ( set @ Val ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Oredundant__set,type,
% 0.28/0.47 irredu2110905762nt_set:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.28/0.47 sup_sup:
% 0.28/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Olist_Oset,type,
% 0.28/0.47 set2:
% 0.28/0.47 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_List_Ozip,type,
% 0.28/0.47 zip:
% 0.28/0.47 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( list @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Map_Odom,type,
% 0.28/0.47 dom:
% 0.28/0.47 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Option_Ooption_ONone,type,
% 0.28/0.47 none:
% 0.28/0.47 !>[A: $tType] : ( option @ A ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Option_Ooption_OSome,type,
% 0.28/0.47 some:
% 0.28/0.47 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.28/0.47 bot_bot:
% 0.28/0.47 !>[A: $tType] : A ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.28/0.47 ord_less_eq:
% 0.28/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Product__Type_OPair,type,
% 0.28/0.47 product_Pair:
% 0.28/0.47 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs,type,
% 0.28/0.47 sSA_CFG_SSA_allDefs:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallUses,type,
% 0.28/0.47 sSA_CFG_SSA_allUses:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallVars,type,
% 0.28/0.47 sSA_CFG_SSA_allVars:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs,type,
% 0.28/0.47 sSA_CFG_SSA_phiDefs:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses,type,
% 0.28/0.47 sSA_CFG_SSA_phiUses:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode,type,
% 0.28/0.47 sSA_CF1081484811efNode:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Node ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OisTrivialPhi,type,
% 0.28/0.47 sSA_CF1297404942ialPhi:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Val > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OliveVal,type,
% 0.28/0.47 sSA_CF722422777iveVal:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Ophi,type,
% 0.28/0.47 sSA_CFG_SSA_wf_phi:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > ( option @ ( list @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg,type,
% 0.28/0.47 sSA_CF1165125185phiArg:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Val > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Opruned,type,
% 0.28/0.47 sSA_CF823892918pruned:
% 0.28/0.47 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Oredundant,type,
% 0.28/0.47 sSA_CF462202545undant:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Otrivial,type,
% 0.28/0.47 sSA_CF1363434349rivial:
% 0.28/0.47 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_SSA__CFG_OCFG__base_Ovars,type,
% 0.28/0.47 sSA_CFG_vars:
% 0.28/0.47 !>[G: $tType,Node: $tType,Var: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Var ) ) > G > ( set @ Var ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_OCollect,type,
% 0.28/0.47 collect:
% 0.28/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Set_Oinsert,type,
% 0.28/0.47 insert:
% 0.28/0.47 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Transitive__Closure_Oacyclic,type,
% 0.28/0.47 transitive_acyclic:
% 0.28/0.47 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_Transitive__Closure_Otranclp,type,
% 0.28/0.47 transitive_tranclp:
% 0.28/0.47 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_c_member,type,
% 0.28/0.47 member:
% 0.28/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v__092_060alpha_062n,type,
% 0.28/0.47 alpha_n: g > ( list @ node ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v__092_060phi_062,type,
% 0.28/0.47 phi: val ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v__092_060phi_062_092_060_094sub_062s,type,
% 0.28/0.47 phi_s: val ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v__092_060phi_062_H____,type,
% 0.28/0.47 phi2: val ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_defs,type,
% 0.28/0.47 defs: g > node > ( set @ val ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_g,type,
% 0.28/0.47 g2: g ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_inEdges_H,type,
% 0.28/0.47 inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_phis,type,
% 0.28/0.47 phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_s,type,
% 0.28/0.47 s: val ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_uses,type,
% 0.28/0.47 uses: g > node > ( set @ val ) ).
% 0.28/0.47
% 0.28/0.47 thf(sy_v_var,type,
% 0.28/0.47 var2: g > val > var ).
% 0.28/0.47
% 0.28/0.47 % Relevant facts (255)
% 0.28/0.47 thf(fact_0_assms_I4_J,axiom,
% 0.28/0.47 phi_s != s ).
% 0.28/0.47
% 0.28/0.47 % assms(4)
% 0.28/0.47 thf(fact_1_False,axiom,
% 0.28/0.47 phi != phi_s ).
% 0.28/0.47
% 0.28/0.47 % False
% 0.28/0.47 thf(fact_2__092_060open_062phiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_092_060close_062,axiom,
% 0.28/0.47 sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s ).
% 0.28/0.47
% 0.28/0.47 % \<open>phiArg g \<phi>' \<phi>\<^sub>s\<close>
% 0.28/0.47 thf(fact_3_assms_I3_J,axiom,
% 0.28/0.47 member @ val @ s @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 0.28/0.47
% 0.28/0.47 % assms(3)
% 0.28/0.47 thf(fact_4_assms_I2_J,axiom,
% 0.28/0.47 member @ val @ phi @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 0.28/0.47
% 0.28/0.47 % assms(2)
% 0.28/0.47 thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.28/0.47 ~ ! [Phi: val] :
% 0.28/0.47 ~ ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ Phi @ phi_s ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>\<And>thesis. (\<And>\<phi>'. phiArg g \<phi>' \<phi>\<^sub>s \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.28/0.47 thf(fact_6_phiArg__in__allVars,axiom,
% 0.28/0.47 ! [G2: g,V: val,V2: val] :
% 0.28/0.47 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ V2 )
% 0.28/0.47 => ( member @ val @ V2 @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiArg_in_allVars
% 0.28/0.47 thf(fact_7_uses__in__vars,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( uses @ G2 @ N ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_vars @ g @ node @ val @ alpha_n @ uses @ G2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % uses_in_vars
% 0.28/0.47 thf(fact_8_trivial__in__allVars,axiom,
% 0.28/0.47 ! [G2: g,V: val] :
% 0.28/0.47 ( ( sSA_CF1363434349rivial @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ V )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % trivial_in_allVars
% 0.28/0.47 thf(fact_9_liveVal__in__allVars,axiom,
% 0.28/0.47 ! [G2: g,V: val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % liveVal_in_allVars
% 0.28/0.47 thf(fact_10_allVars__finite,axiom,
% 0.28/0.47 ! [G2: g] : ( finite_finite2 @ val @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % allVars_finite
% 0.28/0.47 thf(fact_11_uses__in__allUses,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( uses @ G2 @ N ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % uses_in_allUses
% 0.28/0.47 thf(fact_12_redundant__def,axiom,
% 0.28/0.47 ! [G2: g] :
% 0.28/0.47 ( ( sSA_CF462202545undant @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 )
% 0.28/0.47 = ( ? [X: val] :
% 0.28/0.47 ( ( member @ val @ X @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 & ( sSA_CF1363434349rivial @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % redundant_def
% 0.28/0.47 thf(fact_13_trivial__def,axiom,
% 0.28/0.47 ! [G2: g,V: val] :
% 0.28/0.47 ( ( sSA_CF1363434349rivial @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ V )
% 0.28/0.47 = ( ? [X: val] :
% 0.28/0.47 ( ( member @ val @ X @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 & ( sSA_CF1297404942ialPhi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % trivial_def
% 0.28/0.47 thf(fact_14__092_060open_062_092_060not_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062s_A_092_060noteq_062_AdefNode_Ag_As_092_060close_062,axiom,
% 0.28/0.47 ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 0.28/0.47 = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 0.28/0.47
% 0.28/0.47 % \<open>\<not> defNode g \<phi>\<^sub>s \<noteq> defNode g s\<close>
% 0.28/0.47 thf(fact_15_defs__uses__disjoint_H,axiom,
% 0.28/0.47 ! [N: node,G2: g,V: val] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ val @ V @ ( defs @ G2 @ N ) )
% 0.28/0.47 => ~ ( member @ val @ V @ ( uses @ G2 @ N ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % defs_uses_disjoint'
% 0.28/0.47 thf(fact_16_livePhi,axiom,
% 0.28/0.47 ! [G2: g,V: val,V2: val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V )
% 0.28/0.47 => ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ V2 )
% 0.28/0.47 => ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % livePhi
% 0.28/0.47 thf(fact_17_phiArg__distinct__nodes,axiom,
% 0.28/0.47 ! [G2: g,P: val,Q: val] :
% 0.28/0.47 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ Q )
% 0.28/0.47 => ( ( P != Q )
% 0.28/0.47 => ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P )
% 0.28/0.47 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ Q ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiArg_distinct_nodes
% 0.28/0.47 thf(fact_18_phiArgs__def__distinct,axiom,
% 0.28/0.47 ! [G2: g,P: val,Q: val,R: val] :
% 0.28/0.47 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ Q )
% 0.28/0.47 => ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ R )
% 0.28/0.47 => ( ( Q != R )
% 0.28/0.47 => ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ Q )
% 0.28/0.47 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ R ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiArgs_def_distinct
% 0.28/0.47 thf(fact_19_uses__in___092_060alpha_062n,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( uses @ G2 @ N ) )
% 0.28/0.47 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % uses_in_\<alpha>n
% 0.28/0.47 thf(fact_20_defs__finite,axiom,
% 0.28/0.47 ! [G2: g,N: node] : ( finite_finite2 @ val @ ( defs @ G2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % defs_finite
% 0.28/0.47 thf(fact_21_varsE,axiom,
% 0.28/0.47 ! [V: val,G2: g] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_vars @ g @ node @ val @ alpha_n @ uses @ G2 ) )
% 0.28/0.47 => ~ ! [N2: node] :
% 0.28/0.47 ( ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ~ ( member @ val @ V @ ( uses @ G2 @ N2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % varsE
% 0.28/0.47 thf(fact_22_vars__finite,axiom,
% 0.28/0.47 ! [G2: g] : ( finite_finite2 @ val @ ( sSA_CFG_vars @ g @ node @ val @ alpha_n @ uses @ G2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % vars_finite
% 0.28/0.47 thf(fact_23_liveSimple,axiom,
% 0.28/0.47 ! [N: node,G2: g,Val2: val] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ val @ Val2 @ ( uses @ G2 @ N ) )
% 0.28/0.47 => ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ Val2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % liveSimple
% 0.28/0.47 thf(fact_24_liveVal_Osimps,axiom,
% 0.28/0.47 ! [G2: g,A2: val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ A2 )
% 0.28/0.47 = ( ? [N3: node,Val3: val] :
% 0.28/0.47 ( ( A2 = Val3 )
% 0.28/0.47 & ( member @ node @ N3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 & ( member @ val @ Val3 @ ( uses @ G2 @ N3 ) ) )
% 0.28/0.47 | ? [V3: val,V4: val] :
% 0.28/0.47 ( ( A2 = V4 )
% 0.28/0.47 & ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V3 )
% 0.28/0.47 & ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V3 @ V4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % liveVal.simps
% 0.28/0.47 thf(fact_25_liveVal_Oinducts,axiom,
% 0.28/0.47 ! [G2: g,X2: val,P2: val > $o] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ X2 )
% 0.28/0.47 => ( ! [N2: node,Val4: val] :
% 0.28/0.47 ( ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ val @ Val4 @ ( uses @ G2 @ N2 ) )
% 0.28/0.47 => ( P2 @ Val4 ) ) )
% 0.28/0.47 => ( ! [V5: val,V6: val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V5 )
% 0.28/0.47 => ( ( P2 @ V5 )
% 0.28/0.47 => ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V5 @ V6 )
% 0.28/0.47 => ( P2 @ V6 ) ) ) )
% 0.28/0.47 => ( P2 @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % liveVal.inducts
% 0.28/0.47 thf(fact_26_liveVal_Ocases,axiom,
% 0.28/0.47 ! [G2: g,A2: val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ A2 )
% 0.28/0.47 => ( ! [N2: node] :
% 0.28/0.47 ( ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ~ ( member @ val @ A2 @ ( uses @ G2 @ N2 ) ) )
% 0.28/0.47 => ~ ! [V5: val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V5 )
% 0.28/0.47 => ~ ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V5 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % liveVal.cases
% 0.28/0.47 thf(fact_27_allUses__finite,axiom,
% 0.28/0.47 ! [N: node,G2: g] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( finite_finite2 @ val @ ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allUses_finite
% 0.28/0.47 thf(fact_28_defNode_I1_J,axiom,
% 0.28/0.47 ! [V: val,G2: g] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % defNode(1)
% 0.28/0.47 thf(fact_29_uses__finite,axiom,
% 0.28/0.47 ! [G2: g,N: node] : ( finite_finite2 @ val @ ( uses @ G2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % uses_finite
% 0.28/0.47 thf(fact_30_eq,axiom,
% 0.28/0.47 ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 0.28/0.47 = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq
% 0.28/0.47 thf(fact_31_allUses__in__allVars,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N ) )
% 0.28/0.47 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allUses_in_allVars
% 0.28/0.47 thf(fact_32_phiUses__in__allUses,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiUses_in_allUses
% 0.28/0.47 thf(fact_33_phiUses__finite,axiom,
% 0.28/0.47 ! [N: node,G2: g] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( finite_finite2 @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiUses_finite
% 0.28/0.47 thf(fact_34_defNode_I2_J,axiom,
% 0.28/0.47 ! [V: val,G2: g] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % defNode(2)
% 0.28/0.47 thf(fact_35_defNode__ex1,axiom,
% 0.28/0.47 ! [V: val,G2: g] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ? [X3: node] :
% 0.28/0.47 ( ( member @ node @ X3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X3 ) )
% 0.28/0.47 & ! [Y: node] :
% 0.28/0.47 ( ( ( member @ node @ Y @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ Y ) ) )
% 0.28/0.47 => ( Y = X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % defNode_ex1
% 0.28/0.47 thf(fact_36_allVars__in__allDefs,axiom,
% 0.28/0.47 ! [V: val,G2: g] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ? [X3: node] :
% 0.28/0.47 ( ( member @ node @ X3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allVars_in_allDefs
% 0.28/0.47 thf(fact_37_List_Ofinite__set,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A] : ( finite_finite2 @ A @ ( set2 @ A @ Xs ) ) ).
% 0.28/0.47
% 0.28/0.47 % List.finite_set
% 0.28/0.47 thf(fact_38_phiDefs__finite,axiom,
% 0.28/0.47 ! [G2: g,N: node] : ( finite_finite2 @ val @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiDefs_finite
% 0.28/0.47 thf(fact_39_allDefs__finite,axiom,
% 0.28/0.47 ! [N: node,G2: g] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( finite_finite2 @ val @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allDefs_finite
% 0.28/0.47 thf(fact_40_assms_I5_J,axiom,
% 0.28/0.47 ( ( var2 @ g2 @ phi )
% 0.28/0.47 = ( var2 @ g2 @ s ) ) ).
% 0.28/0.47
% 0.28/0.47 % assms(5)
% 0.28/0.47 thf(fact_41_CFG__SSA__wf__base_Oredundant__def,axiom,
% 0.28/0.47 ! [EdgeD: $tType,Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF462202545undant @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( ^ [Alpha_n: G > ( list @ Node ),InEdges: G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ),Defs: G > Node > ( set @ Val ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G] :
% 0.28/0.47 ? [X: Val] :
% 0.28/0.47 ( ( member @ Val @ X @ ( sSA_CFG_SSA_allVars @ G @ Node @ EdgeD @ Val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G3 ) )
% 0.28/0.47 & ( sSA_CF1363434349rivial @ G @ Node @ EdgeD @ Val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G3 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.redundant_def
% 0.28/0.47 thf(fact_42_defs__in__allDefs,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( defs @ G2 @ N ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % defs_in_allDefs
% 0.28/0.47 thf(fact_43_phiDefs__in__allDefs,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiDefs_in_allDefs
% 0.28/0.47 thf(fact_44_allDefs__disjoint_H,axiom,
% 0.28/0.47 ! [N: node,G2: g,M: node,V: val] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 0.28/0.47 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ M ) )
% 0.28/0.47 => ( N = M ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allDefs_disjoint'
% 0.28/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.28/0.47 ! [A: $tType,A2: A,P2: A > $o] :
% 0.28/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.28/0.47 = ( P2 @ A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % mem_Collect_eq
% 0.28/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] :
% 0.28/0.47 ( ( collect @ A
% 0.28/0.47 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 0.28/0.47 = A3 ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mem_eq
% 0.28/0.47 thf(fact_47_Collect__cong,axiom,
% 0.28/0.47 ! [A: $tType,P2: A > $o,Q2: A > $o] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 = ( Q2 @ X3 ) )
% 0.28/0.47 => ( ( collect @ A @ P2 )
% 0.28/0.47 = ( collect @ A @ Q2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_cong
% 0.28/0.47 thf(fact_48_ext,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( F @ X3 )
% 0.28/0.47 = ( G2 @ X3 ) )
% 0.28/0.47 => ( F = G2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % ext
% 0.28/0.47 thf(fact_49_phiArg__same__var,axiom,
% 0.28/0.47 ! [G2: g,P: val,Q: val] :
% 0.28/0.47 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ Q )
% 0.28/0.47 => ( ( var2 @ G2 @ Q )
% 0.28/0.47 = ( var2 @ G2 @ P ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiArg_same_var
% 0.28/0.47 thf(fact_50_vars__eq,axiom,
% 0.28/0.47 ( ( var2 @ g2 @ phi )
% 0.28/0.47 = ( var2 @ g2 @ phi_s ) ) ).
% 0.28/0.47
% 0.28/0.47 % vars_eq
% 0.28/0.47 thf(fact_51_allDefs__var__disjoint,axiom,
% 0.28/0.47 ! [N: node,G2: g,V: val,V2: val] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 0.28/0.47 => ( ( member @ val @ V2 @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 0.28/0.47 => ( ( V != V2 )
% 0.28/0.47 => ( ( var2 @ G2 @ V2 )
% 0.28/0.47 != ( var2 @ G2 @ V ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allDefs_var_disjoint
% 0.28/0.47 thf(fact_52_defNode__var__disjoint,axiom,
% 0.28/0.47 ! [P: val,G2: g,Q: val] :
% 0.28/0.47 ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ( ( member @ val @ Q @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ( ( P != Q )
% 0.28/0.47 => ( ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P )
% 0.28/0.47 = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ Q ) )
% 0.28/0.47 => ( ( var2 @ G2 @ P )
% 0.28/0.47 != ( var2 @ G2 @ Q ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % defNode_var_disjoint
% 0.28/0.47 thf(fact_53_defNode__eq,axiom,
% 0.28/0.47 ! [N: node,G2: g,V: val] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 0.28/0.47 => ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 = N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % defNode_eq
% 0.28/0.47 thf(fact_54_allDefs__in__allVars,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 0.28/0.47 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allDefs_in_allVars
% 0.28/0.47 thf(fact_55_pruned__def,axiom,
% 0.28/0.47 ! [G2: g] :
% 0.28/0.47 ( ( sSA_CF823892918pruned @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 )
% 0.28/0.47 = ( ! [X: node] :
% 0.28/0.47 ( ( member @ node @ X @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ! [Val3: val] :
% 0.28/0.47 ( ( member @ val @ Val3 @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ X ) )
% 0.28/0.47 => ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ Val3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pruned_def
% 0.28/0.47 thf(fact_56_CFG__SSA__base_OphiUses_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_phiUses @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( sSA_CFG_SSA_phiUses @ G @ Node @ EdgeD @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_base.phiUses.cong
% 0.28/0.47 thf(fact_57_CFG__SSA__base_OphiDefs_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_phiDefs @ G @ Node @ Val )
% 0.28/0.47 = ( sSA_CFG_SSA_phiDefs @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_base.phiDefs.cong
% 0.28/0.47 thf(fact_58_CFG__SSA__base_OallDefs_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_allDefs @ G @ Node @ Val )
% 0.28/0.47 = ( sSA_CFG_SSA_allDefs @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_base.allDefs.cong
% 0.28/0.47 thf(fact_59_CFG__SSA__wf__base_OdefNode_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF1081484811efNode @ G @ Node @ Val )
% 0.28/0.47 = ( sSA_CF1081484811efNode @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.defNode.cong
% 0.28/0.47 thf(fact_60_CFG__SSA__base_OallVars_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_allVars @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( sSA_CFG_SSA_allVars @ G @ Node @ EdgeD @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_base.allVars.cong
% 0.28/0.47 thf(fact_61_CFG__SSA__wf__base_OphiArg_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF1165125185phiArg @ G @ Node @ Val )
% 0.28/0.47 = ( sSA_CF1165125185phiArg @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.phiArg.cong
% 0.28/0.47 thf(fact_62_CFG__SSA__base_OallUses_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_allUses @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( sSA_CFG_SSA_allUses @ G @ Node @ EdgeD @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_base.allUses.cong
% 0.28/0.47 thf(fact_63_CFG__SSA__wf__base_OliveVal_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF722422777iveVal @ G @ Node @ Val )
% 0.28/0.47 = ( sSA_CF722422777iveVal @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.liveVal.cong
% 0.28/0.47 thf(fact_64_CFG__SSA__wf__base_Otrivial_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF1363434349rivial @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( sSA_CF1363434349rivial @ G @ Node @ EdgeD @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.trivial.cong
% 0.28/0.47 thf(fact_65_CFG__base_Ovars_Ocong,axiom,
% 0.28/0.47 ! [Var: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Var ) )
% 0.28/0.47 => ( ( sSA_CFG_vars @ G @ Node @ Var )
% 0.28/0.47 = ( sSA_CFG_vars @ G @ Node @ Var ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_base.vars.cong
% 0.28/0.47 thf(fact_66_CFG__SSA__wf__base_OisTrivialPhi_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF1297404942ialPhi @ G @ Node @ Val )
% 0.28/0.47 = ( sSA_CF1297404942ialPhi @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.isTrivialPhi.cong
% 0.28/0.47 thf(fact_67_CFG__SSA__wf__base_Oredundant_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF462202545undant @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( sSA_CF462202545undant @ G @ Node @ EdgeD @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.redundant.cong
% 0.28/0.47 thf(fact_68_finite__list,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ A3 )
% 0.28/0.47 => ? [Xs2: list @ A] :
% 0.28/0.47 ( ( set2 @ A @ Xs2 )
% 0.28/0.47 = A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_list
% 0.28/0.47 thf(fact_69_CFG__SSA__wf__base_OliveSimple,axiom,
% 0.28/0.47 ! [G: $tType,Node: $tType,Val: $tType] :
% 0.28/0.47 ( ( ( linorder @ Val )
% 0.28/0.47 & ( linorder @ Node ) )
% 0.28/0.47 => ! [N: Node,Alpha_n2: G > ( list @ Node ),G2: G,Val2: Val,Uses2: G > Node > ( set @ Val ),Defs2: G > Node > ( set @ Val ),Phis2: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) )] :
% 0.28/0.47 ( ( member @ Node @ N @ ( set2 @ Node @ ( Alpha_n2 @ G2 ) ) )
% 0.28/0.47 => ( ( member @ Val @ Val2 @ ( Uses2 @ G2 @ N ) )
% 0.28/0.47 => ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ Val2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.liveSimple
% 0.28/0.47 thf(fact_70_CFG__SSA__wf__base_OlivePhi,axiom,
% 0.28/0.47 ! [G: $tType,Node: $tType,Val: $tType] :
% 0.28/0.47 ( ( ( linorder @ Val )
% 0.28/0.47 & ( linorder @ Node ) )
% 0.28/0.47 => ! [Alpha_n2: G > ( list @ Node ),Defs2: G > Node > ( set @ Val ),Uses2: G > Node > ( set @ Val ),Phis2: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G2: G,V: Val,V2: Val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ V )
% 0.28/0.47 => ( ( sSA_CF1165125185phiArg @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Phis2 @ G2 @ V @ V2 )
% 0.28/0.47 => ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ V2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.livePhi
% 0.28/0.47 thf(fact_71_CFG__SSA__wf__base_OliveVal_Oinducts,axiom,
% 0.28/0.47 ! [Node: $tType,G: $tType,Val: $tType] :
% 0.28/0.47 ( ( ( linorder @ Val )
% 0.28/0.47 & ( linorder @ Node ) )
% 0.28/0.47 => ! [Alpha_n2: G > ( list @ Node ),Defs2: G > Node > ( set @ Val ),Uses2: G > Node > ( set @ Val ),Phis2: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G2: G,X2: Val,P2: Val > $o] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ X2 )
% 0.28/0.47 => ( ! [N2: Node,Val4: Val] :
% 0.28/0.47 ( ( member @ Node @ N2 @ ( set2 @ Node @ ( Alpha_n2 @ G2 ) ) )
% 0.28/0.47 => ( ( member @ Val @ Val4 @ ( Uses2 @ G2 @ N2 ) )
% 0.28/0.47 => ( P2 @ Val4 ) ) )
% 0.28/0.47 => ( ! [V5: Val,V6: Val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ V5 )
% 0.28/0.47 => ( ( P2 @ V5 )
% 0.28/0.47 => ( ( sSA_CF1165125185phiArg @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Phis2 @ G2 @ V5 @ V6 )
% 0.28/0.47 => ( P2 @ V6 ) ) ) )
% 0.28/0.47 => ( P2 @ X2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.liveVal.inducts
% 0.28/0.47 thf(fact_72_CFG__SSA__wf__base_OliveVal_Osimps,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF722422777iveVal @ G @ Node @ Val )
% 0.28/0.47 = ( ^ [Alpha_n: G > ( list @ Node ),Defs: G > Node > ( set @ Val ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,A4: Val] :
% 0.28/0.47 ( ? [N3: Node,Val3: Val] :
% 0.28/0.47 ( ( A4 = Val3 )
% 0.28/0.47 & ( member @ Node @ N3 @ ( set2 @ Node @ ( Alpha_n @ G3 ) ) )
% 0.28/0.47 & ( member @ Val @ Val3 @ ( Uses @ G3 @ N3 ) ) )
% 0.28/0.47 | ? [V3: Val,V4: Val] :
% 0.28/0.47 ( ( A4 = V4 )
% 0.28/0.47 & ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n @ Defs @ Uses @ Phis @ G3 @ V3 )
% 0.28/0.47 & ( sSA_CF1165125185phiArg @ G @ Node @ Val @ Alpha_n @ Defs @ Phis @ G3 @ V3 @ V4 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.liveVal.simps
% 0.28/0.47 thf(fact_73_CFG__SSA__wf__base_OliveVal_Ocases,axiom,
% 0.28/0.47 ! [Node: $tType,G: $tType,Val: $tType] :
% 0.28/0.47 ( ( ( linorder @ Val )
% 0.28/0.47 & ( linorder @ Node ) )
% 0.28/0.47 => ! [Alpha_n2: G > ( list @ Node ),Defs2: G > Node > ( set @ Val ),Uses2: G > Node > ( set @ Val ),Phis2: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G2: G,A2: Val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ A2 )
% 0.28/0.47 => ( ! [N2: Node] :
% 0.28/0.47 ( ( member @ Node @ N2 @ ( set2 @ Node @ ( Alpha_n2 @ G2 ) ) )
% 0.28/0.47 => ~ ( member @ Val @ A2 @ ( Uses2 @ G2 @ N2 ) ) )
% 0.28/0.47 => ~ ! [V5: Val] :
% 0.28/0.47 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ V5 )
% 0.28/0.47 => ~ ( sSA_CF1165125185phiArg @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Phis2 @ G2 @ V5 @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.liveVal.cases
% 0.28/0.47 thf(fact_74_CFG__SSA__wf__base_Otrivial__def,axiom,
% 0.28/0.47 ! [EdgeD: $tType,Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF1363434349rivial @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( ^ [Alpha_n: G > ( list @ Node ),InEdges: G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ),Defs: G > Node > ( set @ Val ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,V3: Val] :
% 0.28/0.47 ? [X: Val] :
% 0.28/0.47 ( ( member @ Val @ X @ ( sSA_CFG_SSA_allVars @ G @ Node @ EdgeD @ Val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G3 ) )
% 0.28/0.47 & ( sSA_CF1297404942ialPhi @ G @ Node @ Val @ Alpha_n @ Defs @ Phis @ G3 @ V3 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.trivial_def
% 0.28/0.47 thf(fact_75_condensation__finite,axiom,
% 0.28/0.47 ! [G2: g,P2: set @ val] : ( finite_finite2 @ ( product_prod @ ( set @ val ) @ ( set @ val ) ) @ ( irredu280805948_edges @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % condensation_finite
% 0.28/0.47 thf(fact_76_phiUses__exI_H,axiom,
% 0.28/0.47 ! [G2: g,P: val,Q: val] :
% 0.28/0.47 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ Q )
% 0.28/0.47 => ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ~ ! [M2: node] :
% 0.28/0.47 ( ( member @ val @ Q @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ M2 ) )
% 0.28/0.47 => ~ ( member @ node @ M2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiUses_exI'
% 0.28/0.47 thf(fact_77_allUses__def,axiom,
% 0.28/0.47 ! [G2: g,N: node] :
% 0.28/0.47 ( ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N )
% 0.28/0.47 = ( sup_sup @ ( set @ val ) @ ( uses @ G2 @ N ) @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allUses_def
% 0.28/0.47 thf(fact_78_phiArg__trancl__same__var,axiom,
% 0.28/0.47 ! [G2: g,Phi2: val,N: val] :
% 0.28/0.47 ( ( transitive_tranclp @ val @ ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 ) @ Phi2 @ N )
% 0.28/0.47 => ( ( var2 @ G2 @ Phi2 )
% 0.28/0.47 = ( var2 @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiArg_trancl_same_var
% 0.28/0.47 thf(fact_79_allDefs__def,axiom,
% 0.28/0.47 ! [G2: g,N: node] :
% 0.28/0.47 ( ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N )
% 0.28/0.47 = ( sup_sup @ ( set @ val ) @ ( defs @ G2 @ N ) @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % allDefs_def
% 0.28/0.47 thf(fact_80_CFG__SSA__wf__base_Opruned__def,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF823892918pruned @ G @ Node @ Val )
% 0.28/0.47 = ( ^ [Alpha_n: G > ( list @ Node ),Defs: G > Node > ( set @ Val ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G] :
% 0.28/0.47 ! [X: Node] :
% 0.28/0.47 ( ( member @ Node @ X @ ( set2 @ Node @ ( Alpha_n @ G3 ) ) )
% 0.28/0.47 => ! [Val3: Val] :
% 0.28/0.47 ( ( member @ Val @ Val3 @ ( sSA_CFG_SSA_phiDefs @ G @ Node @ Val @ Phis @ G3 @ X ) )
% 0.28/0.47 => ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n @ Defs @ Uses @ Phis @ G3 @ Val3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.pruned_def
% 0.28/0.47 thf(fact_81_finite__code,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( finite_finite @ A )
% 0.28/0.47 => ( ( finite_finite2 @ A )
% 0.28/0.47 = ( ^ [A5: set @ A] : $true ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_code
% 0.28/0.47 thf(fact_82_defNode__cases,axiom,
% 0.28/0.47 ! [V: val,G2: g] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ( ~ ( member @ val @ V @ ( defs @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 != ( none @ ( list @ val ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % defNode_cases
% 0.28/0.47 thf(fact_83_simpleDef__not__phi,axiom,
% 0.28/0.47 ! [N: node,G2: g,V: val] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ val @ V @ ( defs @ G2 @ N ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 = ( none @ ( list @ val ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % simpleDef_not_phi
% 0.28/0.47 thf(fact_84_finite__Un,axiom,
% 0.28/0.47 ! [A: $tType,F2: set @ A,G4: set @ A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ ( sup_sup @ ( set @ A ) @ F2 @ G4 ) )
% 0.28/0.47 = ( ( finite_finite2 @ A @ F2 )
% 0.28/0.47 & ( finite_finite2 @ A @ G4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_Un
% 0.28/0.47 thf(fact_85_trivial__phi,axiom,
% 0.28/0.47 ! [G2: g,V: val] :
% 0.28/0.47 ( ( sSA_CF1363434349rivial @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ V )
% 0.28/0.47 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 != ( none @ ( list @ val ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % trivial_phi
% 0.28/0.47 thf(fact_86_phiArg__exI,axiom,
% 0.28/0.47 ! [M: node,G2: g,V: val] :
% 0.28/0.47 ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) ) ) )
% 0.28/0.47 => ( ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 != ( none @ ( list @ val ) ) )
% 0.28/0.47 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ~ ! [V6: val] :
% 0.28/0.47 ( ( member @ val @ V6 @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ M ) )
% 0.28/0.47 => ~ ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ V6 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiArg_exI
% 0.28/0.47 thf(fact_87_CFG__SSA__wf__base_Ophi_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_wf_phi @ G @ Node @ Val )
% 0.28/0.47 = ( sSA_CFG_SSA_wf_phi @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.phi.cong
% 0.28/0.47 thf(fact_88_infinite__Un,axiom,
% 0.28/0.47 ! [A: $tType,S: set @ A,T: set @ A] :
% 0.28/0.47 ( ( ~ ( finite_finite2 @ A @ ( sup_sup @ ( set @ A ) @ S @ T ) ) )
% 0.28/0.47 = ( ~ ( finite_finite2 @ A @ S )
% 0.28/0.47 | ~ ( finite_finite2 @ A @ T ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % infinite_Un
% 0.28/0.47 thf(fact_89_Un__infinite,axiom,
% 0.28/0.47 ! [A: $tType,S: set @ A,T: set @ A] :
% 0.28/0.47 ( ~ ( finite_finite2 @ A @ S )
% 0.28/0.47 => ~ ( finite_finite2 @ A @ ( sup_sup @ ( set @ A ) @ S @ T ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_infinite
% 0.28/0.47 thf(fact_90_finite__UnI,axiom,
% 0.28/0.47 ! [A: $tType,F2: set @ A,G4: set @ A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ F2 )
% 0.28/0.47 => ( ( finite_finite2 @ A @ G4 )
% 0.28/0.47 => ( finite_finite2 @ A @ ( sup_sup @ ( set @ A ) @ F2 @ G4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_UnI
% 0.28/0.47 thf(fact_91_CFG__SSA__Transformed_Ocondensation__edges_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( irredu280805948_edges @ G @ Node @ Val )
% 0.28/0.47 = ( irredu280805948_edges @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_Transformed.condensation_edges.cong
% 0.28/0.47 thf(fact_92_CFG__SSA__wf__base_Opruned_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF823892918pruned @ G @ Node @ Val )
% 0.28/0.47 = ( sSA_CF823892918pruned @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.pruned.cong
% 0.28/0.47 thf(fact_93_CFG__SSA__base_OallDefs__def,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_allDefs @ G @ Node @ Val )
% 0.28/0.47 = ( ^ [Defs: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,N3: Node] : ( sup_sup @ ( set @ Val ) @ ( Defs @ G3 @ N3 ) @ ( sSA_CFG_SSA_phiDefs @ G @ Node @ Val @ Phis @ G3 @ N3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_base.allDefs_def
% 0.28/0.47 thf(fact_94_CFG__SSA__base_OallUses__def,axiom,
% 0.28/0.47 ! [EdgeD: $tType,Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_allUses @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( ^ [Alpha_n: G > ( list @ Node ),InEdges: G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,N3: Node] : ( sup_sup @ ( set @ Val ) @ ( Uses @ G3 @ N3 ) @ ( sSA_CFG_SSA_phiUses @ G @ Node @ EdgeD @ Val @ Alpha_n @ InEdges @ Phis @ G3 @ N3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_base.allUses_def
% 0.28/0.47 thf(fact_95_finite__set__choice,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,A3: set @ A,P2: A > B > $o] :
% 0.28/0.47 ( ( finite_finite2 @ A @ A3 )
% 0.28/0.47 => ( ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A3 )
% 0.28/0.47 => ? [X_1: B] : ( P2 @ X3 @ X_1 ) )
% 0.28/0.47 => ? [F3: A > B] :
% 0.28/0.47 ! [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ A3 )
% 0.28/0.47 => ( P2 @ X4 @ ( F3 @ X4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_set_choice
% 0.28/0.47 thf(fact_96_finite,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( finite_finite @ A )
% 0.28/0.47 => ! [A3: set @ A] : ( finite_finite2 @ A @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite
% 0.28/0.47 thf(fact_97_phi__phiDefs,axiom,
% 0.28/0.47 ! [G2: g,V: val,Vs: list @ val] :
% 0.28/0.47 ( ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phi_phiDefs
% 0.28/0.47 thf(fact_98_condensation__acyclic,axiom,
% 0.28/0.47 ! [G2: g,P2: set @ val] : ( transitive_acyclic @ ( set @ val ) @ ( irredu280805948_edges @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % condensation_acyclic
% 0.28/0.47 thf(fact_99_phi__def,axiom,
% 0.28/0.47 ! [G2: g,V: val] :
% 0.28/0.47 ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 = ( phis @ G2 @ ( product_Pair @ node @ val @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) @ V ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phi_def
% 0.28/0.47 thf(fact_100_phiArg__def,axiom,
% 0.28/0.47 ! [G2: g,V: val,V2: val] :
% 0.28/0.47 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ V2 )
% 0.28/0.47 = ( ? [Vs2: list @ val] :
% 0.28/0.47 ( ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs2 ) )
% 0.28/0.47 & ( member @ val @ V2 @ ( set2 @ val @ Vs2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiArg_def
% 0.28/0.47 thf(fact_101_phi__finite,axiom,
% 0.28/0.47 ! [G2: g] : ( finite_finite2 @ val @ ( dom @ val @ ( list @ val ) @ ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phi_finite
% 0.28/0.47 thf(fact_102_redundant__scc__phis,axiom,
% 0.28/0.47 ! [G2: g,P2: set @ val,Scc: set @ val,X2: val] :
% 0.28/0.47 ( ( irredu2110905762nt_set @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ P2 )
% 0.28/0.47 => ( ( member @ ( set @ val ) @ Scc @ ( irredu1918690039_nodes @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) )
% 0.28/0.47 => ( ( member @ val @ X2 @ Scc )
% 0.28/0.47 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ X2 )
% 0.28/0.47 != ( none @ ( list @ val ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % redundant_scc_phis
% 0.28/0.47 thf(fact_103_phis__disj_I2_J,axiom,
% 0.28/0.47 ! [G2: g,N: node,V: val,Vs: list @ val,N4: node,Vs3: list @ val] :
% 0.28/0.47 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N4 @ V ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs3 ) )
% 0.28/0.47 => ( Vs = Vs3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phis_disj(2)
% 0.28/0.47 thf(fact_104_phis__disj_I1_J,axiom,
% 0.28/0.47 ! [G2: g,N: node,V: val,Vs: list @ val,N4: node,Vs3: list @ val] :
% 0.28/0.47 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N4 @ V ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs3 ) )
% 0.28/0.47 => ( N = N4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phis_disj(1)
% 0.28/0.47 thf(fact_105_phis__in___092_060alpha_062n,axiom,
% 0.28/0.47 ! [G2: g,N: node,V: val,Vs: list @ val] :
% 0.28/0.47 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phis_in_\<alpha>n
% 0.28/0.47 thf(fact_106_phis__same__var,axiom,
% 0.28/0.47 ! [G2: g,N: node,V: val,Vs: list @ val,V2: val] :
% 0.28/0.47 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( ( member @ val @ V2 @ ( set2 @ val @ Vs ) )
% 0.28/0.47 => ( ( var2 @ G2 @ V2 )
% 0.28/0.47 = ( var2 @ G2 @ V ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phis_same_var
% 0.28/0.47 thf(fact_107_phis__phi,axiom,
% 0.28/0.47 ! [G2: g,N: node,V: val,Vs: list @ val] :
% 0.28/0.47 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phis_phi
% 0.28/0.47 thf(fact_108_phiUses__exI,axiom,
% 0.28/0.47 ! [M: node,G2: g,N: node,V: val,Vs: list @ val] :
% 0.28/0.47 ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 0.28/0.47 => ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ~ ! [V6: val] :
% 0.28/0.47 ( ( member @ val @ V6 @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ M ) )
% 0.28/0.47 => ~ ( member @ val @ V6 @ ( set2 @ val @ Vs ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiUses_exI
% 0.28/0.47 thf(fact_109_CFG__SSA__Transformed_Ocondensation__nodes_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( irredu1918690039_nodes @ G @ Node @ Val )
% 0.28/0.47 = ( irredu1918690039_nodes @ G @ Node @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_Transformed.condensation_nodes.cong
% 0.28/0.47 thf(fact_110_CFG__SSA__Transformed_Oredundant__set_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( irredu2110905762nt_set @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( irredu2110905762nt_set @ G @ Node @ EdgeD @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_Transformed.redundant_set.cong
% 0.28/0.47 thf(fact_111_CFG__SSA__wf__base_Ophi__def,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CFG_SSA_wf_phi @ G @ Node @ Val )
% 0.28/0.47 = ( ^ [Alpha_n: G > ( list @ Node ),Defs: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,V3: Val] : ( Phis @ G3 @ ( product_Pair @ Node @ Val @ ( sSA_CF1081484811efNode @ G @ Node @ Val @ Alpha_n @ Defs @ Phis @ G3 @ V3 ) @ V3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.phi_def
% 0.28/0.47 thf(fact_112_CFG__SSA__wf__base_OphiArg__def,axiom,
% 0.28/0.47 ! [Val: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( sSA_CF1165125185phiArg @ G @ Node @ Val )
% 0.28/0.47 = ( ^ [Alpha_n: G > ( list @ Node ),Defs: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,V3: Val,V4: Val] :
% 0.28/0.47 ? [Vs2: list @ Val] :
% 0.28/0.47 ( ( ( sSA_CFG_SSA_wf_phi @ G @ Node @ Val @ Alpha_n @ Defs @ Phis @ G3 @ V3 )
% 0.28/0.47 = ( some @ ( list @ Val ) @ Vs2 ) )
% 0.28/0.47 & ( member @ Val @ V4 @ ( set2 @ Val @ Vs2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_wf_base.phiArg_def
% 0.28/0.47 thf(fact_113_phiUsesI,axiom,
% 0.28/0.47 ! [N4: node,G2: g,V2: val,Vs: list @ val,N: node,V: val] :
% 0.28/0.47 ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N4 @ V2 ) )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( ( member @ ( product_prod @ node @ val ) @ ( product_Pair @ node @ val @ N @ V ) @ ( set2 @ ( product_prod @ node @ val ) @ ( zip @ node @ val @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N4 ) @ Vs ) ) )
% 0.28/0.47 => ( member @ val @ V @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiUsesI
% 0.28/0.47 thf(fact_114_scc__in__P,axiom,
% 0.28/0.47 ! [Scc: set @ val,G2: g,P2: set @ val] :
% 0.28/0.47 ( ( member @ ( set @ val ) @ Scc @ ( irredu1918690039_nodes @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) )
% 0.28/0.47 => ( ord_less_eq @ ( set @ val ) @ Scc @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % scc_in_P
% 0.28/0.47 thf(fact_115_not__None__eq,axiom,
% 0.28/0.47 ! [A: $tType,X2: option @ A] :
% 0.28/0.47 ( ( X2
% 0.28/0.47 != ( none @ A ) )
% 0.28/0.47 = ( ? [Y2: A] :
% 0.28/0.47 ( X2
% 0.28/0.47 = ( some @ A @ Y2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_None_eq
% 0.28/0.47 thf(fact_116_not__Some__eq,axiom,
% 0.28/0.47 ! [A: $tType,X2: option @ A] :
% 0.28/0.47 ( ( ! [Y2: A] :
% 0.28/0.47 ( X2
% 0.28/0.47 != ( some @ A @ Y2 ) ) )
% 0.28/0.47 = ( X2
% 0.28/0.47 = ( none @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_Some_eq
% 0.28/0.47 thf(fact_117_sup__Some,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( sup @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] :
% 0.28/0.47 ( ( sup_sup @ ( option @ A ) @ ( some @ A @ X2 ) @ ( some @ A @ Y3 ) )
% 0.28/0.47 = ( some @ A @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_Some
% 0.28/0.47 thf(fact_118_option_Oinject,axiom,
% 0.28/0.47 ! [A: $tType,X22: A,Y22: A] :
% 0.28/0.47 ( ( ( some @ A @ X22 )
% 0.28/0.47 = ( some @ A @ Y22 ) )
% 0.28/0.47 = ( X22 = Y22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.inject
% 0.28/0.47 thf(fact_119_less__eq__option__Some,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( option @ A ) @ ( some @ A @ X2 ) @ ( some @ A @ Y3 ) )
% 0.28/0.47 = ( ord_less_eq @ A @ X2 @ Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_option_Some
% 0.28/0.47 thf(fact_120_sup__None__1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( sup @ A )
% 0.28/0.47 => ! [Y3: option @ A] :
% 0.28/0.47 ( ( sup_sup @ ( option @ A ) @ ( none @ A ) @ Y3 )
% 0.28/0.47 = Y3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_None_1
% 0.28/0.47 thf(fact_121_sup__None__2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( sup @ A )
% 0.28/0.47 => ! [X2: option @ A] :
% 0.28/0.47 ( ( sup_sup @ ( option @ A ) @ X2 @ ( none @ A ) )
% 0.28/0.47 = X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_None_2
% 0.28/0.47 thf(fact_122_zip__same,axiom,
% 0.28/0.47 ! [A: $tType,A2: A,B2: A,Xs: list @ A] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( set2 @ ( product_prod @ A @ A ) @ ( zip @ A @ A @ Xs @ Xs ) ) )
% 0.28/0.47 = ( ( member @ A @ A2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 & ( A2 = B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zip_same
% 0.28/0.47 thf(fact_123__C1_C,axiom,
% 0.28/0.47 ! [G2: g,P2: set @ val] :
% 0.28/0.47 ( ( irredu2110905762nt_set @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ P2 )
% 0.28/0.47 => ? [Scc2: set @ val] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ val ) @ Scc2 @ P2 )
% 0.28/0.47 & ( irredu2110774547nt_scc @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ P2 @ Scc2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % "1"
% 0.28/0.47 thf(fact_124_phiUsesE,axiom,
% 0.28/0.47 ! [V: val,G2: g,N: node] :
% 0.28/0.47 ( ( member @ val @ V @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) )
% 0.28/0.47 => ~ ! [N5: node] :
% 0.28/0.47 ( ( member @ node @ N5 @ ( set2 @ node @ ( graph_449533722essors @ g @ node @ edgeD @ alpha_n @ inEdges @ G2 @ N ) ) )
% 0.28/0.47 => ! [V6: val,Vs4: list @ val] :
% 0.28/0.47 ( ( member @ ( product_prod @ node @ val ) @ ( product_Pair @ node @ val @ N @ V ) @ ( set2 @ ( product_prod @ node @ val ) @ ( zip @ node @ val @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N5 ) @ Vs4 ) ) )
% 0.28/0.47 => ( ( phis @ G2 @ ( product_Pair @ node @ val @ N5 @ V6 ) )
% 0.28/0.47 != ( some @ ( list @ val ) @ Vs4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phiUsesE
% 0.28/0.47 thf(fact_125_finite__has__minimal2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [A3: set @ A,A2: A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ A3 )
% 0.28/0.47 => ( ( member @ A @ A2 @ A3 )
% 0.28/0.47 => ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A3 )
% 0.28/0.47 & ( ord_less_eq @ A @ X3 @ A2 )
% 0.28/0.47 & ! [Xa: A] :
% 0.28/0.47 ( ( member @ A @ Xa @ A3 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Xa @ X3 )
% 0.28/0.47 => ( X3 = Xa ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_has_minimal2
% 0.28/0.47 thf(fact_126_finite__has__maximal2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [A3: set @ A,A2: A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ A3 )
% 0.28/0.47 => ( ( member @ A @ A2 @ A3 )
% 0.28/0.47 => ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A3 )
% 0.28/0.47 & ( ord_less_eq @ A @ A2 @ X3 )
% 0.28/0.47 & ! [Xa: A] :
% 0.28/0.47 ( ( member @ A @ Xa @ A3 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ X3 @ Xa )
% 0.28/0.47 => ( X3 = Xa ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_has_maximal2
% 0.28/0.47 thf(fact_127_subset__code_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,Xs: list @ A,B3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ B3 )
% 0.28/0.47 = ( ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ( member @ A @ X @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_code(1)
% 0.28/0.47 thf(fact_128_rev__finite__subset,axiom,
% 0.28/0.47 ! [A: $tType,B3: set @ A,A3: set @ A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ B3 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 => ( finite_finite2 @ A @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % rev_finite_subset
% 0.28/0.47 thf(fact_129_infinite__super,axiom,
% 0.28/0.47 ! [A: $tType,S: set @ A,T: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ S @ T )
% 0.28/0.47 => ( ~ ( finite_finite2 @ A @ S )
% 0.28/0.47 => ~ ( finite_finite2 @ A @ T ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % infinite_super
% 0.28/0.47 thf(fact_130_finite__subset,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 => ( ( finite_finite2 @ A @ B3 )
% 0.28/0.47 => ( finite_finite2 @ A @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_subset
% 0.28/0.47 thf(fact_131_in__set__zipE,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,X2: A,Y3: B,Xs: list @ A,Ys: list @ B] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs @ Ys ) ) )
% 0.28/0.47 => ~ ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.28/0.47 => ~ ( member @ B @ Y3 @ ( set2 @ B @ Ys ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_set_zipE
% 0.28/0.47 thf(fact_132_set__zip__leftD,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,X2: A,Y3: B,Xs: list @ A,Ys: list @ B] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs @ Ys ) ) )
% 0.28/0.47 => ( member @ A @ X2 @ ( set2 @ A @ Xs ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_zip_leftD
% 0.28/0.47 thf(fact_133_set__zip__rightD,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,X2: A,Y3: B,Xs: list @ A,Ys: list @ B] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs @ Ys ) ) )
% 0.28/0.47 => ( member @ B @ Y3 @ ( set2 @ B @ Ys ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_zip_rightD
% 0.28/0.47 thf(fact_134_combine__options__cases,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,X2: option @ A,P2: ( option @ A ) > ( option @ B ) > $o,Y3: option @ B] :
% 0.28/0.47 ( ( ( X2
% 0.28/0.47 = ( none @ A ) )
% 0.28/0.47 => ( P2 @ X2 @ Y3 ) )
% 0.28/0.47 => ( ( ( Y3
% 0.28/0.47 = ( none @ B ) )
% 0.28/0.47 => ( P2 @ X2 @ Y3 ) )
% 0.28/0.47 => ( ! [A6: A,B4: B] :
% 0.28/0.47 ( ( X2
% 0.28/0.47 = ( some @ A @ A6 ) )
% 0.28/0.47 => ( ( Y3
% 0.28/0.47 = ( some @ B @ B4 ) )
% 0.28/0.47 => ( P2 @ X2 @ Y3 ) ) )
% 0.28/0.47 => ( P2 @ X2 @ Y3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % combine_options_cases
% 0.28/0.47 thf(fact_135_split__option__all,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ^ [P3: ( option @ A ) > $o] :
% 0.28/0.47 ! [X5: option @ A] : ( P3 @ X5 ) )
% 0.28/0.47 = ( ^ [P4: ( option @ A ) > $o] :
% 0.28/0.47 ( ( P4 @ ( none @ A ) )
% 0.28/0.47 & ! [X: A] : ( P4 @ ( some @ A @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_option_all
% 0.28/0.47 thf(fact_136_split__option__ex,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ^ [P3: ( option @ A ) > $o] :
% 0.28/0.47 ? [X5: option @ A] : ( P3 @ X5 ) )
% 0.28/0.47 = ( ^ [P4: ( option @ A ) > $o] :
% 0.28/0.47 ( ( P4 @ ( none @ A ) )
% 0.28/0.47 | ? [X: A] : ( P4 @ ( some @ A @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_option_ex
% 0.28/0.47 thf(fact_137_option_Oinducts,axiom,
% 0.28/0.47 ! [A: $tType,P2: ( option @ A ) > $o,Option: option @ A] :
% 0.28/0.47 ( ( P2 @ ( none @ A ) )
% 0.28/0.47 => ( ! [X3: A] : ( P2 @ ( some @ A @ X3 ) )
% 0.28/0.47 => ( P2 @ Option ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.inducts
% 0.28/0.47 thf(fact_138_option_Oexhaust,axiom,
% 0.28/0.47 ! [A: $tType,Y3: option @ A] :
% 0.28/0.47 ( ( Y3
% 0.28/0.47 != ( none @ A ) )
% 0.28/0.47 => ~ ! [X23: A] :
% 0.28/0.47 ( Y3
% 0.28/0.47 != ( some @ A @ X23 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.exhaust
% 0.28/0.47 thf(fact_139_option_OdiscI,axiom,
% 0.28/0.47 ! [A: $tType,Option: option @ A,X22: A] :
% 0.28/0.47 ( ( Option
% 0.28/0.47 = ( some @ A @ X22 ) )
% 0.28/0.47 => ( Option
% 0.28/0.47 != ( none @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.discI
% 0.28/0.47 thf(fact_140_option_Odistinct_I1_J,axiom,
% 0.28/0.47 ! [A: $tType,X22: A] :
% 0.28/0.47 ( ( none @ A )
% 0.28/0.47 != ( some @ A @ X22 ) ) ).
% 0.28/0.47
% 0.28/0.47 % option.distinct(1)
% 0.28/0.47 thf(fact_141_Ex__condensation__leaf,axiom,
% 0.28/0.47 ! [P2: set @ val,G2: g] :
% 0.28/0.47 ( ( P2
% 0.28/0.47 != ( bot_bot @ ( set @ val ) ) )
% 0.28/0.47 => ? [Leaf: set @ val] :
% 0.28/0.47 ( ( member @ ( set @ val ) @ Leaf @ ( irredu1918690039_nodes @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) )
% 0.28/0.47 & ! [Scc3: set @ val] :
% 0.28/0.47 ~ ( member @ ( product_prod @ ( set @ val ) @ ( set @ val ) ) @ ( product_Pair @ ( set @ val ) @ ( set @ val ) @ Leaf @ Scc3 ) @ ( irredu280805948_edges @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Ex_condensation_leaf
% 0.28/0.47 thf(fact_142_Un__subset__iff,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,C: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) @ C )
% 0.28/0.47 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ C )
% 0.28/0.47 & ( ord_less_eq @ ( set @ A ) @ B3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_subset_iff
% 0.28/0.47 thf(fact_143_le__sup__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A,Y3: A,Z: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X2 @ Y3 ) @ Z )
% 0.28/0.47 = ( ( ord_less_eq @ A @ X2 @ Z )
% 0.28/0.47 & ( ord_less_eq @ A @ Y3 @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_sup_iff
% 0.28/0.47 thf(fact_144_sup_Obounded__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [B2: A,C2: A,A2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 )
% 0.28/0.47 = ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.bounded_iff
% 0.28/0.47 thf(fact_145_subset__antisym,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A3 )
% 0.28/0.47 => ( A3 = B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_antisym
% 0.28/0.47 thf(fact_146_subsetI,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A3 )
% 0.28/0.47 => ( member @ A @ X3 @ B3 ) )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_147_sup_Oright__idem,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ B2 )
% 0.28/0.47 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.right_idem
% 0.28/0.47 thf(fact_148_sup__left__idem,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] :
% 0.28/0.47 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ X2 @ Y3 ) )
% 0.28/0.47 = ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_idem
% 0.28/0.47 thf(fact_149_sup_Oleft__idem,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) )
% 0.28/0.47 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_idem
% 0.28/0.47 thf(fact_150_sup__idem,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ X2 @ X2 )
% 0.28/0.47 = X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_idem
% 0.28/0.47 thf(fact_151_sup_Oidem,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ A2 @ A2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.idem
% 0.28/0.47 thf(fact_152_sup__apply,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ B )
% 0.28/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.28/0.47 = ( ^ [F4: A > B,G3: A > B,X: A] : ( sup_sup @ B @ ( F4 @ X ) @ ( G3 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_apply
% 0.28/0.47 thf(fact_153_Un__iff,axiom,
% 0.28/0.47 ! [A: $tType,C2: A,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 0.28/0.47 = ( ( member @ A @ C2 @ A3 )
% 0.28/0.47 | ( member @ A @ C2 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_iff
% 0.28/0.47 thf(fact_154_UnCI,axiom,
% 0.28/0.47 ! [A: $tType,C2: A,B3: set @ A,A3: set @ A] :
% 0.28/0.47 ( ( ~ ( member @ A @ C2 @ B3 )
% 0.28/0.47 => ( member @ A @ C2 @ A3 ) )
% 0.28/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnCI
% 0.28/0.47 thf(fact_155_subset__empty,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.28/0.47 = ( A3
% 0.28/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_empty
% 0.28/0.47 thf(fact_156_empty__subsetI,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 0.28/0.47
% 0.28/0.47 % empty_subsetI
% 0.28/0.47 thf(fact_157_sup__bot__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( bounde1808546759up_bot @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X2 )
% 0.28/0.47 = X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_bot_left
% 0.28/0.47 thf(fact_158_sup__bot__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( bounde1808546759up_bot @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ X2 @ ( bot_bot @ A ) )
% 0.28/0.47 = X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_bot_right
% 0.28/0.47 thf(fact_159_bot__eq__sup__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( bounde1808546759up_bot @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] :
% 0.28/0.47 ( ( ( bot_bot @ A )
% 0.28/0.47 = ( sup_sup @ A @ X2 @ Y3 ) )
% 0.28/0.47 = ( ( X2
% 0.28/0.47 = ( bot_bot @ A ) )
% 0.28/0.47 & ( Y3
% 0.28/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bot_eq_sup_iff
% 0.28/0.47 thf(fact_160_sup__eq__bot__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( bounde1808546759up_bot @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] :
% 0.28/0.47 ( ( ( sup_sup @ A @ X2 @ Y3 )
% 0.28/0.47 = ( bot_bot @ A ) )
% 0.28/0.47 = ( ( X2
% 0.28/0.47 = ( bot_bot @ A ) )
% 0.28/0.47 & ( Y3
% 0.28/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_eq_bot_iff
% 0.28/0.47 thf(fact_161_sup__bot_Oeq__neutr__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( bounde1808546759up_bot @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ( sup_sup @ A @ A2 @ B2 )
% 0.28/0.47 = ( bot_bot @ A ) )
% 0.28/0.47 = ( ( A2
% 0.28/0.47 = ( bot_bot @ A ) )
% 0.28/0.47 & ( B2
% 0.28/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_bot.eq_neutr_iff
% 0.28/0.47 thf(fact_162_sup__bot_Oleft__neutral,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( bounde1808546759up_bot @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_bot.left_neutral
% 0.28/0.47 thf(fact_163_sup__bot_Oneutr__eq__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( bounde1808546759up_bot @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ( bot_bot @ A )
% 0.28/0.47 = ( sup_sup @ A @ A2 @ B2 ) )
% 0.28/0.47 = ( ( A2
% 0.28/0.47 = ( bot_bot @ A ) )
% 0.28/0.47 & ( B2
% 0.28/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_bot.neutr_eq_iff
% 0.28/0.47 thf(fact_164_sup__bot_Oright__neutral,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( bounde1808546759up_bot @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_bot.right_neutral
% 0.28/0.47 thf(fact_165_Un__empty,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.28/0.47 = ( ( A3
% 0.28/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.28/0.47 & ( B3
% 0.28/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_empty
% 0.28/0.47 thf(fact_166_less__eq__option__None__code,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X2: option @ A] : ( ord_less_eq @ ( option @ A ) @ ( none @ A ) @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_option_None_code
% 0.28/0.47 thf(fact_167_less__eq__option__Some__None,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X2: A] :
% 0.28/0.47 ~ ( ord_less_eq @ ( option @ A ) @ ( some @ A @ X2 ) @ ( none @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_option_Some_None
% 0.28/0.47 thf(fact_168_old_Osuccessors__predecessors,axiom,
% 0.28/0.47 ! [N: node,G2: g,M: node] :
% 0.28/0.47 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.28/0.47 => ( ( member @ node @ N @ ( set2 @ node @ ( graph_449533722essors @ g @ node @ edgeD @ alpha_n @ inEdges @ G2 @ M ) ) )
% 0.28/0.47 = ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.successors_predecessors
% 0.28/0.47 thf(fact_169_Un__empty__left,axiom,
% 0.28/0.47 ! [A: $tType,B3: set @ A] :
% 0.28/0.47 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B3 )
% 0.28/0.47 = B3 ) ).
% 0.28/0.47
% 0.28/0.47 % Un_empty_left
% 0.28/0.47 thf(fact_170_Un__empty__right,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] :
% 0.28/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.28/0.47 = A3 ) ).
% 0.28/0.47
% 0.28/0.47 % Un_empty_right
% 0.28/0.47 thf(fact_171_less__eq__option__None__is__None,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X2: option @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( option @ A ) @ X2 @ ( none @ A ) )
% 0.28/0.47 => ( X2
% 0.28/0.47 = ( none @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_option_None_is_None
% 0.28/0.47 thf(fact_172_less__eq__option__None,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X2: option @ A] : ( ord_less_eq @ ( option @ A ) @ ( none @ A ) @ X2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_eq_option_None
% 0.28/0.47 thf(fact_173_infinite__imp__nonempty,axiom,
% 0.28/0.47 ! [A: $tType,S: set @ A] :
% 0.28/0.47 ( ~ ( finite_finite2 @ A @ S )
% 0.28/0.47 => ( S
% 0.28/0.47 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % infinite_imp_nonempty
% 0.28/0.47 thf(fact_174_finite_OemptyI,axiom,
% 0.28/0.47 ! [A: $tType] : ( finite_finite2 @ A @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite.emptyI
% 0.28/0.47 thf(fact_175_CFG__SSA__Transformed_Oredundant__scc_Ocong,axiom,
% 0.28/0.47 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 0.28/0.47 ( ( ( linorder @ Node )
% 0.28/0.47 & ( linorder @ Val ) )
% 0.28/0.47 => ( ( irredu2110774547nt_scc @ G @ Node @ EdgeD @ Val )
% 0.28/0.47 = ( irredu2110774547nt_scc @ G @ Node @ EdgeD @ Val ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % CFG_SSA_Transformed.redundant_scc.cong
% 0.28/0.47 thf(fact_176_finite__has__maximal,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [A3: set @ A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ A3 )
% 0.28/0.47 => ( ( A3
% 0.28/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.28/0.47 => ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A3 )
% 0.28/0.47 & ! [Xa: A] :
% 0.28/0.47 ( ( member @ A @ Xa @ A3 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ X3 @ Xa )
% 0.28/0.47 => ( X3 = Xa ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_has_maximal
% 0.28/0.47 thf(fact_177_finite__has__minimal,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [A3: set @ A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ A3 )
% 0.28/0.47 => ( ( A3
% 0.28/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.28/0.47 => ? [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A3 )
% 0.28/0.47 & ! [Xa: A] :
% 0.28/0.47 ( ( member @ A @ Xa @ A3 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Xa @ X3 )
% 0.28/0.47 => ( X3 = Xa ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_has_minimal
% 0.28/0.47 thf(fact_178_Collect__mono__iff,axiom,
% 0.28/0.47 ! [A: $tType,P2: A > $o,Q2: A > $o] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q2 ) )
% 0.28/0.47 = ( ! [X: A] :
% 0.28/0.47 ( ( P2 @ X )
% 0.28/0.47 => ( Q2 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_179_set__eq__subset,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ^ [Y4: set @ A,Z2: set @ A] : ( Y4 = Z2 ) )
% 0.28/0.47 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.47 & ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_eq_subset
% 0.28/0.47 thf(fact_180_subset__trans,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,C: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_trans
% 0.28/0.47 thf(fact_181_Collect__mono,axiom,
% 0.28/0.47 ! [A: $tType,P2: A > $o,Q2: A > $o] :
% 0.28/0.47 ( ! [X3: A] :
% 0.28/0.47 ( ( P2 @ X3 )
% 0.28/0.47 => ( Q2 @ X3 ) )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_182_subset__refl,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.28/0.47
% 0.28/0.47 % subset_refl
% 0.28/0.47 thf(fact_183_subset__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.28/0.47 ! [T2: A] :
% 0.28/0.47 ( ( member @ A @ T2 @ A5 )
% 0.28/0.47 => ( member @ A @ T2 @ B5 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_184_equalityD2,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( A3 = B3 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD2
% 0.28/0.47 thf(fact_185_equalityD1,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( A3 = B3 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD1
% 0.28/0.47 thf(fact_186_subset__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.28/0.47 ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ A5 )
% 0.28/0.47 => ( member @ A @ X @ B5 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_187_equalityE,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( A3 = B3 )
% 0.28/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityE
% 0.28/0.47 thf(fact_188_subsetD,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 => ( ( member @ A @ C2 @ A3 )
% 0.28/0.47 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_189_in__mono,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,X2: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 => ( ( member @ A @ X2 @ A3 )
% 0.28/0.47 => ( member @ A @ X2 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_190_sup__left__commute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A,Y3: A,Z: A] :
% 0.28/0.47 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y3 @ Z ) )
% 0.28/0.47 = ( sup_sup @ A @ Y3 @ ( sup_sup @ A @ X2 @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_left_commute
% 0.28/0.47 thf(fact_191_sup_Oleft__commute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ B2 @ ( sup_sup @ A @ A2 @ C2 ) )
% 0.28/0.47 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.left_commute
% 0.28/0.47 thf(fact_192_sup__commute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ( ( sup_sup @ A )
% 0.28/0.47 = ( ^ [X: A,Y2: A] : ( sup_sup @ A @ Y2 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_commute
% 0.28/0.47 thf(fact_193_sup_Ocommute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ( ( sup_sup @ A )
% 0.28/0.47 = ( ^ [A4: A,B6: A] : ( sup_sup @ A @ B6 @ A4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.commute
% 0.28/0.47 thf(fact_194_sup__assoc,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A,Y3: A,Z: A] :
% 0.28/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X2 @ Y3 ) @ Z )
% 0.28/0.47 = ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y3 @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_assoc
% 0.28/0.47 thf(fact_195_sup_Oassoc,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ C2 )
% 0.28/0.47 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.assoc
% 0.28/0.47 thf(fact_196_boolean__algebra__cancel_Osup2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [B3: A,K: A,B2: A,A2: A] :
% 0.28/0.47 ( ( B3
% 0.28/0.47 = ( sup_sup @ A @ K @ B2 ) )
% 0.28/0.47 => ( ( sup_sup @ A @ A2 @ B3 )
% 0.28/0.47 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % boolean_algebra_cancel.sup2
% 0.28/0.47 thf(fact_197_boolean__algebra__cancel_Osup1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A3: A,K: A,A2: A,B2: A] :
% 0.28/0.47 ( ( A3
% 0.28/0.47 = ( sup_sup @ A @ K @ A2 ) )
% 0.28/0.47 => ( ( sup_sup @ A @ A3 @ B2 )
% 0.28/0.47 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % boolean_algebra_cancel.sup1
% 0.28/0.47 thf(fact_198_sup__fun__def,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ B )
% 0.28/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.28/0.47 = ( ^ [F4: A > B,G3: A > B,X: A] : ( sup_sup @ B @ ( F4 @ X ) @ ( G3 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_fun_def
% 0.28/0.47 thf(fact_199_inf__sup__aci_I5_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( lattice @ A )
% 0.28/0.47 => ( ( sup_sup @ A )
% 0.28/0.47 = ( ^ [X: A,Y2: A] : ( sup_sup @ A @ Y2 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_aci(5)
% 0.28/0.47 thf(fact_200_inf__sup__aci_I6_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( lattice @ A )
% 0.28/0.47 => ! [X2: A,Y3: A,Z: A] :
% 0.28/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X2 @ Y3 ) @ Z )
% 0.28/0.47 = ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y3 @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_aci(6)
% 0.28/0.47 thf(fact_201_inf__sup__aci_I7_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( lattice @ A )
% 0.28/0.47 => ! [X2: A,Y3: A,Z: A] :
% 0.28/0.47 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y3 @ Z ) )
% 0.28/0.47 = ( sup_sup @ A @ Y3 @ ( sup_sup @ A @ X2 @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_aci(7)
% 0.28/0.47 thf(fact_202_inf__sup__aci_I8_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( lattice @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] :
% 0.28/0.47 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ X2 @ Y3 ) )
% 0.28/0.47 = ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_aci(8)
% 0.28/0.47 thf(fact_203_Un__left__commute,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,C: set @ A] :
% 0.28/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B3 @ C ) )
% 0.28/0.47 = ( sup_sup @ ( set @ A ) @ B3 @ ( sup_sup @ ( set @ A ) @ A3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_left_commute
% 0.28/0.47 thf(fact_204_Un__left__absorb,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 0.28/0.47 = ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_left_absorb
% 0.28/0.47 thf(fact_205_Un__commute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A5: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_commute
% 0.28/0.47 thf(fact_206_Un__absorb,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A] :
% 0.28/0.47 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.28/0.47 = A3 ) ).
% 0.28/0.47
% 0.28/0.47 % Un_absorb
% 0.28/0.47 thf(fact_207_Un__assoc,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,C: set @ A] :
% 0.28/0.47 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) @ C )
% 0.28/0.47 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B3 @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_assoc
% 0.28/0.47 thf(fact_208_ball__Un,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,P2: A > $o] :
% 0.28/0.47 ( ( ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 0.28/0.47 => ( P2 @ X ) ) )
% 0.28/0.47 = ( ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ A3 )
% 0.28/0.47 => ( P2 @ X ) )
% 0.28/0.47 & ! [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ B3 )
% 0.28/0.47 => ( P2 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ball_Un
% 0.28/0.47 thf(fact_209_bex__Un,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A,P2: A > $o] :
% 0.28/0.47 ( ( ? [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 0.28/0.47 & ( P2 @ X ) ) )
% 0.28/0.47 = ( ? [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ A3 )
% 0.28/0.47 & ( P2 @ X ) )
% 0.28/0.47 | ? [X: A] :
% 0.28/0.47 ( ( member @ A @ X @ B3 )
% 0.28/0.47 & ( P2 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % bex_Un
% 0.28/0.47 thf(fact_210_UnI2,axiom,
% 0.28/0.47 ! [A: $tType,C2: A,B3: set @ A,A3: set @ A] :
% 0.28/0.47 ( ( member @ A @ C2 @ B3 )
% 0.28/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnI2
% 0.28/0.47 thf(fact_211_UnI1,axiom,
% 0.28/0.47 ! [A: $tType,C2: A,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( member @ A @ C2 @ A3 )
% 0.28/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnI1
% 0.28/0.47 thf(fact_212_UnE,axiom,
% 0.28/0.47 ! [A: $tType,C2: A,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 0.28/0.47 => ( ~ ( member @ A @ C2 @ A3 )
% 0.28/0.47 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % UnE
% 0.28/0.47 thf(fact_213_sup_OcoboundedI2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [C2: A,B2: A,A2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.28/0.47 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.coboundedI2
% 0.28/0.47 thf(fact_214_sup_OcoboundedI1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [C2: A,A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.28/0.47 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.coboundedI1
% 0.28/0.47 thf(fact_215_sup_Oabsorb__iff2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ( ( ord_less_eq @ A )
% 0.28/0.47 = ( ^ [A4: A,B6: A] :
% 0.28/0.47 ( ( sup_sup @ A @ A4 @ B6 )
% 0.28/0.47 = B6 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.absorb_iff2
% 0.28/0.47 thf(fact_216_sup_Oabsorb__iff1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ( ( ord_less_eq @ A )
% 0.28/0.47 = ( ^ [B6: A,A4: A] :
% 0.28/0.47 ( ( sup_sup @ A @ A4 @ B6 )
% 0.28/0.47 = A4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.absorb_iff1
% 0.28/0.47 thf(fact_217_sup_Ocobounded2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [B2: A,A2: A] : ( ord_less_eq @ A @ B2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.cobounded2
% 0.28/0.47 thf(fact_218_sup_Ocobounded1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.cobounded1
% 0.28/0.47 thf(fact_219_sup_Oorder__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ( ( ord_less_eq @ A )
% 0.28/0.47 = ( ^ [B6: A,A4: A] :
% 0.28/0.47 ( A4
% 0.28/0.47 = ( sup_sup @ A @ A4 @ B6 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.order_iff
% 0.28/0.47 thf(fact_220_sup_OboundedI,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.boundedI
% 0.28/0.47 thf(fact_221_sup_OboundedE,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [B2: A,C2: A,A2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 )
% 0.28/0.47 => ~ ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.boundedE
% 0.28/0.47 thf(fact_222_sup__absorb2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.28/0.47 => ( ( sup_sup @ A @ X2 @ Y3 )
% 0.28/0.47 = Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_absorb2
% 0.28/0.47 thf(fact_223_sup__absorb1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [Y3: A,X2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ Y3 @ X2 )
% 0.28/0.47 => ( ( sup_sup @ A @ X2 @ Y3 )
% 0.28/0.47 = X2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_absorb1
% 0.28/0.47 thf(fact_224_sup_Oabsorb2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.28/0.47 = B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.absorb2
% 0.28/0.47 thf(fact_225_sup_Oabsorb1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [B2: A,A2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.28/0.47 = A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.absorb1
% 0.28/0.47 thf(fact_226_sup__unique,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [F: A > A > A,X2: A,Y3: A] :
% 0.28/0.47 ( ! [X3: A,Y5: A] : ( ord_less_eq @ A @ X3 @ ( F @ X3 @ Y5 ) )
% 0.28/0.47 => ( ! [X3: A,Y5: A] : ( ord_less_eq @ A @ Y5 @ ( F @ X3 @ Y5 ) )
% 0.28/0.47 => ( ! [X3: A,Y5: A,Z3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ Y5 @ X3 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Z3 @ X3 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( F @ Y5 @ Z3 ) @ X3 ) ) )
% 0.28/0.47 => ( ( sup_sup @ A @ X2 @ Y3 )
% 0.28/0.47 = ( F @ X2 @ Y3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_unique
% 0.28/0.47 thf(fact_227_sup_OorderI,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( sup_sup @ A @ A2 @ B2 ) )
% 0.28/0.47 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.orderI
% 0.28/0.47 thf(fact_228_sup_OorderE,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [B2: A,A2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( A2
% 0.28/0.47 = ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.orderE
% 0.28/0.47 thf(fact_229_le__iff__sup,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ( ( ord_less_eq @ A )
% 0.28/0.47 = ( ^ [X: A,Y2: A] :
% 0.28/0.47 ( ( sup_sup @ A @ X @ Y2 )
% 0.28/0.47 = Y2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_iff_sup
% 0.28/0.47 thf(fact_230_sup__least,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [Y3: A,X2: A,Z: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ Y3 @ X2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Z @ X2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y3 @ Z ) @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_least
% 0.28/0.47 thf(fact_231_sup__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,C2: A,B2: A,D: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ D )
% 0.28/0.47 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ ( sup_sup @ A @ C2 @ D ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_mono
% 0.28/0.47 thf(fact_232_sup_Omono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [C2: A,A2: A,D: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ D @ B2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( sup_sup @ A @ C2 @ D ) @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup.mono
% 0.28/0.47 thf(fact_233_le__supI2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A,B2: A,A2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X2 @ B2 )
% 0.28/0.47 => ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_supI2
% 0.28/0.47 thf(fact_234_le__supI1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A,A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X2 @ A2 )
% 0.28/0.47 => ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_supI1
% 0.28/0.47 thf(fact_235_sup__ge2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [Y3: A,X2: A] : ( ord_less_eq @ A @ Y3 @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_ge2
% 0.28/0.47 thf(fact_236_sup__ge1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] : ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % sup_ge1
% 0.28/0.47 thf(fact_237_le__supI,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,X2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ X2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ X2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_supI
% 0.28/0.47 thf(fact_238_le__supE,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A )
% 0.28/0.47 => ! [A2: A,B2: A,X2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X2 )
% 0.28/0.47 => ~ ( ( ord_less_eq @ A @ A2 @ X2 )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ B2 @ X2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_supE
% 0.28/0.47 thf(fact_239_inf__sup__ord_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( lattice @ A )
% 0.28/0.47 => ! [X2: A,Y3: A] : ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_ord(3)
% 0.28/0.47 thf(fact_240_inf__sup__ord_I4_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( lattice @ A )
% 0.28/0.47 => ! [Y3: A,X2: A] : ( ord_less_eq @ A @ Y3 @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % inf_sup_ord(4)
% 0.28/0.47 thf(fact_241_subset__Un__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( sup_sup @ ( set @ A ) @ A5 @ B5 )
% 0.28/0.47 = B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_Un_eq
% 0.28/0.47 thf(fact_242_subset__UnE,axiom,
% 0.28/0.47 ! [A: $tType,C: set @ A,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 0.28/0.47 => ~ ! [A7: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A7 @ A3 )
% 0.28/0.47 => ! [B7: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ B7 @ B3 )
% 0.28/0.47 => ( C
% 0.28/0.47 != ( sup_sup @ ( set @ A ) @ A7 @ B7 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_UnE
% 0.28/0.47 thf(fact_243_Un__absorb2,axiom,
% 0.28/0.47 ! [A: $tType,B3: set @ A,A3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ B3 @ A3 )
% 0.28/0.47 => ( ( sup_sup @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 = A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_absorb2
% 0.28/0.47 thf(fact_244_Un__absorb1,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 => ( ( sup_sup @ ( set @ A ) @ A3 @ B3 )
% 0.28/0.47 = B3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_absorb1
% 0.28/0.47 thf(fact_245_Un__upper2,axiom,
% 0.28/0.47 ! [A: $tType,B3: set @ A,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ B3 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_upper2
% 0.28/0.47 thf(fact_246_Un__upper1,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_upper1
% 0.28/0.47 thf(fact_247_Un__least,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,C: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_least
% 0.28/0.47 thf(fact_248_Un__mono,axiom,
% 0.28/0.47 ! [A: $tType,A3: set @ A,C: set @ A,B3: set @ A,D2: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ D2 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) @ ( sup_sup @ ( set @ A ) @ C @ D2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Un_mono
% 0.28/0.47 thf(fact_249_redundant__set__def,axiom,
% 0.28/0.47 ! [G2: g,P2: set @ val] :
% 0.28/0.47 ( ( irredu2110905762nt_set @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ P2 )
% 0.28/0.47 = ( ( P2
% 0.28/0.47 != ( bot_bot @ ( set @ val ) ) )
% 0.28/0.47 & ( ord_less_eq @ ( set @ val ) @ P2 @ ( dom @ val @ ( list @ val ) @ ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 ) ) )
% 0.28/0.47 & ? [X: val] :
% 0.28/0.47 ( ( member @ val @ X @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 & ! [Y2: val] :
% 0.28/0.47 ( ( member @ val @ Y2 @ P2 )
% 0.28/0.47 => ! [Phi3: val] :
% 0.28/0.47 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ Y2 @ Phi3 )
% 0.28/0.47 => ( member @ val @ Phi3 @ ( sup_sup @ ( set @ val ) @ P2 @ ( insert @ val @ X @ ( bot_bot @ ( set @ val ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % redundant_set_def
% 0.28/0.47 thf(fact_250_phi__no__closed__loop,axiom,
% 0.28/0.47 ! [P: val,G2: g,Vs: list @ val] :
% 0.28/0.47 ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 0.28/0.47 => ( ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P )
% 0.28/0.47 = ( some @ ( list @ val ) @ Vs ) )
% 0.28/0.47 => ( ( set2 @ val @ Vs )
% 0.28/0.47 != ( insert @ val @ P @ ( bot_bot @ ( set @ val ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phi_no_closed_loop
% 0.28/0.47 thf(fact_251_dom__eq__empty__conv,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,F: A > ( option @ B )] :
% 0.28/0.47 ( ( ( dom @ A @ B @ F )
% 0.28/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.28/0.47 = ( F
% 0.28/0.47 = ( ^ [X: A] : ( none @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dom_eq_empty_conv
% 0.28/0.47 thf(fact_252_phis__finite,axiom,
% 0.28/0.47 ! [G2: g] : ( finite_finite2 @ ( product_prod @ node @ val ) @ ( dom @ ( product_prod @ node @ val ) @ ( list @ val ) @ ( phis @ G2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % phis_finite
% 0.28/0.47 thf(fact_253_insert__subset,axiom,
% 0.28/0.47 ! [A: $tType,X2: A,A3: set @ A,B3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X2 @ A3 ) @ B3 )
% 0.28/0.47 = ( ( member @ A @ X2 @ B3 )
% 0.28/0.47 & ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % insert_subset
% 0.28/0.47 thf(fact_254_finite__insert,axiom,
% 0.28/0.47 ! [A: $tType,A2: A,A3: set @ A] :
% 0.28/0.47 ( ( finite_finite2 @ A @ ( insert @ A @ A2 @ A3 ) )
% 0.28/0.47 = ( finite_finite2 @ A @ A3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % finite_insert
% 0.28/0.47
% 0.28/0.47 % Subclasses (3)
% 0.28/0.47 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ( type @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ( order @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ( preorder @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % Type constructors (39)
% 0.28/0.47 thf(tcon_Option_Ooption___Lattices_Obounded__lattice,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( bounded_lattice_top @ A8 )
% 0.28/0.47 => ( bounded_lattice @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_1,axiom,
% 0.28/0.47 bounded_lattice @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice_2,axiom,
% 0.28/0.47 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Lattices_Obounded__lattice_3,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( bounded_lattice @ A9 )
% 0.28/0.47 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( bounded_lattice @ A9 )
% 0.28/0.47 => ( bounded_lattice_top @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_4,axiom,
% 0.28/0.47 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_5,axiom,
% 0.28/0.47 bounded_lattice_top @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Lattices_Obounded__lattice__top_6,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( bounded_lattice_top @ A8 )
% 0.28/0.47 => ( bounded_lattice_top @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( bounded_lattice @ A9 )
% 0.28/0.47 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A9 )
% 0.28/0.47 => ( semilattice_sup @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( preorder @ A9 )
% 0.28/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( finite_finite @ A8 )
% 0.28/0.47 & ( finite_finite @ A9 ) )
% 0.28/0.47 => ( finite_finite @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( lattice @ A9 )
% 0.28/0.47 => ( lattice @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( order @ A9 )
% 0.28/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Lattices_Osup,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A9 )
% 0.28/0.47 => ( sup @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 0.28/0.47 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_8,axiom,
% 0.28/0.47 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_9,axiom,
% 0.28/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Finite__Set_Ofinite_10,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( finite_finite @ A8 )
% 0.28/0.47 => ( finite_finite @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Lattices_Olattice_11,axiom,
% 0.28/0.47 ! [A8: $tType] : ( lattice @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Oorder_12,axiom,
% 0.28/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Lattices_Osup_13,axiom,
% 0.28/0.47 ! [A8: $tType] : ( sup @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14,axiom,
% 0.28/0.47 bounde1808546759up_bot @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_15,axiom,
% 0.28/0.47 semilattice_sup @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_16,axiom,
% 0.28/0.47 preorder @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.28/0.47 linorder @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Finite__Set_Ofinite_17,axiom,
% 0.28/0.47 finite_finite @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Lattices_Olattice_18,axiom,
% 0.28/0.47 lattice @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_19,axiom,
% 0.28/0.47 order @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Lattices_Osup_20,axiom,
% 0.28/0.47 sup @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Lattices_Obounded__semilattice__sup__bot_21,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( lattice @ A8 )
% 0.28/0.47 => ( bounde1808546759up_bot @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Lattices_Osemilattice__sup_22,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( semilattice_sup @ A8 )
% 0.28/0.47 => ( semilattice_sup @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Orderings_Opreorder_23,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( preorder @ A8 )
% 0.28/0.47 => ( preorder @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Orderings_Olinorder_24,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( linorder @ A8 )
% 0.28/0.47 => ( linorder @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Finite__Set_Ofinite_25,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( finite_finite @ A8 )
% 0.28/0.47 => ( finite_finite @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Lattices_Olattice_26,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( lattice @ A8 )
% 0.28/0.47 => ( lattice @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Orderings_Oorder_27,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( order @ A8 )
% 0.28/0.47 => ( order @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Option_Ooption___Lattices_Osup_28,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( sup @ A8 )
% 0.28/0.47 => ( sup @ ( option @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_29,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( finite_finite @ A8 )
% 0.28/0.47 & ( finite_finite @ A9 ) )
% 0.28/0.47 => ( finite_finite @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Free types (3)
% 0.28/0.47 thf(tfree_0,hypothesis,
% 0.28/0.47 linorder @ val ).
% 0.28/0.47
% 0.28/0.47 thf(tfree_1,hypothesis,
% 0.28/0.47 linorder @ node ).
% 0.28/0.47
% 0.28/0.47 thf(tfree_2,hypothesis,
% 0.28/0.47 linorder @ var ).
% 0.28/0.47
% 0.28/0.47 % Conjectures (1)
% 0.28/0.47 thf(conj_0,conjecture,
% 0.28/0.47 member @ val @ phi_s @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.76/1.56 ---- Embedded in THF ---
% 2.76/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.76/1.56 %%% Generated on Tue Feb 24 08:25:46 EST 2026
% 2.76/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.76/1.56 %%% Logic specification used:
% 2.76/1.56 %%% thf(spec, logic, $$dhol).
% 2.76/1.56
% 2.76/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ukvq8Gf8nd/DTF2DTF3462.p
% 2.76/1.56 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.76/1.56 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.76/1.56 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.76/1.56 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.76/1.56 thf(ty_tf_edgeD, type, edgeD: $tType).
% 2.76/1.56 thf(ty_tf_node, type, node: $tType).
% 2.76/1.56 thf(ty_tf_var, type, var: $tType).
% 2.76/1.56 thf(ty_tf_val, type, val: $tType).
% 2.76/1.56 thf(ty_tf_g, type, g: $tType).
% 2.76/1.56 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Lattices_Osup, type, sup: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 2.76/1.56 thf(sy_c_Finite__Set_Ofinite, type, finite_finite2: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.76/1.56 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors, type, graph_1201503639essors: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > (list @ Node))))))).
% 2.76/1.56 thf(sy_c_Graph__path_Ograph__path__base_Osuccessors, type, graph_449533722essors: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > (list @ Node)))))))).
% 2.76/1.56 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Ocondensation__edges, type, irredu280805948_edges: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > ((set @ Val) > (set @ ((product_prod @ (set @ Val)) @ (set @ Val))))))))))).
% 2.76/1.56 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Ocondensation__nodes, type, irredu1918690039_nodes: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > ((set @ Val) > (set @ (set @ Val)))))))))).
% 2.76/1.56 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Oredundant__scc, type, irredu2110774547nt_scc: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (Node > (set @ Val))) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > ((set @ Val) > ((set @ Val) > $o))))))))))).
% 2.76/1.56 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Oredundant__set, type, irredu2110905762nt_set: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (Node > (set @ Val))) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > ((set @ Val) > $o)))))))))).
% 2.76/1.56 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.76/1.56 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.76/1.56 thf(sy_c_List_Ozip, type, zip: (!> [A:$tType,B:$tType]: (((list @ A) > ((list @ B) > (list @ ((product_prod @ A) @ B))))))).
% 2.76/1.56 thf(sy_c_Map_Odom, type, dom: (!> [A:$tType,B:$tType]: (((A > (option @ B)) > (set @ A))))).
% 2.76/1.56 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.76/1.56 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 2.76/1.56 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.76/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.76/1.56 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs, type, sSA_CFG_SSA_allDefs: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (set @ Val)))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallUses, type, sSA_CFG_SSA_allUses: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (set @ Val)))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallVars, type, sSA_CFG_SSA_allVars: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (Node > (set @ Val))) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (set @ Val)))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs, type, sSA_CFG_SSA_phiDefs: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (set @ Val))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses, type, sSA_CFG_SSA_phiUses: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (set @ Val))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode, type, sSA_CF1081484811efNode: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > Node)))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OisTrivialPhi, type, sSA_CF1297404942ialPhi: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > (Val > $o))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OliveVal, type, sSA_CF722422777iveVal: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > $o))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Ophi, type, sSA_CFG_SSA_wf_phi: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > (option @ (list @ Val)))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg, type, sSA_CF1165125185phiArg: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > (Val > $o))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Opruned, type, sSA_CF823892918pruned: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > $o)))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Oredundant, type, sSA_CF462202545undant: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (Node > (set @ Val))) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > $o))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Otrivial, type, sSA_CF1363434349rivial: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (Node > (set @ Val))) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > $o)))))))))).
% 2.76/1.56 thf(sy_c_SSA__CFG_OCFG__base_Ovars, type, sSA_CFG_vars: (!> [G:$tType,Node:$tType,Var:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Var))) > (G > (set @ Var))))))).
% 2.76/1.56 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.76/1.56 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.76/1.56 thf(sy_c_Transitive__Closure_Oacyclic, type, transitive_acyclic: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.76/1.56 thf(sy_c_Transitive__Closure_Otranclp, type, transitive_tranclp: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > $o)))))).
% 2.76/1.56 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.76/1.56 thf(sy_v__092_060alpha_062n, type, alpha_n: (g > (list @ node))).
% 2.76/1.56 thf(sy_v__092_060phi_062, type, phi: val).
% 2.76/1.56 thf(sy_v__092_060phi_062_092_060_094sub_062s, type, phi_s: val).
% 2.76/1.56 thf(sy_v__092_060phi_062_H____, type, phi2: val).
% 2.76/1.56 thf(sy_v_defs, type, defs: (g > (node > (set @ val)))).
% 2.76/1.56 thf(sy_v_g, type, g2: g).
% 2.76/1.56 thf(sy_v_inEdges_H, type, inEdges: (g > (node > (list @ ((product_prod @ node) @ edgeD))))).
% 2.76/1.56 thf(sy_v_phis, type, phis: (g > (((product_prod @ node) @ val) > (option @ (list @ val))))).
% 2.76/1.56 thf(sy_v_s, type, s: val).
% 2.76/1.56 thf(sy_v_uses, type, uses: (g > (node > (set @ val)))).
% 2.76/1.56 thf(sy_v_var, type, var2: (g > (val > var))).
% 2.76/1.56 thf(fact_0_assms_I4_J, axiom, (phi_s != s)).
% 2.76/1.56 thf(fact_1_False, axiom, (phi != phi_s)).
% 2.76/1.56 thf(fact_2__092_060open_062phiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_092_060close_062, axiom, (((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi2) @ phi_s)).
% 2.76/1.56 thf(fact_3_assms_I3_J, axiom, (((member @ val) @ s) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ g2))).
% 2.76/1.56 thf(fact_4_assms_I2_J, axiom, (((member @ val) @ phi) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ g2))).
% 2.76/1.56 thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Phi:val]: ((~ ((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ Phi) @ phi_s)))))))).
% 2.76/1.56 thf(fact_6_phiArg__in__allVars, axiom, (! [G2:g,V:val,V2:val]: (((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) @ V2) => (((member @ val) @ V2) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)))))).
% 2.76/1.56 thf(fact_7_uses__in__vars, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ ((uses @ G2) @ N)) => (((member @ val) @ V) @ ((((((sSA_CFG_vars @ g) @ node) @ val) @ alpha_n) @ uses) @ G2)))))).
% 2.76/1.56 thf(fact_8_trivial__in__allVars, axiom, (! [G2:g,V:val]: (((((((((((((sSA_CF1363434349rivial @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) @ V) => (((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)))))).
% 2.76/1.56 thf(fact_9_liveVal__in__allVars, axiom, (! [G2:g,V:val]: (((((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ V) => (((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)))))).
% 2.76/1.56 thf(fact_10_allVars__finite, axiom, (! [G2:g]: (((finite_finite2 @ val) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2))))).
% 2.76/1.56 thf(fact_11_uses__in__allUses, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ ((uses @ G2) @ N)) => (((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ uses) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_12_redundant__def, axiom, (! [G2:g]: ((((((((((((sSA_CF462202545undant @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) = (? [X:val]: (((((member @ val) @ X) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) & (((((((((((sSA_CF1363434349rivial @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) @ X)))))))).
% 2.76/1.56 thf(fact_13_trivial__def, axiom, (! [G2:g,V:val]: (((((((((((((sSA_CF1363434349rivial @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) @ V) = (? [X:val]: (((((member @ val) @ X) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) & (((((((((sSA_CF1297404942ialPhi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) @ X)))))))).
% 2.76/1.56 thf(fact_14__092_060open_062_092_060not_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062s_A_092_060noteq_062_AdefNode_Ag_As_092_060close_062, axiom, (((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_s) = ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ s))).
% 2.76/1.56 thf(fact_15_defs__uses__disjoint_H, axiom, (! [N:node,G2:g,V:val]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ val) @ V) @ ((defs @ G2) @ N)) => (~ ((((member @ val) @ V) @ ((uses @ G2) @ N))))))))).
% 2.76/1.56 thf(fact_16_livePhi, axiom, (! [G2:g,V:val,V2:val]: (((((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ V) => ((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) @ V2) => (((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ V2)))))).
% 2.76/1.56 thf(fact_17_phiArg__distinct__nodes, axiom, (! [G2:g,P:val,Q:val]: (((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P) @ Q) => ((P != Q) => ((((member @ val) @ P) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => (((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P) != ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ Q)))))))).
% 2.76/1.56 thf(fact_18_phiArgs__def__distinct, axiom, (! [G2:g,P:val,Q:val,R:val]: (((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P) @ Q) => ((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P) @ R) => ((Q != R) => ((((member @ val) @ P) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => (((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ Q) != ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ R))))))))).
% 2.76/1.56 thf(fact_19_uses__in___092_060alpha_062n, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ ((uses @ G2) @ N)) => (((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))))))).
% 2.76/1.56 thf(fact_20_defs__finite, axiom, (! [G2:g,N:node]: (((finite_finite2 @ val) @ ((defs @ G2) @ N))))).
% 2.76/1.56 thf(fact_21_varsE, axiom, (! [V:val,G2:g]: (((((member @ val) @ V) @ ((((((sSA_CFG_vars @ g) @ node) @ val) @ alpha_n) @ uses) @ G2)) => (~ ((! [N2:node]: (((((member @ node) @ N2) @ ((set2 @ node) @ (alpha_n @ G2))) => (~ ((((member @ val) @ V) @ ((uses @ G2) @ N2))))))))))))).
% 2.76/1.56 thf(fact_22_vars__finite, axiom, (! [G2:g]: (((finite_finite2 @ val) @ ((((((sSA_CFG_vars @ g) @ node) @ val) @ alpha_n) @ uses) @ G2))))).
% 2.76/1.56 thf(fact_23_liveSimple, axiom, (! [N:node,G2:g,Val2:val]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ val) @ Val2) @ ((uses @ G2) @ N)) => (((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ Val2)))))).
% 2.76/1.56 thf(fact_24_liveVal_Osimps, axiom, (! [G2:g,A2:val]: (((((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ A2) = ((? [N3:node,Val3:val]: (((A2 = Val3) & ((((member @ node) @ N3) @ ((set2 @ node) @ (alpha_n @ G2))) & (((member @ val) @ Val3) @ ((uses @ G2) @ N3)))))) | (? [V3:val,V4:val]: (((A2 = V4) & ((((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ V3) & (((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V3) @ V4)))))))))).
% 2.76/1.56 thf(fact_25_liveVal_Oinducts, axiom, (! [G2:g,X2:val,P2:(val > $o)]: (((((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ X2) => ((! [N2:node,Val4:val]: (((((member @ node) @ N2) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ val) @ Val4) @ ((uses @ G2) @ N2)) => (P2 @ Val4))))) => ((! [V5:val,V6:val]: (((((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ V5) => ((P2 @ V5) => ((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V5) @ V6) => (P2 @ V6)))))) => (P2 @ X2))))))).
% 2.76/1.56 thf(fact_26_liveVal_Ocases, axiom, (! [G2:g,A2:val]: (((((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ A2) => ((! [N2:node]: (((((member @ node) @ N2) @ ((set2 @ node) @ (alpha_n @ G2))) => (~ ((((member @ val) @ A2) @ ((uses @ G2) @ N2))))))) => (~ ((! [V5:val]: (((((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ V5) => (~ ((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V5) @ A2))))))))))))).
% 2.76/1.56 thf(fact_27_allUses__finite, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((finite_finite2 @ val) @ ((((((((((sSA_CFG_SSA_allUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ uses) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_28_defNode_I1_J, axiom, (! [V:val,G2:g]: (((((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => (((member @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V)) @ ((set2 @ node) @ (alpha_n @ G2))))))).
% 2.76/1.56 thf(fact_29_uses__finite, axiom, (! [G2:g,N:node]: (((finite_finite2 @ val) @ ((uses @ G2) @ N))))).
% 2.76/1.56 thf(fact_30_eq, axiom, (((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_s) = ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ s))).
% 2.76/1.56 thf(fact_31_allUses__in__allVars, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ uses) @ phis) @ G2) @ N)) => ((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => (((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2))))))).
% 2.76/1.56 thf(fact_32_phiUses__in__allUses, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ N)) => (((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ uses) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_33_phiUses__finite, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((finite_finite2 @ val) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_34_defNode_I2_J, axiom, (! [V:val,G2:g]: (((((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V))))))).
% 2.76/1.56 thf(fact_35_defNode__ex1, axiom, (! [V:val,G2:g]: (((((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => (? [X3:node]: (((((member @ node) @ X3) @ ((set2 @ node) @ (alpha_n @ G2))) & ((((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ X3)) & (! [Y:node]: ((((((member @ node) @ Y) @ ((set2 @ node) @ (alpha_n @ G2))) & (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ Y))) => (Y = X3)))))))))))).
% 2.76/1.56 thf(fact_36_allVars__in__allDefs, axiom, (! [V:val,G2:g]: (((((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => (? [X3:node]: (((((member @ node) @ X3) @ ((set2 @ node) @ (alpha_n @ G2))) & (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ X3))))))))).
% 2.76/1.56 thf(fact_37_List_Ofinite__set, axiom, (! [A:$tType,Xs:(list @ A)]: (((finite_finite2 @ A) @ ((set2 @ A) @ Xs))))).
% 2.76/1.56 thf(fact_38_phiDefs__finite, axiom, (! [G2:g,N:node]: (((finite_finite2 @ val) @ ((((((sSA_CFG_SSA_phiDefs @ g) @ node) @ val) @ phis) @ G2) @ N))))).
% 2.76/1.56 thf(fact_39_allDefs__finite, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((finite_finite2 @ val) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_40_assms_I5_J, axiom, (((var2 @ g2) @ phi) = ((var2 @ g2) @ s))).
% 2.76/1.56 thf(fact_41_CFG__SSA__wf__base_Oredundant__def, axiom, (! [EdgeD:$tType,Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((sSA_CF462202545undant @ G) @ Node) @ EdgeD) @ Val) = (^ [Alpha_n:(G > (list @ Node)),InEdges:(G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))),Defs:(G > (Node > (set @ Val))),Uses:(G > (Node > (set @ Val))),Phis:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G3:G]: ((? [X:Val]: (((((member @ Val) @ X) @ ((((((((((sSA_CFG_SSA_allVars @ G) @ Node) @ EdgeD) @ Val) @ Alpha_n) @ InEdges) @ Defs) @ Uses) @ Phis) @ G3)) & (((((((((((sSA_CF1363434349rivial @ G) @ Node) @ EdgeD) @ Val) @ Alpha_n) @ InEdges) @ Defs) @ Uses) @ Phis) @ G3) @ X))))))))))).
% 2.76/1.56 thf(fact_42_defs__in__allDefs, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ ((defs @ G2) @ N)) => (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_43_phiDefs__in__allDefs, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ ((((((sSA_CFG_SSA_phiDefs @ g) @ node) @ val) @ phis) @ G2) @ N)) => (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_44_allDefs__disjoint_H, axiom, (! [N:node,G2:g,M:node,V:val]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ node) @ M) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)) => ((((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ M)) => (N = M)))))))).
% 2.76/1.56 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 2.76/1.56 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A3)))) = A3)))).
% 2.76/1.56 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q2:(A > $o)]: (((! [X3:A]: (((P2 @ X3) = (Q2 @ X3)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q2)))))).
% 2.76/1.56 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G2:(A > B)]: (((! [X3:A]: (((F @ X3) = (G2 @ X3)))) => (F = G2))))).
% 2.76/1.56 thf(fact_49_phiArg__same__var, axiom, (! [G2:g,P:val,Q:val]: (((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P) @ Q) => (((var2 @ G2) @ Q) = ((var2 @ G2) @ P)))))).
% 2.76/1.56 thf(fact_50_vars__eq, axiom, (((var2 @ g2) @ phi) = ((var2 @ g2) @ phi_s))).
% 2.76/1.56 thf(fact_51_allDefs__var__disjoint, axiom, (! [N:node,G2:g,V:val,V2:val]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)) => ((((member @ val) @ V2) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)) => ((V != V2) => (((var2 @ G2) @ V2) != ((var2 @ G2) @ V))))))))).
% 2.76/1.56 thf(fact_52_defNode__var__disjoint, axiom, (! [P:val,G2:g,Q:val]: (((((member @ val) @ P) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => ((((member @ val) @ Q) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => ((P != Q) => ((((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P) = ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ Q)) => (((var2 @ G2) @ P) != ((var2 @ G2) @ Q))))))))).
% 2.76/1.56 thf(fact_53_defNode__eq, axiom, (! [N:node,G2:g,V:val]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)) => (((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) = N)))))).
% 2.76/1.56 thf(fact_54_allDefs__in__allVars, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)) => ((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => (((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2))))))).
% 2.76/1.56 thf(fact_55_pruned__def, axiom, (! [G2:g]: ((((((((((sSA_CF823892918pruned @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) = (! [X:node]: (((((member @ node) @ X) @ ((set2 @ node) @ (alpha_n @ G2))) => (! [Val3:val]: (((((member @ val) @ Val3) @ ((((((sSA_CFG_SSA_phiDefs @ g) @ node) @ val) @ phis) @ G2) @ X)) => (((((((((sSA_CF722422777iveVal @ g) @ node) @ val) @ alpha_n) @ defs) @ uses) @ phis) @ G2) @ Val3))))))))))).
% 2.76/1.56 thf(fact_56_CFG__SSA__base_OphiUses_Ocong, axiom, (! [Val:$tType,EdgeD:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((sSA_CFG_SSA_phiUses @ G) @ Node) @ EdgeD) @ Val) = ((((sSA_CFG_SSA_phiUses @ G) @ Node) @ EdgeD) @ Val)))))).
% 2.76/1.56 thf(fact_57_CFG__SSA__base_OphiDefs_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CFG_SSA_phiDefs @ G) @ Node) @ Val) = (((sSA_CFG_SSA_phiDefs @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_58_CFG__SSA__base_OallDefs_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CFG_SSA_allDefs @ G) @ Node) @ Val) = (((sSA_CFG_SSA_allDefs @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_59_CFG__SSA__wf__base_OdefNode_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CF1081484811efNode @ G) @ Node) @ Val) = (((sSA_CF1081484811efNode @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_60_CFG__SSA__base_OallVars_Ocong, axiom, (! [Val:$tType,EdgeD:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((sSA_CFG_SSA_allVars @ G) @ Node) @ EdgeD) @ Val) = ((((sSA_CFG_SSA_allVars @ G) @ Node) @ EdgeD) @ Val)))))).
% 2.76/1.56 thf(fact_61_CFG__SSA__wf__base_OphiArg_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CF1165125185phiArg @ G) @ Node) @ Val) = (((sSA_CF1165125185phiArg @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_62_CFG__SSA__base_OallUses_Ocong, axiom, (! [Val:$tType,EdgeD:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((sSA_CFG_SSA_allUses @ G) @ Node) @ EdgeD) @ Val) = ((((sSA_CFG_SSA_allUses @ G) @ Node) @ EdgeD) @ Val)))))).
% 2.76/1.56 thf(fact_63_CFG__SSA__wf__base_OliveVal_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CF722422777iveVal @ G) @ Node) @ Val) = (((sSA_CF722422777iveVal @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_64_CFG__SSA__wf__base_Otrivial_Ocong, axiom, (! [Val:$tType,EdgeD:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((sSA_CF1363434349rivial @ G) @ Node) @ EdgeD) @ Val) = ((((sSA_CF1363434349rivial @ G) @ Node) @ EdgeD) @ Val)))))).
% 2.76/1.56 thf(fact_65_CFG__base_Ovars_Ocong, axiom, (! [Var:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Var)) => ((((sSA_CFG_vars @ G) @ Node) @ Var) = (((sSA_CFG_vars @ G) @ Node) @ Var)))))).
% 2.76/1.56 thf(fact_66_CFG__SSA__wf__base_OisTrivialPhi_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CF1297404942ialPhi @ G) @ Node) @ Val) = (((sSA_CF1297404942ialPhi @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_67_CFG__SSA__wf__base_Oredundant_Ocong, axiom, (! [Val:$tType,EdgeD:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((sSA_CF462202545undant @ G) @ Node) @ EdgeD) @ Val) = ((((sSA_CF462202545undant @ G) @ Node) @ EdgeD) @ Val)))))).
% 2.76/1.56 thf(fact_68_finite__list, axiom, (! [A:$tType,A3:(set @ A)]: ((((finite_finite2 @ A) @ A3) => (? [Xs2:(list @ A)]: ((((set2 @ A) @ Xs2) = A3))))))).
% 2.76/1.56 thf(fact_69_CFG__SSA__wf__base_OliveSimple, axiom, (! [G:$tType,Node:$tType,Val:$tType]: ((((linorder @ Val) & (linorder @ Node)) => (! [N:Node,Alpha_n2:(G > (list @ Node)),G2:G,Val2:Val,Uses2:(G > (Node > (set @ Val))),Defs2:(G > (Node > (set @ Val))),Phis2:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val))))]: (((((member @ Node) @ N) @ ((set2 @ Node) @ (Alpha_n2 @ G2))) => ((((member @ Val) @ Val2) @ ((Uses2 @ G2) @ N)) => (((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Uses2) @ Phis2) @ G2) @ Val2))))))))).
% 2.76/1.56 thf(fact_70_CFG__SSA__wf__base_OlivePhi, axiom, (! [G:$tType,Node:$tType,Val:$tType]: ((((linorder @ Val) & (linorder @ Node)) => (! [Alpha_n2:(G > (list @ Node)),Defs2:(G > (Node > (set @ Val))),Uses2:(G > (Node > (set @ Val))),Phis2:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G2:G,V:Val,V2:Val]: (((((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Uses2) @ Phis2) @ G2) @ V) => ((((((((((sSA_CF1165125185phiArg @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Phis2) @ G2) @ V) @ V2) => (((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Uses2) @ Phis2) @ G2) @ V2))))))))).
% 2.76/1.56 thf(fact_71_CFG__SSA__wf__base_OliveVal_Oinducts, axiom, (! [Node:$tType,G:$tType,Val:$tType]: ((((linorder @ Val) & (linorder @ Node)) => (! [Alpha_n2:(G > (list @ Node)),Defs2:(G > (Node > (set @ Val))),Uses2:(G > (Node > (set @ Val))),Phis2:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G2:G,X2:Val,P2:(Val > $o)]: (((((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Uses2) @ Phis2) @ G2) @ X2) => ((! [N2:Node,Val4:Val]: (((((member @ Node) @ N2) @ ((set2 @ Node) @ (Alpha_n2 @ G2))) => ((((member @ Val) @ Val4) @ ((Uses2 @ G2) @ N2)) => (P2 @ Val4))))) => ((! [V5:Val,V6:Val]: (((((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Uses2) @ Phis2) @ G2) @ V5) => ((P2 @ V5) => ((((((((((sSA_CF1165125185phiArg @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Phis2) @ G2) @ V5) @ V6) => (P2 @ V6)))))) => (P2 @ X2)))))))))).
% 2.76/1.56 thf(fact_72_CFG__SSA__wf__base_OliveVal_Osimps, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CF722422777iveVal @ G) @ Node) @ Val) = (^ [Alpha_n:(G > (list @ Node)),Defs:(G > (Node > (set @ Val))),Uses:(G > (Node > (set @ Val))),Phis:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G3:G,A4:Val]: (((? [N3:Node,Val3:Val]: (((A4 = Val3) & ((((member @ Node) @ N3) @ ((set2 @ Node) @ (Alpha_n @ G3))) & (((member @ Val) @ Val3) @ ((Uses @ G3) @ N3)))))) | (? [V3:Val,V4:Val]: (((A4 = V4) & ((((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n) @ Defs) @ Uses) @ Phis) @ G3) @ V3) & (((((((((sSA_CF1165125185phiArg @ G) @ Node) @ Val) @ Alpha_n) @ Defs) @ Phis) @ G3) @ V3) @ V4))))))))))))).
% 2.76/1.56 thf(fact_73_CFG__SSA__wf__base_OliveVal_Ocases, axiom, (! [Node:$tType,G:$tType,Val:$tType]: ((((linorder @ Val) & (linorder @ Node)) => (! [Alpha_n2:(G > (list @ Node)),Defs2:(G > (Node > (set @ Val))),Uses2:(G > (Node > (set @ Val))),Phis2:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G2:G,A2:Val]: (((((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Uses2) @ Phis2) @ G2) @ A2) => ((! [N2:Node]: (((((member @ Node) @ N2) @ ((set2 @ Node) @ (Alpha_n2 @ G2))) => (~ ((((member @ Val) @ A2) @ ((Uses2 @ G2) @ N2))))))) => (~ ((! [V5:Val]: (((((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Uses2) @ Phis2) @ G2) @ V5) => (~ ((((((((((sSA_CF1165125185phiArg @ G) @ Node) @ Val) @ Alpha_n2) @ Defs2) @ Phis2) @ G2) @ V5) @ A2)))))))))))))))).
% 2.76/1.56 thf(fact_74_CFG__SSA__wf__base_Otrivial__def, axiom, (! [EdgeD:$tType,Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((sSA_CF1363434349rivial @ G) @ Node) @ EdgeD) @ Val) = (^ [Alpha_n:(G > (list @ Node)),InEdges:(G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))),Defs:(G > (Node > (set @ Val))),Uses:(G > (Node > (set @ Val))),Phis:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G3:G,V3:Val]: ((? [X:Val]: (((((member @ Val) @ X) @ ((((((((((sSA_CFG_SSA_allVars @ G) @ Node) @ EdgeD) @ Val) @ Alpha_n) @ InEdges) @ Defs) @ Uses) @ Phis) @ G3)) & (((((((((sSA_CF1297404942ialPhi @ G) @ Node) @ Val) @ Alpha_n) @ Defs) @ Phis) @ G3) @ V3) @ X))))))))))).
% 2.76/1.56 thf(fact_75_condensation__finite, axiom, (! [G2:g,P2:(set @ val)]: (((finite_finite2 @ ((product_prod @ (set @ val)) @ (set @ val))) @ ((((((((irredu280805948_edges @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P2))))).
% 2.76/1.56 thf(fact_76_phiUses__exI_H, axiom, (! [G2:g,P:val,Q:val]: (((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P) @ Q) => ((((member @ val) @ P) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => (~ ((! [M2:node]: (((((member @ val) @ Q) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ M2)) => (~ ((((member @ node) @ M2) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P)))))))))))))))).
% 2.76/1.56 thf(fact_77_allUses__def, axiom, (! [G2:g,N:node]: ((((((((((((sSA_CFG_SSA_allUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ uses) @ phis) @ G2) @ N) = (((sup_sup @ (set @ val)) @ ((uses @ G2) @ N)) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_78_phiArg__trancl__same__var, axiom, (! [G2:g,Phi2:val,N:val]: ((((((transitive_tranclp @ val) @ (((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2)) @ Phi2) @ N) => (((var2 @ G2) @ Phi2) = ((var2 @ G2) @ N)))))).
% 2.76/1.56 thf(fact_79_allDefs__def, axiom, (! [G2:g,N:node]: (((((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N) = (((sup_sup @ (set @ val)) @ ((defs @ G2) @ N)) @ ((((((sSA_CFG_SSA_phiDefs @ g) @ node) @ val) @ phis) @ G2) @ N)))))).
% 2.76/1.56 thf(fact_80_CFG__SSA__wf__base_Opruned__def, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CF823892918pruned @ G) @ Node) @ Val) = (^ [Alpha_n:(G > (list @ Node)),Defs:(G > (Node > (set @ Val))),Uses:(G > (Node > (set @ Val))),Phis:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G3:G]: ((! [X:Node]: (((((member @ Node) @ X) @ ((set2 @ Node) @ (Alpha_n @ G3))) => (! [Val3:Val]: (((((member @ Val) @ Val3) @ ((((((sSA_CFG_SSA_phiDefs @ G) @ Node) @ Val) @ Phis) @ G3) @ X)) => (((((((((sSA_CF722422777iveVal @ G) @ Node) @ Val) @ Alpha_n) @ Defs) @ Uses) @ Phis) @ G3) @ Val3)))))))))))))).
% 2.76/1.56 thf(fact_81_finite__code, axiom, (! [A:$tType]: (((finite_finite @ A) => ((finite_finite2 @ A) = (^ [A5:(set @ A)]: ($true))))))).
% 2.76/1.56 thf(fact_82_defNode__cases, axiom, (! [V:val,G2:g]: (((((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => ((~ ((((member @ val) @ V) @ ((defs @ G2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V))))) => (((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) != (none @ (list @ val)))))))).
% 2.76/1.56 thf(fact_83_simpleDef__not__phi, axiom, (! [N:node,G2:g,V:val]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ val) @ V) @ ((defs @ G2) @ N)) => (((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) = (none @ (list @ val)))))))).
% 2.76/1.56 thf(fact_84_finite__Un, axiom, (! [A:$tType,F2:(set @ A),G4:(set @ A)]: ((((finite_finite2 @ A) @ (((sup_sup @ (set @ A)) @ F2) @ G4)) = (((finite_finite2 @ A) @ F2) & ((finite_finite2 @ A) @ G4)))))).
% 2.76/1.56 thf(fact_85_trivial__phi, axiom, (! [G2:g,V:val]: (((((((((((((sSA_CF1363434349rivial @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) @ V) => (((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) != (none @ (list @ val))))))).
% 2.76/1.56 thf(fact_86_phiArg__exI, axiom, (! [M:node,G2:g,V:val]: (((((member @ node) @ M) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V)))) => ((((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) != (none @ (list @ val))) => ((((member @ val) @ V) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => (~ ((! [V6:val]: (((((member @ val) @ V6) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ M)) => (~ ((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) @ V6)))))))))))))).
% 2.76/1.56 thf(fact_87_CFG__SSA__wf__base_Ophi_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CFG_SSA_wf_phi @ G) @ Node) @ Val) = (((sSA_CFG_SSA_wf_phi @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_88_infinite__Un, axiom, (! [A:$tType,S:(set @ A),T:(set @ A)]: (((~ (((finite_finite2 @ A) @ (((sup_sup @ (set @ A)) @ S) @ T)))) = ((~ (((finite_finite2 @ A) @ S))) | (~ (((finite_finite2 @ A) @ T)))))))).
% 2.76/1.56 thf(fact_89_Un__infinite, axiom, (! [A:$tType,S:(set @ A),T:(set @ A)]: (((~ (((finite_finite2 @ A) @ S))) => (~ (((finite_finite2 @ A) @ (((sup_sup @ (set @ A)) @ S) @ T)))))))).
% 2.76/1.56 thf(fact_90_finite__UnI, axiom, (! [A:$tType,F2:(set @ A),G4:(set @ A)]: ((((finite_finite2 @ A) @ F2) => (((finite_finite2 @ A) @ G4) => ((finite_finite2 @ A) @ (((sup_sup @ (set @ A)) @ F2) @ G4))))))).
% 2.76/1.56 thf(fact_91_CFG__SSA__Transformed_Ocondensation__edges_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((irredu280805948_edges @ G) @ Node) @ Val) = (((irredu280805948_edges @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_92_CFG__SSA__wf__base_Opruned_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CF823892918pruned @ G) @ Node) @ Val) = (((sSA_CF823892918pruned @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_93_CFG__SSA__base_OallDefs__def, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CFG_SSA_allDefs @ G) @ Node) @ Val) = (^ [Defs:(G > (Node > (set @ Val))),Phis:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G3:G,N3:Node]: ((((sup_sup @ (set @ Val)) @ ((Defs @ G3) @ N3)) @ ((((((sSA_CFG_SSA_phiDefs @ G) @ Node) @ Val) @ Phis) @ G3) @ N3))))))))).
% 2.76/1.56 thf(fact_94_CFG__SSA__base_OallUses__def, axiom, (! [EdgeD:$tType,Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((sSA_CFG_SSA_allUses @ G) @ Node) @ EdgeD) @ Val) = (^ [Alpha_n:(G > (list @ Node)),InEdges:(G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))),Uses:(G > (Node > (set @ Val))),Phis:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G3:G,N3:Node]: ((((sup_sup @ (set @ Val)) @ ((Uses @ G3) @ N3)) @ (((((((((sSA_CFG_SSA_phiUses @ G) @ Node) @ EdgeD) @ Val) @ Alpha_n) @ InEdges) @ Phis) @ G3) @ N3))))))))).
% 2.76/1.56 thf(fact_95_finite__set__choice, axiom, (! [B:$tType,A:$tType,A3:(set @ A),P2:(A > (B > $o))]: ((((finite_finite2 @ A) @ A3) => ((! [X3:A]: (((((member @ A) @ X3) @ A3) => (? [X_1:B]: (((P2 @ X3) @ X_1)))))) => (? [F3:(A > B)]: ((! [X4:A]: (((((member @ A) @ X4) @ A3) => ((P2 @ X4) @ (F3 @ X4)))))))))))).
% 2.76/1.56 thf(fact_96_finite, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A3:(set @ A)]: (((finite_finite2 @ A) @ A3))))))).
% 2.76/1.56 thf(fact_97_phi__phiDefs, axiom, (! [G2:g,V:val,Vs:(list @ val)]: (((((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) = ((some @ (list @ val)) @ Vs)) => (((member @ val) @ V) @ ((((((sSA_CFG_SSA_phiDefs @ g) @ node) @ val) @ phis) @ G2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V))))))).
% 2.76/1.56 thf(fact_98_condensation__acyclic, axiom, (! [G2:g,P2:(set @ val)]: (((transitive_acyclic @ (set @ val)) @ ((((((((irredu280805948_edges @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P2))))).
% 2.76/1.56 thf(fact_99_phi__def, axiom, (! [G2:g,V:val]: ((((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) = ((phis @ G2) @ ((((product_Pair @ node) @ val) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V)) @ V)))))).
% 2.76/1.56 thf(fact_100_phiArg__def, axiom, (! [G2:g,V:val,V2:val]: (((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) @ V2) = (? [Vs2:(list @ val)]: (((((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) = ((some @ (list @ val)) @ Vs2)) & (((member @ val) @ V2) @ ((set2 @ val) @ Vs2))))))))).
% 2.76/1.56 thf(fact_101_phi__finite, axiom, (! [G2:g]: (((finite_finite2 @ val) @ (((dom @ val) @ (list @ val)) @ (((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2)))))).
% 2.76/1.56 thf(fact_102_redundant__scc__phis, axiom, (! [G2:g,P2:(set @ val),Scc:(set @ val),X2:val]: (((((((((((((irredu2110905762nt_set @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) @ P2) => ((((member @ (set @ val)) @ Scc) @ ((((((((irredu1918690039_nodes @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P2)) => ((((member @ val) @ X2) @ Scc) => (((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ X2) != (none @ (list @ val))))))))).
% 2.76/1.56 thf(fact_103_phis__disj_I2_J, axiom, (! [G2:g,N:node,V:val,Vs:(list @ val),N4:node,Vs3:(list @ val)]: (((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N) @ V)) = ((some @ (list @ val)) @ Vs)) => ((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N4) @ V)) = ((some @ (list @ val)) @ Vs3)) => (Vs = Vs3)))))).
% 2.76/1.56 thf(fact_104_phis__disj_I1_J, axiom, (! [G2:g,N:node,V:val,Vs:(list @ val),N4:node,Vs3:(list @ val)]: (((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N) @ V)) = ((some @ (list @ val)) @ Vs)) => ((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N4) @ V)) = ((some @ (list @ val)) @ Vs3)) => (N = N4)))))).
% 2.76/1.56 thf(fact_105_phis__in___092_060alpha_062n, axiom, (! [G2:g,N:node,V:val,Vs:(list @ val)]: (((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N) @ V)) = ((some @ (list @ val)) @ Vs)) => (((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))))))).
% 2.76/1.56 thf(fact_106_phis__same__var, axiom, (! [G2:g,N:node,V:val,Vs:(list @ val),V2:val]: (((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N) @ V)) = ((some @ (list @ val)) @ Vs)) => ((((member @ val) @ V2) @ ((set2 @ val) @ Vs)) => (((var2 @ G2) @ V2) = ((var2 @ G2) @ V))))))).
% 2.76/1.56 thf(fact_107_phis__phi, axiom, (! [G2:g,N:node,V:val,Vs:(list @ val)]: (((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N) @ V)) = ((some @ (list @ val)) @ Vs)) => (((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ V) = ((some @ (list @ val)) @ Vs)))))).
% 2.76/1.56 thf(fact_108_phiUses__exI, axiom, (! [M:node,G2:g,N:node,V:val,Vs:(list @ val)]: (((((member @ node) @ M) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N))) => ((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N) @ V)) = ((some @ (list @ val)) @ Vs)) => ((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => (~ ((! [V6:val]: (((((member @ val) @ V6) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ M)) => (~ ((((member @ val) @ V6) @ ((set2 @ val) @ Vs))))))))))))))).
% 2.76/1.56 thf(fact_109_CFG__SSA__Transformed_Ocondensation__nodes_Ocong, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((irredu1918690039_nodes @ G) @ Node) @ Val) = (((irredu1918690039_nodes @ G) @ Node) @ Val)))))).
% 2.76/1.56 thf(fact_110_CFG__SSA__Transformed_Oredundant__set_Ocong, axiom, (! [Val:$tType,EdgeD:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((irredu2110905762nt_set @ G) @ Node) @ EdgeD) @ Val) = ((((irredu2110905762nt_set @ G) @ Node) @ EdgeD) @ Val)))))).
% 2.76/1.56 thf(fact_111_CFG__SSA__wf__base_Ophi__def, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CFG_SSA_wf_phi @ G) @ Node) @ Val) = (^ [Alpha_n:(G > (list @ Node)),Defs:(G > (Node > (set @ Val))),Phis:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G3:G,V3:Val]: (((Phis @ G3) @ ((((product_Pair @ Node) @ Val) @ ((((((((sSA_CF1081484811efNode @ G) @ Node) @ Val) @ Alpha_n) @ Defs) @ Phis) @ G3) @ V3)) @ V3))))))))).
% 2.76/1.56 thf(fact_112_CFG__SSA__wf__base_OphiArg__def, axiom, (! [Val:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => ((((sSA_CF1165125185phiArg @ G) @ Node) @ Val) = (^ [Alpha_n:(G > (list @ Node)),Defs:(G > (Node > (set @ Val))),Phis:(G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))),G3:G,V3:Val,V4:Val]: ((? [Vs2:(list @ Val)]: (((((((((((sSA_CFG_SSA_wf_phi @ G) @ Node) @ Val) @ Alpha_n) @ Defs) @ Phis) @ G3) @ V3) = ((some @ (list @ Val)) @ Vs2)) & (((member @ Val) @ V4) @ ((set2 @ Val) @ Vs2)))))))))))).
% 2.76/1.56 thf(fact_113_phiUsesI, axiom, (! [N4:node,G2:g,V2:val,Vs:(list @ val),N:node,V:val]: (((((member @ node) @ N4) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((phis @ G2) @ ((((product_Pair @ node) @ val) @ N4) @ V2)) = ((some @ (list @ val)) @ Vs)) => ((((member @ ((product_prod @ node) @ val)) @ ((((product_Pair @ node) @ val) @ N) @ V)) @ ((set2 @ ((product_prod @ node) @ val)) @ ((((zip @ node) @ val) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N4)) @ Vs))) => (((member @ val) @ V) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ N)))))))).
% 2.76/1.56 thf(fact_114_scc__in__P, axiom, (! [Scc:(set @ val),G2:g,P2:(set @ val)]: (((((member @ (set @ val)) @ Scc) @ ((((((((irredu1918690039_nodes @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P2)) => (((ord_less_eq @ (set @ val)) @ Scc) @ P2))))).
% 2.76/1.56 thf(fact_115_not__None__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((X2 != (none @ A)) = (? [Y2:A]: ((X2 = ((some @ A) @ Y2)))))))).
% 2.76/1.56 thf(fact_116_not__Some__eq, axiom, (! [A:$tType,X2:(option @ A)]: (((! [Y2:A]: ((X2 != ((some @ A) @ Y2)))) = (X2 = (none @ A)))))).
% 2.76/1.56 thf(fact_117_sup__Some, axiom, (! [A:$tType]: (((sup @ A) => (! [X2:A,Y3:A]: (((((sup_sup @ (option @ A)) @ ((some @ A) @ X2)) @ ((some @ A) @ Y3)) = ((some @ A) @ (((sup_sup @ A) @ X2) @ Y3))))))))).
% 2.76/1.56 thf(fact_118_option_Oinject, axiom, (! [A:$tType,X22:A,Y22:A]: (((((some @ A) @ X22) = ((some @ A) @ Y22)) = (X22 = Y22))))).
% 2.76/1.56 thf(fact_119_less__eq__option__Some, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y3:A]: (((((ord_less_eq @ (option @ A)) @ ((some @ A) @ X2)) @ ((some @ A) @ Y3)) = (((ord_less_eq @ A) @ X2) @ Y3)))))))).
% 2.76/1.56 thf(fact_120_sup__None__1, axiom, (! [A:$tType]: (((sup @ A) => (! [Y3:(option @ A)]: (((((sup_sup @ (option @ A)) @ (none @ A)) @ Y3) = Y3))))))).
% 2.76/1.56 thf(fact_121_sup__None__2, axiom, (! [A:$tType]: (((sup @ A) => (! [X2:(option @ A)]: (((((sup_sup @ (option @ A)) @ X2) @ (none @ A)) = X2))))))).
% 2.76/1.56 thf(fact_122_zip__same, axiom, (! [A:$tType,A2:A,B2:A,Xs:(list @ A)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ ((set2 @ ((product_prod @ A) @ A)) @ ((((zip @ A) @ A) @ Xs) @ Xs))) = ((((member @ A) @ A2) @ ((set2 @ A) @ Xs)) & (A2 = B2)))))).
% 2.76/1.56 thf(fact_123__C1_C, axiom, (! [G2:g,P2:(set @ val)]: (((((((((((((irredu2110905762nt_set @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) @ P2) => (? [Scc2:(set @ val)]: (((((ord_less_eq @ (set @ val)) @ Scc2) @ P2) & ((((((((((((irredu2110774547nt_scc @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) @ P2) @ Scc2)))))))).
% 2.76/1.56 thf(fact_124_phiUsesE, axiom, (! [V:val,G2:g,N:node]: (((((member @ val) @ V) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ N)) => (~ ((! [N5:node]: (((((member @ node) @ N5) @ ((set2 @ node) @ (((((((graph_449533722essors @ g) @ node) @ edgeD) @ alpha_n) @ inEdges) @ G2) @ N))) => (! [V6:val,Vs4:(list @ val)]: (((((member @ ((product_prod @ node) @ val)) @ ((((product_Pair @ node) @ val) @ N) @ V)) @ ((set2 @ ((product_prod @ node) @ val)) @ ((((zip @ node) @ val) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N5)) @ Vs4))) => (((phis @ G2) @ ((((product_Pair @ node) @ val) @ N5) @ V6)) != ((some @ (list @ val)) @ Vs4)))))))))))))).
% 2.76/1.56 thf(fact_125_finite__has__minimal2, axiom, (! [A:$tType]: (((order @ A) => (! [A3:(set @ A),A2:A]: ((((finite_finite2 @ A) @ A3) => ((((member @ A) @ A2) @ A3) => (? [X3:A]: (((((member @ A) @ X3) @ A3) & ((((ord_less_eq @ A) @ X3) @ A2) & (! [Xa:A]: (((((member @ A) @ Xa) @ A3) => ((((ord_less_eq @ A) @ Xa) @ X3) => (X3 = Xa))))))))))))))))).
% 2.76/1.56 thf(fact_126_finite__has__maximal2, axiom, (! [A:$tType]: (((order @ A) => (! [A3:(set @ A),A2:A]: ((((finite_finite2 @ A) @ A3) => ((((member @ A) @ A2) @ A3) => (? [X3:A]: (((((member @ A) @ X3) @ A3) & ((((ord_less_eq @ A) @ A2) @ X3) & (! [Xa:A]: (((((member @ A) @ Xa) @ A3) => ((((ord_less_eq @ A) @ X3) @ Xa) => (X3 = Xa))))))))))))))))).
% 2.76/1.56 thf(fact_127_subset__code_I1_J, axiom, (! [A:$tType,Xs:(list @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ B3) = (! [X:A]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (((member @ A) @ X) @ B3)))))))).
% 2.76/1.56 thf(fact_128_rev__finite__subset, axiom, (! [A:$tType,B3:(set @ A),A3:(set @ A)]: ((((finite_finite2 @ A) @ B3) => ((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((finite_finite2 @ A) @ A3)))))).
% 2.76/1.56 thf(fact_129_infinite__super, axiom, (! [A:$tType,S:(set @ A),T:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ S) @ T) => ((~ (((finite_finite2 @ A) @ S))) => (~ (((finite_finite2 @ A) @ T)))))))).
% 2.76/1.56 thf(fact_130_finite__subset, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => (((finite_finite2 @ A) @ B3) => ((finite_finite2 @ A) @ A3)))))).
% 2.76/1.56 thf(fact_131_in__set__zipE, axiom, (! [A:$tType,B:$tType,X2:A,Y3:B,Xs:(list @ A),Ys:(list @ B)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ ((set2 @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs) @ Ys))) => (~ (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => (~ ((((member @ B) @ Y3) @ ((set2 @ B) @ Ys))))))))))).
% 2.76/1.56 thf(fact_132_set__zip__leftD, axiom, (! [B:$tType,A:$tType,X2:A,Y3:B,Xs:(list @ A),Ys:(list @ B)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ ((set2 @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs) @ Ys))) => (((member @ A) @ X2) @ ((set2 @ A) @ Xs)))))).
% 2.76/1.56 thf(fact_133_set__zip__rightD, axiom, (! [A:$tType,B:$tType,X2:A,Y3:B,Xs:(list @ A),Ys:(list @ B)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ ((set2 @ ((product_prod @ A) @ B)) @ ((((zip @ A) @ B) @ Xs) @ Ys))) => (((member @ B) @ Y3) @ ((set2 @ B) @ Ys)))))).
% 2.76/1.56 thf(fact_134_combine__options__cases, axiom, (! [A:$tType,B:$tType,X2:(option @ A),P2:((option @ A) > ((option @ B) > $o)),Y3:(option @ B)]: ((((X2 = (none @ A)) => ((P2 @ X2) @ Y3)) => (((Y3 = (none @ B)) => ((P2 @ X2) @ Y3)) => ((! [A6:A,B4:B]: (((X2 = ((some @ A) @ A6)) => ((Y3 = ((some @ B) @ B4)) => ((P2 @ X2) @ Y3))))) => ((P2 @ X2) @ Y3))))))).
% 2.76/1.56 thf(fact_135_split__option__all, axiom, (! [A:$tType]: (((^ [P3:((option @ A) > $o)]: ((! [X5:(option @ A)]: ((P3 @ X5))))) = (^ [P4:((option @ A) > $o)]: (((P4 @ (none @ A)) & (! [X:A]: ((P4 @ ((some @ A) @ X))))))))))).
% 2.76/1.56 thf(fact_136_split__option__ex, axiom, (! [A:$tType]: (((^ [P3:((option @ A) > $o)]: ((? [X5:(option @ A)]: ((P3 @ X5))))) = (^ [P4:((option @ A) > $o)]: (((P4 @ (none @ A)) | (? [X:A]: ((P4 @ ((some @ A) @ X))))))))))).
% 2.76/1.56 thf(fact_137_option_Oinducts, axiom, (! [A:$tType,P2:((option @ A) > $o),Option:(option @ A)]: (((P2 @ (none @ A)) => ((! [X3:A]: ((P2 @ ((some @ A) @ X3)))) => (P2 @ Option)))))).
% 2.76/1.56 thf(fact_138_option_Oexhaust, axiom, (! [A:$tType,Y3:(option @ A)]: (((Y3 != (none @ A)) => (~ ((! [X23:A]: ((Y3 != ((some @ A) @ X23)))))))))).
% 2.76/1.56 thf(fact_139_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X22:A]: (((Option = ((some @ A) @ X22)) => (Option != (none @ A)))))).
% 2.76/1.56 thf(fact_140_option_Odistinct_I1_J, axiom, (! [A:$tType,X22:A]: (((none @ A) != ((some @ A) @ X22))))).
% 2.76/1.56 thf(fact_141_Ex__condensation__leaf, axiom, (! [P2:(set @ val),G2:g]: (((P2 != (bot_bot @ (set @ val))) => (? [Leaf:(set @ val)]: (((((member @ (set @ val)) @ Leaf) @ ((((((((irredu1918690039_nodes @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P2)) & (! [Scc3:(set @ val)]: ((~ ((((member @ ((product_prod @ (set @ val)) @ (set @ val))) @ ((((product_Pair @ (set @ val)) @ (set @ val)) @ Leaf) @ Scc3)) @ ((((((((irredu280805948_edges @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P2))))))))))))).
% 2.76/1.56 thf(fact_142_Un__subset__iff, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) @ C) = ((((ord_less_eq @ (set @ A)) @ A3) @ C) & (((ord_less_eq @ (set @ A)) @ B3) @ C)))))).
% 2.76/1.56 thf(fact_143_le__sup__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y3:A,Z:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X2) @ Y3)) @ Z) = ((((ord_less_eq @ A) @ X2) @ Z) & (((ord_less_eq @ A) @ Y3) @ Z))))))))).
% 2.76/1.56 thf(fact_144_sup_Obounded__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,C2:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C2)) @ A2) = ((((ord_less_eq @ A) @ B2) @ A2) & (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.76/1.56 thf(fact_145_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ A3) => (A3 = B3)))))).
% 2.76/1.56 thf(fact_146_subsetI, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A3) => (((member @ A) @ X3) @ B3)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B3))))).
% 2.76/1.56 thf(fact_147_sup_Oright__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ B2) = (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.76/1.56 thf(fact_148_sup__left__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y3:A]: (((((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ X2) @ Y3)) = (((sup_sup @ A) @ X2) @ Y3)))))))).
% 2.76/1.56 thf(fact_149_sup_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: (((((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B2)) = (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.76/1.56 thf(fact_150_sup__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A]: (((((sup_sup @ A) @ X2) @ X2) = X2))))))).
% 2.76/1.56 thf(fact_151_sup_Oidem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ A2) = A2))))))).
% 2.76/1.56 thf(fact_152_sup__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F4:(A > B),G3:(A > B),X:A]: ((((sup_sup @ B) @ (F4 @ X)) @ (G3 @ X))))))))).
% 2.76/1.56 thf(fact_153_Un__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) = ((((member @ A) @ C2) @ A3) | (((member @ A) @ C2) @ B3)))))).
% 2.76/1.56 thf(fact_154_UnCI, axiom, (! [A:$tType,C2:A,B3:(set @ A),A3:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B3))) => (((member @ A) @ C2) @ A3)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B3)))))).
% 2.76/1.56 thf(fact_155_subset__empty, axiom, (! [A:$tType,A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = (A3 = (bot_bot @ (set @ A))))))).
% 2.76/1.56 thf(fact_156_empty__subsetI, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A3)))).
% 2.76/1.56 thf(fact_157_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X2) = X2))))))).
% 2.76/1.56 thf(fact_158_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X2:A]: (((((sup_sup @ A) @ X2) @ (bot_bot @ A)) = X2))))))).
% 2.76/1.56 thf(fact_159_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X2:A,Y3:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X2) @ Y3)) = ((X2 = (bot_bot @ A)) & (Y3 = (bot_bot @ A)))))))))).
% 2.76/1.56 thf(fact_160_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X2:A,Y3:A]: ((((((sup_sup @ A) @ X2) @ Y3) = (bot_bot @ A)) = ((X2 = (bot_bot @ A)) & (Y3 = (bot_bot @ A)))))))))).
% 2.76/1.56 thf(fact_161_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B2:A]: ((((((sup_sup @ A) @ A2) @ B2) = (bot_bot @ A)) = ((A2 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 2.76/1.56 thf(fact_162_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A2) = A2))))))).
% 2.76/1.56 thf(fact_163_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B2:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A2) @ B2)) = ((A2 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 2.76/1.56 thf(fact_164_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ (bot_bot @ A)) = A2))))))).
% 2.76/1.56 thf(fact_165_Un__empty, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A3) @ B3) = (bot_bot @ (set @ A))) = ((A3 = (bot_bot @ (set @ A))) & (B3 = (bot_bot @ (set @ A)))))))).
% 2.76/1.56 thf(fact_166_less__eq__option__None__code, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:(option @ A)]: ((((ord_less_eq @ (option @ A)) @ (none @ A)) @ X2))))))).
% 2.76/1.56 thf(fact_167_less__eq__option__Some__None, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((~ ((((ord_less_eq @ (option @ A)) @ ((some @ A) @ X2)) @ (none @ A)))))))))).
% 2.76/1.56 thf(fact_168_old_Osuccessors__predecessors, axiom, (! [N:node,G2:g,M:node]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((member @ node) @ N) @ ((set2 @ node) @ (((((((graph_449533722essors @ g) @ node) @ edgeD) @ alpha_n) @ inEdges) @ G2) @ M))) = (((member @ node) @ M) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N)))))))).
% 2.76/1.56 thf(fact_169_Un__empty__left, axiom, (! [A:$tType,B3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B3) = B3)))).
% 2.76/1.56 thf(fact_170_Un__empty__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = A3)))).
% 2.76/1.56 thf(fact_171_less__eq__option__None__is__None, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:(option @ A)]: (((((ord_less_eq @ (option @ A)) @ X2) @ (none @ A)) => (X2 = (none @ A))))))))).
% 2.76/1.56 thf(fact_172_less__eq__option__None, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:(option @ A)]: ((((ord_less_eq @ (option @ A)) @ (none @ A)) @ X2))))))).
% 2.76/1.56 thf(fact_173_infinite__imp__nonempty, axiom, (! [A:$tType,S:(set @ A)]: (((~ (((finite_finite2 @ A) @ S))) => (S != (bot_bot @ (set @ A))))))).
% 2.76/1.56 thf(fact_174_finite_OemptyI, axiom, (! [A:$tType]: (((finite_finite2 @ A) @ (bot_bot @ (set @ A)))))).
% 2.76/1.56 thf(fact_175_CFG__SSA__Transformed_Oredundant__scc_Ocong, axiom, (! [Val:$tType,EdgeD:$tType,Node:$tType,G:$tType]: ((((linorder @ Node) & (linorder @ Val)) => (((((irredu2110774547nt_scc @ G) @ Node) @ EdgeD) @ Val) = ((((irredu2110774547nt_scc @ G) @ Node) @ EdgeD) @ Val)))))).
% 2.76/1.56 thf(fact_176_finite__has__maximal, axiom, (! [A:$tType]: (((order @ A) => (! [A3:(set @ A)]: ((((finite_finite2 @ A) @ A3) => ((A3 != (bot_bot @ (set @ A))) => (? [X3:A]: (((((member @ A) @ X3) @ A3) & (! [Xa:A]: (((((member @ A) @ Xa) @ A3) => ((((ord_less_eq @ A) @ X3) @ Xa) => (X3 = Xa)))))))))))))))).
% 2.76/1.56 thf(fact_177_finite__has__minimal, axiom, (! [A:$tType]: (((order @ A) => (! [A3:(set @ A)]: ((((finite_finite2 @ A) @ A3) => ((A3 != (bot_bot @ (set @ A))) => (? [X3:A]: (((((member @ A) @ X3) @ A3) & (! [Xa:A]: (((((member @ A) @ Xa) @ A3) => ((((ord_less_eq @ A) @ Xa) @ X3) => (X3 = Xa)))))))))))))))).
% 2.76/1.56 thf(fact_178_Collect__mono__iff, axiom, (! [A:$tType,P2:(A > $o),Q2:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q2)) = (! [X:A]: (((P2 @ X) => (Q2 @ X)))))))).
% 2.76/1.56 thf(fact_179_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z2:(set @ A)]: ((Y4 = Z2))) = (^ [A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A5)))))))).
% 2.76/1.56 thf(fact_180_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ C) => (((ord_less_eq @ (set @ A)) @ A3) @ C)))))).
% 2.76/1.56 thf(fact_181_Collect__mono, axiom, (! [A:$tType,P2:(A > $o),Q2:(A > $o)]: (((! [X3:A]: (((P2 @ X3) => (Q2 @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P2)) @ ((collect @ A) @ Q2)))))).
% 2.76/1.56 thf(fact_182_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 2.76/1.56 thf(fact_183_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A5) => (((member @ A) @ T2) @ B5)))))))))).
% 2.76/1.56 thf(fact_184_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (((ord_less_eq @ (set @ A)) @ B3) @ A3))))).
% 2.76/1.56 thf(fact_185_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (((ord_less_eq @ (set @ A)) @ A3) @ B3))))).
% 2.76/1.56 thf(fact_186_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ A5) => (((member @ A) @ X) @ B5)))))))))).
% 2.76/1.56 thf(fact_187_equalityE, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((A3 = B3) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => (~ ((((ord_less_eq @ (set @ A)) @ B3) @ A3)))))))))).
% 2.76/1.56 thf(fact_188_subsetD, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B3)))))).
% 2.76/1.56 thf(fact_189_in__mono, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((member @ A) @ X2) @ A3) => (((member @ A) @ X2) @ B3)))))).
% 2.76/1.56 thf(fact_190_sup__left__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y3:A,Z:A]: (((((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ Y3) @ Z)) = (((sup_sup @ A) @ Y3) @ (((sup_sup @ A) @ X2) @ Z))))))))).
% 2.76/1.56 thf(fact_191_sup_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A,C2:A]: (((((sup_sup @ A) @ B2) @ (((sup_sup @ A) @ A2) @ C2)) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B2) @ C2))))))))).
% 2.76/1.56 thf(fact_192_sup__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [X:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X)))))))).
% 2.76/1.56 thf(fact_193_sup_Ocommute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [A4:A,B6:A]: ((((sup_sup @ A) @ B6) @ A4)))))))).
% 2.76/1.56 thf(fact_194_sup__assoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y3:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X2) @ Y3)) @ Z) = (((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ Y3) @ Z))))))))).
% 2.76/1.56 thf(fact_195_sup_Oassoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ C2) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B2) @ C2))))))))).
% 2.76/1.56 thf(fact_196_boolean__algebra__cancel_Osup2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,K:A,B2:A,A2:A]: (((B3 = (((sup_sup @ A) @ K) @ B2)) => ((((sup_sup @ A) @ A2) @ B3) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A2) @ B2)))))))))).
% 2.76/1.56 thf(fact_197_boolean__algebra__cancel_Osup1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,K:A,A2:A,B2:A]: (((A3 = (((sup_sup @ A) @ K) @ A2)) => ((((sup_sup @ A) @ A3) @ B2) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A2) @ B2)))))))))).
% 2.76/1.56 thf(fact_198_sup__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F4:(A > B),G3:(A > B),X:A]: ((((sup_sup @ B) @ (F4 @ X)) @ (G3 @ X))))))))).
% 2.76/1.56 thf(fact_199_inf__sup__aci_I5_J, axiom, (! [A:$tType]: (((lattice @ A) => ((sup_sup @ A) = (^ [X:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X)))))))).
% 2.76/1.56 thf(fact_200_inf__sup__aci_I6_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y3:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X2) @ Y3)) @ Z) = (((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ Y3) @ Z))))))))).
% 2.76/1.56 thf(fact_201_inf__sup__aci_I7_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y3:A,Z:A]: (((((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ Y3) @ Z)) = (((sup_sup @ A) @ Y3) @ (((sup_sup @ A) @ X2) @ Z))))))))).
% 2.76/1.56 thf(fact_202_inf__sup__aci_I8_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y3:A]: (((((sup_sup @ A) @ X2) @ (((sup_sup @ A) @ X2) @ Y3)) = (((sup_sup @ A) @ X2) @ Y3)))))))).
% 2.76/1.56 thf(fact_203_Un__left__commute, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B3) @ C)) = (((sup_sup @ (set @ A)) @ B3) @ (((sup_sup @ (set @ A)) @ A3) @ C)))))).
% 2.76/1.56 thf(fact_204_Un__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) = (((sup_sup @ (set @ A)) @ A3) @ B3))))).
% 2.76/1.56 thf(fact_205_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A5))))))).
% 2.76/1.56 thf(fact_206_Un__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ A3) = A3)))).
% 2.76/1.56 thf(fact_207_Un__assoc, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),C:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) @ C) = (((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B3) @ C)))))).
% 2.76/1.56 thf(fact_208_ball__Un, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),P2:(A > $o)]: (((! [X:A]: (((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) => (P2 @ X)))) = ((! [X:A]: (((((member @ A) @ X) @ A3) => (P2 @ X)))) & (! [X:A]: (((((member @ A) @ X) @ B3) => (P2 @ X))))))))).
% 2.76/1.56 thf(fact_209_bex__Un, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A),P2:(A > $o)]: (((? [X:A]: (((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) & (P2 @ X)))) = ((? [X:A]: (((((member @ A) @ X) @ A3) & (P2 @ X)))) | (? [X:A]: (((((member @ A) @ X) @ B3) & (P2 @ X))))))))).
% 2.76/1.56 thf(fact_210_UnI2, axiom, (! [A:$tType,C2:A,B3:(set @ A),A3:(set @ A)]: (((((member @ A) @ C2) @ B3) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B3)))))).
% 2.76/1.56 thf(fact_211_UnI1, axiom, (! [A:$tType,C2:A,A3:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B3)))))).
% 2.76/1.56 thf(fact_212_UnE, axiom, (! [A:$tType,C2:A,A3:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) => ((~ ((((member @ A) @ C2) @ A3))) => (((member @ A) @ C2) @ B3)))))).
% 2.76/1.56 thf(fact_213_sup_OcoboundedI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.76/1.56 thf(fact_214_sup_OcoboundedI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ C2) @ A2) => (((ord_less_eq @ A) @ C2) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.76/1.56 thf(fact_215_sup_Oabsorb__iff2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [A4:A,B6:A]: (((((sup_sup @ A) @ A4) @ B6) = B6)))))))).
% 2.76/1.56 thf(fact_216_sup_Oabsorb__iff1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B6:A,A4:A]: (((((sup_sup @ A) @ A4) @ B6) = A4)))))))).
% 2.76/1.56 thf(fact_217_sup_Ocobounded2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A]: ((((ord_less_eq @ A) @ B2) @ (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.76/1.56 thf(fact_218_sup_Ocobounded1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.76/1.56 thf(fact_219_sup_Oorder__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [B6:A,A4:A]: ((A4 = (((sup_sup @ A) @ A4) @ B6))))))))).
% 2.76/1.56 thf(fact_220_sup_OboundedI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ A2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C2)) @ A2))))))))).
% 2.76/1.56 thf(fact_221_sup_OboundedE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,C2:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C2)) @ A2) => (~ (((((ord_less_eq @ A) @ B2) @ A2) => (~ ((((ord_less_eq @ A) @ C2) @ A2))))))))))))).
% 2.76/1.56 thf(fact_222_sup__absorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => ((((sup_sup @ A) @ X2) @ Y3) = Y3)))))))).
% 2.76/1.56 thf(fact_223_sup__absorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y3:A,X2:A]: (((((ord_less_eq @ A) @ Y3) @ X2) => ((((sup_sup @ A) @ X2) @ Y3) = X2)))))))).
% 2.76/1.56 thf(fact_224_sup_Oabsorb2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((sup_sup @ A) @ A2) @ B2) = B2)))))))).
% 2.76/1.56 thf(fact_225_sup_Oabsorb1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((sup_sup @ A) @ A2) @ B2) = A2)))))))).
% 2.76/1.56 thf(fact_226_sup__unique, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [F:(A > (A > A)),X2:A,Y3:A]: (((! [X3:A,Y5:A]: ((((ord_less_eq @ A) @ X3) @ ((F @ X3) @ Y5)))) => ((! [X3:A,Y5:A]: ((((ord_less_eq @ A) @ Y5) @ ((F @ X3) @ Y5)))) => ((! [X3:A,Y5:A,Z3:A]: (((((ord_less_eq @ A) @ Y5) @ X3) => ((((ord_less_eq @ A) @ Z3) @ X3) => (((ord_less_eq @ A) @ ((F @ Y5) @ Z3)) @ X3))))) => ((((sup_sup @ A) @ X2) @ Y3) = ((F @ X2) @ Y3))))))))))).
% 2.76/1.56 thf(fact_227_sup_OorderI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A]: (((A2 = (((sup_sup @ A) @ A2) @ B2)) => (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 2.76/1.56 thf(fact_228_sup_OorderE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => (A2 = (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.76/1.56 thf(fact_229_le__iff__sup, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less_eq @ A) = (^ [X:A,Y2:A]: (((((sup_sup @ A) @ X) @ Y2) = Y2)))))))).
% 2.76/1.56 thf(fact_230_sup__least, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y3:A,X2:A,Z:A]: (((((ord_less_eq @ A) @ Y3) @ X2) => ((((ord_less_eq @ A) @ Z) @ X2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ Y3) @ Z)) @ X2))))))))).
% 2.76/1.56 thf(fact_231_sup__mono, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,C2:A,B2:A,D:A]: (((((ord_less_eq @ A) @ A2) @ C2) => ((((ord_less_eq @ A) @ B2) @ D) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ (((sup_sup @ A) @ C2) @ D)))))))))).
% 2.76/1.56 thf(fact_232_sup_Omono, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,A2:A,D:A,B2:A]: (((((ord_less_eq @ A) @ C2) @ A2) => ((((ord_less_eq @ A) @ D) @ B2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ C2) @ D)) @ (((sup_sup @ A) @ A2) @ B2)))))))))).
% 2.76/1.56 thf(fact_233_le__supI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ X2) @ B2) => (((ord_less_eq @ A) @ X2) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.76/1.56 thf(fact_234_le__supI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ X2) @ A2) => (((ord_less_eq @ A) @ X2) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.76/1.56 thf(fact_235_sup__ge2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [Y3:A,X2:A]: ((((ord_less_eq @ A) @ Y3) @ (((sup_sup @ A) @ X2) @ Y3)))))))).
% 2.76/1.56 thf(fact_236_sup__ge1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X2:A,Y3:A]: ((((ord_less_eq @ A) @ X2) @ (((sup_sup @ A) @ X2) @ Y3)))))))).
% 2.76/1.56 thf(fact_237_le__supI, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,X2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ X2) => ((((ord_less_eq @ A) @ B2) @ X2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ X2))))))))).
% 2.76/1.56 thf(fact_238_le__supE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A2:A,B2:A,X2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ X2) => (~ (((((ord_less_eq @ A) @ A2) @ X2) => (~ ((((ord_less_eq @ A) @ B2) @ X2))))))))))))).
% 2.76/1.56 thf(fact_239_inf__sup__ord_I3_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X2:A,Y3:A]: ((((ord_less_eq @ A) @ X2) @ (((sup_sup @ A) @ X2) @ Y3)))))))).
% 2.76/1.56 thf(fact_240_inf__sup__ord_I4_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [Y3:A,X2:A]: ((((ord_less_eq @ A) @ Y3) @ (((sup_sup @ A) @ X2) @ Y3)))))))).
% 2.76/1.56 thf(fact_241_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ B5) = B5))))))).
% 2.76/1.56 thf(fact_242_subset__UnE, axiom, (! [A:$tType,C:(set @ A),A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) => (~ ((! [A7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ A3) => (! [B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B7) @ B3) => (C != (((sup_sup @ (set @ A)) @ A7) @ B7)))))))))))))).
% 2.76/1.56 thf(fact_243_Un__absorb2, axiom, (! [A:$tType,B3:(set @ A),A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B3) @ A3) => ((((sup_sup @ (set @ A)) @ A3) @ B3) = A3))))).
% 2.76/1.56 thf(fact_244_Un__absorb1, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B3) => ((((sup_sup @ (set @ A)) @ A3) @ B3) = B3))))).
% 2.76/1.56 thf(fact_245_Un__upper2, axiom, (! [A:$tType,B3:(set @ A),A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B3) @ (((sup_sup @ (set @ A)) @ A3) @ B3))))).
% 2.76/1.56 thf(fact_246_Un__upper1, axiom, (! [A:$tType,A3:(set @ A),B3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B3))))).
% 2.76/1.56 thf(fact_247_Un__least, axiom, (! [A:$tType,A3:(set @ A),C:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C) => ((((ord_less_eq @ (set @ A)) @ B3) @ C) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) @ C)))))).
% 2.76/1.56 thf(fact_248_Un__mono, axiom, (! [A:$tType,A3:(set @ A),C:(set @ A),B3:(set @ A),D2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C) => ((((ord_less_eq @ (set @ A)) @ B3) @ D2) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B3)) @ (((sup_sup @ (set @ A)) @ C) @ D2))))))).
% 2.76/1.56 thf(fact_249_redundant__set__def, axiom, (! [G2:g,P2:(set @ val)]: (((((((((((((irredu2110905762nt_set @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2) @ P2) = ((P2 != (bot_bot @ (set @ val))) & ((((ord_less_eq @ (set @ val)) @ P2) @ (((dom @ val) @ (list @ val)) @ (((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2))) & (? [X:val]: (((((member @ val) @ X) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) & (! [Y2:val]: (((((member @ val) @ Y2) @ P2) => (! [Phi3:val]: (((((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ Y2) @ Phi3) => (((member @ val) @ Phi3) @ (((sup_sup @ (set @ val)) @ P2) @ (((insert @ val) @ X) @ (bot_bot @ (set @ val)))))))))))))))))))).
% 2.76/1.56 thf(fact_250_phi__no__closed__loop, axiom, (! [P:val,G2:g,Vs:(list @ val)]: (((((member @ val) @ P) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ G2)) => ((((((((((sSA_CFG_SSA_wf_phi @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ G2) @ P) = ((some @ (list @ val)) @ Vs)) => (((set2 @ val) @ Vs) != (((insert @ val) @ P) @ (bot_bot @ (set @ val))))))))).
% 2.76/1.56 thf(fact_251_dom__eq__empty__conv, axiom, (! [B:$tType,A:$tType,F:(A > (option @ B))]: ((((((dom @ A) @ B) @ F) = (bot_bot @ (set @ A))) = (F = (^ [X:A]: ((none @ B)))))))).
% 2.76/1.56 thf(fact_252_phis__finite, axiom, (! [G2:g]: (((finite_finite2 @ ((product_prod @ node) @ val)) @ (((dom @ ((product_prod @ node) @ val)) @ (list @ val)) @ (phis @ G2)))))).
% 2.76/1.56 thf(fact_253_insert__subset, axiom, (! [A:$tType,X2:A,A3:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X2) @ A3)) @ B3) = ((((member @ A) @ X2) @ B3) & (((ord_less_eq @ (set @ A)) @ A3) @ B3)))))).
% 2.76/1.56 thf(fact_254_finite__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: ((((finite_finite2 @ A) @ (((insert @ A) @ A2) @ A3)) = ((finite_finite2 @ A) @ A3))))).
% 2.76/1.56 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 2.76/1.56 thf(subcl_Orderings_Olinorder___Orderings_Oorder, axiom, (! [A:$tType]: (((linorder @ A) => (order @ A))))).
% 2.76/1.56 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: (((linorder @ A) => (preorder @ A))))).
% 2.76/1.56 thf(tcon_Option_Ooption___Lattices_Obounded__lattice, axiom, (! [A8:$tType]: (((bounded_lattice_top @ A8) => (bounded_lattice @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_1, axiom, (bounded_lattice @ $o)).
% 2.76/1.56 thf(tcon_Set_Oset___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 2.76/1.56 thf(tcon_fun___Lattices_Obounded__lattice_3, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_fun___Lattices_Obounded__lattice__top, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice_top @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_4, axiom, (! [A8:$tType]: ((bounded_lattice_top @ (set @ A8))))).
% 2.76/1.56 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_5, axiom, (bounded_lattice_top @ $o)).
% 2.76/1.56 thf(tcon_Option_Ooption___Lattices_Obounded__lattice__top_6, axiom, (! [A8:$tType]: (((bounded_lattice_top @ A8) => (bounded_lattice_top @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounde1808546759up_bot @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_sup @ A9) => (semilattice_sup @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A8:$tType,A9:$tType]: ((((finite_finite @ A8) & (finite_finite @ A9)) => (finite_finite @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: (((lattice @ A9) => (lattice @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_fun___Lattices_Osup, axiom, (! [A8:$tType,A9:$tType]: (((semilattice_sup @ A9) => (sup @ (A8 > A9)))))).
% 2.76/1.56 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7, axiom, (! [A8:$tType]: ((bounde1808546759up_bot @ (set @ A8))))).
% 2.76/1.56 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_8, axiom, (! [A8:$tType]: ((semilattice_sup @ (set @ A8))))).
% 2.76/1.56 thf(tcon_Set_Oset___Orderings_Opreorder_9, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 2.76/1.56 thf(tcon_Set_Oset___Finite__Set_Ofinite_10, axiom, (! [A8:$tType]: (((finite_finite @ A8) => (finite_finite @ (set @ A8)))))).
% 2.76/1.56 thf(tcon_Set_Oset___Lattices_Olattice_11, axiom, (! [A8:$tType]: ((lattice @ (set @ A8))))).
% 2.76/1.56 thf(tcon_Set_Oset___Orderings_Oorder_12, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 2.76/1.56 thf(tcon_Set_Oset___Lattices_Osup_13, axiom, (! [A8:$tType]: ((sup @ (set @ A8))))).
% 2.76/1.56 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14, axiom, (bounde1808546759up_bot @ $o)).
% 2.76/1.56 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_15, axiom, (semilattice_sup @ $o)).
% 2.76/1.56 thf(tcon_HOL_Obool___Orderings_Opreorder_16, axiom, (preorder @ $o)).
% 2.76/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.76/1.56 thf(tcon_HOL_Obool___Finite__Set_Ofinite_17, axiom, (finite_finite @ $o)).
% 2.76/1.56 thf(tcon_HOL_Obool___Lattices_Olattice_18, axiom, (lattice @ $o)).
% 2.76/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_19, axiom, (order @ $o)).
% 2.76/1.56 thf(tcon_HOL_Obool___Lattices_Osup_20, axiom, (sup @ $o)).
% 2.76/1.56 thf(tcon_Option_Ooption___Lattices_Obounded__semilattice__sup__bot_21, axiom, (! [A8:$tType]: (((lattice @ A8) => (bounde1808546759up_bot @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_Option_Ooption___Lattices_Osemilattice__sup_22, axiom, (! [A8:$tType]: (((semilattice_sup @ A8) => (semilattice_sup @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_Option_Ooption___Orderings_Opreorder_23, axiom, (! [A8:$tType]: (((preorder @ A8) => (preorder @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_Option_Ooption___Orderings_Olinorder_24, axiom, (! [A8:$tType]: (((linorder @ A8) => (linorder @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_Option_Ooption___Finite__Set_Ofinite_25, axiom, (! [A8:$tType]: (((finite_finite @ A8) => (finite_finite @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_Option_Ooption___Lattices_Olattice_26, axiom, (! [A8:$tType]: (((lattice @ A8) => (lattice @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_Option_Ooption___Orderings_Oorder_27, axiom, (! [A8:$tType]: (((order @ A8) => (order @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_Option_Ooption___Lattices_Osup_28, axiom, (! [A8:$tType]: (((sup @ A8) => (sup @ (option @ A8)))))).
% 2.76/1.56 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_29, axiom, (! [A8:$tType,A9:$tType]: ((((finite_finite @ A8) & (finite_finite @ A9)) => (finite_finite @ ((product_prod @ A8) @ A9)))))).
% 2.76/1.56 thf(tfree_0, hypothesis, (linorder @ val)).
% 2.76/1.56 thf(tfree_1, hypothesis, (linorder @ node)).
% 2.76/1.56 thf(tfree_2, hypothesis, (linorder @ var)).
% 2.76/1.56 thf(conj_0, conjecture, (((member @ val) @ phi_s) @ ((((((((((sSA_CFG_SSA_allVars @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ defs) @ uses) @ phis) @ g2))).
% 2.76/1.56 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ukvq8Gf8nd/DTF2DTF3462.p
% 2.76/1.56 ------------------------
% 2.76/1.59 ---- Cleaned THF ---
% 2.76/1.59 thf(ty_t_Product__Type_Oprod,type,
% 2.76/1.59 product_prod: $tType > $tType > $tType ).
% 2.76/1.59
% 2.76/1.59 thf(ty_t_Option_Ooption,type,
% 2.76/1.59 option: $tType > $tType ).
% 2.76/1.59
% 2.76/1.59 thf(ty_t_List_Olist,type,
% 2.76/1.59 list: $tType > $tType ).
% 2.76/1.59
% 2.76/1.59 thf(ty_t_Set_Oset,type,
% 2.76/1.59 set: $tType > $tType ).
% 2.76/1.59
% 2.76/1.59 thf(ty_tf_edgeD,type,
% 2.76/1.59 edgeD: $tType ).
% 2.76/1.59
% 2.76/1.59 thf(ty_tf_node,type,
% 2.76/1.59 node: $tType ).
% 2.76/1.59
% 2.76/1.59 thf(ty_tf_var,type,
% 2.76/1.59 var: $tType ).
% 2.76/1.59
% 2.76/1.59 thf(ty_tf_val,type,
% 2.76/1.59 val: $tType ).
% 2.76/1.59
% 2.76/1.59 thf(ty_tf_g,type,
% 2.76/1.59 g: $tType ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 2.76/1.59 bounded_lattice_top:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.76/1.59 bounded_lattice:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_HOL_Otype,type,
% 2.76/1.59 type:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Lattices_Osup,type,
% 2.76/1.59 sup:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Orderings_Oorder,type,
% 2.76/1.59 order:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Lattices_Olattice,type,
% 2.76/1.59 lattice:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Finite__Set_Ofinite,type,
% 2.76/1.59 finite_finite:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Orderings_Olinorder,type,
% 2.76/1.59 linorder:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Orderings_Opreorder,type,
% 2.76/1.59 preorder:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.76/1.59 semilattice_sup:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 2.76/1.59 bounde1808546759up_bot:
% 2.76/1.59 !>[A: $tType] : $o ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Finite__Set_Ofinite,type,
% 2.76/1.59 finite_finite2:
% 2.76/1.59 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors,type,
% 2.76/1.59 graph_1201503639essors:
% 2.76/1.59 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Graph__path_Ograph__path__base_Osuccessors,type,
% 2.76/1.59 graph_449533722essors:
% 2.76/1.59 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Ocondensation__edges,type,
% 2.76/1.59 irredu280805948_edges:
% 2.76/1.59 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) > ( set @ ( product_prod @ ( set @ Val ) @ ( set @ Val ) ) ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Ocondensation__nodes,type,
% 2.76/1.59 irredu1918690039_nodes:
% 2.76/1.59 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) > ( set @ ( set @ Val ) ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Oredundant__scc,type,
% 2.76/1.59 irredu2110774547nt_scc:
% 2.76/1.59 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) > ( set @ Val ) > $o ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Irreducible__Mirabelle__vdklcywumt_OCFG__SSA__Transformed_Oredundant__set,type,
% 2.76/1.59 irredu2110905762nt_set:
% 2.76/1.59 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) > $o ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.76/1.59 sup_sup:
% 2.76/1.59 !>[A: $tType] : ( A > A > A ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_List_Olist_Oset,type,
% 2.76/1.59 set2:
% 2.76/1.59 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_List_Ozip,type,
% 2.76/1.59 zip:
% 2.76/1.59 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( list @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Map_Odom,type,
% 2.76/1.59 dom:
% 2.76/1.59 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Option_Ooption_ONone,type,
% 2.76/1.59 none:
% 2.76/1.59 !>[A: $tType] : ( option @ A ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Option_Ooption_OSome,type,
% 2.76/1.59 some:
% 2.76/1.59 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.76/1.59 bot_bot:
% 2.76/1.59 !>[A: $tType] : A ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.76/1.59 ord_less_eq:
% 2.76/1.59 !>[A: $tType] : ( A > A > $o ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_Product__Type_OPair,type,
% 2.76/1.59 product_Pair:
% 2.76/1.59 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs,type,
% 2.76/1.59 sSA_CFG_SSA_allDefs:
% 2.76/1.59 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 2.76/1.59
% 2.76/1.59 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallUses,type,
% 2.76/1.59 sSA_CFG_SSA_allUses:
% 2.76/1.59 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallVars,type,
% 2.76/1.60 sSA_CFG_SSA_allVars:
% 2.76/1.60 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > ( set @ Val ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs,type,
% 2.76/1.60 sSA_CFG_SSA_phiDefs:
% 2.76/1.60 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses,type,
% 2.76/1.60 sSA_CFG_SSA_phiUses:
% 2.76/1.60 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode,type,
% 2.76/1.60 sSA_CF1081484811efNode:
% 2.76/1.60 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Node ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OisTrivialPhi,type,
% 2.76/1.60 sSA_CF1297404942ialPhi:
% 2.76/1.60 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Val > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OliveVal,type,
% 2.76/1.60 sSA_CF722422777iveVal:
% 2.76/1.60 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Ophi,type,
% 2.76/1.60 sSA_CFG_SSA_wf_phi:
% 2.76/1.60 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > ( option @ ( list @ Val ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg,type,
% 2.76/1.60 sSA_CF1165125185phiArg:
% 2.76/1.60 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Val > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Opruned,type,
% 2.76/1.60 sSA_CF823892918pruned:
% 2.76/1.60 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Oredundant,type,
% 2.76/1.60 sSA_CF462202545undant:
% 2.76/1.60 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Otrivial,type,
% 2.76/1.60 sSA_CF1363434349rivial:
% 2.76/1.60 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node > ( set @ Val ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_SSA__CFG_OCFG__base_Ovars,type,
% 2.76/1.60 sSA_CFG_vars:
% 2.76/1.60 !>[G: $tType,Node: $tType,Var: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Var ) ) > G > ( set @ Var ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_Set_OCollect,type,
% 2.76/1.60 collect:
% 2.76/1.60 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_Set_Oinsert,type,
% 2.76/1.60 insert:
% 2.76/1.60 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_Transitive__Closure_Oacyclic,type,
% 2.76/1.60 transitive_acyclic:
% 2.76/1.60 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_Transitive__Closure_Otranclp,type,
% 2.76/1.60 transitive_tranclp:
% 2.76/1.60 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_c_member,type,
% 2.76/1.60 member:
% 2.76/1.60 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v__092_060alpha_062n,type,
% 2.76/1.60 alpha_n: g > ( list @ node ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v__092_060phi_062,type,
% 2.76/1.60 phi: val ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v__092_060phi_062_092_060_094sub_062s,type,
% 2.76/1.60 phi_s: val ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v__092_060phi_062_H____,type,
% 2.76/1.60 phi2: val ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v_defs,type,
% 2.76/1.60 defs: g > node > ( set @ val ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v_g,type,
% 2.76/1.60 g2: g ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v_inEdges_H,type,
% 2.76/1.60 inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v_phis,type,
% 2.76/1.60 phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v_s,type,
% 2.76/1.60 s: val ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v_uses,type,
% 2.76/1.60 uses: g > node > ( set @ val ) ).
% 2.76/1.60
% 2.76/1.60 thf(sy_v_var,type,
% 2.76/1.60 var2: g > val > var ).
% 2.76/1.60
% 2.76/1.60 thf(fact_0_assms_I4_J,axiom,
% 2.76/1.60 phi_s != s ).
% 2.76/1.60
% 2.76/1.60 thf(fact_1_False,axiom,
% 2.76/1.60 phi != phi_s ).
% 2.76/1.60
% 2.76/1.60 thf(fact_2__092_060open_062phiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_092_060close_062,axiom,
% 2.76/1.60 sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s ).
% 2.76/1.60
% 2.76/1.60 thf(fact_3_assms_I3_J,axiom,
% 2.76/1.60 member @ val @ s @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_4_assms_I2_J,axiom,
% 2.76/1.60 member @ val @ phi @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.76/1.60 ~ ! [Phi: val] :
% 2.76/1.60 ~ ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ Phi @ phi_s ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_6_phiArg__in__allVars,axiom,
% 2.76/1.60 ! [G2: g,V: val,V2: val] :
% 2.76/1.60 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ V2 )
% 2.76/1.60 => ( member @ val @ V2 @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_7_uses__in__vars,axiom,
% 2.76/1.60 ! [V: val,G2: g,N: node] :
% 2.76/1.60 ( ( member @ val @ V @ ( uses @ G2 @ N ) )
% 2.76/1.60 => ( member @ val @ V @ ( sSA_CFG_vars @ g @ node @ val @ alpha_n @ uses @ G2 ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_8_trivial__in__allVars,axiom,
% 2.76/1.60 ! [G2: g,V: val] :
% 2.76/1.60 ( ( sSA_CF1363434349rivial @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ V )
% 2.76/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_9_liveVal__in__allVars,axiom,
% 2.76/1.60 ! [G2: g,V: val] :
% 2.76/1.60 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V )
% 2.76/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_10_allVars__finite,axiom,
% 2.76/1.60 ! [G2: g] : ( finite_finite2 @ val @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_11_uses__in__allUses,axiom,
% 2.76/1.60 ! [V: val,G2: g,N: node] :
% 2.76/1.60 ( ( member @ val @ V @ ( uses @ G2 @ N ) )
% 2.76/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_12_redundant__def,axiom,
% 2.76/1.60 ! [G2: g] :
% 2.76/1.60 ( ( sSA_CF462202545undant @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 )
% 2.76/1.60 = ( ? [X: val] :
% 2.76/1.60 ( ( member @ val @ X @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.76/1.60 & ( sSA_CF1363434349rivial @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ X ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_13_trivial__def,axiom,
% 2.76/1.60 ! [G2: g,V: val] :
% 2.76/1.60 ( ( sSA_CF1363434349rivial @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ V )
% 2.76/1.60 = ( ? [X: val] :
% 2.76/1.60 ( ( member @ val @ X @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.76/1.60 & ( sSA_CF1297404942ialPhi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ X ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_14__092_060open_062_092_060not_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062s_A_092_060noteq_062_AdefNode_Ag_As_092_060close_062,axiom,
% 2.76/1.60 ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 2.76/1.60 = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_15_defs__uses__disjoint_H,axiom,
% 2.76/1.60 ! [N: node,G2: g,V: val] :
% 2.76/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ( ( member @ val @ V @ ( defs @ G2 @ N ) )
% 2.76/1.60 => ~ ( member @ val @ V @ ( uses @ G2 @ N ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_16_livePhi,axiom,
% 2.76/1.60 ! [G2: g,V: val,V2: val] :
% 2.76/1.60 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V )
% 2.76/1.60 => ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ V2 )
% 2.76/1.60 => ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V2 ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_17_phiArg__distinct__nodes,axiom,
% 2.76/1.60 ! [G2: g,P: val,Q: val] :
% 2.76/1.60 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ Q )
% 2.76/1.60 => ( ( P != Q )
% 2.76/1.60 => ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.76/1.60 => ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P )
% 2.76/1.60 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ Q ) ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_18_phiArgs__def__distinct,axiom,
% 2.76/1.60 ! [G2: g,P: val,Q: val,R: val] :
% 2.76/1.60 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ Q )
% 2.76/1.60 => ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ R )
% 2.76/1.60 => ( ( Q != R )
% 2.76/1.60 => ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.76/1.60 => ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ Q )
% 2.76/1.60 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ R ) ) ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_19_uses__in___092_060alpha_062n,axiom,
% 2.76/1.60 ! [V: val,G2: g,N: node] :
% 2.76/1.60 ( ( member @ val @ V @ ( uses @ G2 @ N ) )
% 2.76/1.60 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_20_defs__finite,axiom,
% 2.76/1.60 ! [G2: g,N: node] : ( finite_finite2 @ val @ ( defs @ G2 @ N ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_21_varsE,axiom,
% 2.76/1.60 ! [V: val,G2: g] :
% 2.76/1.60 ( ( member @ val @ V @ ( sSA_CFG_vars @ g @ node @ val @ alpha_n @ uses @ G2 ) )
% 2.76/1.60 => ~ ! [N2: node] :
% 2.76/1.60 ( ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ~ ( member @ val @ V @ ( uses @ G2 @ N2 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_22_vars__finite,axiom,
% 2.76/1.60 ! [G2: g] : ( finite_finite2 @ val @ ( sSA_CFG_vars @ g @ node @ val @ alpha_n @ uses @ G2 ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_23_liveSimple,axiom,
% 2.76/1.60 ! [N: node,G2: g,Val2: val] :
% 2.76/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ( ( member @ val @ Val2 @ ( uses @ G2 @ N ) )
% 2.76/1.60 => ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ Val2 ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_24_liveVal_Osimps,axiom,
% 2.76/1.60 ! [G2: g,A2: val] :
% 2.76/1.60 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ A2 )
% 2.76/1.60 = ( ? [N3: node,Val3: val] :
% 2.76/1.60 ( ( A2 = Val3 )
% 2.76/1.60 & ( member @ node @ N3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 & ( member @ val @ Val3 @ ( uses @ G2 @ N3 ) ) )
% 2.76/1.60 | ? [V3: val,V4: val] :
% 2.76/1.60 ( ( A2 = V4 )
% 2.76/1.60 & ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V3 )
% 2.76/1.60 & ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V3 @ V4 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_25_liveVal_Oinducts,axiom,
% 2.76/1.60 ! [G2: g,X2: val,P2: val > $o] :
% 2.76/1.60 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ X2 )
% 2.76/1.60 => ( ! [N2: node,Val4: val] :
% 2.76/1.60 ( ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ( ( member @ val @ Val4 @ ( uses @ G2 @ N2 ) )
% 2.76/1.60 => ( P2 @ Val4 ) ) )
% 2.76/1.60 => ( ! [V5: val,V6: val] :
% 2.76/1.60 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V5 )
% 2.76/1.60 => ( ( P2 @ V5 )
% 2.76/1.60 => ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V5 @ V6 )
% 2.76/1.60 => ( P2 @ V6 ) ) ) )
% 2.76/1.60 => ( P2 @ X2 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_26_liveVal_Ocases,axiom,
% 2.76/1.60 ! [G2: g,A2: val] :
% 2.76/1.60 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ A2 )
% 2.76/1.60 => ( ! [N2: node] :
% 2.76/1.60 ( ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ~ ( member @ val @ A2 @ ( uses @ G2 @ N2 ) ) )
% 2.76/1.60 => ~ ! [V5: val] :
% 2.76/1.60 ( ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ V5 )
% 2.76/1.60 => ~ ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V5 @ A2 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_27_allUses__finite,axiom,
% 2.76/1.60 ! [N: node,G2: g] :
% 2.76/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ( finite_finite2 @ val @ ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_28_defNode_I1_J,axiom,
% 2.76/1.60 ! [V: val,G2: g] :
% 2.76/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.76/1.60 => ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_29_uses__finite,axiom,
% 2.76/1.60 ! [G2: g,N: node] : ( finite_finite2 @ val @ ( uses @ G2 @ N ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_30_eq,axiom,
% 2.76/1.60 ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 2.76/1.60 = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_31_allUses__in__allVars,axiom,
% 2.76/1.60 ! [V: val,G2: g,N: node] :
% 2.76/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N ) )
% 2.76/1.60 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_32_phiUses__in__allUses,axiom,
% 2.76/1.60 ! [V: val,G2: g,N: node] :
% 2.76/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) )
% 2.76/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_33_phiUses__finite,axiom,
% 2.76/1.60 ! [N: node,G2: g] :
% 2.76/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ( finite_finite2 @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_34_defNode_I2_J,axiom,
% 2.76/1.60 ! [V: val,G2: g] :
% 2.76/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.76/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_35_defNode__ex1,axiom,
% 2.76/1.60 ! [V: val,G2: g] :
% 2.76/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.76/1.60 => ? [X3: node] :
% 2.76/1.60 ( ( member @ node @ X3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X3 ) )
% 2.76/1.60 & ! [Y: node] :
% 2.76/1.60 ( ( ( member @ node @ Y @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ Y ) ) )
% 2.76/1.60 => ( Y = X3 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_36_allVars__in__allDefs,axiom,
% 2.76/1.60 ! [V: val,G2: g] :
% 2.76/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.76/1.60 => ? [X3: node] :
% 2.76/1.60 ( ( member @ node @ X3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X3 ) ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_37_List_Ofinite__set,axiom,
% 2.76/1.60 ! [A: $tType,Xs: list @ A] : ( finite_finite2 @ A @ ( set2 @ A @ Xs ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_38_phiDefs__finite,axiom,
% 2.76/1.60 ! [G2: g,N: node] : ( finite_finite2 @ val @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_39_allDefs__finite,axiom,
% 2.76/1.60 ! [N: node,G2: g] :
% 2.76/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.76/1.60 => ( finite_finite2 @ val @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_40_assms_I5_J,axiom,
% 2.76/1.60 ( ( var2 @ g2 @ phi )
% 2.76/1.60 = ( var2 @ g2 @ s ) ) ).
% 2.76/1.60
% 2.76/1.60 thf(fact_41_CFG__SSA__wf__base_Oredundant__def,axiom,
% 2.76/1.60 ! [EdgeD: $tType,Val: $tType,Node: $tType,G: $tType] :
% 2.76/1.60 ( ( ( linorder @ Node )
% 2.76/1.60 & ( linorder @ Val ) )
% 2.76/1.60 => ( ( sSA_CF462202545undant @ G @ Node @ EdgeD @ Val )
% 2.76/1.60 = ( ^ [Alpha_n: G > ( list @ Node ),InEdges: G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ),Defs: G > Node > ( set @ Val ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G] :
% 2.96/1.60 ? [X: Val] :
% 2.96/1.60 ( ( member @ Val @ X @ ( sSA_CFG_SSA_allVars @ G @ Node @ EdgeD @ Val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G3 ) )
% 2.96/1.60 & ( sSA_CF1363434349rivial @ G @ Node @ EdgeD @ Val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G3 @ X ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_42_defs__in__allDefs,axiom,
% 2.96/1.60 ! [V: val,G2: g,N: node] :
% 2.96/1.60 ( ( member @ val @ V @ ( defs @ G2 @ N ) )
% 2.96/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_43_phiDefs__in__allDefs,axiom,
% 2.96/1.60 ! [V: val,G2: g,N: node] :
% 2.96/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) )
% 2.96/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_44_allDefs__disjoint_H,axiom,
% 2.96/1.60 ! [N: node,G2: g,M: node,V: val] :
% 2.96/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 2.96/1.60 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ M ) )
% 2.96/1.60 => ( N = M ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_45_mem__Collect__eq,axiom,
% 2.96/1.60 ! [A: $tType,A2: A,P2: A > $o] :
% 2.96/1.60 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 2.96/1.60 = ( P2 @ A2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_46_Collect__mem__eq,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A] :
% 2.96/1.60 ( ( collect @ A
% 2.96/1.60 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 2.96/1.60 = A3 ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_47_Collect__cong,axiom,
% 2.96/1.60 ! [A: $tType,P2: A > $o,Q2: A > $o] :
% 2.96/1.60 ( ! [X3: A] :
% 2.96/1.60 ( ( P2 @ X3 )
% 2.96/1.60 = ( Q2 @ X3 ) )
% 2.96/1.60 => ( ( collect @ A @ P2 )
% 2.96/1.60 = ( collect @ A @ Q2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_48_ext,axiom,
% 2.96/1.60 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 2.96/1.60 ( ! [X3: A] :
% 2.96/1.60 ( ( F @ X3 )
% 2.96/1.60 = ( G2 @ X3 ) )
% 2.96/1.60 => ( F = G2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_49_phiArg__same__var,axiom,
% 2.96/1.60 ! [G2: g,P: val,Q: val] :
% 2.96/1.60 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ Q )
% 2.96/1.60 => ( ( var2 @ G2 @ Q )
% 2.96/1.60 = ( var2 @ G2 @ P ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_50_vars__eq,axiom,
% 2.96/1.60 ( ( var2 @ g2 @ phi )
% 2.96/1.60 = ( var2 @ g2 @ phi_s ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_51_allDefs__var__disjoint,axiom,
% 2.96/1.60 ! [N: node,G2: g,V: val,V2: val] :
% 2.96/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 2.96/1.60 => ( ( member @ val @ V2 @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 2.96/1.60 => ( ( V != V2 )
% 2.96/1.60 => ( ( var2 @ G2 @ V2 )
% 2.96/1.60 != ( var2 @ G2 @ V ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_52_defNode__var__disjoint,axiom,
% 2.96/1.60 ! [P: val,G2: g,Q: val] :
% 2.96/1.60 ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.96/1.60 => ( ( member @ val @ Q @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.96/1.60 => ( ( P != Q )
% 2.96/1.60 => ( ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P )
% 2.96/1.60 = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ Q ) )
% 2.96/1.60 => ( ( var2 @ G2 @ P )
% 2.96/1.60 != ( var2 @ G2 @ Q ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_53_defNode__eq,axiom,
% 2.96/1.60 ! [N: node,G2: g,V: val] :
% 2.96/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 2.96/1.60 => ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 = N ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_54_allDefs__in__allVars,axiom,
% 2.96/1.60 ! [V: val,G2: g,N: node] :
% 2.96/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 2.96/1.60 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_55_pruned__def,axiom,
% 2.96/1.60 ! [G2: g] :
% 2.96/1.60 ( ( sSA_CF823892918pruned @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 )
% 2.96/1.60 = ( ! [X: node] :
% 2.96/1.60 ( ( member @ node @ X @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ! [Val3: val] :
% 2.96/1.60 ( ( member @ val @ Val3 @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ X ) )
% 2.96/1.60 => ( sSA_CF722422777iveVal @ g @ node @ val @ alpha_n @ defs @ uses @ phis @ G2 @ Val3 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_56_CFG__SSA__base_OphiUses_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_phiUses @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( sSA_CFG_SSA_phiUses @ G @ Node @ EdgeD @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_57_CFG__SSA__base_OphiDefs_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_phiDefs @ G @ Node @ Val )
% 2.96/1.60 = ( sSA_CFG_SSA_phiDefs @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_58_CFG__SSA__base_OallDefs_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_allDefs @ G @ Node @ Val )
% 2.96/1.60 = ( sSA_CFG_SSA_allDefs @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_59_CFG__SSA__wf__base_OdefNode_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF1081484811efNode @ G @ Node @ Val )
% 2.96/1.60 = ( sSA_CF1081484811efNode @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_60_CFG__SSA__base_OallVars_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_allVars @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( sSA_CFG_SSA_allVars @ G @ Node @ EdgeD @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_61_CFG__SSA__wf__base_OphiArg_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF1165125185phiArg @ G @ Node @ Val )
% 2.96/1.60 = ( sSA_CF1165125185phiArg @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_62_CFG__SSA__base_OallUses_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_allUses @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( sSA_CFG_SSA_allUses @ G @ Node @ EdgeD @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_63_CFG__SSA__wf__base_OliveVal_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF722422777iveVal @ G @ Node @ Val )
% 2.96/1.60 = ( sSA_CF722422777iveVal @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_64_CFG__SSA__wf__base_Otrivial_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF1363434349rivial @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( sSA_CF1363434349rivial @ G @ Node @ EdgeD @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_65_CFG__base_Ovars_Ocong,axiom,
% 2.96/1.60 ! [Var: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Var ) )
% 2.96/1.60 => ( ( sSA_CFG_vars @ G @ Node @ Var )
% 2.96/1.60 = ( sSA_CFG_vars @ G @ Node @ Var ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_66_CFG__SSA__wf__base_OisTrivialPhi_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF1297404942ialPhi @ G @ Node @ Val )
% 2.96/1.60 = ( sSA_CF1297404942ialPhi @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_67_CFG__SSA__wf__base_Oredundant_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF462202545undant @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( sSA_CF462202545undant @ G @ Node @ EdgeD @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_68_finite__list,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ A3 )
% 2.96/1.60 => ? [Xs2: list @ A] :
% 2.96/1.60 ( ( set2 @ A @ Xs2 )
% 2.96/1.60 = A3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_69_CFG__SSA__wf__base_OliveSimple,axiom,
% 2.96/1.60 ! [G: $tType,Node: $tType,Val: $tType] :
% 2.96/1.60 ( ( ( linorder @ Val )
% 2.96/1.60 & ( linorder @ Node ) )
% 2.96/1.60 => ! [N: Node,Alpha_n2: G > ( list @ Node ),G2: G,Val2: Val,Uses2: G > Node > ( set @ Val ),Defs2: G > Node > ( set @ Val ),Phis2: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) )] :
% 2.96/1.60 ( ( member @ Node @ N @ ( set2 @ Node @ ( Alpha_n2 @ G2 ) ) )
% 2.96/1.60 => ( ( member @ Val @ Val2 @ ( Uses2 @ G2 @ N ) )
% 2.96/1.60 => ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ Val2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_70_CFG__SSA__wf__base_OlivePhi,axiom,
% 2.96/1.60 ! [G: $tType,Node: $tType,Val: $tType] :
% 2.96/1.60 ( ( ( linorder @ Val )
% 2.96/1.60 & ( linorder @ Node ) )
% 2.96/1.60 => ! [Alpha_n2: G > ( list @ Node ),Defs2: G > Node > ( set @ Val ),Uses2: G > Node > ( set @ Val ),Phis2: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G2: G,V: Val,V2: Val] :
% 2.96/1.60 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ V )
% 2.96/1.60 => ( ( sSA_CF1165125185phiArg @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Phis2 @ G2 @ V @ V2 )
% 2.96/1.60 => ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ V2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_71_CFG__SSA__wf__base_OliveVal_Oinducts,axiom,
% 2.96/1.60 ! [Node: $tType,G: $tType,Val: $tType] :
% 2.96/1.60 ( ( ( linorder @ Val )
% 2.96/1.60 & ( linorder @ Node ) )
% 2.96/1.60 => ! [Alpha_n2: G > ( list @ Node ),Defs2: G > Node > ( set @ Val ),Uses2: G > Node > ( set @ Val ),Phis2: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G2: G,X2: Val,P2: Val > $o] :
% 2.96/1.60 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ X2 )
% 2.96/1.60 => ( ! [N2: Node,Val4: Val] :
% 2.96/1.60 ( ( member @ Node @ N2 @ ( set2 @ Node @ ( Alpha_n2 @ G2 ) ) )
% 2.96/1.60 => ( ( member @ Val @ Val4 @ ( Uses2 @ G2 @ N2 ) )
% 2.96/1.60 => ( P2 @ Val4 ) ) )
% 2.96/1.60 => ( ! [V5: Val,V6: Val] :
% 2.96/1.60 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ V5 )
% 2.96/1.60 => ( ( P2 @ V5 )
% 2.96/1.60 => ( ( sSA_CF1165125185phiArg @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Phis2 @ G2 @ V5 @ V6 )
% 2.96/1.60 => ( P2 @ V6 ) ) ) )
% 2.96/1.60 => ( P2 @ X2 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_72_CFG__SSA__wf__base_OliveVal_Osimps,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF722422777iveVal @ G @ Node @ Val )
% 2.96/1.60 = ( ^ [Alpha_n: G > ( list @ Node ),Defs: G > Node > ( set @ Val ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,A4: Val] :
% 2.96/1.60 ( ? [N3: Node,Val3: Val] :
% 2.96/1.60 ( ( A4 = Val3 )
% 2.96/1.60 & ( member @ Node @ N3 @ ( set2 @ Node @ ( Alpha_n @ G3 ) ) )
% 2.96/1.60 & ( member @ Val @ Val3 @ ( Uses @ G3 @ N3 ) ) )
% 2.96/1.60 | ? [V3: Val,V4: Val] :
% 2.96/1.60 ( ( A4 = V4 )
% 2.96/1.60 & ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n @ Defs @ Uses @ Phis @ G3 @ V3 )
% 2.96/1.60 & ( sSA_CF1165125185phiArg @ G @ Node @ Val @ Alpha_n @ Defs @ Phis @ G3 @ V3 @ V4 ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_73_CFG__SSA__wf__base_OliveVal_Ocases,axiom,
% 2.96/1.60 ! [Node: $tType,G: $tType,Val: $tType] :
% 2.96/1.60 ( ( ( linorder @ Val )
% 2.96/1.60 & ( linorder @ Node ) )
% 2.96/1.60 => ! [Alpha_n2: G > ( list @ Node ),Defs2: G > Node > ( set @ Val ),Uses2: G > Node > ( set @ Val ),Phis2: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G2: G,A2: Val] :
% 2.96/1.60 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ A2 )
% 2.96/1.60 => ( ! [N2: Node] :
% 2.96/1.60 ( ( member @ Node @ N2 @ ( set2 @ Node @ ( Alpha_n2 @ G2 ) ) )
% 2.96/1.60 => ~ ( member @ Val @ A2 @ ( Uses2 @ G2 @ N2 ) ) )
% 2.96/1.60 => ~ ! [V5: Val] :
% 2.96/1.60 ( ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G2 @ V5 )
% 2.96/1.60 => ~ ( sSA_CF1165125185phiArg @ G @ Node @ Val @ Alpha_n2 @ Defs2 @ Phis2 @ G2 @ V5 @ A2 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_74_CFG__SSA__wf__base_Otrivial__def,axiom,
% 2.96/1.60 ! [EdgeD: $tType,Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF1363434349rivial @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( ^ [Alpha_n: G > ( list @ Node ),InEdges: G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ),Defs: G > Node > ( set @ Val ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,V3: Val] :
% 2.96/1.60 ? [X: Val] :
% 2.96/1.60 ( ( member @ Val @ X @ ( sSA_CFG_SSA_allVars @ G @ Node @ EdgeD @ Val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G3 ) )
% 2.96/1.60 & ( sSA_CF1297404942ialPhi @ G @ Node @ Val @ Alpha_n @ Defs @ Phis @ G3 @ V3 @ X ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_75_condensation__finite,axiom,
% 2.96/1.60 ! [G2: g,P2: set @ val] : ( finite_finite2 @ ( product_prod @ ( set @ val ) @ ( set @ val ) ) @ ( irredu280805948_edges @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_76_phiUses__exI_H,axiom,
% 2.96/1.60 ! [G2: g,P: val,Q: val] :
% 2.96/1.60 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P @ Q )
% 2.96/1.60 => ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.96/1.60 => ~ ! [M2: node] :
% 2.96/1.60 ( ( member @ val @ Q @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ M2 ) )
% 2.96/1.60 => ~ ( member @ node @ M2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P ) ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_77_allUses__def,axiom,
% 2.96/1.60 ! [G2: g,N: node] :
% 2.96/1.60 ( ( sSA_CFG_SSA_allUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ uses @ phis @ G2 @ N )
% 2.96/1.60 = ( sup_sup @ ( set @ val ) @ ( uses @ G2 @ N ) @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_78_phiArg__trancl__same__var,axiom,
% 2.96/1.60 ! [G2: g,Phi2: val,N: val] :
% 2.96/1.60 ( ( transitive_tranclp @ val @ ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 ) @ Phi2 @ N )
% 2.96/1.60 => ( ( var2 @ G2 @ Phi2 )
% 2.96/1.60 = ( var2 @ G2 @ N ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_79_allDefs__def,axiom,
% 2.96/1.60 ! [G2: g,N: node] :
% 2.96/1.60 ( ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N )
% 2.96/1.60 = ( sup_sup @ ( set @ val ) @ ( defs @ G2 @ N ) @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_80_CFG__SSA__wf__base_Opruned__def,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF823892918pruned @ G @ Node @ Val )
% 2.96/1.60 = ( ^ [Alpha_n: G > ( list @ Node ),Defs: G > Node > ( set @ Val ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G] :
% 2.96/1.60 ! [X: Node] :
% 2.96/1.60 ( ( member @ Node @ X @ ( set2 @ Node @ ( Alpha_n @ G3 ) ) )
% 2.96/1.60 => ! [Val3: Val] :
% 2.96/1.60 ( ( member @ Val @ Val3 @ ( sSA_CFG_SSA_phiDefs @ G @ Node @ Val @ Phis @ G3 @ X ) )
% 2.96/1.60 => ( sSA_CF722422777iveVal @ G @ Node @ Val @ Alpha_n @ Defs @ Uses @ Phis @ G3 @ Val3 ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_81_finite__code,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( finite_finite @ A )
% 2.96/1.60 => ( ( finite_finite2 @ A )
% 2.96/1.60 = ( ^ [A5: set @ A] : $true ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_82_defNode__cases,axiom,
% 2.96/1.60 ! [V: val,G2: g] :
% 2.96/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.96/1.60 => ( ~ ( member @ val @ V @ ( defs @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 != ( none @ ( list @ val ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_83_simpleDef__not__phi,axiom,
% 2.96/1.60 ! [N: node,G2: g,V: val] :
% 2.96/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ( ( member @ val @ V @ ( defs @ G2 @ N ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 = ( none @ ( list @ val ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_84_finite__Un,axiom,
% 2.96/1.60 ! [A: $tType,F2: set @ A,G4: set @ A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ ( sup_sup @ ( set @ A ) @ F2 @ G4 ) )
% 2.96/1.60 = ( ( finite_finite2 @ A @ F2 )
% 2.96/1.60 & ( finite_finite2 @ A @ G4 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_85_trivial__phi,axiom,
% 2.96/1.60 ! [G2: g,V: val] :
% 2.96/1.60 ( ( sSA_CF1363434349rivial @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ V )
% 2.96/1.60 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 != ( none @ ( list @ val ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_86_phiArg__exI,axiom,
% 2.96/1.60 ! [M: node,G2: g,V: val] :
% 2.96/1.60 ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) ) ) )
% 2.96/1.60 => ( ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 != ( none @ ( list @ val ) ) )
% 2.96/1.60 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.96/1.60 => ~ ! [V6: val] :
% 2.96/1.60 ( ( member @ val @ V6 @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ M ) )
% 2.96/1.60 => ~ ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ V6 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_87_CFG__SSA__wf__base_Ophi_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_wf_phi @ G @ Node @ Val )
% 2.96/1.60 = ( sSA_CFG_SSA_wf_phi @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_88_infinite__Un,axiom,
% 2.96/1.60 ! [A: $tType,S: set @ A,T: set @ A] :
% 2.96/1.60 ( ( ~ ( finite_finite2 @ A @ ( sup_sup @ ( set @ A ) @ S @ T ) ) )
% 2.96/1.60 = ( ~ ( finite_finite2 @ A @ S )
% 2.96/1.60 | ~ ( finite_finite2 @ A @ T ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_89_Un__infinite,axiom,
% 2.96/1.60 ! [A: $tType,S: set @ A,T: set @ A] :
% 2.96/1.60 ( ~ ( finite_finite2 @ A @ S )
% 2.96/1.60 => ~ ( finite_finite2 @ A @ ( sup_sup @ ( set @ A ) @ S @ T ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_90_finite__UnI,axiom,
% 2.96/1.60 ! [A: $tType,F2: set @ A,G4: set @ A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ F2 )
% 2.96/1.60 => ( ( finite_finite2 @ A @ G4 )
% 2.96/1.60 => ( finite_finite2 @ A @ ( sup_sup @ ( set @ A ) @ F2 @ G4 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_91_CFG__SSA__Transformed_Ocondensation__edges_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( irredu280805948_edges @ G @ Node @ Val )
% 2.96/1.60 = ( irredu280805948_edges @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_92_CFG__SSA__wf__base_Opruned_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF823892918pruned @ G @ Node @ Val )
% 2.96/1.60 = ( sSA_CF823892918pruned @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_93_CFG__SSA__base_OallDefs__def,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_allDefs @ G @ Node @ Val )
% 2.96/1.60 = ( ^ [Defs: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,N3: Node] : ( sup_sup @ ( set @ Val ) @ ( Defs @ G3 @ N3 ) @ ( sSA_CFG_SSA_phiDefs @ G @ Node @ Val @ Phis @ G3 @ N3 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_94_CFG__SSA__base_OallUses__def,axiom,
% 2.96/1.60 ! [EdgeD: $tType,Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_allUses @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( ^ [Alpha_n: G > ( list @ Node ),InEdges: G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ),Uses: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,N3: Node] : ( sup_sup @ ( set @ Val ) @ ( Uses @ G3 @ N3 ) @ ( sSA_CFG_SSA_phiUses @ G @ Node @ EdgeD @ Val @ Alpha_n @ InEdges @ Phis @ G3 @ N3 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_95_finite__set__choice,axiom,
% 2.96/1.60 ! [B: $tType,A: $tType,A3: set @ A,P2: A > B > $o] :
% 2.96/1.60 ( ( finite_finite2 @ A @ A3 )
% 2.96/1.60 => ( ! [X3: A] :
% 2.96/1.60 ( ( member @ A @ X3 @ A3 )
% 2.96/1.60 => ? [X_1: B] : ( P2 @ X3 @ X_1 ) )
% 2.96/1.60 => ? [F3: A > B] :
% 2.96/1.60 ! [X4: A] :
% 2.96/1.60 ( ( member @ A @ X4 @ A3 )
% 2.96/1.60 => ( P2 @ X4 @ ( F3 @ X4 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_96_finite,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( finite_finite @ A )
% 2.96/1.60 => ! [A3: set @ A] : ( finite_finite2 @ A @ A3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_97_phi__phiDefs,axiom,
% 2.96/1.60 ! [G2: g,V: val,Vs: list @ val] :
% 2.96/1.60 ( ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_98_condensation__acyclic,axiom,
% 2.96/1.60 ! [G2: g,P2: set @ val] : ( transitive_acyclic @ ( set @ val ) @ ( irredu280805948_edges @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_99_phi__def,axiom,
% 2.96/1.60 ! [G2: g,V: val] :
% 2.96/1.60 ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 = ( phis @ G2 @ ( product_Pair @ node @ val @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V ) @ V ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_100_phiArg__def,axiom,
% 2.96/1.60 ! [G2: g,V: val,V2: val] :
% 2.96/1.60 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V @ V2 )
% 2.96/1.60 = ( ? [Vs2: list @ val] :
% 2.96/1.60 ( ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs2 ) )
% 2.96/1.60 & ( member @ val @ V2 @ ( set2 @ val @ Vs2 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_101_phi__finite,axiom,
% 2.96/1.60 ! [G2: g] : ( finite_finite2 @ val @ ( dom @ val @ ( list @ val ) @ ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_102_redundant__scc__phis,axiom,
% 2.96/1.60 ! [G2: g,P2: set @ val,Scc: set @ val,X2: val] :
% 2.96/1.60 ( ( irredu2110905762nt_set @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ P2 )
% 2.96/1.60 => ( ( member @ ( set @ val ) @ Scc @ ( irredu1918690039_nodes @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) )
% 2.96/1.60 => ( ( member @ val @ X2 @ Scc )
% 2.96/1.60 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ X2 )
% 2.96/1.60 != ( none @ ( list @ val ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_103_phis__disj_I2_J,axiom,
% 2.96/1.60 ! [G2: g,N: node,V: val,Vs: list @ val,N4: node,Vs3: list @ val] :
% 2.96/1.60 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N4 @ V ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs3 ) )
% 2.96/1.60 => ( Vs = Vs3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_104_phis__disj_I1_J,axiom,
% 2.96/1.60 ! [G2: g,N: node,V: val,Vs: list @ val,N4: node,Vs3: list @ val] :
% 2.96/1.60 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N4 @ V ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs3 ) )
% 2.96/1.60 => ( N = N4 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_105_phis__in___092_060alpha_062n,axiom,
% 2.96/1.60 ! [G2: g,N: node,V: val,Vs: list @ val] :
% 2.96/1.60 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_106_phis__same__var,axiom,
% 2.96/1.60 ! [G2: g,N: node,V: val,Vs: list @ val,V2: val] :
% 2.96/1.60 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( ( member @ val @ V2 @ ( set2 @ val @ Vs ) )
% 2.96/1.60 => ( ( var2 @ G2 @ V2 )
% 2.96/1.60 = ( var2 @ G2 @ V ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_107_phis__phi,axiom,
% 2.96/1.60 ! [G2: g,N: node,V: val,Vs: list @ val] :
% 2.96/1.60 ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_108_phiUses__exI,axiom,
% 2.96/1.60 ! [M: node,G2: g,N: node,V: val,Vs: list @ val] :
% 2.96/1.60 ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 2.96/1.60 => ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N @ V ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ~ ! [V6: val] :
% 2.96/1.60 ( ( member @ val @ V6 @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ M ) )
% 2.96/1.60 => ~ ( member @ val @ V6 @ ( set2 @ val @ Vs ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_109_CFG__SSA__Transformed_Ocondensation__nodes_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( irredu1918690039_nodes @ G @ Node @ Val )
% 2.96/1.60 = ( irredu1918690039_nodes @ G @ Node @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_110_CFG__SSA__Transformed_Oredundant__set_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( irredu2110905762nt_set @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( irredu2110905762nt_set @ G @ Node @ EdgeD @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_111_CFG__SSA__wf__base_Ophi__def,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CFG_SSA_wf_phi @ G @ Node @ Val )
% 2.96/1.60 = ( ^ [Alpha_n: G > ( list @ Node ),Defs: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,V3: Val] : ( Phis @ G3 @ ( product_Pair @ Node @ Val @ ( sSA_CF1081484811efNode @ G @ Node @ Val @ Alpha_n @ Defs @ Phis @ G3 @ V3 ) @ V3 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_112_CFG__SSA__wf__base_OphiArg__def,axiom,
% 2.96/1.60 ! [Val: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( sSA_CF1165125185phiArg @ G @ Node @ Val )
% 2.96/1.60 = ( ^ [Alpha_n: G > ( list @ Node ),Defs: G > Node > ( set @ Val ),Phis: G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ),G3: G,V3: Val,V4: Val] :
% 2.96/1.60 ? [Vs2: list @ Val] :
% 2.96/1.60 ( ( ( sSA_CFG_SSA_wf_phi @ G @ Node @ Val @ Alpha_n @ Defs @ Phis @ G3 @ V3 )
% 2.96/1.60 = ( some @ ( list @ Val ) @ Vs2 ) )
% 2.96/1.60 & ( member @ Val @ V4 @ ( set2 @ Val @ Vs2 ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_113_phiUsesI,axiom,
% 2.96/1.60 ! [N4: node,G2: g,V2: val,Vs: list @ val,N: node,V: val] :
% 2.96/1.60 ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ( ( ( phis @ G2 @ ( product_Pair @ node @ val @ N4 @ V2 ) )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( ( member @ ( product_prod @ node @ val ) @ ( product_Pair @ node @ val @ N @ V ) @ ( set2 @ ( product_prod @ node @ val ) @ ( zip @ node @ val @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N4 ) @ Vs ) ) )
% 2.96/1.60 => ( member @ val @ V @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_114_scc__in__P,axiom,
% 2.96/1.60 ! [Scc: set @ val,G2: g,P2: set @ val] :
% 2.96/1.60 ( ( member @ ( set @ val ) @ Scc @ ( irredu1918690039_nodes @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) )
% 2.96/1.60 => ( ord_less_eq @ ( set @ val ) @ Scc @ P2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_115_not__None__eq,axiom,
% 2.96/1.60 ! [A: $tType,X2: option @ A] :
% 2.96/1.60 ( ( X2
% 2.96/1.60 != ( none @ A ) )
% 2.96/1.60 = ( ? [Y2: A] :
% 2.96/1.60 ( X2
% 2.96/1.60 = ( some @ A @ Y2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_116_not__Some__eq,axiom,
% 2.96/1.60 ! [A: $tType,X2: option @ A] :
% 2.96/1.60 ( ( ! [Y2: A] :
% 2.96/1.60 ( X2
% 2.96/1.60 != ( some @ A @ Y2 ) ) )
% 2.96/1.60 = ( X2
% 2.96/1.60 = ( none @ A ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_117_sup__Some,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( sup @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] :
% 2.96/1.60 ( ( sup_sup @ ( option @ A ) @ ( some @ A @ X2 ) @ ( some @ A @ Y3 ) )
% 2.96/1.60 = ( some @ A @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_118_option_Oinject,axiom,
% 2.96/1.60 ! [A: $tType,X22: A,Y22: A] :
% 2.96/1.60 ( ( ( some @ A @ X22 )
% 2.96/1.60 = ( some @ A @ Y22 ) )
% 2.96/1.60 = ( X22 = Y22 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_119_less__eq__option__Some,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( preorder @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] :
% 2.96/1.60 ( ( ord_less_eq @ ( option @ A ) @ ( some @ A @ X2 ) @ ( some @ A @ Y3 ) )
% 2.96/1.60 = ( ord_less_eq @ A @ X2 @ Y3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_120_sup__None__1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( sup @ A )
% 2.96/1.60 => ! [Y3: option @ A] :
% 2.96/1.60 ( ( sup_sup @ ( option @ A ) @ ( none @ A ) @ Y3 )
% 2.96/1.60 = Y3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_121_sup__None__2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( sup @ A )
% 2.96/1.60 => ! [X2: option @ A] :
% 2.96/1.60 ( ( sup_sup @ ( option @ A ) @ X2 @ ( none @ A ) )
% 2.96/1.60 = X2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_122_zip__same,axiom,
% 2.96/1.60 ! [A: $tType,A2: A,B2: A,Xs: list @ A] :
% 2.96/1.60 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( set2 @ ( product_prod @ A @ A ) @ ( zip @ A @ A @ Xs @ Xs ) ) )
% 2.96/1.60 = ( ( member @ A @ A2 @ ( set2 @ A @ Xs ) )
% 2.96/1.60 & ( A2 = B2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_123__C1_C,axiom,
% 2.96/1.60 ! [G2: g,P2: set @ val] :
% 2.96/1.60 ( ( irredu2110905762nt_set @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ P2 )
% 2.96/1.60 => ? [Scc2: set @ val] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ val ) @ Scc2 @ P2 )
% 2.96/1.60 & ( irredu2110774547nt_scc @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ P2 @ Scc2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_124_phiUsesE,axiom,
% 2.96/1.60 ! [V: val,G2: g,N: node] :
% 2.96/1.60 ( ( member @ val @ V @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) )
% 2.96/1.60 => ~ ! [N5: node] :
% 2.96/1.60 ( ( member @ node @ N5 @ ( set2 @ node @ ( graph_449533722essors @ g @ node @ edgeD @ alpha_n @ inEdges @ G2 @ N ) ) )
% 2.96/1.60 => ! [V6: val,Vs4: list @ val] :
% 2.96/1.60 ( ( member @ ( product_prod @ node @ val ) @ ( product_Pair @ node @ val @ N @ V ) @ ( set2 @ ( product_prod @ node @ val ) @ ( zip @ node @ val @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N5 ) @ Vs4 ) ) )
% 2.96/1.60 => ( ( phis @ G2 @ ( product_Pair @ node @ val @ N5 @ V6 ) )
% 2.96/1.60 != ( some @ ( list @ val ) @ Vs4 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_125_finite__has__minimal2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( order @ A )
% 2.96/1.60 => ! [A3: set @ A,A2: A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ A3 )
% 2.96/1.60 => ( ( member @ A @ A2 @ A3 )
% 2.96/1.60 => ? [X3: A] :
% 2.96/1.60 ( ( member @ A @ X3 @ A3 )
% 2.96/1.60 & ( ord_less_eq @ A @ X3 @ A2 )
% 2.96/1.60 & ! [Xa: A] :
% 2.96/1.60 ( ( member @ A @ Xa @ A3 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ Xa @ X3 )
% 2.96/1.60 => ( X3 = Xa ) ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_126_finite__has__maximal2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( order @ A )
% 2.96/1.60 => ! [A3: set @ A,A2: A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ A3 )
% 2.96/1.60 => ( ( member @ A @ A2 @ A3 )
% 2.96/1.60 => ? [X3: A] :
% 2.96/1.60 ( ( member @ A @ X3 @ A3 )
% 2.96/1.60 & ( ord_less_eq @ A @ A2 @ X3 )
% 2.96/1.60 & ! [Xa: A] :
% 2.96/1.60 ( ( member @ A @ Xa @ A3 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ X3 @ Xa )
% 2.96/1.60 => ( X3 = Xa ) ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_127_subset__code_I1_J,axiom,
% 2.96/1.60 ! [A: $tType,Xs: list @ A,B3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ B3 )
% 2.96/1.60 = ( ! [X: A] :
% 2.96/1.60 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.96/1.60 => ( member @ A @ X @ B3 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_128_rev__finite__subset,axiom,
% 2.96/1.60 ! [A: $tType,B3: set @ A,A3: set @ A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ B3 )
% 2.96/1.60 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 => ( finite_finite2 @ A @ A3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_129_infinite__super,axiom,
% 2.96/1.60 ! [A: $tType,S: set @ A,T: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ S @ T )
% 2.96/1.60 => ( ~ ( finite_finite2 @ A @ S )
% 2.96/1.60 => ~ ( finite_finite2 @ A @ T ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_130_finite__subset,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 => ( ( finite_finite2 @ A @ B3 )
% 2.96/1.60 => ( finite_finite2 @ A @ A3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_131_in__set__zipE,axiom,
% 2.96/1.60 ! [A: $tType,B: $tType,X2: A,Y3: B,Xs: list @ A,Ys: list @ B] :
% 2.96/1.60 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs @ Ys ) ) )
% 2.96/1.60 => ~ ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.96/1.60 => ~ ( member @ B @ Y3 @ ( set2 @ B @ Ys ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_132_set__zip__leftD,axiom,
% 2.96/1.60 ! [B: $tType,A: $tType,X2: A,Y3: B,Xs: list @ A,Ys: list @ B] :
% 2.96/1.60 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs @ Ys ) ) )
% 2.96/1.60 => ( member @ A @ X2 @ ( set2 @ A @ Xs ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_133_set__zip__rightD,axiom,
% 2.96/1.60 ! [A: $tType,B: $tType,X2: A,Y3: B,Xs: list @ A,Ys: list @ B] :
% 2.96/1.60 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( zip @ A @ B @ Xs @ Ys ) ) )
% 2.96/1.60 => ( member @ B @ Y3 @ ( set2 @ B @ Ys ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_134_combine__options__cases,axiom,
% 2.96/1.60 ! [A: $tType,B: $tType,X2: option @ A,P2: ( option @ A ) > ( option @ B ) > $o,Y3: option @ B] :
% 2.96/1.60 ( ( ( X2
% 2.96/1.60 = ( none @ A ) )
% 2.96/1.60 => ( P2 @ X2 @ Y3 ) )
% 2.96/1.60 => ( ( ( Y3
% 2.96/1.60 = ( none @ B ) )
% 2.96/1.60 => ( P2 @ X2 @ Y3 ) )
% 2.96/1.60 => ( ! [A6: A,B4: B] :
% 2.96/1.60 ( ( X2
% 2.96/1.60 = ( some @ A @ A6 ) )
% 2.96/1.60 => ( ( Y3
% 2.96/1.60 = ( some @ B @ B4 ) )
% 2.96/1.60 => ( P2 @ X2 @ Y3 ) ) )
% 2.96/1.60 => ( P2 @ X2 @ Y3 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_135_split__option__all,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( ^ [P3: ( option @ A ) > $o] :
% 2.96/1.60 ! [X5: option @ A] : ( P3 @ X5 ) )
% 2.96/1.60 = ( ^ [P4: ( option @ A ) > $o] :
% 2.96/1.60 ( ( P4 @ ( none @ A ) )
% 2.96/1.60 & ! [X: A] : ( P4 @ ( some @ A @ X ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_136_split__option__ex,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( ^ [P3: ( option @ A ) > $o] :
% 2.96/1.60 ? [X5: option @ A] : ( P3 @ X5 ) )
% 2.96/1.60 = ( ^ [P4: ( option @ A ) > $o] :
% 2.96/1.60 ( ( P4 @ ( none @ A ) )
% 2.96/1.60 | ? [X: A] : ( P4 @ ( some @ A @ X ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_137_option_Oinducts,axiom,
% 2.96/1.60 ! [A: $tType,P2: ( option @ A ) > $o,Option: option @ A] :
% 2.96/1.60 ( ( P2 @ ( none @ A ) )
% 2.96/1.60 => ( ! [X3: A] : ( P2 @ ( some @ A @ X3 ) )
% 2.96/1.60 => ( P2 @ Option ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_138_option_Oexhaust,axiom,
% 2.96/1.60 ! [A: $tType,Y3: option @ A] :
% 2.96/1.60 ( ( Y3
% 2.96/1.60 != ( none @ A ) )
% 2.96/1.60 => ~ ! [X23: A] :
% 2.96/1.60 ( Y3
% 2.96/1.60 != ( some @ A @ X23 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_139_option_OdiscI,axiom,
% 2.96/1.60 ! [A: $tType,Option: option @ A,X22: A] :
% 2.96/1.60 ( ( Option
% 2.96/1.60 = ( some @ A @ X22 ) )
% 2.96/1.60 => ( Option
% 2.96/1.60 != ( none @ A ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_140_option_Odistinct_I1_J,axiom,
% 2.96/1.60 ! [A: $tType,X22: A] :
% 2.96/1.60 ( ( none @ A )
% 2.96/1.60 != ( some @ A @ X22 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_141_Ex__condensation__leaf,axiom,
% 2.96/1.60 ! [P2: set @ val,G2: g] :
% 2.96/1.60 ( ( P2
% 2.96/1.60 != ( bot_bot @ ( set @ val ) ) )
% 2.96/1.60 => ? [Leaf: set @ val] :
% 2.96/1.60 ( ( member @ ( set @ val ) @ Leaf @ ( irredu1918690039_nodes @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) )
% 2.96/1.60 & ! [Scc3: set @ val] :
% 2.96/1.60 ~ ( member @ ( product_prod @ ( set @ val ) @ ( set @ val ) ) @ ( product_Pair @ ( set @ val ) @ ( set @ val ) @ Leaf @ Scc3 ) @ ( irredu280805948_edges @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_142_Un__subset__iff,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A,C: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) @ C )
% 2.96/1.60 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ C )
% 2.96/1.60 & ( ord_less_eq @ ( set @ A ) @ B3 @ C ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_143_le__sup__iff,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A,Y3: A,Z: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X2 @ Y3 ) @ Z )
% 2.96/1.60 = ( ( ord_less_eq @ A @ X2 @ Z )
% 2.96/1.60 & ( ord_less_eq @ A @ Y3 @ Z ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_144_sup_Obounded__iff,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [B2: A,C2: A,A2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 )
% 2.96/1.60 = ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.96/1.60 & ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_145_subset__antisym,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A3 )
% 2.96/1.60 => ( A3 = B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_146_subsetI,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ! [X3: A] :
% 2.96/1.60 ( ( member @ A @ X3 @ A3 )
% 2.96/1.60 => ( member @ A @ X3 @ B3 ) )
% 2.96/1.60 => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_147_sup_Oright__idem,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,B2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ B2 )
% 2.96/1.60 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_148_sup__left__idem,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] :
% 2.96/1.60 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ X2 @ Y3 ) )
% 2.96/1.60 = ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_149_sup_Oleft__idem,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,B2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) )
% 2.96/1.60 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_150_sup__idem,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ X2 @ X2 )
% 2.96/1.60 = X2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_151_sup_Oidem,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ A2 @ A2 )
% 2.96/1.60 = A2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_152_sup__apply,axiom,
% 2.96/1.60 ! [B: $tType,A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ B )
% 2.96/1.60 => ( ( sup_sup @ ( A > B ) )
% 2.96/1.60 = ( ^ [F4: A > B,G3: A > B,X: A] : ( sup_sup @ B @ ( F4 @ X ) @ ( G3 @ X ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_153_Un__iff,axiom,
% 2.96/1.60 ! [A: $tType,C2: A,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 2.96/1.60 = ( ( member @ A @ C2 @ A3 )
% 2.96/1.60 | ( member @ A @ C2 @ B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_154_UnCI,axiom,
% 2.96/1.60 ! [A: $tType,C2: A,B3: set @ A,A3: set @ A] :
% 2.96/1.60 ( ( ~ ( member @ A @ C2 @ B3 )
% 2.96/1.60 => ( member @ A @ C2 @ A3 ) )
% 2.96/1.60 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_155_subset__empty,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.96/1.60 = ( A3
% 2.96/1.60 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_156_empty__subsetI,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_157_sup__bot__left,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( bounde1808546759up_bot @ A )
% 2.96/1.60 => ! [X2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X2 )
% 2.96/1.60 = X2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_158_sup__bot__right,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( bounde1808546759up_bot @ A )
% 2.96/1.60 => ! [X2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ X2 @ ( bot_bot @ A ) )
% 2.96/1.60 = X2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_159_bot__eq__sup__iff,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( bounde1808546759up_bot @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] :
% 2.96/1.60 ( ( ( bot_bot @ A )
% 2.96/1.60 = ( sup_sup @ A @ X2 @ Y3 ) )
% 2.96/1.60 = ( ( X2
% 2.96/1.60 = ( bot_bot @ A ) )
% 2.96/1.60 & ( Y3
% 2.96/1.60 = ( bot_bot @ A ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_160_sup__eq__bot__iff,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( bounde1808546759up_bot @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] :
% 2.96/1.60 ( ( ( sup_sup @ A @ X2 @ Y3 )
% 2.96/1.60 = ( bot_bot @ A ) )
% 2.96/1.60 = ( ( X2
% 2.96/1.60 = ( bot_bot @ A ) )
% 2.96/1.60 & ( Y3
% 2.96/1.60 = ( bot_bot @ A ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_161_sup__bot_Oeq__neutr__iff,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( bounde1808546759up_bot @ A )
% 2.96/1.60 => ! [A2: A,B2: A] :
% 2.96/1.60 ( ( ( sup_sup @ A @ A2 @ B2 )
% 2.96/1.60 = ( bot_bot @ A ) )
% 2.96/1.60 = ( ( A2
% 2.96/1.60 = ( bot_bot @ A ) )
% 2.96/1.60 & ( B2
% 2.96/1.60 = ( bot_bot @ A ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_162_sup__bot_Oleft__neutral,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( bounde1808546759up_bot @ A )
% 2.96/1.60 => ! [A2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 2.96/1.60 = A2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_163_sup__bot_Oneutr__eq__iff,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( bounde1808546759up_bot @ A )
% 2.96/1.60 => ! [A2: A,B2: A] :
% 2.96/1.60 ( ( ( bot_bot @ A )
% 2.96/1.60 = ( sup_sup @ A @ A2 @ B2 ) )
% 2.96/1.60 = ( ( A2
% 2.96/1.60 = ( bot_bot @ A ) )
% 2.96/1.60 & ( B2
% 2.96/1.60 = ( bot_bot @ A ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_164_sup__bot_Oright__neutral,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( bounde1808546759up_bot @ A )
% 2.96/1.60 => ! [A2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 2.96/1.60 = A2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_165_Un__empty,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.60 = ( ( A3
% 2.96/1.60 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.60 & ( B3
% 2.96/1.60 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_166_less__eq__option__None__code,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( preorder @ A )
% 2.96/1.60 => ! [X2: option @ A] : ( ord_less_eq @ ( option @ A ) @ ( none @ A ) @ X2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_167_less__eq__option__Some__None,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( preorder @ A )
% 2.96/1.60 => ! [X2: A] :
% 2.96/1.60 ~ ( ord_less_eq @ ( option @ A ) @ ( some @ A @ X2 ) @ ( none @ A ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_168_old_Osuccessors__predecessors,axiom,
% 2.96/1.60 ! [N: node,G2: g,M: node] :
% 2.96/1.60 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.96/1.60 => ( ( member @ node @ N @ ( set2 @ node @ ( graph_449533722essors @ g @ node @ edgeD @ alpha_n @ inEdges @ G2 @ M ) ) )
% 2.96/1.60 = ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_169_Un__empty__left,axiom,
% 2.96/1.60 ! [A: $tType,B3: set @ A] :
% 2.96/1.60 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B3 )
% 2.96/1.60 = B3 ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_170_Un__empty__right,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A] :
% 2.96/1.60 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.96/1.60 = A3 ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_171_less__eq__option__None__is__None,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( preorder @ A )
% 2.96/1.60 => ! [X2: option @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( option @ A ) @ X2 @ ( none @ A ) )
% 2.96/1.60 => ( X2
% 2.96/1.60 = ( none @ A ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_172_less__eq__option__None,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( preorder @ A )
% 2.96/1.60 => ! [X2: option @ A] : ( ord_less_eq @ ( option @ A ) @ ( none @ A ) @ X2 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_173_infinite__imp__nonempty,axiom,
% 2.96/1.60 ! [A: $tType,S: set @ A] :
% 2.96/1.60 ( ~ ( finite_finite2 @ A @ S )
% 2.96/1.60 => ( S
% 2.96/1.60 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_174_finite_OemptyI,axiom,
% 2.96/1.60 ! [A: $tType] : ( finite_finite2 @ A @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_175_CFG__SSA__Transformed_Oredundant__scc_Ocong,axiom,
% 2.96/1.60 ! [Val: $tType,EdgeD: $tType,Node: $tType,G: $tType] :
% 2.96/1.60 ( ( ( linorder @ Node )
% 2.96/1.60 & ( linorder @ Val ) )
% 2.96/1.60 => ( ( irredu2110774547nt_scc @ G @ Node @ EdgeD @ Val )
% 2.96/1.60 = ( irredu2110774547nt_scc @ G @ Node @ EdgeD @ Val ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_176_finite__has__maximal,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( order @ A )
% 2.96/1.60 => ! [A3: set @ A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ A3 )
% 2.96/1.60 => ( ( A3
% 2.96/1.60 != ( bot_bot @ ( set @ A ) ) )
% 2.96/1.60 => ? [X3: A] :
% 2.96/1.60 ( ( member @ A @ X3 @ A3 )
% 2.96/1.60 & ! [Xa: A] :
% 2.96/1.60 ( ( member @ A @ Xa @ A3 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ X3 @ Xa )
% 2.96/1.60 => ( X3 = Xa ) ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_177_finite__has__minimal,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( order @ A )
% 2.96/1.60 => ! [A3: set @ A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ A3 )
% 2.96/1.60 => ( ( A3
% 2.96/1.60 != ( bot_bot @ ( set @ A ) ) )
% 2.96/1.60 => ? [X3: A] :
% 2.96/1.60 ( ( member @ A @ X3 @ A3 )
% 2.96/1.60 & ! [Xa: A] :
% 2.96/1.60 ( ( member @ A @ Xa @ A3 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ Xa @ X3 )
% 2.96/1.60 => ( X3 = Xa ) ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_178_Collect__mono__iff,axiom,
% 2.96/1.60 ! [A: $tType,P2: A > $o,Q2: A > $o] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q2 ) )
% 2.96/1.60 = ( ! [X: A] :
% 2.96/1.60 ( ( P2 @ X )
% 2.96/1.60 => ( Q2 @ X ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_179_set__eq__subset,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( ^ [Y4: set @ A,Z2: set @ A] : ( Y4 = Z2 ) )
% 2.96/1.60 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.96/1.60 & ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_180_subset__trans,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A,C: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C )
% 2.96/1.60 => ( ord_less_eq @ ( set @ A ) @ A3 @ C ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_181_Collect__mono,axiom,
% 2.96/1.60 ! [A: $tType,P2: A > $o,Q2: A > $o] :
% 2.96/1.60 ( ! [X3: A] :
% 2.96/1.60 ( ( P2 @ X3 )
% 2.96/1.60 => ( Q2 @ X3 ) )
% 2.96/1.60 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P2 ) @ ( collect @ A @ Q2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_182_subset__refl,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_183_subset__iff,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.60 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.60 ! [T2: A] :
% 2.96/1.60 ( ( member @ A @ T2 @ A5 )
% 2.96/1.60 => ( member @ A @ T2 @ B5 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_184_equalityD2,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( A3 = B3 )
% 2.96/1.60 => ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_185_equalityD1,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( A3 = B3 )
% 2.96/1.60 => ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_186_subset__eq,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.60 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.60 ! [X: A] :
% 2.96/1.60 ( ( member @ A @ X @ A5 )
% 2.96/1.60 => ( member @ A @ X @ B5 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_187_equalityE,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( A3 = B3 )
% 2.96/1.60 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_188_subsetD,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A,C2: A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 => ( ( member @ A @ C2 @ A3 )
% 2.96/1.60 => ( member @ A @ C2 @ B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_189_in__mono,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A,X2: A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 => ( ( member @ A @ X2 @ A3 )
% 2.96/1.60 => ( member @ A @ X2 @ B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_190_sup__left__commute,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A,Y3: A,Z: A] :
% 2.96/1.60 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y3 @ Z ) )
% 2.96/1.60 = ( sup_sup @ A @ Y3 @ ( sup_sup @ A @ X2 @ Z ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_191_sup_Oleft__commute,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [B2: A,A2: A,C2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ B2 @ ( sup_sup @ A @ A2 @ C2 ) )
% 2.96/1.60 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_192_sup__commute,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ( ( sup_sup @ A )
% 2.96/1.60 = ( ^ [X: A,Y2: A] : ( sup_sup @ A @ Y2 @ X ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_193_sup_Ocommute,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ( ( sup_sup @ A )
% 2.96/1.60 = ( ^ [A4: A,B6: A] : ( sup_sup @ A @ B6 @ A4 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_194_sup__assoc,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A,Y3: A,Z: A] :
% 2.96/1.60 ( ( sup_sup @ A @ ( sup_sup @ A @ X2 @ Y3 ) @ Z )
% 2.96/1.60 = ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y3 @ Z ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_195_sup_Oassoc,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,B2: A,C2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ C2 )
% 2.96/1.60 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_196_boolean__algebra__cancel_Osup2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [B3: A,K: A,B2: A,A2: A] :
% 2.96/1.60 ( ( B3
% 2.96/1.60 = ( sup_sup @ A @ K @ B2 ) )
% 2.96/1.60 => ( ( sup_sup @ A @ A2 @ B3 )
% 2.96/1.60 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_197_boolean__algebra__cancel_Osup1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A3: A,K: A,A2: A,B2: A] :
% 2.96/1.60 ( ( A3
% 2.96/1.60 = ( sup_sup @ A @ K @ A2 ) )
% 2.96/1.60 => ( ( sup_sup @ A @ A3 @ B2 )
% 2.96/1.60 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_198_sup__fun__def,axiom,
% 2.96/1.60 ! [B: $tType,A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ B )
% 2.96/1.60 => ( ( sup_sup @ ( A > B ) )
% 2.96/1.60 = ( ^ [F4: A > B,G3: A > B,X: A] : ( sup_sup @ B @ ( F4 @ X ) @ ( G3 @ X ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_199_inf__sup__aci_I5_J,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( lattice @ A )
% 2.96/1.60 => ( ( sup_sup @ A )
% 2.96/1.60 = ( ^ [X: A,Y2: A] : ( sup_sup @ A @ Y2 @ X ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_200_inf__sup__aci_I6_J,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( lattice @ A )
% 2.96/1.60 => ! [X2: A,Y3: A,Z: A] :
% 2.96/1.60 ( ( sup_sup @ A @ ( sup_sup @ A @ X2 @ Y3 ) @ Z )
% 2.96/1.60 = ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y3 @ Z ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_201_inf__sup__aci_I7_J,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( lattice @ A )
% 2.96/1.60 => ! [X2: A,Y3: A,Z: A] :
% 2.96/1.60 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ Y3 @ Z ) )
% 2.96/1.60 = ( sup_sup @ A @ Y3 @ ( sup_sup @ A @ X2 @ Z ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_202_inf__sup__aci_I8_J,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( lattice @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] :
% 2.96/1.60 ( ( sup_sup @ A @ X2 @ ( sup_sup @ A @ X2 @ Y3 ) )
% 2.96/1.60 = ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_203_Un__left__commute,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A,C: set @ A] :
% 2.96/1.60 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B3 @ C ) )
% 2.96/1.60 = ( sup_sup @ ( set @ A ) @ B3 @ ( sup_sup @ ( set @ A ) @ A3 @ C ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_204_Un__left__absorb,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 2.96/1.60 = ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_205_Un__commute,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( sup_sup @ ( set @ A ) )
% 2.96/1.60 = ( ^ [A5: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_206_Un__absorb,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A] :
% 2.96/1.60 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 2.96/1.60 = A3 ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_207_Un__assoc,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A,C: set @ A] :
% 2.96/1.60 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) @ C )
% 2.96/1.60 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B3 @ C ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_208_ball__Un,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A,P2: A > $o] :
% 2.96/1.60 ( ( ! [X: A] :
% 2.96/1.60 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 2.96/1.60 => ( P2 @ X ) ) )
% 2.96/1.60 = ( ! [X: A] :
% 2.96/1.60 ( ( member @ A @ X @ A3 )
% 2.96/1.60 => ( P2 @ X ) )
% 2.96/1.60 & ! [X: A] :
% 2.96/1.60 ( ( member @ A @ X @ B3 )
% 2.96/1.60 => ( P2 @ X ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_209_bex__Un,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A,P2: A > $o] :
% 2.96/1.60 ( ( ? [X: A] :
% 2.96/1.60 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 2.96/1.60 & ( P2 @ X ) ) )
% 2.96/1.60 = ( ? [X: A] :
% 2.96/1.60 ( ( member @ A @ X @ A3 )
% 2.96/1.60 & ( P2 @ X ) )
% 2.96/1.60 | ? [X: A] :
% 2.96/1.60 ( ( member @ A @ X @ B3 )
% 2.96/1.60 & ( P2 @ X ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_210_UnI2,axiom,
% 2.96/1.60 ! [A: $tType,C2: A,B3: set @ A,A3: set @ A] :
% 2.96/1.60 ( ( member @ A @ C2 @ B3 )
% 2.96/1.60 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_211_UnI1,axiom,
% 2.96/1.60 ! [A: $tType,C2: A,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( member @ A @ C2 @ A3 )
% 2.96/1.60 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_212_UnE,axiom,
% 2.96/1.60 ! [A: $tType,C2: A,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 2.96/1.60 => ( ~ ( member @ A @ C2 @ A3 )
% 2.96/1.60 => ( member @ A @ C2 @ B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_213_sup_OcoboundedI2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [C2: A,B2: A,A2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ C2 @ B2 )
% 2.96/1.60 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_214_sup_OcoboundedI1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [C2: A,A2: A,B2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ C2 @ A2 )
% 2.96/1.60 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_215_sup_Oabsorb__iff2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ( ( ord_less_eq @ A )
% 2.96/1.60 = ( ^ [A4: A,B6: A] :
% 2.96/1.60 ( ( sup_sup @ A @ A4 @ B6 )
% 2.96/1.60 = B6 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_216_sup_Oabsorb__iff1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ( ( ord_less_eq @ A )
% 2.96/1.60 = ( ^ [B6: A,A4: A] :
% 2.96/1.60 ( ( sup_sup @ A @ A4 @ B6 )
% 2.96/1.60 = A4 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_217_sup_Ocobounded2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [B2: A,A2: A] : ( ord_less_eq @ A @ B2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_218_sup_Ocobounded1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_219_sup_Oorder__iff,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ( ( ord_less_eq @ A )
% 2.96/1.60 = ( ^ [B6: A,A4: A] :
% 2.96/1.60 ( A4
% 2.96/1.60 = ( sup_sup @ A @ A4 @ B6 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_220_sup_OboundedI,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [B2: A,A2: A,C2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ C2 @ A2 )
% 2.96/1.60 => ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_221_sup_OboundedE,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [B2: A,C2: A,A2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 )
% 2.96/1.60 => ~ ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.96/1.60 => ~ ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_222_sup__absorb2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.96/1.60 => ( ( sup_sup @ A @ X2 @ Y3 )
% 2.96/1.60 = Y3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_223_sup__absorb1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [Y3: A,X2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ Y3 @ X2 )
% 2.96/1.60 => ( ( sup_sup @ A @ X2 @ Y3 )
% 2.96/1.60 = X2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_224_sup_Oabsorb2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,B2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.96/1.60 => ( ( sup_sup @ A @ A2 @ B2 )
% 2.96/1.60 = B2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_225_sup_Oabsorb1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [B2: A,A2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.96/1.60 => ( ( sup_sup @ A @ A2 @ B2 )
% 2.96/1.60 = A2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_226_sup__unique,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [F: A > A > A,X2: A,Y3: A] :
% 2.96/1.60 ( ! [X3: A,Y5: A] : ( ord_less_eq @ A @ X3 @ ( F @ X3 @ Y5 ) )
% 2.96/1.60 => ( ! [X3: A,Y5: A] : ( ord_less_eq @ A @ Y5 @ ( F @ X3 @ Y5 ) )
% 2.96/1.60 => ( ! [X3: A,Y5: A,Z3: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ Y5 @ X3 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ Z3 @ X3 )
% 2.96/1.60 => ( ord_less_eq @ A @ ( F @ Y5 @ Z3 ) @ X3 ) ) )
% 2.96/1.60 => ( ( sup_sup @ A @ X2 @ Y3 )
% 2.96/1.60 = ( F @ X2 @ Y3 ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_227_sup_OorderI,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,B2: A] :
% 2.96/1.60 ( ( A2
% 2.96/1.60 = ( sup_sup @ A @ A2 @ B2 ) )
% 2.96/1.60 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_228_sup_OorderE,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [B2: A,A2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.96/1.60 => ( A2
% 2.96/1.60 = ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_229_le__iff__sup,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ( ( ord_less_eq @ A )
% 2.96/1.60 = ( ^ [X: A,Y2: A] :
% 2.96/1.60 ( ( sup_sup @ A @ X @ Y2 )
% 2.96/1.60 = Y2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_230_sup__least,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [Y3: A,X2: A,Z: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ Y3 @ X2 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ Z @ X2 )
% 2.96/1.60 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y3 @ Z ) @ X2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_231_sup__mono,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,C2: A,B2: A,D: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ A2 @ C2 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ B2 @ D )
% 2.96/1.60 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ ( sup_sup @ A @ C2 @ D ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_232_sup_Omono,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [C2: A,A2: A,D: A,B2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ C2 @ A2 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ D @ B2 )
% 2.96/1.60 => ( ord_less_eq @ A @ ( sup_sup @ A @ C2 @ D ) @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_233_le__supI2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A,B2: A,A2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ X2 @ B2 )
% 2.96/1.60 => ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_234_le__supI1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A,A2: A,B2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ X2 @ A2 )
% 2.96/1.60 => ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_235_sup__ge2,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [Y3: A,X2: A] : ( ord_less_eq @ A @ Y3 @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_236_sup__ge1,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] : ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_237_le__supI,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,X2: A,B2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ A2 @ X2 )
% 2.96/1.60 => ( ( ord_less_eq @ A @ B2 @ X2 )
% 2.96/1.60 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_238_le__supE,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A )
% 2.96/1.60 => ! [A2: A,B2: A,X2: A] :
% 2.96/1.60 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X2 )
% 2.96/1.60 => ~ ( ( ord_less_eq @ A @ A2 @ X2 )
% 2.96/1.60 => ~ ( ord_less_eq @ A @ B2 @ X2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_239_inf__sup__ord_I3_J,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( lattice @ A )
% 2.96/1.60 => ! [X2: A,Y3: A] : ( ord_less_eq @ A @ X2 @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_240_inf__sup__ord_I4_J,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( lattice @ A )
% 2.96/1.60 => ! [Y3: A,X2: A] : ( ord_less_eq @ A @ Y3 @ ( sup_sup @ A @ X2 @ Y3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_241_subset__Un__eq,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.60 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.96/1.60 ( ( sup_sup @ ( set @ A ) @ A5 @ B5 )
% 2.96/1.60 = B5 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_242_subset__UnE,axiom,
% 2.96/1.60 ! [A: $tType,C: set @ A,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) )
% 2.96/1.60 => ~ ! [A7: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A7 @ A3 )
% 2.96/1.60 => ! [B7: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ B7 @ B3 )
% 2.96/1.60 => ( C
% 2.96/1.60 != ( sup_sup @ ( set @ A ) @ A7 @ B7 ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_243_Un__absorb2,axiom,
% 2.96/1.60 ! [A: $tType,B3: set @ A,A3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ B3 @ A3 )
% 2.96/1.60 => ( ( sup_sup @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 = A3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_244_Un__absorb1,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 => ( ( sup_sup @ ( set @ A ) @ A3 @ B3 )
% 2.96/1.60 = B3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_245_Un__upper2,axiom,
% 2.96/1.60 ! [A: $tType,B3: set @ A,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ B3 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_246_Un__upper1,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_247_Un__least,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,C: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C )
% 2.96/1.60 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ C )
% 2.96/1.60 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) @ C ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_248_Un__mono,axiom,
% 2.96/1.60 ! [A: $tType,A3: set @ A,C: set @ A,B3: set @ A,D2: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C )
% 2.96/1.60 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ D2 )
% 2.96/1.60 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B3 ) @ ( sup_sup @ ( set @ A ) @ C @ D2 ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_249_redundant__set__def,axiom,
% 2.96/1.60 ! [G2: g,P2: set @ val] :
% 2.96/1.60 ( ( irredu2110905762nt_set @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 @ P2 )
% 2.96/1.60 = ( ( P2
% 2.96/1.60 != ( bot_bot @ ( set @ val ) ) )
% 2.96/1.60 & ( ord_less_eq @ ( set @ val ) @ P2 @ ( dom @ val @ ( list @ val ) @ ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 ) ) )
% 2.96/1.60 & ? [X: val] :
% 2.96/1.60 ( ( member @ val @ X @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.96/1.60 & ! [Y2: val] :
% 2.96/1.60 ( ( member @ val @ Y2 @ P2 )
% 2.96/1.60 => ! [Phi3: val] :
% 2.96/1.60 ( ( sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ Y2 @ Phi3 )
% 2.96/1.60 => ( member @ val @ Phi3 @ ( sup_sup @ ( set @ val ) @ P2 @ ( insert @ val @ X @ ( bot_bot @ ( set @ val ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_250_phi__no__closed__loop,axiom,
% 2.96/1.60 ! [P: val,G2: g,Vs: list @ val] :
% 2.96/1.60 ( ( member @ val @ P @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ G2 ) )
% 2.96/1.60 => ( ( ( sSA_CFG_SSA_wf_phi @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ P )
% 2.96/1.60 = ( some @ ( list @ val ) @ Vs ) )
% 2.96/1.60 => ( ( set2 @ val @ Vs )
% 2.96/1.60 != ( insert @ val @ P @ ( bot_bot @ ( set @ val ) ) ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_251_dom__eq__empty__conv,axiom,
% 2.96/1.60 ! [B: $tType,A: $tType,F: A > ( option @ B )] :
% 2.96/1.60 ( ( ( dom @ A @ B @ F )
% 2.96/1.60 = ( bot_bot @ ( set @ A ) ) )
% 2.96/1.60 = ( F
% 2.96/1.60 = ( ^ [X: A] : ( none @ B ) ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_252_phis__finite,axiom,
% 2.96/1.60 ! [G2: g] : ( finite_finite2 @ ( product_prod @ node @ val ) @ ( dom @ ( product_prod @ node @ val ) @ ( list @ val ) @ ( phis @ G2 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_253_insert__subset,axiom,
% 2.96/1.60 ! [A: $tType,X2: A,A3: set @ A,B3: set @ A] :
% 2.96/1.60 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X2 @ A3 ) @ B3 )
% 2.96/1.60 = ( ( member @ A @ X2 @ B3 )
% 2.96/1.60 & ( ord_less_eq @ ( set @ A ) @ A3 @ B3 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(fact_254_finite__insert,axiom,
% 2.96/1.60 ! [A: $tType,A2: A,A3: set @ A] :
% 2.96/1.60 ( ( finite_finite2 @ A @ ( insert @ A @ A2 @ A3 ) )
% 2.96/1.60 = ( finite_finite2 @ A @ A3 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( linorder @ A )
% 2.96/1.60 => ( type @ A ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( linorder @ A )
% 2.96/1.60 => ( order @ A ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 2.96/1.60 ! [A: $tType] :
% 2.96/1.60 ( ( linorder @ A )
% 2.96/1.60 => ( preorder @ A ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Lattices_Obounded__lattice,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( bounded_lattice_top @ A8 )
% 2.96/1.60 => ( bounded_lattice @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Lattices_Obounded__lattice_1,axiom,
% 2.96/1.60 bounded_lattice @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Lattices_Obounded__lattice_2,axiom,
% 2.96/1.60 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Lattices_Obounded__lattice_3,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( bounded_lattice @ A9 )
% 2.96/1.60 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( bounded_lattice @ A9 )
% 2.96/1.60 => ( bounded_lattice_top @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_4,axiom,
% 2.96/1.60 ! [A8: $tType] : ( bounded_lattice_top @ ( set @ A8 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_5,axiom,
% 2.96/1.60 bounded_lattice_top @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Lattices_Obounded__lattice__top_6,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( bounded_lattice_top @ A8 )
% 2.96/1.60 => ( bounded_lattice_top @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( bounded_lattice @ A9 )
% 2.96/1.60 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A9 )
% 2.96/1.60 => ( semilattice_sup @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( preorder @ A9 )
% 2.96/1.60 => ( preorder @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( ( finite_finite @ A8 )
% 2.96/1.60 & ( finite_finite @ A9 ) )
% 2.96/1.60 => ( finite_finite @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( lattice @ A9 )
% 2.96/1.60 => ( lattice @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( order @ A9 )
% 2.96/1.60 => ( order @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_fun___Lattices_Osup,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A9 )
% 2.96/1.60 => ( sup @ ( A8 > A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 2.96/1.60 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_8,axiom,
% 2.96/1.60 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Orderings_Opreorder_9,axiom,
% 2.96/1.60 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Finite__Set_Ofinite_10,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( finite_finite @ A8 )
% 2.96/1.60 => ( finite_finite @ ( set @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Lattices_Olattice_11,axiom,
% 2.96/1.60 ! [A8: $tType] : ( lattice @ ( set @ A8 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Orderings_Oorder_12,axiom,
% 2.96/1.60 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Set_Oset___Lattices_Osup_13,axiom,
% 2.96/1.60 ! [A8: $tType] : ( sup @ ( set @ A8 ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14,axiom,
% 2.96/1.60 bounde1808546759up_bot @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_15,axiom,
% 2.96/1.60 semilattice_sup @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Orderings_Opreorder_16,axiom,
% 2.96/1.60 preorder @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.96/1.60 linorder @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Finite__Set_Ofinite_17,axiom,
% 2.96/1.60 finite_finite @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Lattices_Olattice_18,axiom,
% 2.96/1.60 lattice @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Orderings_Oorder_19,axiom,
% 2.96/1.60 order @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_HOL_Obool___Lattices_Osup_20,axiom,
% 2.96/1.60 sup @ $o ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Lattices_Obounded__semilattice__sup__bot_21,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( lattice @ A8 )
% 2.96/1.60 => ( bounde1808546759up_bot @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Lattices_Osemilattice__sup_22,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( semilattice_sup @ A8 )
% 2.96/1.60 => ( semilattice_sup @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Orderings_Opreorder_23,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( preorder @ A8 )
% 2.96/1.60 => ( preorder @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Orderings_Olinorder_24,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( linorder @ A8 )
% 2.96/1.60 => ( linorder @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Finite__Set_Ofinite_25,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( finite_finite @ A8 )
% 2.96/1.60 => ( finite_finite @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Lattices_Olattice_26,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( lattice @ A8 )
% 2.96/1.60 => ( lattice @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Orderings_Oorder_27,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( order @ A8 )
% 2.96/1.60 => ( order @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Option_Ooption___Lattices_Osup_28,axiom,
% 2.96/1.60 ! [A8: $tType] :
% 2.96/1.60 ( ( sup @ A8 )
% 2.96/1.60 => ( sup @ ( option @ A8 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tcon_Product__Type_Oprod___Finite__Set_Ofinite_29,axiom,
% 2.96/1.60 ! [A8: $tType,A9: $tType] :
% 2.96/1.60 ( ( ( finite_finite @ A8 )
% 2.96/1.60 & ( finite_finite @ A9 ) )
% 2.96/1.60 => ( finite_finite @ ( product_prod @ A8 @ A9 ) ) ) ).
% 2.96/1.60
% 2.96/1.60 thf(tfree_0,hypothesis,
% 2.96/1.60 linorder @ val ).
% 2.96/1.60
% 2.96/1.60 thf(tfree_1,hypothesis,
% 2.96/1.60 linorder @ node ).
% 2.96/1.60
% 2.96/1.60 thf(tfree_2,hypothesis,
% 2.96/1.60 linorder @ var ).
% 2.96/1.60
% 2.96/1.60 thf(conj_0,conjecture,
% 2.96/1.60 member @ val @ phi_s @ ( sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 2.96/1.60 ------------------------
% 2.96/1.64 % (3727)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/27Mi)
% 2.96/1.64 % (3726)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/4Mi)
% 2.96/1.64 % (3729)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/2Mi)
% 2.96/1.64 % (3726)Instruction limit reached!
% 2.96/1.64 % (3726)------------------------------
% 2.96/1.64 % (3726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.64 % (3726)Termination reason: Unknown
% 2.96/1.64 % (3726)Termination phase: shuffling
% 2.96/1.64
% 2.96/1.64 % (3726)Memory used [KB]: 1407
% 2.96/1.64 % (3726)Time elapsed: 0.003 s
% 2.96/1.64 % (3726)Instructions burned: 4 (million)
% 2.96/1.64 % (3726)------------------------------
% 2.96/1.64 % (3726)------------------------------
% 2.96/1.64 % (3729)Instruction limit reached!
% 2.96/1.64 % (3729)------------------------------
% 2.96/1.64 % (3729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.64 % (3729)Termination reason: Unknown
% 2.96/1.64 % (3729)Termination phase: shuffling
% 2.96/1.64
% 2.96/1.64 % (3729)Memory used [KB]: 1407
% 2.96/1.64 % (3729)Time elapsed: 0.002 s
% 2.96/1.64 % (3729)Instructions burned: 3 (million)
% 2.96/1.64 % (3729)------------------------------
% 2.96/1.64 % (3729)------------------------------
% 2.96/1.64 % (3725)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/183Mi)
% 2.96/1.64 % (3728)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/2Mi)
% 2.96/1.64 % (3730)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/275Mi)
% 2.96/1.64 % (3731)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/18Mi)
% 2.96/1.65 % (3727)Instruction limit reached!
% 2.96/1.65 % (3727)------------------------------
% 2.96/1.65 % (3727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.65 % (3727)Termination reason: Unknown
% 2.96/1.65 % (3727)Termination phase: shuffling
% 2.96/1.65
% 2.96/1.65 % (3727)Memory used [KB]: 1791
% 2.96/1.65 % (3727)Time elapsed: 0.011 s
% 2.96/1.65 % (3727)Instructions burned: 29 (million)
% 2.96/1.65 % (3727)------------------------------
% 2.96/1.65 % (3727)------------------------------
% 2.96/1.65 % (3728)Instruction limit reached!
% 2.96/1.65 % (3728)------------------------------
% 2.96/1.65 % (3728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.65 % (3728)Termination reason: Unknown
% 2.96/1.65 % (3728)Termination phase: shuffling
% 2.96/1.65
% 2.96/1.65 % (3728)Memory used [KB]: 1407
% 2.96/1.65 % (3728)Time elapsed: 0.004 s
% 2.96/1.65 % (3728)Instructions burned: 3 (million)
% 2.96/1.65 % (3728)------------------------------
% 2.96/1.65 % (3728)------------------------------
% 2.96/1.65 % (3733)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/37Mi)
% 2.96/1.66 % (3731)Instruction limit reached!
% 2.96/1.66 % (3731)------------------------------
% 2.96/1.66 % (3731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.66 % (3731)Termination reason: Unknown
% 2.96/1.66 % (3731)Termination phase: shuffling
% 2.96/1.66
% 2.96/1.66 % (3731)Memory used [KB]: 1535
% 2.96/1.66 % (3731)Time elapsed: 0.013 s
% 2.96/1.66 % (3731)Instructions burned: 18 (million)
% 2.96/1.66 % (3731)------------------------------
% 2.96/1.66 % (3731)------------------------------
% 2.96/1.66 % (3734)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/15Mi)
% 2.96/1.66 % (3732)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/3Mi)
% 2.96/1.66 % (3732)Instruction limit reached!
% 2.96/1.66 % (3732)------------------------------
% 2.96/1.66 % (3732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.66 % (3732)Termination reason: Unknown
% 2.96/1.66 % (3732)Termination phase: shuffling
% 2.96/1.66
% 2.96/1.66 % (3732)Memory used [KB]: 1407
% 2.96/1.66 % (3732)Time elapsed: 0.004 s
% 2.96/1.66 % (3732)Instructions burned: 3 (million)
% 2.96/1.66 % (3732)------------------------------
% 2.96/1.66 % (3732)------------------------------
% 2.96/1.66 % (3733)Instruction limit reached!
% 2.96/1.66 % (3733)------------------------------
% 2.96/1.66 % (3733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.66 % (3733)Termination reason: Unknown
% 2.96/1.66 % (3733)Termination phase: shuffling
% 2.96/1.66
% 2.96/1.66 % (3733)Memory used [KB]: 2174
% 2.96/1.66 % (3733)Time elapsed: 0.013 s
% 2.96/1.66 % (3733)Instructions burned: 37 (million)
% 2.96/1.66 % (3733)------------------------------
% 2.96/1.66 % (3733)------------------------------
% 2.96/1.66 % (3734)Instruction limit reached!
% 2.96/1.66 % (3734)------------------------------
% 2.96/1.66 % (3734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.66 % (3734)Termination reason: Unknown
% 2.96/1.66 % (3734)Termination phase: shuffling
% 2.96/1.66
% 2.96/1.66 % (3734)Memory used [KB]: 1535
% 2.96/1.66 % (3734)Time elapsed: 0.006 s
% 2.96/1.66 % (3734)Instructions burned: 15 (million)
% 2.96/1.66 % (3734)------------------------------
% 2.96/1.66 % (3734)------------------------------
% 2.96/1.66 % (3735)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/3Mi)
% 2.96/1.67 % (3735)Instruction limit reached!
% 2.96/1.67 % (3735)------------------------------
% 2.96/1.67 % (3735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.67 % (3735)Termination reason: Unknown
% 2.96/1.67 % (3735)Termination phase: shuffling
% 2.96/1.67
% 2.96/1.67 % (3735)Memory used [KB]: 1407
% 2.96/1.67 % (3735)Time elapsed: 0.004 s
% 2.96/1.67 % (3735)Instructions burned: 4 (million)
% 2.96/1.67 % (3735)------------------------------
% 2.96/1.67 % (3735)------------------------------
% 2.96/1.67 % (3738)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/16Mi)
% 2.96/1.67 % (3739)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/3Mi)
% 2.96/1.67 % (3739)Instruction limit reached!
% 2.96/1.67 % (3739)------------------------------
% 2.96/1.67 % (3739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.67 % (3739)Termination reason: Unknown
% 2.96/1.67 % (3739)Termination phase: shuffling
% 2.96/1.67
% 2.96/1.67 % (3739)Memory used [KB]: 1407
% 2.96/1.67 % (3739)Time elapsed: 0.002 s
% 2.96/1.67 % (3739)Instructions burned: 3 (million)
% 2.96/1.67 % (3739)------------------------------
% 2.96/1.67 % (3739)------------------------------
% 2.96/1.67 % (3736)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/1041Mi)
% 2.96/1.68 % (3737)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/7Mi)
% 2.96/1.68 % (3738)Instruction limit reached!
% 2.96/1.68 % (3738)------------------------------
% 2.96/1.68 % (3738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.68 % (3738)Termination reason: Unknown
% 2.96/1.68 % (3738)Termination phase: shuffling
% 2.96/1.68
% 2.96/1.68 % (3738)Memory used [KB]: 1535
% 2.96/1.68 % (3738)Time elapsed: 0.008 s
% 2.96/1.68 % (3738)Instructions burned: 18 (million)
% 2.96/1.68 % (3738)------------------------------
% 2.96/1.68 % (3738)------------------------------
% 2.96/1.68 % (3740)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/3Mi)
% 2.96/1.68 % (3737)Instruction limit reached!
% 2.96/1.68 % (3737)------------------------------
% 2.96/1.68 % (3737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.68 % (3737)Termination reason: Unknown
% 2.96/1.68 % (3737)Termination phase: shuffling
% 2.96/1.68
% 2.96/1.68 % (3737)Memory used [KB]: 1407
% 2.96/1.68 % (3737)Time elapsed: 0.006 s
% 2.96/1.68 % (3737)Instructions burned: 7 (million)
% 2.96/1.68 % (3737)------------------------------
% 2.96/1.68 % (3737)------------------------------
% 2.96/1.68 % (3740)Instruction limit reached!
% 2.96/1.68 % (3740)------------------------------
% 2.96/1.68 % (3740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.68 % (3740)Termination reason: Unknown
% 2.96/1.68 % (3740)Termination phase: shuffling
% 2.96/1.68
% 2.96/1.68 % (3740)Memory used [KB]: 1407
% 2.96/1.68 % (3740)Time elapsed: 0.003 s
% 2.96/1.68 % (3740)Instructions burned: 4 (million)
% 2.96/1.68 % (3740)------------------------------
% 2.96/1.68 % (3740)------------------------------
% 2.96/1.68 % (3730)First to succeed.
% 2.96/1.68 % (3741)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3462 for (2999ds/7Mi)
% 2.96/1.68 % (3730)Refutation found. Thanks to Tanya!
% 2.96/1.68 % SZS status Theorem for DTF2THF_3462
% 2.96/1.68 % SZS output start Proof for DTF2THF_3462
% 2.96/1.68 thf(type_def_5, type, set: ($tType) > $tType).
% 2.96/1.68 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 2.96/1.68 thf(type_def_8, type, list: ($tType) > $tType).
% 2.96/1.68 thf(type_def_9, type, option: ($tType) > $tType).
% 2.96/1.68 thf(type_def_10, type, g: $tType).
% 2.96/1.68 thf(type_def_11, type, node: $tType).
% 2.96/1.68 thf(type_def_12, type, val: $tType).
% 2.96/1.68 thf(type_def_13, type, edgeD: $tType).
% 2.96/1.68 thf(type_def_14, type, var: $tType).
% 2.96/1.68 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 2.96/1.68 thf(func_def_1, type, option: ($tType) > $tType).
% 2.96/1.68 thf(func_def_2, type, list: ($tType) > $tType).
% 2.96/1.68 thf(func_def_3, type, set: ($tType) > $tType).
% 2.96/1.68 thf(func_def_4, type, edgeD: $tType).
% 2.96/1.68 thf(func_def_5, type, node: $tType).
% 2.96/1.68 thf(func_def_6, type, var: $tType).
% 2.96/1.68 thf(func_def_7, type, val: $tType).
% 2.96/1.68 thf(func_def_8, type, g: $tType).
% 2.96/1.68 thf(func_def_9, type, bounded_lattice_top: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_10, type, bounded_lattice: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_11, type, type: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_12, type, sup: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_14, type, lattice: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_15, type, finite_finite: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_16, type, linorder: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_17, type, preorder: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_18, type, semilattice_sup: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_19, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 2.96/1.68 thf(func_def_20, type, finite_finite2: !>[X0: $tType]:(set @ X0 > $o)).
% 2.96/1.68 thf(func_def_21, type, graph_1201503639essors: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1)).
% 2.96/1.68 thf(func_def_22, type, graph_449533722essors: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1)).
% 2.96/1.68 thf(func_def_23, type, irredu280805948_edges: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > set @ X2 > set @ product_prod @ set @ X2 @ set @ X2)).
% 2.96/1.68 thf(func_def_24, type, irredu1918690039_nodes: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > set @ X2 > set @ set @ X2)).
% 2.96/1.68 thf(func_def_25, type, irredu2110774547nt_scc: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > set @ X3 > set @ X3 > $o)).
% 2.96/1.68 thf(func_def_26, type, irredu2110905762nt_set: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > set @ X3 > $o)).
% 2.96/1.68 thf(func_def_27, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.96/1.68 thf(func_def_28, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 2.96/1.68 thf(func_def_29, type, zip: !>[X0: $tType, X1: $tType]:(list @ X0 > list @ X1 > list @ product_prod @ X0 @ X1)).
% 2.96/1.68 thf(func_def_30, type, dom: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > set @ X0)).
% 2.96/1.68 thf(func_def_31, type, none: !>[X0: $tType]:(option @ X0)).
% 2.96/1.68 thf(func_def_32, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 2.96/1.68 thf(func_def_33, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.96/1.68 thf(func_def_34, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.96/1.68 thf(func_def_35, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.96/1.68 thf(func_def_36, type, sSA_CFG_SSA_allDefs: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X1 > set @ X2)).
% 2.96/1.68 thf(func_def_37, type, sSA_CFG_SSA_allUses: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > X1 > set @ X3)).
% 2.96/1.68 thf(func_def_38, type, sSA_CFG_SSA_allVars: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > set @ X3)).
% 2.96/1.68 thf(func_def_39, type, sSA_CFG_SSA_phiDefs: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X1 > set @ X2)).
% 2.96/1.68 thf(func_def_40, type, sSA_CFG_SSA_phiUses: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > X1 > set @ X3)).
% 2.96/1.68 thf(func_def_41, type, sSA_CF1081484811efNode: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > X1)).
% 2.96/1.68 thf(func_def_42, type, sSA_CF1297404942ialPhi: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > X2 > $o)).
% 2.96/1.68 thf(func_def_43, type, sSA_CF722422777iveVal: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > $o)).
% 2.96/1.68 thf(func_def_44, type, sSA_CFG_SSA_wf_phi: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > option @ list @ X2)).
% 2.96/1.68 thf(func_def_45, type, sSA_CF1165125185phiArg: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > X2 > $o)).
% 2.96/1.68 thf(func_def_46, type, sSA_CF823892918pruned: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > $o)).
% 2.96/1.68 thf(func_def_47, type, sSA_CF462202545undant: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > $o)).
% 2.96/1.68 thf(func_def_48, type, sSA_CF1363434349rivial: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > X3 > $o)).
% 2.96/1.68 thf(func_def_49, type, sSA_CFG_vars: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > X0 > set @ X2)).
% 2.96/1.68 thf(func_def_50, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.96/1.68 thf(func_def_51, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.96/1.68 thf(func_def_52, type, transitive_acyclic: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 2.96/1.68 thf(func_def_53, type, transitive_tranclp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 2.96/1.68 thf(func_def_54, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.96/1.68 thf(func_def_55, type, alpha_n: g > list @ node).
% 2.96/1.68 thf(func_def_56, type, phi: val).
% 2.96/1.68 thf(func_def_57, type, phi_s: val).
% 2.96/1.68 thf(func_def_58, type, phi2: val).
% 2.96/1.68 thf(func_def_59, type, defs: g > node > set @ val).
% 2.96/1.68 thf(func_def_60, type, g2: g).
% 2.96/1.68 thf(func_def_61, type, inEdges: g > node > list @ product_prod @ node @ edgeD).
% 2.96/1.68 thf(func_def_62, type, phis: g > product_prod @ node @ val > option @ list @ val).
% 2.96/1.68 thf(func_def_63, type, s: val).
% 2.96/1.68 thf(func_def_64, type, uses: g > node > set @ val).
% 2.96/1.68 thf(func_def_65, type, var2: g > val > var).
% 2.96/1.68 thf(func_def_84, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X1 > X1)).
% 2.96/1.68 thf(func_def_85, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X1 > X1 > X0)).
% 2.96/1.68 thf(func_def_86, type, sK2: !>[X0: $tType]:(set @ X0 > list @ X0)).
% 2.96/1.68 thf(func_def_87, type, sK3: !>[X0: $tType]:(set @ X0 > list @ X0 > X0)).
% 2.96/1.68 thf(func_def_88, type, sK4: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.96/1.68 thf(func_def_89, type, sK5: !>[X0: $tType]:((X0 > $o) > set @ X0 > set @ X0 > X0)).
% 2.96/1.68 thf(func_def_90, type, sK6: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.96/1.68 thf(func_def_91, type, sK7: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.96/1.68 thf(func_def_92, type, sK8: val).
% 2.96/1.68 thf(func_def_93, type, sK9: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.96/1.68 thf(func_def_94, type, sK10: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 2.96/1.68 thf(func_def_95, type, sK11: !>[X0: $tType]:((X0 > $o) > set @ X0 > set @ X0 > X0)).
% 2.96/1.68 thf(func_def_97, type, ph13: !>[X0: $tType]:(X0)).
% 2.96/1.68 thf(f997,plain,(
% 2.96/1.68 $false),
% 2.96/1.68 inference(trivial_inequality_removal,[status(thm)],[f996])).
% 2.96/1.68 thf(f996,plain,(
% 2.96/1.68 ($true != $true)),
% 2.96/1.68 inference(superposition,[status(thm)],[f995,f984])).
% 2.96/1.68 thf(f984,plain,(
% 2.96/1.68 ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ sK8 @ phi_s) = $true)),
% 2.96/1.68 inference(cnf_transformation,[status(thm)],[f924])).
% 2.96/1.68 thf(f924,plain,(
% 2.96/1.68 ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ sK8 @ phi_s) = $true)),
% 2.96/1.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f870,f923])).
% 2.96/1.68 thf(f923,plain,(
% 2.96/1.68 ? [X0 : val] : ($true = (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s)) => ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ sK8 @ phi_s) = $true)),
% 2.96/1.68 introduced(definition,[],[choice_axiom])).
% 2.96/1.68 thf(f870,plain,(
% 2.96/1.68 ? [X0 : val] : ($true = (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s))),
% 2.96/1.68 inference(ennf_transformation,[status(thm)],[f859])).
% 2.96/1.68 thf(f859,plain,(
% 2.96/1.68 ~! [X0 : val] : ($true != (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s))),
% 2.96/1.68 inference(flattening,[status(thm)],[f663])).
% 2.96/1.68 thf(f663,plain,(
% 2.96/1.68 ~! [X0 : val] : ~($true = (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s))),
% 2.96/1.68 inference(fool_elimination,[status(thm)],[f662])).
% 2.96/1.68 thf(f662,plain,(
% 2.96/1.68 ~! [X0 : val] : ~(sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s)),
% 2.96/1.68 inference(rectify,[status(thm)],[f6])).
% 2.96/1.68 thf(f6,axiom,(
% 2.96/1.68 ~! [X7 : val] : ~(sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X7 @ phi_s)),
% 2.96/1.68 file('/export/starexec/sandbox/tmp/tmp.Ukvq8Gf8nd/DTF2THF_3462.p',fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 2.96/1.68 thf(f995,plain,(
% 2.96/1.68 ( ! [X0 : val] : (($true != (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s))) )),
% 2.96/1.68 inference(trivial_inequality_removal,[status(thm)],[f994])).
% 2.96/1.68 thf(f994,plain,(
% 2.96/1.68 ( ! [X0 : val] : (($true != (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s)) | ($true != $true)) )),
% 2.96/1.68 inference(superposition,[status(thm)],[f933,f951])).
% 2.96/1.68 thf(f951,plain,(
% 2.96/1.68 ( ! [X2 : val,X0 : g,X1 : val] : (($true = (member @ val @ X2 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X0))) | ($true != (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X0 @ X1 @ X2))) )),
% 2.96/1.68 inference(cnf_transformation,[status(thm)],[f883])).
% 2.96/1.68 thf(f883,plain,(
% 2.96/1.68 ! [X0 : g,X1 : val,X2 : val] : (($true = (member @ val @ X2 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X0))) | ($true != (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X0 @ X1 @ X2)))),
% 2.96/1.68 inference(ennf_transformation,[status(thm)],[f437])).
% 2.96/1.68 thf(f437,plain,(
% 2.96/1.68 ! [X0 : g,X1 : val,X2 : val] : (($true = (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X0 @ X1 @ X2)) => ($true = (member @ val @ X2 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X0))))),
% 2.96/1.68 inference(fool_elimination,[status(thm)],[f436])).
% 2.96/1.68 thf(f436,plain,(
% 2.96/1.68 ! [X0 : g,X1 : val,X2 : val] : ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X0 @ X1 @ X2) => (member @ val @ X2 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X0)))),
% 2.96/1.68 inference(rectify,[status(thm)],[f7])).
% 2.96/1.68 thf(f7,axiom,(
% 2.96/1.68 ! [X8 : g,X9 : val,X10 : val] : ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X8 @ X9 @ X10) => (member @ val @ X10 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X8)))),
% 2.96/1.68 file('/export/starexec/sandbox/tmp/tmp.Ukvq8Gf8nd/DTF2THF_3462.p',fact_6_phiArg__in__allVars)).
% 2.96/1.68 thf(f933,plain,(
% 2.96/1.68 ((member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2)) != $true)),
% 2.96/1.68 inference(cnf_transformation,[status(thm)],[f856])).
% 2.96/1.68 thf(f856,plain,(
% 2.96/1.68 ((member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2)) != $true)),
% 2.96/1.68 inference(flattening,[status(thm)],[f645])).
% 2.96/1.68 thf(f645,plain,(
% 2.96/1.68 ~((member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2)) = $true)),
% 2.96/1.68 inference(fool_elimination,[status(thm)],[f644])).
% 2.96/1.68 thf(f644,plain,(
% 2.96/1.68 ~(member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 2.96/1.68 inference(rectify,[status(thm)],[f302])).
% 2.96/1.68 thf(f302,negated_conjecture,(
% 2.96/1.68 ~(member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 2.96/1.68 inference(negated_conjecture,[status(cth)],[f301])).
% 2.96/1.68 thf(f301,conjecture,(
% 2.96/1.68 (member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 2.96/1.68 file('/export/starexec/sandbox/tmp/tmp.Ukvq8Gf8nd/DTF2THF_3462.p',conj_0)).
% 2.96/1.68 % SZS output end Proof for DTF2THF_3462
% 2.96/1.68 % (3730)------------------------------
% 2.96/1.68 % (3730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.68 % (3730)Termination reason: Refutation
% 2.96/1.68
% 2.96/1.68 % (3730)Memory used [KB]: 6524
% 2.96/1.68 % (3730)Time elapsed: 0.037 s
% 2.96/1.68 % (3730)Instructions burned: 81 (million)
% 2.96/1.68 % (3730)------------------------------
% 2.96/1.68 % (3730)------------------------------
% 2.96/1.68 % (3724)Success in time 0.073 s
%------------------------------------------------------------------------------