%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP080^2 : 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 : n022.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 08:55:23 AM UTC 2026
% Result : Theorem 50.05s 8.60s
% Output : Refutation 50.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP080^2 : TPTP v9.2.1. Released v7.5.0.
% 0.10/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:25:36 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.24/0.45 ---- Original DTF file ---
% 0.24/0.45 thf(spec,logic,$$dhol).
% 0.24/0.45 %------------------------------------------------------------------------------
% 0.24/0.45 % File : ITP080^2 : TPTP v9.2.1. Released v7.5.0.
% 0.24/0.45 % Domain : Interactive Theorem Proving
% 0.24/0.45 % Problem : Sledgehammer Irreducible problem prob_414__6626236_1
% 0.24/0.45 % Version : Especial.
% 0.24/0.45 % English :
% 0.24/0.45
% 0.24/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.24/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.24/0.45 % Source : [Des21]
% 0.24/0.45 % Names : Irreducible/prob_414__6626236_1 [Des21]
% 0.24/0.45
% 0.24/0.45 % Status : Theorem
% 0.24/0.45 % Rating : 0.00 v7.5.0
% 0.24/0.45 % Syntax : Number of formulae : 317 ( 89 unt; 53 typ; 0 def)
% 0.24/0.45 % Number of atoms : 861 ( 354 equ; 0 cnn)
% 0.24/0.45 % Maximal formula atoms : 10 ( 3 avg)
% 0.24/0.45 % Number of connectives : 5561 ( 156 ~; 13 |; 84 &;4871 @)
% 0.24/0.45 % ( 0 <=>; 437 =>; 0 <=; 0 <~>)
% 0.24/0.45 % Maximal formula depth : 25 ( 10 avg)
% 0.24/0.45 % Number of types : 5 ( 4 usr)
% 0.24/0.45 % Number of type conns : 303 ( 303 >; 0 *; 0 +; 0 <<)
% 0.24/0.45 % Number of symbols : 50 ( 49 usr; 11 con; 0-13 aty)
% 0.24/0.45 % Number of variables : 1217 ( 16 ^;1069 !; 73 ?;1217 :)
% 0.24/0.45 % ( 59 !>; 0 ?*; 0 @-; 0 @+)
% 0.24/0.45 % SPC : TH1_THM_EQU_NAR
% 0.24/0.45
% 0.24/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:24:38.328
% 0.24/0.45 %------------------------------------------------------------------------------
% 0.24/0.45 % Could-be-implicit typings (8)
% 0.24/0.45 thf(ty_t_Product__Type_Oprod,type,
% 0.24/0.45 product_prod: $tType > $tType > $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_t_Option_Ooption,type,
% 0.24/0.45 option: $tType > $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_t_List_Olist,type,
% 0.24/0.45 list: $tType > $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_t_Set_Oset,type,
% 0.24/0.45 set: $tType > $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_tf_edgeD,type,
% 0.24/0.45 edgeD: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_tf_node,type,
% 0.24/0.45 node: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_tf_val,type,
% 0.24/0.45 val: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_tf_g,type,
% 0.24/0.45 g: $tType ).
% 0.24/0.45
% 0.24/0.45 % Explicit typings (45)
% 0.24/0.45 thf(sy_cl_HOL_Otype,type,
% 0.24/0.45 type:
% 0.24/0.45 !>[A: $tType] : $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.24/0.45 ord:
% 0.24/0.45 !>[A: $tType] : $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.24/0.45 linorder:
% 0.24/0.45 !>[A: $tType] : $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite,type,
% 0.24/0.45 finite_finite:
% 0.24/0.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Graph__path_Ograph__Entry_OEntryPath,type,
% 0.24/0.45 graph_2081878492ryPath:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > G > ( list @ Node ) > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Graph__path_Ograph__Entry_OisIdom,type,
% 0.24/0.45 graph_graph_isIdom:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > G > Node > Node > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Graph__path_Ograph__Entry__base_Odominates,type,
% 0.24/0.45 graph_709200220inates:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > G > Node > Node > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Graph__path_Ograph__path__base_OinEdges,type,
% 0.24/0.45 graph_1822314308nEdges:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ ( product_prod @ Node @ ( product_prod @ EdgeD @ Node ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Graph__path_Ograph__path__base_Opath2,type,
% 0.24/0.45 graph_1661282752_path2:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) > Node > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors,type,
% 0.24/0.45 graph_1201503639essors:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_List_Oappend,type,
% 0.24/0.45 append:
% 0.24/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_List_Odistinct,type,
% 0.24/0.45 distinct:
% 0.24/0.45 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_List_Olist_OCons,type,
% 0.24/0.45 cons:
% 0.24/0.45 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_List_Olist_ONil,type,
% 0.24/0.45 nil:
% 0.24/0.45 !>[A: $tType] : ( list @ A ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_List_Olist_Ohd,type,
% 0.24/0.45 hd:
% 0.24/0.45 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_List_Olist_Oset,type,
% 0.24/0.45 set2:
% 0.24/0.45 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_List_Olist_Otl,type,
% 0.24/0.45 tl:
% 0.24/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Minimality_Ograph__Entry_Oreducible,type,
% 0.24/0.45 graph_reducible:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > G > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs,type,
% 0.24/0.45 sSA_CFG_SSA_allDefs:
% 0.24/0.45 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_SSA__CFG_OCFG__SSA__base_OdefAss,type,
% 0.24/0.45 sSA_CFG_SSA_defAss:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > Val > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs,type,
% 0.24/0.45 sSA_CFG_SSA_phiDefs:
% 0.24/0.45 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses,type,
% 0.24/0.45 sSA_CFG_SSA_phiUses:
% 0.24/0.45 !>[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 ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode,type,
% 0.24/0.45 sSA_CF1081484811efNode:
% 0.24/0.45 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Node ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg,type,
% 0.24/0.45 sSA_CF1165125185phiArg:
% 0.24/0.45 !>[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 ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_SSA__CFG_OCFG__base_OdefAss_H,type,
% 0.24/0.45 sSA_CFG_defAss:
% 0.24/0.45 !>[G: $tType,Node: $tType,EdgeD: $tType,Var: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > ( G > Node > ( set @ Var ) ) > G > Node > Var > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Set_OCollect,type,
% 0.24/0.45 collect:
% 0.24/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Sublist_Osuffix,type,
% 0.24/0.45 suffix:
% 0.24/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_member,type,
% 0.24/0.45 member:
% 0.24/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_Entry,type,
% 0.24/0.45 entry: g > node ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v__092_060alpha_062n,type,
% 0.24/0.45 alpha_n: g > ( list @ node ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 0.24/0.45 phi_r: val ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_defs,type,
% 0.24/0.45 defs: g > node > ( set @ val ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_g,type,
% 0.24/0.45 g2: g ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_inEdges_H,type,
% 0.24/0.45 inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_invar,type,
% 0.24/0.45 invar: g > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_m,type,
% 0.24/0.45 m: node ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_ms,type,
% 0.24/0.45 ms: list @ node ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_n,type,
% 0.24/0.45 n: node ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_ns,type,
% 0.24/0.45 ns: list @ node ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_phis,type,
% 0.24/0.45 phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 0.24/0.45 pred_phi_r: node ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_r,type,
% 0.24/0.45 r: val ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_rs_H____,type,
% 0.24/0.45 rs: list @ node ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_rs____,type,
% 0.24/0.45 rs2: list @ node ).
% 0.24/0.45
% 0.24/0.45 thf(sy_v_s,type,
% 0.24/0.45 s: val ).
% 0.24/0.45
% 0.24/0.45 % Relevant facts (255)
% 0.24/0.45 thf(fact_0_old_Opath2__hd,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( N
% 0.24/0.45 = ( hd @ node @ Ns ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_hd
% 0.24/0.45 thf(fact_1_False,axiom,
% 0.24/0.45 r != phi_r ).
% 0.24/0.45
% 0.24/0.45 % False
% 0.24/0.45 thf(fact_2_old_OEntry__in__graph,axiom,
% 0.24/0.45 ! [G2: g] : ( member @ node @ ( entry @ G2 ) @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Entry_in_graph
% 0.24/0.45 thf(fact_3_rs_H__props_I2_J,axiom,
% 0.24/0.45 graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs ).
% 0.24/0.45
% 0.24/0.45 % rs'_props(2)
% 0.24/0.45 thf(fact_4_rs_H__props_I1_J,axiom,
% 0.24/0.45 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 0.24/0.45
% 0.24/0.45 % rs'_props(1)
% 0.24/0.45 thf(fact_5_old_OEntryPath__distinct,axiom,
% 0.24/0.45 ! [G2: g,Ns: list @ node] :
% 0.24/0.45 ( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ Ns )
% 0.24/0.45 => ( distinct @ node @ Ns ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.EntryPath_distinct
% 0.24/0.45 thf(fact_6_old_O_092_060alpha_062n__distinct,axiom,
% 0.24/0.45 ! [G2: g] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( distinct @ node @ ( alpha_n @ G2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.\<alpha>n_distinct
% 0.24/0.45 thf(fact_7_rs_H__props_I3_J,axiom,
% 0.24/0.45 member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 0.24/0.45
% 0.24/0.45 % rs'_props(3)
% 0.24/0.45 thf(fact_8_assms_I10_J,axiom,
% 0.24/0.45 sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 0.24/0.45
% 0.24/0.45 % assms(10)
% 0.24/0.45 thf(fact_9_allDefs__disjoint_H,axiom,
% 0.24/0.45 ! [N: node,G2: g,M: node,V: val] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 0.24/0.45 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ M ) )
% 0.24/0.45 => ( N = M ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % allDefs_disjoint'
% 0.24/0.45 thf(fact_10_assms_I7_J,axiom,
% 0.24/0.45 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 0.24/0.45
% 0.24/0.45 % assms(7)
% 0.24/0.45 thf(fact_11_defNode__eq,axiom,
% 0.24/0.45 ! [N: node,G2: g,V: val] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 0.24/0.45 => ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 0.24/0.45 = N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defNode_eq
% 0.24/0.45 thf(fact_12_rs_H__props_I4_J,axiom,
% 0.24/0.45 member @ node @ pred_phi_r @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % rs'_props(4)
% 0.24/0.45 thf(fact_13_defs__in__allDefs,axiom,
% 0.24/0.45 ! [V: val,G2: g,N: node] :
% 0.24/0.45 ( ( member @ val @ V @ ( defs @ G2 @ N ) )
% 0.24/0.45 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defs_in_allDefs
% 0.24/0.45 thf(fact_14_FormalSSA__Misc_Oin__set__tlD,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) )
% 0.24/0.45 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % FormalSSA_Misc.in_set_tlD
% 0.24/0.45 thf(fact_15_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_hd_in_\<alpha>n
% 0.24/0.45 thf(fact_16_old_Opath2__hd__in__ns,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( member @ node @ N @ ( set2 @ node @ Ns ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_hd_in_ns
% 0.24/0.45 thf(fact_17_old_Opath2__in___092_060alpha_062n,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node,L: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ( member @ node @ L @ ( set2 @ node @ Ns ) )
% 0.24/0.45 => ( member @ node @ L @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_in_\<alpha>n
% 0.24/0.45 thf(fact_18_old_Oinvar,axiom,
% 0.24/0.45 ! [G2: g] : ( invar @ G2 ) ).
% 0.24/0.45
% 0.24/0.45 % old.invar
% 0.24/0.45 thf(fact_19_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_tl_in_\<alpha>n
% 0.24/0.45 thf(fact_20_old_Opath2__last__in__ns,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( member @ node @ M @ ( set2 @ node @ Ns ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_last_in_ns
% 0.24/0.45 thf(fact_21_old_Osuccessor__is__node,axiom,
% 0.24/0.45 ! [N: node,G2: g,N2: node] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 0.24/0.45 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( invar @ G2 )
% 0.24/0.45 => ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.successor_is_node
% 0.24/0.45 thf(fact_22_old_Opredecessor__is__node,axiom,
% 0.24/0.45 ! [N: node,G2: g,N2: node] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 0.24/0.45 => ( ( invar @ G2 )
% 0.24/0.45 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.predecessor_is_node
% 0.24/0.45 thf(fact_23_old_Opath2__forget__hd,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ Ns ) @ Ns @ M ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_forget_hd
% 0.24/0.45 thf(fact_24_old_OEntry__reachesE,axiom,
% 0.24/0.45 ! [N: node,G2: g] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( invar @ G2 )
% 0.24/0.45 => ~ ! [Ns2: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ N )
% 0.24/0.45 => ~ ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ Ns2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Entry_reachesE
% 0.24/0.45 thf(fact_25__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.24/0.45 ~ ! [Rs: list @ node,Pred_phi_r: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ Rs @ Pred_phi_r )
% 0.24/0.45 => ( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ Rs )
% 0.24/0.45 => ( ( member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ Pred_phi_r ) )
% 0.24/0.45 => ~ ( member @ node @ Pred_phi_r @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % \<open>\<And>thesis. (\<And>rs' pred\<^sub>\<phi>\<^sub>r. \<lbrakk>g \<turnstile> defNode g r-rs'\<rightarrow>pred\<^sub>\<phi>\<^sub>r; old.EntryPath g rs'; r \<in> phiUses g pred\<^sub>\<phi>\<^sub>r; pred\<^sub>\<phi>\<^sub>r \<in> set (old.predecessors g (defNode g \<phi>\<^sub>r))\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.24/0.45 thf(fact_26_old_OEntry__reaches,axiom,
% 0.24/0.45 ! [N: node,G2: g] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( invar @ G2 )
% 0.24/0.45 => ? [Ns2: list @ node] : ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Entry_reaches
% 0.24/0.45 thf(fact_27_old_Oidom__ex,axiom,
% 0.24/0.45 ! [G2: g,N: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( N
% 0.24/0.45 != ( entry @ G2 ) )
% 0.24/0.45 => ? [X2: node] :
% 0.24/0.45 ( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ X2 )
% 0.24/0.45 & ! [Y: node] :
% 0.24/0.45 ( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ Y )
% 0.24/0.45 => ( Y = X2 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.idom_ex
% 0.24/0.45 thf(fact_28_FormalSSA__Misc_Odistinct__hd__tl,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( distinct @ A @ Xs )
% 0.24/0.45 => ~ ( member @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % FormalSSA_Misc.distinct_hd_tl
% 0.24/0.45 thf(fact_29_defAss_H__extend,axiom,
% 0.24/0.45 ! [G2: g,M: node,V: val,N: node,Ns: list @ node] :
% 0.24/0.45 ( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ M @ V )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ! [X2: node] :
% 0.24/0.45 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ns ) ) )
% 0.24/0.45 => ~ ( member @ val @ V @ ( defs @ G2 @ X2 ) ) )
% 0.24/0.45 => ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ N @ V ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAss'_extend
% 0.24/0.45 thf(fact_30_defAss_H__def,axiom,
% 0.24/0.45 ! [G2: g,M: node,V: val] :
% 0.24/0.45 ( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ M @ V )
% 0.24/0.45 = ( ! [Ns3: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns3 @ M )
% 0.24/0.45 => ? [X3: node] :
% 0.24/0.45 ( ( member @ node @ X3 @ ( set2 @ node @ Ns3 ) )
% 0.24/0.45 & ( member @ val @ V @ ( defs @ G2 @ X3 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAss'_def
% 0.24/0.45 thf(fact_31_defAss_HI,axiom,
% 0.24/0.45 ! [G2: g,M: node,V: val] :
% 0.24/0.45 ( ! [Ns2: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ M )
% 0.24/0.45 => ? [X4: node] :
% 0.24/0.45 ( ( member @ node @ X4 @ ( set2 @ node @ Ns2 ) )
% 0.24/0.45 & ( member @ val @ V @ ( defs @ G2 @ X4 ) ) ) )
% 0.24/0.45 => ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ M @ V ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAss'I
% 0.24/0.45 thf(fact_32_defAss_HE,axiom,
% 0.24/0.45 ! [G2: g,M: node,V: val,Ns: list @ node] :
% 0.24/0.45 ( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ M @ V )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns @ M )
% 0.24/0.45 => ~ ! [N3: node] :
% 0.24/0.45 ( ( member @ node @ N3 @ ( set2 @ node @ Ns ) )
% 0.24/0.45 => ~ ( member @ val @ V @ ( defs @ G2 @ N3 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAss'E
% 0.24/0.45 thf(fact_33_defAss__extend,axiom,
% 0.24/0.45 ! [G2: g,M: node,V: val,N: node,Ns: list @ node] :
% 0.24/0.45 ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ M @ V )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ! [X2: node] :
% 0.24/0.45 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ns ) ) )
% 0.24/0.45 => ~ ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X2 ) ) )
% 0.24/0.45 => ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ N @ V ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAss_extend
% 0.24/0.45 thf(fact_34_assms_I8_J,axiom,
% 0.24/0.45 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 0.24/0.45
% 0.24/0.45 % assms(8)
% 0.24/0.45 thf(fact_35_defAss__def,axiom,
% 0.24/0.45 ! [G2: g,M: node,V: val] :
% 0.24/0.45 ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ M @ V )
% 0.24/0.45 = ( ! [Ns3: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns3 @ M )
% 0.24/0.45 => ? [X3: node] :
% 0.24/0.45 ( ( member @ node @ X3 @ ( set2 @ node @ Ns3 ) )
% 0.24/0.45 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X3 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAss_def
% 0.24/0.45 thf(fact_36_defAssI,axiom,
% 0.24/0.45 ! [G2: g,M: node,V: val] :
% 0.24/0.45 ( ! [Ns2: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ M )
% 0.24/0.45 => ? [X4: node] :
% 0.24/0.45 ( ( member @ node @ X4 @ ( set2 @ node @ Ns2 ) )
% 0.24/0.45 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X4 ) ) ) )
% 0.24/0.45 => ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ M @ V ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAssI
% 0.24/0.45 thf(fact_37_defAssD,axiom,
% 0.24/0.45 ! [G2: g,M: node,V: val,Ns: list @ node] :
% 0.24/0.45 ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ M @ V )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns @ M )
% 0.24/0.45 => ? [X2: node] :
% 0.24/0.45 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 0.24/0.45 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAssD
% 0.24/0.45 thf(fact_38_phiDefs__in__allDefs,axiom,
% 0.24/0.45 ! [V: val,G2: g,N: node] :
% 0.24/0.45 ( ( member @ val @ V @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) )
% 0.24/0.45 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % phiDefs_in_allDefs
% 0.24/0.45 thf(fact_39_defAss__dominating,axiom,
% 0.24/0.45 ! [N: node,G2: g,V: val] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ N @ V )
% 0.24/0.45 = ( ? [X3: node] :
% 0.24/0.45 ( ( member @ node @ X3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X3 @ N )
% 0.24/0.45 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X3 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % defAss_dominating
% 0.24/0.45 thf(fact_40_old_Osuccessor__in___092_060alpha_062n,axiom,
% 0.24/0.45 ! [G2: g,N: node] :
% 0.24/0.45 ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N )
% 0.24/0.45 != ( nil @ node ) )
% 0.24/0.45 => ( ( invar @ G2 )
% 0.24/0.45 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.successor_in_\<alpha>n
% 0.24/0.45 thf(fact_41_phiUses__finite,axiom,
% 0.24/0.45 ! [N: node,G2: g] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( finite_finite @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % phiUses_finite
% 0.24/0.45 thf(fact_42_old_Opath2__split__last__prop,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ? [X4: node] :
% 0.24/0.45 ( ( member @ node @ X4 @ ( set2 @ node @ Ns ) )
% 0.24/0.45 & ( P @ X4 ) )
% 0.24/0.45 => ~ ! [N4: node,Ns4: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N4 @ Ns4 @ M )
% 0.24/0.45 => ( ( P @ N4 )
% 0.24/0.45 => ( ! [X4: node] :
% 0.24/0.45 ( ( member @ node @ X4 @ ( set2 @ node @ ( tl @ node @ Ns4 ) ) )
% 0.24/0.45 => ~ ( P @ X4 ) )
% 0.24/0.45 => ~ ( suffix @ node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_split_last_prop
% 0.24/0.45 thf(fact_43_allDefs__finite,axiom,
% 0.24/0.45 ! [N: node,G2: g] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( finite_finite @ val @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % allDefs_finite
% 0.24/0.45 thf(fact_44_old_Opath2__not__Nil,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( Ns
% 0.24/0.45 != ( nil @ node ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_not_Nil
% 0.24/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.24/0.45 ! [A: $tType,A2: A,P: A > $o] :
% 0.24/0.45 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.24/0.45 = ( P @ A2 ) ) ).
% 0.24/0.45
% 0.24/0.45 % mem_Collect_eq
% 0.24/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.24/0.45 ! [A: $tType,A3: set @ A] :
% 0.24/0.45 ( ( collect @ A
% 0.24/0.45 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.24/0.45 = A3 ) ).
% 0.24/0.45
% 0.24/0.45 % Collect_mem_eq
% 0.24/0.45 thf(fact_47_Collect__cong,axiom,
% 0.24/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.24/0.45 ( ! [X2: A] :
% 0.24/0.45 ( ( P @ X2 )
% 0.24/0.45 = ( Q @ X2 ) )
% 0.24/0.45 => ( ( collect @ A @ P )
% 0.24/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % Collect_cong
% 0.24/0.45 thf(fact_48_ext,axiom,
% 0.24/0.45 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.24/0.45 ( ! [X2: A] :
% 0.24/0.45 ( ( F @ X2 )
% 0.24/0.45 = ( G2 @ X2 ) )
% 0.24/0.45 => ( F = G2 ) ) ).
% 0.24/0.45
% 0.24/0.45 % ext
% 0.24/0.45 thf(fact_49_old_Opath2__not__Nil2,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node] :
% 0.24/0.45 ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( nil @ node ) @ M ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_not_Nil2
% 0.24/0.45 thf(fact_50_old_Opath2__app,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 0.24/0.45 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( tl @ node @ Ms ) ) @ L ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_app
% 0.24/0.45 thf(fact_51_defs__finite,axiom,
% 0.24/0.45 ! [G2: g,N: node] : ( finite_finite @ val @ ( defs @ G2 @ N ) ) ).
% 0.24/0.45
% 0.24/0.45 % defs_finite
% 0.24/0.45 thf(fact_52_phiDefs__finite,axiom,
% 0.24/0.45 ! [G2: g,N: node] : ( finite_finite @ val @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) ) ).
% 0.24/0.45
% 0.24/0.45 % phiDefs_finite
% 0.24/0.45 thf(fact_53_strict__dom__trans_H,axiom,
% 0.24/0.45 ! [N: node,M: node,G2: g,M2: node] :
% 0.24/0.45 ( ( ( N != M )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M ) )
% 0.24/0.45 => ( ( ( M != M2 )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ M @ M2 ) )
% 0.24/0.45 => ( ( N != M2 )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % strict_dom_trans'
% 0.24/0.45 thf(fact_54_old_Ostrict__dom__trans,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node,M2: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( ( N != M )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M ) )
% 0.24/0.45 => ( ( ( M != M2 )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ M @ M2 ) )
% 0.24/0.45 => ( ( N != M2 )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.strict_dom_trans
% 0.24/0.45 thf(fact_55_old_Odominates__trans,axiom,
% 0.24/0.45 ! [G2: g,N: node,N2: node,N5: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N2 @ N5 )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N5 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_trans
% 0.24/0.45 thf(fact_56_old_Odominates__antitrans,axiom,
% 0.24/0.45 ! [G2: g,N_1: node,M: node,N_2: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N_1 @ M )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N_2 @ M )
% 0.24/0.45 => ( ~ ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N_1 @ N_2 )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N_2 @ N_1 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_antitrans
% 0.24/0.45 thf(fact_57_old_Odominates__antisymm,axiom,
% 0.24/0.45 ! [G2: g,N: node,N2: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N2 @ N )
% 0.24/0.45 => ( N = N2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_antisymm
% 0.24/0.45 thf(fact_58_dominates__trans_H,axiom,
% 0.24/0.45 ! [G2: g,N: node,N2: node,N5: node] :
% 0.24/0.45 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N2 @ N5 )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N5 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % dominates_trans'
% 0.24/0.45 thf(fact_59_dominates__antisymm_H,axiom,
% 0.24/0.45 ! [G2: g,N: node,N2: node] :
% 0.24/0.45 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N2 @ N )
% 0.24/0.45 => ( N = N2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % dominates_antisymm'
% 0.24/0.45 thf(fact_60_dominates__refl_H,axiom,
% 0.24/0.45 ! [N: node,G2: g] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N ) ) ).
% 0.24/0.45
% 0.24/0.45 % dominates_refl'
% 0.24/0.45 thf(fact_61_old_Odominates__path,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node] :
% 0.24/0.45 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 0.24/0.45 => ( ( invar @ G2 )
% 0.24/0.45 => ~ ! [Ns2: list @ node] :
% 0.24/0.45 ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns2 @ M ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_path
% 0.24/0.45 thf(fact_62_old_Odominates__mid,axiom,
% 0.24/0.45 ! [G2: g,N: node,X: node,M: node,Ns: list @ node] :
% 0.24/0.45 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ X )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X @ M )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ( invar @ G2 )
% 0.24/0.45 => ( member @ node @ X @ ( set2 @ node @ Ns ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_mid
% 0.24/0.45 thf(fact_63_old_Odominates__def,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node] :
% 0.24/0.45 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 0.24/0.45 = ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 & ! [Ns3: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns3 @ M )
% 0.24/0.45 => ( member @ node @ N @ ( set2 @ node @ Ns3 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_def
% 0.24/0.45 thf(fact_64_old_OdominatesE,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node] :
% 0.24/0.45 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 0.24/0.45 => ~ ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ~ ! [Ns5: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns5 @ M )
% 0.24/0.45 => ( member @ node @ N @ ( set2 @ node @ Ns5 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominatesE
% 0.24/0.45 thf(fact_65_old_Odominates__unsnoc,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node,M2: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 0.24/0.45 => ( ( member @ node @ M2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M ) ) )
% 0.24/0.45 => ( ( N != M )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_unsnoc
% 0.24/0.45 thf(fact_66_non__dominated__predecessor,axiom,
% 0.24/0.45 ! [N: node,G2: g] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( N
% 0.24/0.45 != ( entry @ G2 ) )
% 0.24/0.45 => ~ ! [M3: node] :
% 0.24/0.45 ( ( member @ node @ M3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M3 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % non_dominated_predecessor
% 0.24/0.45 thf(fact_67_old_OisIdom__def,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node] :
% 0.24/0.45 ( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 0.24/0.45 = ( ( M != N )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ M @ N )
% 0.24/0.45 & ! [X3: node] :
% 0.24/0.45 ( ( member @ node @ X3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( ( X3 != N )
% 0.24/0.45 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X3 @ N ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X3 @ M ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.isIdom_def
% 0.24/0.45 thf(fact_68_old_OEntryPath__suffix,axiom,
% 0.24/0.45 ! [G2: g,Ns: list @ node,Ns6: list @ node] :
% 0.24/0.45 ( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ Ns )
% 0.24/0.45 => ( ( suffix @ node @ Ns6 @ Ns )
% 0.24/0.45 => ( ( Ns6
% 0.24/0.45 != ( nil @ node ) )
% 0.24/0.45 => ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ Ns6 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.EntryPath_suffix
% 0.24/0.45 thf(fact_69_old_Odominates__unsnoc_H,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node,M2: node,Ms: list @ node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M2 @ Ms @ M )
% 0.24/0.45 => ( ! [X2: node] :
% 0.24/0.45 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ms ) ) )
% 0.24/0.45 => ( X2 != N ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_unsnoc'
% 0.24/0.45 thf(fact_70_old_Odominates__extend,axiom,
% 0.24/0.45 ! [G2: g,N: node,M: node,M2: node,Ms: list @ node] :
% 0.24/0.45 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M2 @ Ms @ M )
% 0.24/0.45 => ( ~ ( member @ node @ N @ ( set2 @ node @ ( tl @ node @ Ms ) ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_extend
% 0.24/0.45 thf(fact_71_old_OEntry__no__predecessor,axiom,
% 0.24/0.45 ! [G2: g] :
% 0.24/0.45 ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( entry @ G2 ) )
% 0.24/0.45 = ( nil @ node ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Entry_no_predecessor
% 0.24/0.45 thf(fact_72_old_Odominates__refl,axiom,
% 0.24/0.45 ! [G2: g,N: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominates_refl
% 0.24/0.45 thf(fact_73_old_OEntry__dominates,axiom,
% 0.24/0.45 ! [G2: g,N: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ ( entry @ G2 ) @ N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Entry_dominates
% 0.24/0.45 thf(fact_74_old_OdominatesI,axiom,
% 0.24/0.45 ! [M: node,G2: g,N: node] :
% 0.24/0.45 ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ! [Ns2: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ M )
% 0.24/0.45 => ( member @ node @ N @ ( set2 @ node @ Ns2 ) ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.dominatesI
% 0.24/0.45 thf(fact_75_old_OEntry__iff__unreachable,axiom,
% 0.24/0.45 ! [G2: g,N: node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N )
% 0.24/0.45 = ( nil @ node ) )
% 0.24/0.45 = ( N
% 0.24/0.45 = ( entry @ G2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Entry_iff_unreachable
% 0.24/0.45 thf(fact_76_old_Oreducible__def,axiom,
% 0.24/0.45 ! [G2: g] :
% 0.24/0.45 ( ( graph_reducible @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 )
% 0.24/0.45 = ( ! [N6: node,Ns3: list @ node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N6 @ Ns3 @ N6 )
% 0.24/0.45 => ? [X3: node] :
% 0.24/0.45 ( ( member @ node @ X3 @ ( set2 @ node @ Ns3 ) )
% 0.24/0.45 & ! [Y2: node] :
% 0.24/0.45 ( ( member @ node @ Y2 @ ( set2 @ node @ Ns3 ) )
% 0.24/0.45 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X3 @ Y2 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.reducible_def
% 0.24/0.45 thf(fact_77_in__hd__or__tl__conv,axiom,
% 0.24/0.45 ! [A: $tType,L: list @ A,X: A] :
% 0.24/0.45 ( ( L
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( ( X
% 0.24/0.45 = ( hd @ A @ L ) )
% 0.24/0.45 | ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ L ) ) ) )
% 0.24/0.45 = ( member @ A @ X @ ( set2 @ A @ L ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % in_hd_or_tl_conv
% 0.24/0.45 thf(fact_78_old_Opath2__cases,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ( ( Ns
% 0.24/0.45 = ( cons @ node @ N @ ( nil @ node ) ) )
% 0.24/0.45 => ( M != N ) )
% 0.24/0.45 => ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) @ ( tl @ node @ Ns ) @ M )
% 0.24/0.45 => ~ ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_cases
% 0.24/0.45 thf(fact_79_old_Opath2__snoc,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node,M2: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M2 ) ) )
% 0.24/0.45 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ M2 @ ( nil @ node ) ) ) @ M2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_snoc
% 0.24/0.45 thf(fact_80_old_Opath2__rev__induct,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( P @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) )
% 0.24/0.45 => ( ! [Ns2: list @ node,M4: node,M3: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns2 @ M4 )
% 0.24/0.45 => ( ( P @ N @ Ns2 @ M4 )
% 0.24/0.45 => ( ( member @ node @ M4 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M3 ) ) )
% 0.24/0.45 => ( P @ N @ ( append @ node @ Ns2 @ ( cons @ node @ M3 @ ( nil @ node ) ) ) @ M3 ) ) ) )
% 0.24/0.45 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_rev_induct
% 0.24/0.45 thf(fact_81_tl__append2,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( tl @ A @ ( append @ A @ Xs @ Ys ) )
% 0.24/0.45 = ( append @ A @ ( tl @ A @ Xs ) @ Ys ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % tl_append2
% 0.24/0.45 thf(fact_82_hd__append2,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.24/0.45 = ( hd @ A @ Xs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % hd_append2
% 0.24/0.45 thf(fact_83_same__suffix__nil,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ Xs )
% 0.24/0.45 = ( Ys
% 0.24/0.45 = ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % same_suffix_nil
% 0.24/0.45 thf(fact_84_old_Opath2__induct,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ( ( invar @ G2 )
% 0.24/0.45 => ( P @ M @ ( cons @ node @ M @ ( nil @ node ) ) @ M ) )
% 0.24/0.45 => ( ! [Ns2: list @ node,N4: node,N3: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N3 @ Ns2 @ M )
% 0.24/0.45 => ( ( P @ N3 @ Ns2 @ M )
% 0.24/0.45 => ( ( member @ node @ N4 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N3 ) ) )
% 0.24/0.45 => ( P @ N4 @ ( cons @ node @ N4 @ Ns2 ) @ M ) ) ) )
% 0.24/0.45 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_induct
% 0.24/0.45 thf(fact_85_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Y3: A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ ( append @ A @ Ys @ ( cons @ A @ Y3 @ Xs ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.elem_set_implies_elem_tl_app_cons
% 0.24/0.45 thf(fact_86_list_Oinject,axiom,
% 0.24/0.45 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.24/0.45 ( ( ( cons @ A @ X21 @ X22 )
% 0.24/0.45 = ( cons @ A @ Y21 @ Y22 ) )
% 0.24/0.45 = ( ( X21 = Y21 )
% 0.24/0.45 & ( X22 = Y22 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.inject
% 0.24/0.45 thf(fact_87_same__append__eq,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.24/0.45 = ( append @ A @ Xs @ Zs ) )
% 0.24/0.45 = ( Ys = Zs ) ) ).
% 0.24/0.45
% 0.24/0.45 % same_append_eq
% 0.24/0.45 thf(fact_88_append__same__eq,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Ys @ Xs )
% 0.24/0.45 = ( append @ A @ Zs @ Xs ) )
% 0.24/0.45 = ( Ys = Zs ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_same_eq
% 0.24/0.45 thf(fact_89_append__assoc,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 0.24/0.45 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_assoc
% 0.24/0.45 thf(fact_90_append_Oassoc,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.24/0.45 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C )
% 0.24/0.45 = ( append @ A @ A2 @ ( append @ A @ B2 @ C ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append.assoc
% 0.24/0.45 thf(fact_91_suffix__order_Odual__order_Orefl,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A] : ( suffix @ A @ A2 @ A2 ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.dual_order.refl
% 0.24/0.45 thf(fact_92_suffix__order_Oorder__refl,axiom,
% 0.24/0.45 ! [A: $tType,X: list @ A] : ( suffix @ A @ X @ X ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.order_refl
% 0.24/0.45 thf(fact_93_old_Opath2__split_I2_J,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns6: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns6 ) ) @ M )
% 0.24/0.45 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns6 ) @ M ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_split(2)
% 0.24/0.45 thf(fact_94_List_Ofinite__set,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] : ( finite_finite @ A @ ( set2 @ A @ Xs ) ) ).
% 0.24/0.45
% 0.24/0.45 % List.finite_set
% 0.24/0.45 thf(fact_95_append_Oright__neutral,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A] :
% 0.24/0.45 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.24/0.45 = A2 ) ).
% 0.24/0.45
% 0.24/0.45 % append.right_neutral
% 0.24/0.45 thf(fact_96_empty__append__eq__id,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( append @ A @ ( nil @ A ) )
% 0.24/0.45 = ( ^ [X3: list @ A] : X3 ) ) ).
% 0.24/0.45
% 0.24/0.45 % empty_append_eq_id
% 0.24/0.45 thf(fact_97_append__is__Nil__conv,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 = ( ( Xs
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( Ys
% 0.24/0.45 = ( nil @ A ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_is_Nil_conv
% 0.24/0.45 thf(fact_98_Nil__is__append__conv,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( ( nil @ A )
% 0.24/0.45 = ( append @ A @ Xs @ Ys ) )
% 0.24/0.45 = ( ( Xs
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( Ys
% 0.24/0.45 = ( nil @ A ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % Nil_is_append_conv
% 0.24/0.45 thf(fact_99_self__append__conv2,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.24/0.45 ( ( Ys
% 0.24/0.45 = ( append @ A @ Xs @ Ys ) )
% 0.24/0.45 = ( Xs
% 0.24/0.45 = ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % self_append_conv2
% 0.24/0.45 thf(fact_100_append__self__conv2,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.24/0.45 = Ys )
% 0.24/0.45 = ( Xs
% 0.24/0.45 = ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_self_conv2
% 0.24/0.45 thf(fact_101_self__append__conv,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Xs @ Ys ) )
% 0.24/0.45 = ( Ys
% 0.24/0.45 = ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % self_append_conv
% 0.24/0.45 thf(fact_102_append__self__conv,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.24/0.45 = Xs )
% 0.24/0.45 = ( Ys
% 0.24/0.45 = ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_self_conv
% 0.24/0.45 thf(fact_103_append__Nil2,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.24/0.45 = Xs ) ).
% 0.24/0.45
% 0.24/0.45 % append_Nil2
% 0.24/0.45 thf(fact_104_suffix__bot_Obot_Oextremum__unique,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 0.24/0.45 = ( A2
% 0.24/0.45 = ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_bot.bot.extremum_unique
% 0.24/0.45 thf(fact_105_suffix__Nil,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ Xs @ ( nil @ A ) )
% 0.24/0.45 = ( Xs
% 0.24/0.45 = ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_Nil
% 0.24/0.45 thf(fact_106_same__suffix__suffix,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ ( append @ A @ Zs @ Xs ) )
% 0.24/0.45 = ( suffix @ A @ Ys @ Zs ) ) ).
% 0.24/0.45
% 0.24/0.45 % same_suffix_suffix
% 0.24/0.45 thf(fact_107_old_Opath2__split_I1_J,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns6: list @ node,M: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns6 ) ) @ M )
% 0.24/0.45 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ ( nil @ node ) ) ) @ N2 ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.path2_split(1)
% 0.24/0.45 thf(fact_108_old_OEntry__loop,axiom,
% 0.24/0.45 ! [G2: g,Ns: list @ node] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns @ ( entry @ G2 ) )
% 0.24/0.45 => ( Ns
% 0.24/0.45 = ( cons @ node @ ( entry @ G2 ) @ ( nil @ node ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Entry_loop
% 0.24/0.45 thf(fact_109_old_OEntryPath__triv,axiom,
% 0.24/0.45 ! [G2: g,N: node] : ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.EntryPath_triv
% 0.24/0.45 thf(fact_110_append1__eq__conv,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y3: A] :
% 0.24/0.45 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.24/0.45 = ( append @ A @ Ys @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 0.24/0.45 = ( ( Xs = Ys )
% 0.24/0.45 & ( X = Y3 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append1_eq_conv
% 0.24/0.45 thf(fact_111_list__ee__eq__leel_I1_J,axiom,
% 0.24/0.45 ! [A: $tType,E1: A,E2: A,L1: list @ A,E12: A,E22: A,L2: list @ A] :
% 0.24/0.45 ( ( ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) )
% 0.24/0.45 = ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) ) )
% 0.24/0.45 = ( ( L1
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( E1 = E12 )
% 0.24/0.45 & ( E2 = E22 )
% 0.24/0.45 & ( L2
% 0.24/0.45 = ( nil @ A ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_ee_eq_leel(1)
% 0.24/0.45 thf(fact_112_list__ee__eq__leel_I2_J,axiom,
% 0.24/0.45 ! [A: $tType,L1: list @ A,E12: A,E22: A,L2: list @ A,E1: A,E2: A] :
% 0.24/0.45 ( ( ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) )
% 0.24/0.45 = ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) ) )
% 0.24/0.45 = ( ( L1
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( E1 = E12 )
% 0.24/0.45 & ( E2 = E22 )
% 0.24/0.45 & ( L2
% 0.24/0.45 = ( nil @ A ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_ee_eq_leel(2)
% 0.24/0.45 thf(fact_113_list__se__match_I1_J,axiom,
% 0.24/0.45 ! [A: $tType,L1: list @ A,L2: list @ A,A2: A] :
% 0.24/0.45 ( ( L1
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( ( append @ A @ L1 @ L2 )
% 0.24/0.45 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.24/0.45 = ( ( L1
% 0.24/0.45 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.24/0.45 & ( L2
% 0.24/0.45 = ( nil @ A ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_se_match(1)
% 0.24/0.45 thf(fact_114_list__se__match_I2_J,axiom,
% 0.24/0.45 ! [A: $tType,L2: list @ A,L1: list @ A,A2: A] :
% 0.24/0.45 ( ( L2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( ( append @ A @ L1 @ L2 )
% 0.24/0.45 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.24/0.45 = ( ( L1
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( L2
% 0.24/0.45 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_se_match(2)
% 0.24/0.45 thf(fact_115_list__se__match_I3_J,axiom,
% 0.24/0.45 ! [A: $tType,L1: list @ A,A2: A,L2: list @ A] :
% 0.24/0.45 ( ( L1
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 0.24/0.45 = ( append @ A @ L1 @ L2 ) )
% 0.24/0.45 = ( ( L1
% 0.24/0.45 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.24/0.45 & ( L2
% 0.24/0.45 = ( nil @ A ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_se_match(3)
% 0.24/0.45 thf(fact_116_list__se__match_I4_J,axiom,
% 0.24/0.45 ! [A: $tType,L2: list @ A,A2: A,L1: list @ A] :
% 0.24/0.45 ( ( L2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 0.24/0.45 = ( append @ A @ L1 @ L2 ) )
% 0.24/0.45 = ( ( L1
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( L2
% 0.24/0.45 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_se_match(4)
% 0.24/0.45 thf(fact_117_list__e__eq__lel_I1_J,axiom,
% 0.24/0.45 ! [A: $tType,E: A,L1: list @ A,E3: A,L2: list @ A] :
% 0.24/0.45 ( ( ( cons @ A @ E @ ( nil @ A ) )
% 0.24/0.45 = ( append @ A @ L1 @ ( cons @ A @ E3 @ L2 ) ) )
% 0.24/0.45 = ( ( L1
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( E3 = E )
% 0.24/0.45 & ( L2
% 0.24/0.45 = ( nil @ A ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_e_eq_lel(1)
% 0.24/0.45 thf(fact_118_list__e__eq__lel_I2_J,axiom,
% 0.24/0.45 ! [A: $tType,L1: list @ A,E3: A,L2: list @ A,E: A] :
% 0.24/0.45 ( ( ( append @ A @ L1 @ ( cons @ A @ E3 @ L2 ) )
% 0.24/0.45 = ( cons @ A @ E @ ( nil @ A ) ) )
% 0.24/0.45 = ( ( L1
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( E3 = E )
% 0.24/0.45 & ( L2
% 0.24/0.45 = ( nil @ A ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_e_eq_lel(2)
% 0.24/0.45 thf(fact_119_snoc__suffix__snoc,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y3: A] :
% 0.24/0.45 ( ( suffix @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 0.24/0.45 = ( ( X = Y3 )
% 0.24/0.45 & ( suffix @ A @ Xs @ Ys ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % snoc_suffix_snoc
% 0.24/0.45 thf(fact_120_suffix__snoc,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y3: A] :
% 0.24/0.45 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 0.24/0.45 = ( ( Xs
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 | ? [Zs2: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Zs2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 0.24/0.45 & ( suffix @ A @ Zs2 @ Ys ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_snoc
% 0.24/0.45 thf(fact_121_list_Ocollapse,axiom,
% 0.24/0.45 ! [A: $tType,List: list @ A] :
% 0.24/0.45 ( ( List
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 0.24/0.45 = List ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.collapse
% 0.24/0.45 thf(fact_122_hd__Cons__tl,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 0.24/0.45 = Xs ) ) ).
% 0.24/0.45
% 0.24/0.45 % hd_Cons_tl
% 0.24/0.45 thf(fact_123_rs__def,axiom,
% 0.24/0.45 ( rs2
% 0.24/0.45 = ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % rs_def
% 0.24/0.45 thf(fact_124_old_Oempty__path2,axiom,
% 0.24/0.45 ! [N: node,G2: g] :
% 0.24/0.45 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.24/0.45 => ( ( invar @ G2 )
% 0.24/0.45 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.empty_path2
% 0.24/0.45 thf(fact_125_old_OCons__path2,axiom,
% 0.24/0.45 ! [G2: g,N: node,Ns: list @ node,M: node,N2: node] :
% 0.24/0.45 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.24/0.45 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 0.24/0.45 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns ) @ M ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Cons_path2
% 0.24/0.45 thf(fact_126_list_Odistinct_I1_J,axiom,
% 0.24/0.45 ! [A: $tType,X21: A,X22: list @ A] :
% 0.24/0.45 ( ( nil @ A )
% 0.24/0.45 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.distinct(1)
% 0.24/0.45 thf(fact_127_neq__NilE,axiom,
% 0.24/0.45 ! [A: $tType,L: list @ A] :
% 0.24/0.45 ( ( L
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ~ ! [X2: A,Xs2: list @ A] :
% 0.24/0.45 ( L
% 0.24/0.45 != ( cons @ A @ X2 @ Xs2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % neq_NilE
% 0.24/0.45 thf(fact_128_list_OdiscI,axiom,
% 0.24/0.45 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.24/0.45 ( ( List
% 0.24/0.45 = ( cons @ A @ X21 @ X22 ) )
% 0.24/0.45 => ( List
% 0.24/0.45 != ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.discI
% 0.24/0.45 thf(fact_129_revg_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.24/0.45 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.24/0.45 => ( ! [A4: A,As: list @ A,B3: list @ A] :
% 0.24/0.45 ( ( P @ As @ ( cons @ A @ A4 @ B3 ) )
% 0.24/0.45 => ( P @ ( cons @ A @ A4 @ As ) @ B3 ) )
% 0.24/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % revg.induct
% 0.24/0.45 thf(fact_130_zipf_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,C2: $tType,B: $tType,P: ( A > B > C2 ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > C2,A1: list @ A,A22: list @ B] :
% 0.24/0.45 ( ! [F2: A > B > C2] : ( P @ F2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [F2: A > B > C2,A4: A,As: list @ A,B3: B,Bs: list @ B] :
% 0.24/0.45 ( ( P @ F2 @ As @ Bs )
% 0.24/0.45 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B @ B3 @ Bs ) ) )
% 0.24/0.45 => ( ! [A4: A > B > C2,V2: A,Va: list @ A] : ( P @ A4 @ ( cons @ A @ V2 @ Va ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [A4: A > B > C2,V2: B,Va: list @ B] : ( P @ A4 @ ( nil @ A ) @ ( cons @ B @ V2 @ Va ) )
% 0.24/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % zipf.induct
% 0.24/0.45 thf(fact_131_list_Oexhaust,axiom,
% 0.24/0.45 ! [A: $tType,Y3: list @ A] :
% 0.24/0.45 ( ( Y3
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ~ ! [X212: A,X222: list @ A] :
% 0.24/0.45 ( Y3
% 0.24/0.45 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.exhaust
% 0.24/0.45 thf(fact_132_list_Oinducts,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.24/0.45 ( ( P @ ( nil @ A ) )
% 0.24/0.45 => ( ! [X1: A,X23: list @ A] :
% 0.24/0.45 ( ( P @ X23 )
% 0.24/0.45 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 0.24/0.45 => ( P @ List ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.inducts
% 0.24/0.45 thf(fact_133_neq__Nil__conv,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 = ( ? [Y2: A,Ys2: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( cons @ A @ Y2 @ Ys2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % neq_Nil_conv
% 0.24/0.45 thf(fact_134_list__induct2_H,axiom,
% 0.24/0.45 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.24/0.45 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [Y4: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys3 ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 0.24/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) )
% 0.24/0.45 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_induct2'
% 0.24/0.45 thf(fact_135_splice_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.24/0.45 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Ys3: list @ A] :
% 0.24/0.45 ( ( P @ Ys3 @ Xs2 )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ Ys3 ) )
% 0.24/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % splice.induct
% 0.24/0.45 thf(fact_136_induct__list012,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.24/0.45 ( ( P @ ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.24/0.45 => ( ! [X2: A,Y4: A,Zs3: list @ A] :
% 0.24/0.45 ( ( P @ Zs3 )
% 0.24/0.45 => ( ( P @ ( cons @ A @ Y4 @ Zs3 ) )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Zs3 ) ) ) ) )
% 0.24/0.45 => ( P @ Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % induct_list012
% 0.24/0.45 thf(fact_137_min__list_Ocases,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( ord @ A )
% 0.24/0.45 => ! [X: list @ A] :
% 0.24/0.45 ( ! [X2: A,Xs2: list @ A] :
% 0.24/0.45 ( X
% 0.24/0.45 != ( cons @ A @ X2 @ Xs2 ) )
% 0.24/0.45 => ( X
% 0.24/0.45 = ( nil @ A ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % min_list.cases
% 0.24/0.45 thf(fact_138_suffix__Cons,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Y3: A,Ys: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ Xs @ ( cons @ A @ Y3 @ Ys ) )
% 0.24/0.45 = ( ( Xs
% 0.24/0.45 = ( cons @ A @ Y3 @ Ys ) )
% 0.24/0.45 | ( suffix @ A @ Xs @ Ys ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_Cons
% 0.24/0.45 thf(fact_139_Cons__eq__appendI,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( ( cons @ A @ X @ Xs1 )
% 0.24/0.45 = Ys )
% 0.24/0.45 => ( ( Xs
% 0.24/0.45 = ( append @ A @ Xs1 @ Zs ) )
% 0.24/0.45 => ( ( cons @ A @ X @ Xs )
% 0.24/0.45 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % Cons_eq_appendI
% 0.24/0.45 thf(fact_140_min__list_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( ord @ A )
% 0.24/0.45 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.24/0.45 ( ! [X2: A,Xs2: list @ A] :
% 0.24/0.45 ( ! [X213: A,X223: list @ A] :
% 0.24/0.45 ( ( Xs2
% 0.24/0.45 = ( cons @ A @ X213 @ X223 ) )
% 0.24/0.45 => ( P @ Xs2 ) )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.24/0.45 => ( ( P @ ( nil @ A ) )
% 0.24/0.45 => ( P @ A0 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % min_list.induct
% 0.24/0.45 thf(fact_141_shuffles_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.24/0.45 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.24/0.45 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 0.24/0.45 ( ( P @ Xs2 @ ( cons @ A @ Y4 @ Ys3 ) )
% 0.24/0.45 => ( ( P @ ( cons @ A @ X2 @ Xs2 ) @ Ys3 )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) )
% 0.24/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % shuffles.induct
% 0.24/0.45 thf(fact_142_transpose_Ocases,axiom,
% 0.24/0.45 ! [A: $tType,X: list @ ( list @ A )] :
% 0.24/0.45 ( ( X
% 0.24/0.45 != ( nil @ ( list @ A ) ) )
% 0.24/0.45 => ( ! [Xss: list @ ( list @ A )] :
% 0.24/0.45 ( X
% 0.24/0.45 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.24/0.45 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.24/0.45 ( X
% 0.24/0.45 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % transpose.cases
% 0.24/0.45 thf(fact_143_suffix__ConsD,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.24/0.45 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_ConsD
% 0.24/0.45 thf(fact_144_suffix__ConsI,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y3: A] :
% 0.24/0.45 ( ( suffix @ A @ Xs @ Ys )
% 0.24/0.45 => ( suffix @ A @ Xs @ ( cons @ A @ Y3 @ Ys ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_ConsI
% 0.24/0.45 thf(fact_145_list__2pre__induct,axiom,
% 0.24/0.45 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,W1: list @ A,W2: list @ B] :
% 0.24/0.45 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [E4: A,W12: list @ A,W22: list @ B] :
% 0.24/0.45 ( ( P @ W12 @ W22 )
% 0.24/0.45 => ( P @ ( cons @ A @ E4 @ W12 ) @ W22 ) )
% 0.24/0.45 => ( ! [E4: B,W13: list @ A,W23: list @ B] :
% 0.24/0.45 ( ( P @ W13 @ W23 )
% 0.24/0.45 => ( P @ W13 @ ( cons @ B @ E4 @ W23 ) ) )
% 0.24/0.45 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_2pre_induct
% 0.24/0.45 thf(fact_146_suffix__ConsD2,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A,Y3: A,Ys: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y3 @ Ys ) )
% 0.24/0.45 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_ConsD2
% 0.24/0.45 thf(fact_147_remdups__adj_Ocases,axiom,
% 0.24/0.45 ! [A: $tType,X: list @ A] :
% 0.24/0.45 ( ( X
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A] :
% 0.24/0.45 ( X
% 0.24/0.45 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.24/0.45 => ~ ! [X2: A,Y4: A,Xs2: list @ A] :
% 0.24/0.45 ( X
% 0.24/0.45 != ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % remdups_adj.cases
% 0.24/0.45 thf(fact_148_sorted__wrt_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.24/0.45 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.24/0.45 => ( ! [P2: A > A > $o,X2: A,Ys3: list @ A] :
% 0.24/0.45 ( ( P @ P2 @ Ys3 )
% 0.24/0.45 => ( P @ P2 @ ( cons @ A @ X2 @ Ys3 ) ) )
% 0.24/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % sorted_wrt.induct
% 0.24/0.45 thf(fact_149_append__Cons,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.24/0.45 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_Cons
% 0.24/0.45 thf(fact_150_remdups__adj_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.24/0.45 ( ( P @ ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.24/0.45 => ( ! [X2: A,Y4: A,Xs2: list @ A] :
% 0.24/0.45 ( ( ( X2 = Y4 )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.24/0.45 => ( ( ( X2 != Y4 )
% 0.24/0.45 => ( P @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 0.24/0.45 => ( P @ A0 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % remdups_adj.induct
% 0.24/0.45 thf(fact_151_list__induct__first2,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.24/0.45 ( ( P @ ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.24/0.45 => ( ! [X1: A,X23: A,Xs2: list @ A] :
% 0.24/0.45 ( ( P @ Xs2 )
% 0.24/0.45 => ( P @ ( cons @ A @ X1 @ ( cons @ A @ X23 @ Xs2 ) ) ) )
% 0.24/0.45 => ( P @ Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_induct_first2
% 0.24/0.45 thf(fact_152_list__match__lel__lel,axiom,
% 0.24/0.45 ! [A: $tType,C1: list @ A,Qs: A,C22: list @ A,C12: list @ A,Qs2: A,C23: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ C1 @ ( cons @ A @ Qs @ C22 ) )
% 0.24/0.45 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C23 ) ) )
% 0.24/0.45 => ( ! [C21: list @ A] :
% 0.24/0.45 ( ( C1
% 0.24/0.45 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C21 ) ) )
% 0.24/0.45 => ( C23
% 0.24/0.45 != ( append @ A @ C21 @ ( cons @ A @ Qs @ C22 ) ) ) )
% 0.24/0.45 => ( ( ( C12 = C1 )
% 0.24/0.45 => ( ( Qs2 = Qs )
% 0.24/0.45 => ( C23 != C22 ) ) )
% 0.24/0.45 => ~ ! [C212: list @ A] :
% 0.24/0.45 ( ( C12
% 0.24/0.45 = ( append @ A @ C1 @ ( cons @ A @ Qs @ C212 ) ) )
% 0.24/0.45 => ( C22
% 0.24/0.45 != ( append @ A @ C212 @ ( cons @ A @ Qs2 @ C23 ) ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_match_lel_lel
% 0.24/0.45 thf(fact_153_arg__min__list_Oinduct,axiom,
% 0.24/0.45 ! [B: $tType,A: $tType] :
% 0.24/0.45 ( ( linorder @ B )
% 0.24/0.45 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.24/0.45 ( ! [F2: A > B,X2: A] : ( P @ F2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.24/0.45 => ( ! [F2: A > B,X2: A,Y4: A,Zs3: list @ A] :
% 0.24/0.45 ( ( P @ F2 @ ( cons @ A @ Y4 @ Zs3 ) )
% 0.24/0.45 => ( P @ F2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Zs3 ) ) ) )
% 0.24/0.45 => ( ! [A4: A > B] : ( P @ A4 @ ( nil @ A ) )
% 0.24/0.45 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % arg_min_list.induct
% 0.24/0.45 thf(fact_154_successively_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.24/0.45 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.24/0.45 => ( ! [P2: A > A > $o,X2: A] : ( P @ P2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.24/0.45 => ( ! [P2: A > A > $o,X2: A,Y4: A,Xs2: list @ A] :
% 0.24/0.45 ( ( P @ P2 @ ( cons @ A @ Y4 @ Xs2 ) )
% 0.24/0.45 => ( P @ P2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) )
% 0.24/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % successively.induct
% 0.24/0.45 thf(fact_155_list__all__zip_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,B: $tType,P: ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > $o,A1: list @ A,A22: list @ B] :
% 0.24/0.45 ( ! [P2: A > B > $o] : ( P @ P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [P2: A > B > $o,A4: A,As: list @ A,B3: B,Bs: list @ B] :
% 0.24/0.45 ( ( P @ P2 @ As @ Bs )
% 0.24/0.45 => ( P @ P2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B @ B3 @ Bs ) ) )
% 0.24/0.45 => ( ! [P2: A > B > $o,V2: A,Va: list @ A] : ( P @ P2 @ ( cons @ A @ V2 @ Va ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [P2: A > B > $o,V2: B,Va: list @ B] : ( P @ P2 @ ( nil @ A ) @ ( cons @ B @ V2 @ Va ) )
% 0.24/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_all_zip.induct
% 0.24/0.45 thf(fact_156_list__nonempty__induct,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A] :
% 0.24/0.45 ( ( Xs2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( P @ Xs2 )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 0.24/0.45 => ( P @ Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_nonempty_induct
% 0.24/0.45 thf(fact_157_map__tailrec__rev_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.24/0.45 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 0.24/0.45 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.24/0.45 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 0.24/0.45 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.24/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % map_tailrec_rev.induct
% 0.24/0.45 thf(fact_158_mergesort__by__rel__merge_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.24/0.45 ( ! [R: A > A > $o,X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 0.24/0.45 ( ( ( R @ X2 @ Y4 )
% 0.24/0.45 => ( P @ R @ Xs2 @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.24/0.45 => ( ( ~ ( R @ X2 @ Y4 )
% 0.24/0.45 => ( P @ R @ ( cons @ A @ X2 @ Xs2 ) @ Ys3 ) )
% 0.24/0.45 => ( P @ R @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) )
% 0.24/0.45 => ( ! [R: A > A > $o,Xs2: list @ A] : ( P @ R @ Xs2 @ ( nil @ A ) )
% 0.24/0.45 => ( ! [R: A > A > $o,V2: A,Va: list @ A] : ( P @ R @ ( nil @ A ) @ ( cons @ A @ V2 @ Va ) )
% 0.24/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % mergesort_by_rel_merge.induct
% 0.24/0.45 thf(fact_159_mergesort__by__rel__merge__induct,axiom,
% 0.24/0.45 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,R2: A > B > $o,Xs: list @ A,Ys: list @ B] :
% 0.24/0.45 ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ B ) )
% 0.24/0.45 => ( ! [X_1: list @ B] : ( P @ ( nil @ A ) @ X_1 )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 0.24/0.45 ( ( R2 @ X2 @ Y4 )
% 0.24/0.45 => ( ( P @ Xs2 @ ( cons @ B @ Y4 @ Ys3 ) )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 0.24/0.45 ( ~ ( R2 @ X2 @ Y4 )
% 0.24/0.45 => ( ( P @ ( cons @ A @ X2 @ Xs2 ) @ Ys3 )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) ) )
% 0.24/0.45 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % mergesort_by_rel_merge_induct
% 0.24/0.45 thf(fact_160_longest__common__prefix_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.24/0.45 ( ! [X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 0.24/0.45 ( ( ( X2 = Y4 )
% 0.24/0.45 => ( P @ Xs2 @ Ys3 ) )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.24/0.45 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.24/0.45 => ( ! [Uu: list @ A] : ( P @ Uu @ ( nil @ A ) )
% 0.24/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % longest_common_prefix.induct
% 0.24/0.45 thf(fact_161_strict__sorted_Oinduct,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( linorder @ A )
% 0.24/0.45 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.24/0.45 ( ( P @ ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A,Ys3: list @ A] :
% 0.24/0.45 ( ( P @ Ys3 )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ Ys3 ) ) )
% 0.24/0.45 => ( P @ A0 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % strict_sorted.induct
% 0.24/0.45 thf(fact_162_list_Osel_I1_J,axiom,
% 0.24/0.45 ! [A: $tType,X21: A,X22: list @ A] :
% 0.24/0.45 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.24/0.45 = X21 ) ).
% 0.24/0.45
% 0.24/0.45 % list.sel(1)
% 0.24/0.45 thf(fact_163_list_Osel_I3_J,axiom,
% 0.24/0.45 ! [A: $tType,X21: A,X22: list @ A] :
% 0.24/0.45 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.24/0.45 = X22 ) ).
% 0.24/0.45
% 0.24/0.45 % list.sel(3)
% 0.24/0.45 thf(fact_164_list__tail__coinc,axiom,
% 0.24/0.45 ! [A: $tType,N1: A,R1: list @ A,N22: A,R22: list @ A] :
% 0.24/0.45 ( ( ( cons @ A @ N1 @ R1 )
% 0.24/0.45 = ( cons @ A @ N22 @ R22 ) )
% 0.24/0.45 => ( ( N1 = N22 )
% 0.24/0.45 & ( R1 = R22 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_tail_coinc
% 0.24/0.45 thf(fact_165_not__Cons__self2,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( cons @ A @ X @ Xs )
% 0.24/0.45 != Xs ) ).
% 0.24/0.45
% 0.24/0.45 % not_Cons_self2
% 0.24/0.45 thf(fact_166_distinct__length__2__or__more,axiom,
% 0.24/0.45 ! [A: $tType,A2: A,B2: A,Xs: list @ A] :
% 0.24/0.45 ( ( distinct @ A @ ( cons @ A @ A2 @ ( cons @ A @ B2 @ Xs ) ) )
% 0.24/0.45 = ( ( A2 != B2 )
% 0.24/0.45 & ( distinct @ A @ ( cons @ A @ A2 @ Xs ) )
% 0.24/0.45 & ( distinct @ A @ ( cons @ A @ B2 @ Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % distinct_length_2_or_more
% 0.24/0.45 thf(fact_167_list_Oset__cases,axiom,
% 0.24/0.45 ! [A: $tType,E: A,A2: list @ A] :
% 0.24/0.45 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 0.24/0.45 => ( ! [Z2: list @ A] :
% 0.24/0.45 ( A2
% 0.24/0.45 != ( cons @ A @ E @ Z2 ) )
% 0.24/0.45 => ~ ! [Z1: A,Z2: list @ A] :
% 0.24/0.45 ( ( A2
% 0.24/0.45 = ( cons @ A @ Z1 @ Z2 ) )
% 0.24/0.45 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.set_cases
% 0.24/0.45 thf(fact_168_set__ConsD,axiom,
% 0.24/0.45 ! [A: $tType,Y3: A,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( member @ A @ Y3 @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 0.24/0.45 => ( ( Y3 = X )
% 0.24/0.45 | ( member @ A @ Y3 @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % set_ConsD
% 0.24/0.45 thf(fact_169_list_Oset__intros_I1_J,axiom,
% 0.24/0.45 ! [A: $tType,X21: A,X22: list @ A] : ( member @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.set_intros(1)
% 0.24/0.45 thf(fact_170_list_Oset__intros_I2_J,axiom,
% 0.24/0.45 ! [A: $tType,Y3: A,X22: list @ A,X21: A] :
% 0.24/0.45 ( ( member @ A @ Y3 @ ( set2 @ A @ X22 ) )
% 0.24/0.45 => ( member @ A @ Y3 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.set_intros(2)
% 0.24/0.45 thf(fact_171_list__append__eq__Cons__cases,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Ys @ Zs )
% 0.24/0.45 = ( cons @ A @ X @ Xs ) )
% 0.24/0.45 => ( ( ( Ys
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 => ( Zs
% 0.24/0.45 != ( cons @ A @ X @ Xs ) ) )
% 0.24/0.45 => ~ ! [Ys4: list @ A] :
% 0.24/0.45 ( ( Ys
% 0.24/0.45 = ( cons @ A @ X @ Ys4 ) )
% 0.24/0.45 => ( ( append @ A @ Ys4 @ Zs )
% 0.24/0.45 != Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_append_eq_Cons_cases
% 0.24/0.45 thf(fact_172_list__Cons__eq__append__cases,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( ( cons @ A @ X @ Xs )
% 0.24/0.45 = ( append @ A @ Ys @ Zs ) )
% 0.24/0.45 => ( ( ( Ys
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 => ( Zs
% 0.24/0.45 != ( cons @ A @ X @ Xs ) ) )
% 0.24/0.45 => ~ ! [Ys4: list @ A] :
% 0.24/0.45 ( ( Ys
% 0.24/0.45 = ( cons @ A @ X @ Ys4 ) )
% 0.24/0.45 => ( ( append @ A @ Ys4 @ Zs )
% 0.24/0.45 != Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list_Cons_eq_append_cases
% 0.24/0.45 thf(fact_173_rev__nonempty__induct2_H,axiom,
% 0.24/0.45 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( Ys
% 0.24/0.45 != ( nil @ B ) )
% 0.24/0.45 => ( ! [X2: A,Y4: B] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) @ ( cons @ B @ Y4 @ ( nil @ B ) ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: B] :
% 0.24/0.45 ( ( Xs2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) )
% 0.24/0.45 => ( ! [X2: A,Y4: B,Ys3: list @ B] :
% 0.24/0.45 ( ( Ys3
% 0.24/0.45 != ( nil @ B ) )
% 0.24/0.45 => ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 0.24/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.24/0.45 => ( ( Xs2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( Ys3
% 0.24/0.45 != ( nil @ B ) )
% 0.24/0.45 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) ) ) ) )
% 0.24/0.45 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % rev_nonempty_induct2'
% 0.24/0.45 thf(fact_174_rev__nonempty__induct,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A] :
% 0.24/0.45 ( ( Xs2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( P @ Xs2 )
% 0.24/0.45 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ) )
% 0.24/0.45 => ( P @ Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % rev_nonempty_induct
% 0.24/0.45 thf(fact_175_append__eq__Cons__conv,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Ys @ Zs )
% 0.24/0.45 = ( cons @ A @ X @ Xs ) )
% 0.24/0.45 = ( ( ( Ys
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( Zs
% 0.24/0.45 = ( cons @ A @ X @ Xs ) ) )
% 0.24/0.45 | ? [Ys5: list @ A] :
% 0.24/0.45 ( ( Ys
% 0.24/0.45 = ( cons @ A @ X @ Ys5 ) )
% 0.24/0.45 & ( ( append @ A @ Ys5 @ Zs )
% 0.24/0.45 = Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_eq_Cons_conv
% 0.24/0.45 thf(fact_176_Cons__eq__append__conv,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( ( cons @ A @ X @ Xs )
% 0.24/0.45 = ( append @ A @ Ys @ Zs ) )
% 0.24/0.45 = ( ( ( Ys
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 & ( ( cons @ A @ X @ Xs )
% 0.24/0.45 = Zs ) )
% 0.24/0.45 | ? [Ys5: list @ A] :
% 0.24/0.45 ( ( ( cons @ A @ X @ Ys5 )
% 0.24/0.45 = Ys )
% 0.24/0.45 & ( Xs
% 0.24/0.45 = ( append @ A @ Ys5 @ Zs ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % Cons_eq_append_conv
% 0.24/0.45 thf(fact_177_neq__Nil__rev__conv,axiom,
% 0.24/0.45 ! [A: $tType,L: list @ A] :
% 0.24/0.45 ( ( L
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 = ( ? [Xs3: list @ A,X3: A] :
% 0.24/0.45 ( L
% 0.24/0.45 = ( append @ A @ Xs3 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % neq_Nil_rev_conv
% 0.24/0.45 thf(fact_178_rev__induct2_H,axiom,
% 0.24/0.45 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.24/0.45 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( nil @ B ) )
% 0.24/0.45 => ( ! [Y4: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 0.24/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.24/0.45 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) ) )
% 0.24/0.45 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % rev_induct2'
% 0.24/0.45 thf(fact_179_neq__Nil__revE,axiom,
% 0.24/0.45 ! [A: $tType,L: list @ A] :
% 0.24/0.45 ( ( L
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ~ ! [Ll: list @ A,E4: A] :
% 0.24/0.45 ( L
% 0.24/0.45 != ( append @ A @ Ll @ ( cons @ A @ E4 @ ( nil @ A ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % neq_Nil_revE
% 0.24/0.45 thf(fact_180_rev__exhaust,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ~ ! [Ys3: list @ A,Y4: A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 != ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % rev_exhaust
% 0.24/0.45 thf(fact_181_rev__induct,axiom,
% 0.24/0.45 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.24/0.45 ( ( P @ ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A] :
% 0.24/0.45 ( ( P @ Xs2 )
% 0.24/0.45 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) )
% 0.24/0.45 => ( P @ Xs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % rev_induct
% 0.24/0.45 thf(fact_182_split__list,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 => ? [Ys3: list @ A,Zs3: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list
% 0.24/0.45 thf(fact_183_split__list__last,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 => ? [Ys3: list @ A,Zs3: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.24/0.45 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_last
% 0.24/0.45 thf(fact_184_split__list__prop,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.24/0.45 ( ? [X4: A] :
% 0.24/0.45 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( P @ X4 ) )
% 0.24/0.45 => ? [Ys3: list @ A,X2: A] :
% 0.24/0.45 ( ? [Zs3: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.24/0.45 & ( P @ X2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_prop
% 0.24/0.45 thf(fact_185_xy__in__set__cases,axiom,
% 0.24/0.45 ! [A: $tType,X: A,L: list @ A,Y3: A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ L ) )
% 0.24/0.45 => ( ( member @ A @ Y3 @ ( set2 @ A @ L ) )
% 0.24/0.45 => ( ( ( X = Y3 )
% 0.24/0.45 => ! [L12: list @ A,L22: list @ A] :
% 0.24/0.45 ( L
% 0.24/0.45 != ( append @ A @ L12 @ ( cons @ A @ Y3 @ L22 ) ) ) )
% 0.24/0.45 => ( ( ( X != Y3 )
% 0.24/0.45 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 0.24/0.45 ( L
% 0.24/0.45 != ( append @ A @ L12 @ ( cons @ A @ X @ ( append @ A @ L22 @ ( cons @ A @ Y3 @ L3 ) ) ) ) ) )
% 0.24/0.45 => ~ ( ( X != Y3 )
% 0.24/0.45 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 0.24/0.45 ( L
% 0.24/0.45 != ( append @ A @ L12 @ ( cons @ A @ Y3 @ ( append @ A @ L22 @ ( cons @ A @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % xy_in_set_cases
% 0.24/0.45 thf(fact_186_split__list__first,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 => ? [Ys3: list @ A,Zs3: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.24/0.45 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_first
% 0.24/0.45 thf(fact_187_split__list__propE,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.24/0.45 ( ? [X4: A] :
% 0.24/0.45 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( P @ X4 ) )
% 0.24/0.45 => ~ ! [Ys3: list @ A,X2: A] :
% 0.24/0.45 ( ? [Zs3: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.24/0.45 => ~ ( P @ X2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_propE
% 0.24/0.45 thf(fact_188_append__Cons__eq__iff,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Xs4: list @ A,Ys6: list @ A] :
% 0.24/0.45 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 => ( ~ ( member @ A @ X @ ( set2 @ A @ Ys ) )
% 0.24/0.45 => ( ( ( append @ A @ Xs @ ( cons @ A @ X @ Ys ) )
% 0.24/0.45 = ( append @ A @ Xs4 @ ( cons @ A @ X @ Ys6 ) ) )
% 0.24/0.45 = ( ( Xs = Xs4 )
% 0.24/0.45 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_Cons_eq_iff
% 0.24/0.45 thf(fact_189_in__set__conv__decomp,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 = ( ? [Ys2: list @ A,Zs2: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % in_set_conv_decomp
% 0.24/0.45 thf(fact_190_in__set__list__format,axiom,
% 0.24/0.45 ! [A: $tType,E: A,L: list @ A] :
% 0.24/0.45 ( ( member @ A @ E @ ( set2 @ A @ L ) )
% 0.24/0.45 => ~ ! [L12: list @ A,L22: list @ A] :
% 0.24/0.45 ( L
% 0.24/0.45 != ( append @ A @ L12 @ ( cons @ A @ E @ L22 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % in_set_list_format
% 0.24/0.45 thf(fact_191_split__list__last__prop,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.24/0.45 ( ? [X4: A] :
% 0.24/0.45 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( P @ X4 ) )
% 0.24/0.45 => ? [Ys3: list @ A,X2: A,Zs3: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.24/0.45 & ( P @ X2 )
% 0.24/0.45 & ! [Xa: A] :
% 0.24/0.45 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 0.24/0.45 => ~ ( P @ Xa ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_last_prop
% 0.24/0.45 thf(fact_192_split__list__first__prop,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.24/0.45 ( ? [X4: A] :
% 0.24/0.45 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( P @ X4 ) )
% 0.24/0.45 => ? [Ys3: list @ A,X2: A] :
% 0.24/0.45 ( ? [Zs3: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.24/0.45 & ( P @ X2 )
% 0.24/0.45 & ! [Xa: A] :
% 0.24/0.45 ( ( member @ A @ Xa @ ( set2 @ A @ Ys3 ) )
% 0.24/0.45 => ~ ( P @ Xa ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_first_prop
% 0.24/0.45 thf(fact_193_split__list__last__propE,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.24/0.45 ( ? [X4: A] :
% 0.24/0.45 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( P @ X4 ) )
% 0.24/0.45 => ~ ! [Ys3: list @ A,X2: A,Zs3: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.24/0.45 => ( ( P @ X2 )
% 0.24/0.45 => ~ ! [Xa: A] :
% 0.24/0.45 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 0.24/0.45 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_last_propE
% 0.24/0.45 thf(fact_194_split__list__first__propE,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.24/0.45 ( ? [X4: A] :
% 0.24/0.45 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( P @ X4 ) )
% 0.24/0.45 => ~ ! [Ys3: list @ A,X2: A] :
% 0.24/0.45 ( ? [Zs3: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 0.24/0.45 => ( ( P @ X2 )
% 0.24/0.45 => ~ ! [Xa: A] :
% 0.24/0.45 ( ( member @ A @ Xa @ ( set2 @ A @ Ys3 ) )
% 0.24/0.45 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_first_propE
% 0.24/0.45 thf(fact_195_in__set__conv__decomp__last,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 = ( ? [Ys2: list @ A,Zs2: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.24/0.45 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % in_set_conv_decomp_last
% 0.24/0.45 thf(fact_196_in__set__conv__decomp__first,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 = ( ? [Ys2: list @ A,Zs2: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.24/0.45 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % in_set_conv_decomp_first
% 0.24/0.45 thf(fact_197_split__list__last__prop__iff,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.24/0.45 ( ( ? [X3: A] :
% 0.24/0.45 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( P @ X3 ) ) )
% 0.24/0.45 = ( ? [Ys2: list @ A,X3: A,Zs2: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 0.24/0.45 & ( P @ X3 )
% 0.24/0.45 & ! [Y2: A] :
% 0.24/0.45 ( ( member @ A @ Y2 @ ( set2 @ A @ Zs2 ) )
% 0.24/0.45 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_last_prop_iff
% 0.24/0.45 thf(fact_198_split__list__first__prop__iff,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.24/0.45 ( ( ? [X3: A] :
% 0.24/0.45 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( P @ X3 ) ) )
% 0.24/0.45 = ( ? [Ys2: list @ A,X3: A] :
% 0.24/0.45 ( ? [Zs2: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 0.24/0.45 & ( P @ X3 )
% 0.24/0.45 & ! [Y2: A] :
% 0.24/0.45 ( ( member @ A @ Y2 @ ( set2 @ A @ Ys2 ) )
% 0.24/0.45 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % split_list_first_prop_iff
% 0.24/0.45 thf(fact_199_distinct__singleton,axiom,
% 0.24/0.45 ! [A: $tType,X: A] : ( distinct @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % distinct_singleton
% 0.24/0.45 thf(fact_200_distinct_Osimps_I2_J,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( distinct @ A @ ( cons @ A @ X @ Xs ) )
% 0.24/0.45 = ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 & ( distinct @ A @ Xs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % distinct.simps(2)
% 0.24/0.45 thf(fact_201_distinct__match,axiom,
% 0.24/0.45 ! [A: $tType,Al: list @ A,E: A,Bl: list @ A,Al2: list @ A,Bl2: list @ A] :
% 0.24/0.45 ( ( distinct @ A @ ( append @ A @ Al @ ( cons @ A @ E @ Bl ) ) )
% 0.24/0.45 => ( ( ( append @ A @ Al @ ( cons @ A @ E @ Bl ) )
% 0.24/0.45 = ( append @ A @ Al2 @ ( cons @ A @ E @ Bl2 ) ) )
% 0.24/0.45 = ( ( Al = Al2 )
% 0.24/0.45 & ( Bl = Bl2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % distinct_match
% 0.24/0.45 thf(fact_202_Nil__tl,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( ( nil @ A )
% 0.24/0.45 = ( tl @ A @ Xs ) )
% 0.24/0.45 = ( ( Xs
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 | ? [X3: A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % Nil_tl
% 0.24/0.45 thf(fact_203_tl__Nil,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( ( tl @ A @ Xs )
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 = ( ( Xs
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 | ? [X3: A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % tl_Nil
% 0.24/0.45 thf(fact_204_tl__obtain__elem,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( ( tl @ A @ Xs )
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 => ~ ! [E4: A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 != ( cons @ A @ E4 @ ( nil @ A ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % tl_obtain_elem
% 0.24/0.45 thf(fact_205_not__distinct__decomp,axiom,
% 0.24/0.45 ! [A: $tType,Ws: list @ A] :
% 0.24/0.45 ( ~ ( distinct @ A @ Ws )
% 0.24/0.45 => ? [Xs2: list @ A,Ys3: list @ A,Zs3: list @ A,Y4: A] :
% 0.24/0.45 ( Ws
% 0.24/0.45 = ( append @ A @ Xs2 @ ( append @ A @ ( cons @ A @ Y4 @ ( nil @ A ) ) @ ( append @ A @ Ys3 @ ( append @ A @ ( cons @ A @ Y4 @ ( nil @ A ) ) @ Zs3 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % not_distinct_decomp
% 0.24/0.45 thf(fact_206_not__distinct__conv__prefix,axiom,
% 0.24/0.45 ! [A: $tType,As2: list @ A] :
% 0.24/0.45 ( ( ~ ( distinct @ A @ As2 ) )
% 0.24/0.45 = ( ? [Xs3: list @ A,Y2: A,Ys2: list @ A] :
% 0.24/0.45 ( ( member @ A @ Y2 @ ( set2 @ A @ Xs3 ) )
% 0.24/0.45 & ( distinct @ A @ Xs3 )
% 0.24/0.45 & ( As2
% 0.24/0.45 = ( append @ A @ Xs3 @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % not_distinct_conv_prefix
% 0.24/0.45 thf(fact_207_not__suffix__induct,axiom,
% 0.24/0.45 ! [A: $tType,Ps: list @ A,Ls: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.24/0.45 ( ~ ( suffix @ A @ Ps @ Ls )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( nil @ A ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 0.24/0.45 ( ( X2 != Y4 )
% 0.24/0.45 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) )
% 0.24/0.45 => ( ! [X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 0.24/0.45 ( ( X2 = Y4 )
% 0.24/0.45 => ( ~ ( suffix @ A @ Xs2 @ Ys3 )
% 0.24/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.24/0.45 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ) )
% 0.24/0.45 => ( P @ Ps @ Ls ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % not_suffix_induct
% 0.24/0.45 thf(fact_208_not__suffix__cases,axiom,
% 0.24/0.45 ! [A: $tType,Ps: list @ A,Ls: list @ A] :
% 0.24/0.45 ( ~ ( suffix @ A @ Ps @ Ls )
% 0.24/0.45 => ( ( ( Ps
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( Ls
% 0.24/0.45 != ( nil @ A ) ) )
% 0.24/0.45 => ( ! [A4: A,As: list @ A] :
% 0.24/0.45 ( ( Ps
% 0.24/0.45 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 0.24/0.45 => ! [X2: A,Xs2: list @ A] :
% 0.24/0.45 ( ( Ls
% 0.24/0.45 = ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 0.24/0.45 => ( ( X2 = A4 )
% 0.24/0.45 => ( suffix @ A @ As @ Xs2 ) ) ) )
% 0.24/0.45 => ~ ! [A4: A] :
% 0.24/0.45 ( ? [As: list @ A] :
% 0.24/0.45 ( Ps
% 0.24/0.45 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 0.24/0.45 => ! [X2: A] :
% 0.24/0.45 ( ? [Xs2: list @ A] :
% 0.24/0.45 ( Ls
% 0.24/0.45 = ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 0.24/0.45 => ( X2 = A4 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % not_suffix_cases
% 0.24/0.45 thf(fact_209_list_Oexhaust__sel,axiom,
% 0.24/0.45 ! [A: $tType,List: list @ A] :
% 0.24/0.45 ( ( List
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( List
% 0.24/0.45 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.exhaust_sel
% 0.24/0.45 thf(fact_210_not__distinct__split__distinct,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ~ ( distinct @ A @ Xs )
% 0.24/0.45 => ~ ! [Y4: A,Ys3: list @ A] :
% 0.24/0.45 ( ( distinct @ A @ Ys3 )
% 0.24/0.45 => ( ( member @ A @ Y4 @ ( set2 @ A @ Ys3 ) )
% 0.24/0.45 => ! [Zs3: list @ A] :
% 0.24/0.45 ( Xs
% 0.24/0.45 != ( append @ A @ Ys3 @ ( append @ A @ ( cons @ A @ Y4 @ ( nil @ A ) ) @ Zs3 ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % not_distinct_split_distinct
% 0.24/0.45 thf(fact_211_append__eq__append__conv2,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.24/0.45 = ( append @ A @ Zs @ Ts ) )
% 0.24/0.45 = ( ? [Us: list @ A] :
% 0.24/0.45 ( ( ( Xs
% 0.24/0.45 = ( append @ A @ Zs @ Us ) )
% 0.24/0.45 & ( ( append @ A @ Us @ Ys )
% 0.24/0.45 = Ts ) )
% 0.24/0.45 | ( ( ( append @ A @ Xs @ Us )
% 0.24/0.45 = Zs )
% 0.24/0.45 & ( Ys
% 0.24/0.45 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_eq_append_conv2
% 0.24/0.45 thf(fact_212_append__eq__appendI,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us2: list @ A] :
% 0.24/0.45 ( ( ( append @ A @ Xs @ Xs1 )
% 0.24/0.45 = Zs )
% 0.24/0.45 => ( ( Ys
% 0.24/0.45 = ( append @ A @ Xs1 @ Us2 ) )
% 0.24/0.45 => ( ( append @ A @ Xs @ Ys )
% 0.24/0.45 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % append_eq_appendI
% 0.24/0.45 thf(fact_213_suffix__order_Odual__order_Oantisym,axiom,
% 0.24/0.45 ! [A: $tType,B2: list @ A,A2: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ B2 @ A2 )
% 0.24/0.45 => ( ( suffix @ A @ A2 @ B2 )
% 0.24/0.45 => ( A2 = B2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.dual_order.antisym
% 0.24/0.45 thf(fact_214_suffix__order_Odual__order_Oeq__iff,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( ^ [Y5: list @ A,Z: list @ A] : ( Y5 = Z ) )
% 0.24/0.45 = ( ^ [A5: list @ A,B4: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ B4 @ A5 )
% 0.24/0.45 & ( suffix @ A @ A5 @ B4 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.dual_order.eq_iff
% 0.24/0.45 thf(fact_215_suffix__order_Odual__order_Otrans,axiom,
% 0.24/0.45 ! [A: $tType,B2: list @ A,A2: list @ A,C: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ B2 @ A2 )
% 0.24/0.45 => ( ( suffix @ A @ C @ B2 )
% 0.24/0.45 => ( suffix @ A @ C @ A2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.dual_order.trans
% 0.24/0.45 thf(fact_216_suffix__order_Oord__le__eq__trans,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ A2 @ B2 )
% 0.24/0.45 => ( ( B2 = C )
% 0.24/0.45 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.ord_le_eq_trans
% 0.24/0.45 thf(fact_217_suffix__order_Oord__eq__le__trans,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.24/0.45 ( ( A2 = B2 )
% 0.24/0.45 => ( ( suffix @ A @ B2 @ C )
% 0.24/0.45 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.ord_eq_le_trans
% 0.24/0.45 thf(fact_218_suffix__order_Oorder_Oantisym,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A,B2: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ A2 @ B2 )
% 0.24/0.45 => ( ( suffix @ A @ B2 @ A2 )
% 0.24/0.45 => ( A2 = B2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.order.antisym
% 0.24/0.45 thf(fact_219_suffix__order_Oorder_Oeq__iff,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( ^ [Y5: list @ A,Z: list @ A] : ( Y5 = Z ) )
% 0.24/0.45 = ( ^ [A5: list @ A,B4: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ A5 @ B4 )
% 0.24/0.45 & ( suffix @ A @ B4 @ A5 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.order.eq_iff
% 0.24/0.45 thf(fact_220_suffix__order_Oantisym__conv,axiom,
% 0.24/0.45 ! [A: $tType,Y3: list @ A,X: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ Y3 @ X )
% 0.24/0.45 => ( ( suffix @ A @ X @ Y3 )
% 0.24/0.45 = ( X = Y3 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.antisym_conv
% 0.24/0.45 thf(fact_221_suffix__order_Oorder__trans,axiom,
% 0.24/0.45 ! [A: $tType,X: list @ A,Y3: list @ A,Z3: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ X @ Y3 )
% 0.24/0.45 => ( ( suffix @ A @ Y3 @ Z3 )
% 0.24/0.45 => ( suffix @ A @ X @ Z3 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.order_trans
% 0.24/0.45 thf(fact_222_suffix__order_Oorder_Otrans,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ A2 @ B2 )
% 0.24/0.45 => ( ( suffix @ A @ B2 @ C )
% 0.24/0.45 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.order.trans
% 0.24/0.45 thf(fact_223_suffix__order_Oeq__refl,axiom,
% 0.24/0.45 ! [A: $tType,X: list @ A,Y3: list @ A] :
% 0.24/0.45 ( ( X = Y3 )
% 0.24/0.45 => ( suffix @ A @ X @ Y3 ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.eq_refl
% 0.24/0.45 thf(fact_224_suffix__order_Oantisym,axiom,
% 0.24/0.45 ! [A: $tType,X: list @ A,Y3: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ X @ Y3 )
% 0.24/0.45 => ( ( suffix @ A @ Y3 @ X )
% 0.24/0.45 => ( X = Y3 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.antisym
% 0.24/0.45 thf(fact_225_suffix__order_Oeq__iff,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( ^ [Y5: list @ A,Z: list @ A] : ( Y5 = Z ) )
% 0.24/0.45 = ( ^ [X3: list @ A,Y2: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ X3 @ Y2 )
% 0.24/0.45 & ( suffix @ A @ Y2 @ X3 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_order.eq_iff
% 0.24/0.45 thf(fact_226_suffix__same__cases,axiom,
% 0.24/0.45 ! [A: $tType,Xs_1: list @ A,Ys: list @ A,Xs_2: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ Xs_1 @ Ys )
% 0.24/0.45 => ( ( suffix @ A @ Xs_2 @ Ys )
% 0.24/0.45 => ( ( suffix @ A @ Xs_1 @ Xs_2 )
% 0.24/0.45 | ( suffix @ A @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_same_cases
% 0.24/0.45 thf(fact_227_finite__list,axiom,
% 0.24/0.45 ! [A: $tType,A3: set @ A] :
% 0.24/0.45 ( ( finite_finite @ A @ A3 )
% 0.24/0.45 => ? [Xs2: list @ A] :
% 0.24/0.45 ( ( set2 @ A @ Xs2 )
% 0.24/0.45 = A3 ) ) ).
% 0.24/0.45
% 0.24/0.45 % finite_list
% 0.24/0.45 thf(fact_228_append_Oleft__neutral,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A] :
% 0.24/0.45 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.24/0.45 = A2 ) ).
% 0.24/0.45
% 0.24/0.45 % append.left_neutral
% 0.24/0.45 thf(fact_229_append__Nil,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A] :
% 0.24/0.45 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.24/0.45 = Ys ) ).
% 0.24/0.45
% 0.24/0.45 % append_Nil
% 0.24/0.45 thf(fact_230_eq__Nil__appendI,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( Xs = Ys )
% 0.24/0.45 => ( Xs
% 0.24/0.45 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % eq_Nil_appendI
% 0.24/0.45 thf(fact_231_distinct_Osimps_I1_J,axiom,
% 0.24/0.45 ! [A: $tType] : ( distinct @ A @ ( nil @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 % distinct.simps(1)
% 0.24/0.45 thf(fact_232_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 0.24/0.45 => ( A2
% 0.24/0.45 = ( nil @ A ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_bot.bot.extremum_uniqueI
% 0.24/0.45 thf(fact_233_suffix__bot_Obot_Oextremum,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A] : ( suffix @ A @ ( nil @ A ) @ A2 ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_bot.bot.extremum
% 0.24/0.45 thf(fact_234_Nil__suffix,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( nil @ A ) @ Xs ) ).
% 0.24/0.45
% 0.24/0.45 % Nil_suffix
% 0.24/0.45 thf(fact_235_list_Osel_I2_J,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( tl @ A @ ( nil @ A ) )
% 0.24/0.45 = ( nil @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.sel(2)
% 0.24/0.45 thf(fact_236_suffix__appendI,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ Xs @ Ys )
% 0.24/0.45 => ( suffix @ A @ Xs @ ( append @ A @ Zs @ Ys ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_appendI
% 0.24/0.45 thf(fact_237_suffix__appendD,axiom,
% 0.24/0.45 ! [A: $tType,Zs: list @ A,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ ( append @ A @ Zs @ Xs ) @ Ys )
% 0.24/0.45 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_appendD
% 0.24/0.45 thf(fact_238_suffix__append,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ Zs ) )
% 0.24/0.45 = ( ( suffix @ A @ Xs @ Zs )
% 0.24/0.45 | ? [Xs5: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Xs5 @ Zs ) )
% 0.24/0.45 & ( suffix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_append
% 0.24/0.45 thf(fact_239_Sublist_Osuffix__def,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( suffix @ A )
% 0.24/0.45 = ( ^ [Xs3: list @ A,Ys2: list @ A] :
% 0.24/0.45 ? [Zs2: list @ A] :
% 0.24/0.45 ( Ys2
% 0.24/0.45 = ( append @ A @ Zs2 @ Xs3 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % Sublist.suffix_def
% 0.24/0.45 thf(fact_240_suffixI,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A,Zs: list @ A,Xs: list @ A] :
% 0.24/0.45 ( ( Ys
% 0.24/0.45 = ( append @ A @ Zs @ Xs ) )
% 0.24/0.45 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffixI
% 0.24/0.45 thf(fact_241_suffixE,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( suffix @ A @ Xs @ Ys )
% 0.24/0.45 => ~ ! [Zs3: list @ A] :
% 0.24/0.45 ( Ys
% 0.24/0.45 != ( append @ A @ Zs3 @ Xs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % suffixE
% 0.24/0.45 thf(fact_242_distinct__suffix,axiom,
% 0.24/0.45 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.24/0.45 ( ( distinct @ A @ Ys )
% 0.24/0.45 => ( ( suffix @ A @ Xs @ Ys )
% 0.24/0.45 => ( distinct @ A @ Xs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % distinct_suffix
% 0.24/0.45 thf(fact_243_distinct__tl,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( distinct @ A @ Xs )
% 0.24/0.45 => ( distinct @ A @ ( tl @ A @ Xs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % distinct_tl
% 0.24/0.45 thf(fact_244_suffix__tl,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( tl @ A @ Xs ) @ Xs ) ).
% 0.24/0.45
% 0.24/0.45 % suffix_tl
% 0.24/0.45 thf(fact_245_finite__distinct__list,axiom,
% 0.24/0.45 ! [A: $tType,A3: set @ A] :
% 0.24/0.45 ( ( finite_finite @ A @ A3 )
% 0.24/0.45 => ? [Xs2: list @ A] :
% 0.24/0.45 ( ( ( set2 @ A @ Xs2 )
% 0.24/0.45 = A3 )
% 0.24/0.45 & ( distinct @ A @ Xs2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % finite_distinct_list
% 0.24/0.45 thf(fact_246_list_Oset__sel_I1_J,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A] :
% 0.24/0.45 ( ( A2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( member @ A @ ( hd @ A @ A2 ) @ ( set2 @ A @ A2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.set_sel(1)
% 0.24/0.45 thf(fact_247_hd__in__set,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( member @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ Xs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % hd_in_set
% 0.24/0.45 thf(fact_248_list_Oset__sel_I2_J,axiom,
% 0.24/0.45 ! [A: $tType,A2: list @ A,X: A] :
% 0.24/0.45 ( ( A2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ A2 ) ) )
% 0.24/0.45 => ( member @ A @ X @ ( set2 @ A @ A2 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.set_sel(2)
% 0.24/0.45 thf(fact_249_longest__common__prefix,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ? [Ps2: list @ A,Xs6: list @ A,Ys4: list @ A] :
% 0.24/0.45 ( ( Xs
% 0.24/0.45 = ( append @ A @ Ps2 @ Xs6 ) )
% 0.24/0.45 & ( Ys
% 0.24/0.45 = ( append @ A @ Ps2 @ Ys4 ) )
% 0.24/0.45 & ( ( Xs6
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 | ( Ys4
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 | ( ( hd @ A @ Xs6 )
% 0.24/0.45 != ( hd @ A @ Ys4 ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % longest_common_prefix
% 0.24/0.45 thf(fact_250_hd__append,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.24/0.45 ( ( ( Xs
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.24/0.45 = ( hd @ A @ Ys ) ) )
% 0.24/0.45 & ( ( Xs
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.24/0.45 = ( hd @ A @ Xs ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % hd_append
% 0.24/0.45 thf(fact_251_list_Oexpand,axiom,
% 0.24/0.45 ! [A: $tType,List: list @ A,List2: list @ A] :
% 0.24/0.45 ( ( ( List
% 0.24/0.45 = ( nil @ A ) )
% 0.24/0.45 = ( List2
% 0.24/0.45 = ( nil @ A ) ) )
% 0.24/0.45 => ( ( ( List
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( List2
% 0.24/0.45 != ( nil @ A ) )
% 0.24/0.45 => ( ( ( hd @ A @ List )
% 0.24/0.45 = ( hd @ A @ List2 ) )
% 0.24/0.45 & ( ( tl @ A @ List )
% 0.24/0.45 = ( tl @ A @ List2 ) ) ) ) )
% 0.24/0.45 => ( List = List2 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % list.expand
% 0.24/0.45 thf(fact_252_not__hd__in__tl,axiom,
% 0.24/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.24/0.45 ( ( X
% 0.24/0.45 != ( hd @ A @ Xs ) )
% 0.24/0.45 => ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.24/0.45 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % not_hd_in_tl
% 0.24/0.45 thf(fact_253_Misc_Odistinct__hd__tl,axiom,
% 0.24/0.45 ! [A: $tType,Xs: list @ A,X: A] :
% 0.24/0.45 ( ( distinct @ A @ Xs )
% 0.24/0.45 => ( ( X
% 0.24/0.45 = ( hd @ A @ Xs ) )
% 0.24/0.45 => ~ ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % Misc.distinct_hd_tl
% 0.24/0.45 thf(fact_254_old_OEntry__unreachable,axiom,
% 0.24/0.45 ! [G2: g] :
% 0.24/0.45 ( ( invar @ G2 )
% 0.24/0.45 => ( ( graph_1822314308nEdges @ g @ node @ edgeD @ inEdges @ G2 @ ( entry @ G2 ) )
% 0.24/0.45 = ( nil @ ( product_prod @ node @ ( product_prod @ edgeD @ node ) ) ) ) ) ).
% 0.24/0.45
% 0.24/0.45 % old.Entry_unreachable
% 0.24/0.45
% 0.24/0.45 % Subclasses (2)
% 0.24/0.45 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( linorder @ A )
% 0.24/0.45 => ( type @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.24/0.45 ! [A: $tType] :
% 0.24/0.45 ( ( linorder @ A )
% 0.24/0.45 => ( ord @ A ) ) ).
% 0.24/0.45
% 0.24/0.45 % Type constructors (4)
% 0.24/0.45 thf(tcon_fun___Orderings_Oord,axiom,
% 0.24/0.45 ! [A6: $tType,A7: $tType] :
% 0.24/0.45 ( ( ord @ A7 )
% 0.24/0.45 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_Set_Oset___Orderings_Oord_1,axiom,
% 0.24/0.45 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.24/0.45 linorder @ $o ).
% 0.24/0.45
% 0.24/0.45 thf(tcon_HOL_Obool___Orderings_Oord_2,axiom,
% 0.24/0.45 ord @ $o ).
% 0.24/0.45
% 0.24/0.45 % Free types (2)
% 0.24/0.45 thf(tfree_0,hypothesis,
% 0.24/0.45 linorder @ node ).
% 0.24/0.45
% 0.24/0.45 thf(tfree_1,hypothesis,
% 0.24/0.45 linorder @ val ).
% 0.24/0.45
% 0.24/0.45 % Conjectures (1)
% 0.24/0.45 thf(conj_0,conjecture,
% 0.24/0.45 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ) ).
% 0.24/0.45
% 0.24/0.45 %------------------------------------------------------------------------------
% 0.24/0.45 ------------------------
% 2.85/1.54 ---- Embedded in THF ---
% 2.85/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.85/1.54 %%% Generated on Tue Feb 24 08:25:37 EST 2026
% 2.85/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.85/1.54 %%% Logic specification used:
% 2.85/1.54 %%% thf(spec, logic, $$dhol).
% 2.85/1.54
% 2.85/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cRKnHLkZP0/DTF2DTF20598.p
% 2.85/1.54 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.85/1.54 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.85/1.54 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.85/1.54 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.85/1.54 thf(ty_tf_edgeD, type, edgeD: $tType).
% 2.85/1.54 thf(ty_tf_node, type, node: $tType).
% 2.85/1.54 thf(ty_tf_val, type, val: $tType).
% 2.85/1.54 thf(ty_tf_g, type, g: $tType).
% 2.85/1.54 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.85/1.54 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.85/1.54 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.85/1.54 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.85/1.54 thf(sy_c_Graph__path_Ograph__Entry_OEntryPath, type, graph_2081878492ryPath: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > Node) > (G > ((list @ Node) > $o))))))))).
% 2.85/1.54 thf(sy_c_Graph__path_Ograph__Entry_OisIdom, type, graph_graph_isIdom: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > Node) > (G > (Node > (Node > $o)))))))))).
% 2.85/1.54 thf(sy_c_Graph__path_Ograph__Entry__base_Odominates, type, graph_709200220inates: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > Node) > (G > (Node > (Node > $o)))))))))).
% 2.85/1.54 thf(sy_c_Graph__path_Ograph__path__base_OinEdges, type, graph_1822314308nEdges: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > (list @ ((product_prod @ Node) @ ((product_prod @ EdgeD) @ Node))))))))).
% 2.85/1.54 thf(sy_c_Graph__path_Ograph__path__base_Opath2, type, graph_1661282752_path2: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > ((list @ Node) > (Node > $o)))))))))).
% 2.85/1.54 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors, type, graph_1201503639essors: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > (list @ Node))))))).
% 2.85/1.54 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.85/1.54 thf(sy_c_List_Odistinct, type, distinct: (!> [A:$tType]: (((list @ A) > $o)))).
% 2.85/1.54 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.85/1.54 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.85/1.54 thf(sy_c_List_Olist_Ohd, type, hd: (!> [A:$tType]: (((list @ A) > A)))).
% 2.85/1.54 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.85/1.54 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.85/1.54 thf(sy_c_Minimality_Ograph__Entry_Oreducible, type, graph_reducible: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > Node) > (G > $o)))))))).
% 2.85/1.54 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs, type, sSA_CFG_SSA_allDefs: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (set @ Val)))))))).
% 2.85/1.54 thf(sy_c_SSA__CFG_OCFG__SSA__base_OdefAss, type, sSA_CFG_SSA_defAss: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > Node) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (Val > $o)))))))))))).
% 2.85/1.54 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs, type, sSA_CFG_SSA_phiDefs: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (set @ Val))))))).
% 2.85/1.54 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))))))))).
% 2.85/1.54 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode, type, sSA_CF1081484811efNode: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > Node)))))))).
% 2.85/1.54 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg, type, sSA_CF1165125185phiArg: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > (Val > $o))))))))).
% 2.85/1.54 thf(sy_c_SSA__CFG_OCFG__base_OdefAss_H, type, sSA_CFG_defAss: (!> [G:$tType,Node:$tType,EdgeD:$tType,Var:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > Node) > ((G > (Node > (set @ Var))) > (G > (Node > (Var > $o))))))))))).
% 2.85/1.54 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.85/1.54 thf(sy_c_Sublist_Osuffix, type, suffix: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.85/1.54 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.85/1.54 thf(sy_v_Entry, type, entry: (g > node)).
% 2.85/1.54 thf(sy_v__092_060alpha_062n, type, alpha_n: (g > (list @ node))).
% 2.85/1.54 thf(sy_v__092_060phi_062_092_060_094sub_062r, type, phi_r: val).
% 2.85/1.54 thf(sy_v_defs, type, defs: (g > (node > (set @ val)))).
% 2.85/1.54 thf(sy_v_g, type, g2: g).
% 2.85/1.54 thf(sy_v_inEdges_H, type, inEdges: (g > (node > (list @ ((product_prod @ node) @ edgeD))))).
% 2.85/1.54 thf(sy_v_invar, type, invar: (g > $o)).
% 2.85/1.54 thf(sy_v_m, type, m: node).
% 2.85/1.54 thf(sy_v_ms, type, ms: (list @ node)).
% 2.85/1.54 thf(sy_v_n, type, n: node).
% 2.85/1.54 thf(sy_v_ns, type, ns: (list @ node)).
% 2.85/1.54 thf(sy_v_phis, type, phis: (g > (((product_prod @ node) @ val) > (option @ (list @ val))))).
% 2.85/1.54 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____, type, pred_phi_r: node).
% 2.85/1.54 thf(sy_v_r, type, r: val).
% 2.85/1.54 thf(sy_v_rs_H____, type, rs: (list @ node)).
% 2.85/1.54 thf(sy_v_rs____, type, rs2: (list @ node)).
% 2.85/1.54 thf(sy_v_s, type, s: val).
% 2.85/1.54 thf(fact_0_old_Opath2__hd, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (N = ((hd @ node) @ Ns)))))).
% 2.85/1.54 thf(fact_1_False, axiom, (r != phi_r)).
% 2.85/1.54 thf(fact_2_old_OEntry__in__graph, axiom, (! [G2:g]: ((((member @ node) @ (entry @ G2)) @ ((set2 @ node) @ (alpha_n @ G2)))))).
% 2.85/1.54 thf(fact_3_rs_H__props_I2_J, axiom, (((((((((graph_2081878492ryPath @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ g2) @ rs)).
% 2.85/1.54 thf(fact_4_rs_H__props_I1_J, axiom, ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r)) @ rs) @ pred_phi_r)).
% 2.85/1.54 thf(fact_5_old_OEntryPath__distinct, axiom, (! [G2:g,Ns:(list @ node)]: (((((((((((graph_2081878492ryPath @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ Ns) => ((distinct @ node) @ Ns))))).
% 2.85/1.54 thf(fact_6_old_O_092_060alpha_062n__distinct, axiom, (! [G2:g]: (((invar @ G2) => ((distinct @ node) @ (alpha_n @ G2)))))).
% 2.85/1.54 thf(fact_7_rs_H__props_I3_J, axiom, (((member @ val) @ r) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ g2) @ pred_phi_r))).
% 2.85/1.54 thf(fact_8_assms_I10_J, axiom, (((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r) @ r)).
% 2.85/1.54 thf(fact_9_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)))))))).
% 2.85/1.54 thf(fact_10_assms_I7_J, axiom, ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ n) @ ns) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r))).
% 2.85/1.54 thf(fact_11_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)))))).
% 2.85/1.54 thf(fact_12_rs_H__props_I4_J, axiom, (((member @ node) @ pred_phi_r) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ g2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r))))).
% 2.85/1.54 thf(fact_13_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)))))).
% 2.85/1.54 thf(fact_14_FormalSSA__Misc_Oin__set__tlD, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ Xs))) => (((member @ A) @ X) @ ((set2 @ A) @ Xs)))))).
% 2.85/1.54 thf(fact_15_old_Opath2__hd__in___092_060alpha_062n, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))))))).
% 2.85/1.54 thf(fact_16_old_Opath2__hd__in__ns, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((member @ node) @ N) @ ((set2 @ node) @ Ns)))))).
% 2.85/1.54 thf(fact_17_old_Opath2__in___092_060alpha_062n, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,L:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ L) @ ((set2 @ node) @ Ns)) => (((member @ node) @ L) @ ((set2 @ node) @ (alpha_n @ G2)))))))).
% 2.85/1.54 thf(fact_18_old_Oinvar, axiom, (! [G2:g]: ((invar @ G2)))).
% 2.85/1.54 thf(fact_19_old_Opath2__tl__in___092_060alpha_062n, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((member @ node) @ M) @ ((set2 @ node) @ (alpha_n @ G2))))))).
% 2.85/1.54 thf(fact_20_old_Opath2__last__in__ns, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((member @ node) @ M) @ ((set2 @ node) @ Ns)))))).
% 2.85/1.54 thf(fact_21_old_Osuccessor__is__node, axiom, (! [N:node,G2:g,N2:node]: (((((member @ node) @ N) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N2))) => ((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((invar @ G2) => (((member @ node) @ N2) @ ((set2 @ node) @ (alpha_n @ G2))))))))).
% 2.85/1.54 thf(fact_22_old_Opredecessor__is__node, axiom, (! [N:node,G2:g,N2:node]: (((((member @ node) @ N) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N2))) => ((invar @ G2) => (((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2)))))))).
% 2.85/1.54 thf(fact_23_old_Opath2__forget__hd, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ ((hd @ node) @ Ns)) @ Ns) @ M))))).
% 2.85/1.54 thf(fact_24_old_OEntry__reachesE, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((invar @ G2) => (~ ((! [Ns2:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns2) @ N) => (~ ((((((((((graph_2081878492ryPath @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ Ns2))))))))))))).
% 2.85/1.54 thf(fact_25__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Rs:(list @ node),Pred_phi_r:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r)) @ Rs) @ Pred_phi_r) => ((((((((((graph_2081878492ryPath @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ g2) @ Rs) => ((((member @ val) @ r) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ g2) @ Pred_phi_r)) => (~ ((((member @ node) @ Pred_phi_r) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ g2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r)))))))))))))).
% 2.85/1.54 thf(fact_26_old_OEntry__reaches, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((invar @ G2) => (? [Ns2:(list @ node)]: (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns2) @ N)))))))).
% 2.85/1.54 thf(fact_27_old_Oidom__ex, axiom, (! [G2:g,N:node]: (((invar @ G2) => ((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((N != (entry @ G2)) => (? [X2:node]: ((((((((((((graph_graph_isIdom @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ X2) & (! [Y:node]: ((((((((((((graph_graph_isIdom @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ Y) => (Y = X2))))))))))))).
% 2.85/1.54 thf(fact_28_FormalSSA__Misc_Odistinct__hd__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((distinct @ A) @ Xs) => (~ ((((member @ A) @ ((hd @ A) @ Xs)) @ ((set2 @ A) @ ((tl @ A) @ Xs))))))))).
% 2.85/1.54 thf(fact_29_defAss_H__extend, axiom, (! [G2:g,M:node,V:val,N:node,Ns:(list @ node)]: ((((((((((((((sSA_CFG_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ G2) @ M) @ V) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((tl @ node) @ Ns))) => (~ ((((member @ val) @ V) @ ((defs @ G2) @ X2))))))) => ((((((((((((sSA_CFG_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ G2) @ N) @ V))))))).
% 2.85/1.54 thf(fact_30_defAss_H__def, axiom, (! [G2:g,M:node,V:val]: ((((((((((((((sSA_CFG_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ G2) @ M) @ V) = (! [Ns3:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns3) @ M) => (? [X3:node]: (((((member @ node) @ X3) @ ((set2 @ node) @ Ns3)) & (((member @ val) @ V) @ ((defs @ G2) @ X3)))))))))))).
% 2.85/1.54 thf(fact_31_defAss_HI, axiom, (! [G2:g,M:node,V:val]: (((! [Ns2:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns2) @ M) => (? [X4:node]: (((((member @ node) @ X4) @ ((set2 @ node) @ Ns2)) & (((member @ val) @ V) @ ((defs @ G2) @ X4)))))))) => ((((((((((((sSA_CFG_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ G2) @ M) @ V))))).
% 2.85/1.54 thf(fact_32_defAss_HE, axiom, (! [G2:g,M:node,V:val,Ns:(list @ node)]: ((((((((((((((sSA_CFG_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ G2) @ M) @ V) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns) @ M) => (~ ((! [N3:node]: (((((member @ node) @ N3) @ ((set2 @ node) @ Ns)) => (~ ((((member @ val) @ V) @ ((defs @ G2) @ N3)))))))))))))).
% 2.85/1.54 thf(fact_33_defAss__extend, axiom, (! [G2:g,M:node,V:val,N:node,Ns:(list @ node)]: (((((((((((((((sSA_CFG_SSA_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ phis) @ G2) @ M) @ V) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((tl @ node) @ Ns))) => (~ ((((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ X2))))))) => (((((((((((((sSA_CFG_SSA_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ phis) @ G2) @ N) @ V))))))).
% 2.85/1.54 thf(fact_34_assms_I8_J, axiom, ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ m) @ ms) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ s))).
% 2.85/1.54 thf(fact_35_defAss__def, axiom, (! [G2:g,M:node,V:val]: (((((((((((((((sSA_CFG_SSA_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ phis) @ G2) @ M) @ V) = (! [Ns3:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns3) @ M) => (? [X3:node]: (((((member @ node) @ X3) @ ((set2 @ node) @ Ns3)) & (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ X3)))))))))))).
% 2.85/1.54 thf(fact_36_defAssI, axiom, (! [G2:g,M:node,V:val]: (((! [Ns2:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns2) @ M) => (? [X4:node]: (((((member @ node) @ X4) @ ((set2 @ node) @ Ns2)) & (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ X4)))))))) => (((((((((((((sSA_CFG_SSA_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ phis) @ G2) @ M) @ V))))).
% 2.85/1.54 thf(fact_37_defAssD, axiom, (! [G2:g,M:node,V:val,Ns:(list @ node)]: (((((((((((((((sSA_CFG_SSA_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ phis) @ G2) @ M) @ V) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns) @ M) => (? [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ Ns)) & (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ X2)))))))))).
% 2.85/1.54 thf(fact_38_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)))))).
% 2.85/1.54 thf(fact_39_defAss__dominating, axiom, (! [N:node,G2:g,V:val]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((((((((((((sSA_CFG_SSA_defAss @ g) @ node) @ edgeD) @ val) @ alpha_n) @ invar) @ inEdges) @ entry) @ defs) @ phis) @ G2) @ N) @ V) = (? [X3:node]: (((((member @ node) @ X3) @ ((set2 @ node) @ (alpha_n @ G2))) & (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ X3) @ N) & (((member @ val) @ V) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ X3))))))))))).
% 2.85/1.54 thf(fact_40_old_Osuccessor__in___092_060alpha_062n, axiom, (! [G2:g,N:node]: (((((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N) != (nil @ node)) => ((invar @ G2) => (((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2)))))))).
% 2.85/1.54 thf(fact_41_phiUses__finite, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((finite_finite @ val) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ N)))))).
% 2.85/1.54 thf(fact_42_old_Opath2__split__last__prop, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,P:(node > $o)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((? [X4:node]: (((((member @ node) @ X4) @ ((set2 @ node) @ Ns)) & (P @ X4)))) => (~ ((! [N4:node,Ns4:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N4) @ Ns4) @ M) => ((P @ N4) => ((! [X4:node]: (((((member @ node) @ X4) @ ((set2 @ node) @ ((tl @ node) @ Ns4))) => (~ ((P @ X4)))))) => (~ ((((suffix @ node) @ Ns4) @ Ns))))))))))))))).
% 2.85/1.54 thf(fact_43_allDefs__finite, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((finite_finite @ val) @ (((((((sSA_CFG_SSA_allDefs @ g) @ node) @ val) @ defs) @ phis) @ G2) @ N)))))).
% 2.85/1.54 thf(fact_44_old_Opath2__not__Nil, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (Ns != (nil @ node)))))).
% 2.85/1.54 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.85/1.54 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) = A3)))).
% 2.85/1.54 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.85/1.54 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G2:(A > B)]: (((! [X2:A]: (((F @ X2) = (G2 @ X2)))) => (F = G2))))).
% 2.85/1.54 thf(fact_49_old_Opath2__not__Nil2, axiom, (! [G2:g,N:node,M:node]: ((~ (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (nil @ node)) @ M)))))).
% 2.85/1.54 thf(fact_50_old_Opath2__app, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,Ms:(list @ node),L:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ M) @ Ms) @ L) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ ((tl @ node) @ Ms))) @ L)))))).
% 2.85/1.54 thf(fact_51_defs__finite, axiom, (! [G2:g,N:node]: (((finite_finite @ val) @ ((defs @ G2) @ N))))).
% 2.85/1.54 thf(fact_52_phiDefs__finite, axiom, (! [G2:g,N:node]: (((finite_finite @ val) @ ((((((sSA_CFG_SSA_phiDefs @ g) @ node) @ val) @ phis) @ G2) @ N))))).
% 2.85/1.54 thf(fact_53_strict__dom__trans_H, axiom, (! [N:node,M:node,G2:g,M2:node]: ((((N != M) & ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M)) => (((M != M2) & ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ M) @ M2)) => ((N != M2) & ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M2))))))).
% 2.85/1.54 thf(fact_54_old_Ostrict__dom__trans, axiom, (! [G2:g,N:node,M:node,M2:node]: (((invar @ G2) => (((N != M) & ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M)) => (((M != M2) & ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ M) @ M2)) => ((N != M2) & ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M2)))))))).
% 2.85/1.54 thf(fact_55_old_Odominates__trans, axiom, (! [G2:g,N:node,N2:node,N5:node]: (((invar @ G2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ N2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N2) @ N5) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ N5))))))).
% 2.85/1.54 thf(fact_56_old_Odominates__antitrans, axiom, (! [G2:g,N_1:node,M:node,N_2:node]: (((invar @ G2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N_1) @ M) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N_2) @ M) => ((~ (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N_1) @ N_2))) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N_2) @ N_1)))))))).
% 2.85/1.54 thf(fact_57_old_Odominates__antisymm, axiom, (! [G2:g,N:node,N2:node]: (((invar @ G2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ N2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N2) @ N) => (N = N2))))))).
% 2.85/1.54 thf(fact_58_dominates__trans_H, axiom, (! [G2:g,N:node,N2:node,N5:node]: ((((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ N2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N2) @ N5) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ N5)))))).
% 2.85/1.54 thf(fact_59_dominates__antisymm_H, axiom, (! [G2:g,N:node,N2:node]: ((((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ N2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N2) @ N) => (N = N2)))))).
% 2.85/1.54 thf(fact_60_dominates__refl_H, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ N))))).
% 2.85/1.54 thf(fact_61_old_Odominates__path, axiom, (! [G2:g,N:node,M:node]: ((((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M) => ((invar @ G2) => (~ ((! [Ns2:(list @ node)]: ((~ (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns2) @ M)))))))))))).
% 2.85/1.54 thf(fact_62_old_Odominates__mid, axiom, (! [G2:g,N:node,X:node,M:node,Ns:(list @ node)]: ((((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ X) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ X) @ M) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((invar @ G2) => (((member @ node) @ X) @ ((set2 @ node) @ Ns))))))))).
% 2.85/1.54 thf(fact_63_old_Odominates__def, axiom, (! [G2:g,N:node,M:node]: ((((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M) = ((((member @ node) @ M) @ ((set2 @ node) @ (alpha_n @ G2))) & (! [Ns3:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns3) @ M) => (((member @ node) @ N) @ ((set2 @ node) @ Ns3)))))))))).
% 2.85/1.54 thf(fact_64_old_OdominatesE, axiom, (! [G2:g,N:node,M:node]: ((((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M) => (~ (((((member @ node) @ M) @ ((set2 @ node) @ (alpha_n @ G2))) => (~ ((! [Ns5:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns5) @ M) => (((member @ node) @ N) @ ((set2 @ node) @ Ns5)))))))))))))).
% 2.85/1.54 thf(fact_65_old_Odominates__unsnoc, axiom, (! [G2:g,N:node,M:node,M2:node]: (((invar @ G2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M) => ((((member @ node) @ M2) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ M))) => ((N != M) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M2)))))))).
% 2.85/1.54 thf(fact_66_non__dominated__predecessor, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((N != (entry @ G2)) => (~ ((! [M3:node]: (((((member @ node) @ M3) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N))) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M3))))))))))).
% 2.85/1.54 thf(fact_67_old_OisIdom__def, axiom, (! [G2:g,N:node,M:node]: ((((((((((((graph_graph_isIdom @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M) = ((M != N) & (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ M) @ N) & (! [X3:node]: (((((member @ node) @ X3) @ ((set2 @ node) @ (alpha_n @ G2))) => (((X3 != N) & ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ X3) @ N)) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ X3) @ M))))))))))).
% 2.85/1.54 thf(fact_68_old_OEntryPath__suffix, axiom, (! [G2:g,Ns:(list @ node),Ns6:(list @ node)]: (((((((((((graph_2081878492ryPath @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ Ns) => ((((suffix @ node) @ Ns6) @ Ns) => ((Ns6 != (nil @ node)) => (((((((((graph_2081878492ryPath @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ Ns6))))))).
% 2.85/1.54 thf(fact_69_old_Odominates__unsnoc_H, axiom, (! [G2:g,N:node,M:node,M2:node,Ms:(list @ node)]: (((invar @ G2) => (((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ M2) @ Ms) @ M) => ((! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((tl @ node) @ Ms))) => (X2 != N)))) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M2)))))))).
% 2.85/1.54 thf(fact_70_old_Odominates__extend, axiom, (! [G2:g,N:node,M:node,M2:node,Ms:(list @ node)]: ((((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ M2) @ Ms) @ M) => ((~ ((((member @ node) @ N) @ ((set2 @ node) @ ((tl @ node) @ Ms))))) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M2))))))).
% 2.85/1.54 thf(fact_71_old_OEntry__no__predecessor, axiom, (! [G2:g]: ((((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ (entry @ G2)) = (nil @ node))))).
% 2.85/1.54 thf(fact_72_old_Odominates__refl, axiom, (! [G2:g,N:node]: (((invar @ G2) => ((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ N)))))).
% 2.85/1.54 thf(fact_73_old_OEntry__dominates, axiom, (! [G2:g,N:node]: (((invar @ G2) => ((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ (entry @ G2)) @ N)))))).
% 2.85/1.54 thf(fact_74_old_OdominatesI, axiom, (! [M:node,G2:g,N:node]: (((((member @ node) @ M) @ ((set2 @ node) @ (alpha_n @ G2))) => ((! [Ns2:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns2) @ M) => (((member @ node) @ N) @ ((set2 @ node) @ Ns2))))) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ N) @ M)))))).
% 2.85/1.54 thf(fact_75_old_OEntry__iff__unreachable, axiom, (! [G2:g,N:node]: (((invar @ G2) => ((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N) = (nil @ node)) = (N = (entry @ G2)))))))).
% 2.85/1.54 thf(fact_76_old_Oreducible__def, axiom, (! [G2:g]: ((((((((((graph_reducible @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) = (! [N6:node,Ns3:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N6) @ Ns3) @ N6) => (? [X3:node]: (((((member @ node) @ X3) @ ((set2 @ node) @ Ns3)) & (! [Y2:node]: (((((member @ node) @ Y2) @ ((set2 @ node) @ Ns3)) => ((((((((((graph_709200220inates @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ X3) @ Y2)))))))))))))).
% 2.85/1.54 thf(fact_77_in__hd__or__tl__conv, axiom, (! [A:$tType,L:(list @ A),X:A]: (((L != (nil @ A)) => (((X = ((hd @ A) @ L)) | (((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ L)))) = (((member @ A) @ X) @ ((set2 @ A) @ L))))))).
% 2.85/1.54 thf(fact_78_old_Opath2__cases, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((Ns = (((cons @ node) @ N) @ (nil @ node))) => (M != N)) => (~ ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ ((hd @ node) @ ((tl @ node) @ Ns))) @ ((tl @ node) @ Ns)) @ M) => (~ ((((member @ node) @ N) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((hd @ node) @ ((tl @ node) @ Ns))))))))))))))).
% 2.85/1.54 thf(fact_79_old_Opath2__snoc, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,M2:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ M) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ M2))) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ M2) @ (nil @ node)))) @ M2)))))).
% 2.85/1.54 thf(fact_80_old_Opath2__rev__induct, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,P:(node > ((list @ node) > (node > $o)))]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => (((P @ N) @ (((cons @ node) @ N) @ (nil @ node))) @ N)) => ((! [Ns2:(list @ node),M4:node,M3:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns2) @ M4) => ((((P @ N) @ Ns2) @ M4) => ((((member @ node) @ M4) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ M3))) => (((P @ N) @ (((append @ node) @ Ns2) @ (((cons @ node) @ M3) @ (nil @ node)))) @ M3)))))) => (((P @ N) @ Ns) @ M))))))).
% 2.85/1.54 thf(fact_81_tl__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != (nil @ A)) => (((tl @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ ((tl @ A) @ Xs)) @ Ys)))))).
% 2.85/1.54 thf(fact_82_hd__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Xs)))))).
% 2.85/1.54 thf(fact_83_same__suffix__nil, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Ys) @ Xs)) @ Xs) = (Ys = (nil @ A)))))).
% 2.85/1.54 thf(fact_84_old_Opath2__induct, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,P:(node > ((list @ node) > (node > $o)))]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((invar @ G2) => (((P @ M) @ (((cons @ node) @ M) @ (nil @ node))) @ M)) => ((! [Ns2:(list @ node),N4:node,N3:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N3) @ Ns2) @ M) => ((((P @ N3) @ Ns2) @ M) => ((((member @ node) @ N4) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N3))) => (((P @ N4) @ (((cons @ node) @ N4) @ Ns2)) @ M)))))) => (((P @ N) @ Ns) @ M))))))).
% 2.85/1.54 thf(fact_85_old_Oelem__set__implies__elem__tl__app__cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Y3:A]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y3) @ Xs))))))))).
% 2.85/1.54 thf(fact_86_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.85/1.54 thf(fact_87_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs)) = (Ys = Zs))))).
% 2.85/1.54 thf(fact_88_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs) @ Xs)) = (Ys = Zs))))).
% 2.85/1.54 thf(fact_89_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)))))).
% 2.85/1.54 thf(fact_90_append_Oassoc, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((((append @ A) @ (((append @ A) @ A2) @ B2)) @ C) = (((append @ A) @ A2) @ (((append @ A) @ B2) @ C)))))).
% 2.85/1.54 thf(fact_91_suffix__order_Odual__order_Orefl, axiom, (! [A:$tType,A2:(list @ A)]: ((((suffix @ A) @ A2) @ A2)))).
% 2.85/1.54 thf(fact_92_suffix__order_Oorder__refl, axiom, (! [A:$tType,X:(list @ A)]: ((((suffix @ A) @ X) @ X)))).
% 2.85/1.54 thf(fact_93_old_Opath2__split_I2_J, axiom, (! [G2:g,N:node,Ns:(list @ node),N2:node,Ns6:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ N2) @ Ns6))) @ M) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N2) @ (((cons @ node) @ N2) @ Ns6)) @ M))))).
% 2.85/1.54 thf(fact_94_List_Ofinite__set, axiom, (! [A:$tType,Xs:(list @ A)]: (((finite_finite @ A) @ ((set2 @ A) @ Xs))))).
% 2.85/1.54 thf(fact_95_append_Oright__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ A2) @ (nil @ A)) = A2)))).
% 2.85/1.54 thf(fact_96_empty__append__eq__id, axiom, (! [A:$tType]: ((((append @ A) @ (nil @ A)) = (^ [X3:(list @ A)]: (X3)))))).
% 2.85/1.54 thf(fact_97_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.85/1.54 thf(fact_98_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.85/1.54 thf(fact_99_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.85/1.54 thf(fact_100_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.85/1.54 thf(fact_101_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.85/1.54 thf(fact_102_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.85/1.54 thf(fact_103_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.85/1.54 thf(fact_104_suffix__bot_Obot_Oextremum__unique, axiom, (! [A:$tType,A2:(list @ A)]: (((((suffix @ A) @ A2) @ (nil @ A)) = (A2 = (nil @ A)))))).
% 2.85/1.54 thf(fact_105_suffix__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((suffix @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.85/1.54 thf(fact_106_same__suffix__suffix, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Ys) @ Xs)) @ (((append @ A) @ Zs) @ Xs)) = (((suffix @ A) @ Ys) @ Zs))))).
% 2.85/1.54 thf(fact_107_old_Opath2__split_I1_J, axiom, (! [G2:g,N:node,Ns:(list @ node),N2:node,Ns6:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ N2) @ Ns6))) @ M) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ N2) @ (nil @ node)))) @ N2))))).
% 2.85/1.54 thf(fact_108_old_OEntry__loop, axiom, (! [G2:g,Ns:(list @ node)]: (((invar @ G2) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (entry @ G2)) @ Ns) @ (entry @ G2)) => (Ns = (((cons @ node) @ (entry @ G2)) @ (nil @ node)))))))).
% 2.85/1.54 thf(fact_109_old_OEntryPath__triv, axiom, (! [G2:g,N:node]: ((((((((((graph_2081878492ryPath @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ entry) @ G2) @ (((cons @ node) @ N) @ (nil @ node)))))).
% 2.85/1.54 thf(fact_110_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y3:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y3) @ (nil @ A)))) = ((Xs = Ys) & (X = Y3)))))).
% 2.85/1.54 thf(fact_111_list__ee__eq__leel_I1_J, axiom, (! [A:$tType,E1:A,E2:A,L1:(list @ A),E12:A,E22:A,L2:(list @ A)]: ((((((cons @ A) @ E1) @ (((cons @ A) @ E2) @ (nil @ A))) = (((append @ A) @ L1) @ (((cons @ A) @ E12) @ (((cons @ A) @ E22) @ L2)))) = ((L1 = (nil @ A)) & ((E1 = E12) & ((E2 = E22) & (L2 = (nil @ A))))))))).
% 2.85/1.54 thf(fact_112_list__ee__eq__leel_I2_J, axiom, (! [A:$tType,L1:(list @ A),E12:A,E22:A,L2:(list @ A),E1:A,E2:A]: ((((((append @ A) @ L1) @ (((cons @ A) @ E12) @ (((cons @ A) @ E22) @ L2))) = (((cons @ A) @ E1) @ (((cons @ A) @ E2) @ (nil @ A)))) = ((L1 = (nil @ A)) & ((E1 = E12) & ((E2 = E22) & (L2 = (nil @ A))))))))).
% 2.85/1.54 thf(fact_113_list__se__match_I1_J, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A),A2:A]: (((L1 != (nil @ A)) => (((((append @ A) @ L1) @ L2) = (((cons @ A) @ A2) @ (nil @ A))) = ((L1 = (((cons @ A) @ A2) @ (nil @ A))) & (L2 = (nil @ A)))))))).
% 2.85/1.54 thf(fact_114_list__se__match_I2_J, axiom, (! [A:$tType,L2:(list @ A),L1:(list @ A),A2:A]: (((L2 != (nil @ A)) => (((((append @ A) @ L1) @ L2) = (((cons @ A) @ A2) @ (nil @ A))) = ((L1 = (nil @ A)) & (L2 = (((cons @ A) @ A2) @ (nil @ A))))))))).
% 2.85/1.54 thf(fact_115_list__se__match_I3_J, axiom, (! [A:$tType,L1:(list @ A),A2:A,L2:(list @ A)]: (((L1 != (nil @ A)) => (((((cons @ A) @ A2) @ (nil @ A)) = (((append @ A) @ L1) @ L2)) = ((L1 = (((cons @ A) @ A2) @ (nil @ A))) & (L2 = (nil @ A)))))))).
% 2.85/1.54 thf(fact_116_list__se__match_I4_J, axiom, (! [A:$tType,L2:(list @ A),A2:A,L1:(list @ A)]: (((L2 != (nil @ A)) => (((((cons @ A) @ A2) @ (nil @ A)) = (((append @ A) @ L1) @ L2)) = ((L1 = (nil @ A)) & (L2 = (((cons @ A) @ A2) @ (nil @ A))))))))).
% 2.85/1.54 thf(fact_117_list__e__eq__lel_I1_J, axiom, (! [A:$tType,E:A,L1:(list @ A),E3:A,L2:(list @ A)]: ((((((cons @ A) @ E) @ (nil @ A)) = (((append @ A) @ L1) @ (((cons @ A) @ E3) @ L2))) = ((L1 = (nil @ A)) & ((E3 = E) & (L2 = (nil @ A)))))))).
% 2.85/1.54 thf(fact_118_list__e__eq__lel_I2_J, axiom, (! [A:$tType,L1:(list @ A),E3:A,L2:(list @ A),E:A]: ((((((append @ A) @ L1) @ (((cons @ A) @ E3) @ L2)) = (((cons @ A) @ E) @ (nil @ A))) = ((L1 = (nil @ A)) & ((E3 = E) & (L2 = (nil @ A)))))))).
% 2.85/1.54 thf(fact_119_snoc__suffix__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y3:A]: (((((suffix @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y3) @ (nil @ A)))) = ((X = Y3) & (((suffix @ A) @ Xs) @ Ys)))))).
% 2.85/1.54 thf(fact_120_suffix__snoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Y3:A]: (((((suffix @ A) @ Xs) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y3) @ (nil @ A)))) = ((Xs = (nil @ A)) | (? [Zs2:(list @ A)]: (((Xs = (((append @ A) @ Zs2) @ (((cons @ A) @ Y3) @ (nil @ A)))) & (((suffix @ A) @ Zs2) @ Ys))))))))).
% 2.85/1.54 thf(fact_121_list_Ocollapse, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List)) = List))))).
% 2.85/1.54 thf(fact_122_hd__Cons__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ Xs)) @ ((tl @ A) @ Xs)) = Xs))))).
% 2.85/1.54 thf(fact_123_rs__def, axiom, (rs2 = (((append @ node) @ rs) @ (((cons @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r)) @ (nil @ node))))).
% 2.85/1.54 thf(fact_124_old_Oempty__path2, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((invar @ G2) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((cons @ node) @ N) @ (nil @ node))) @ N)))))).
% 2.85/1.54 thf(fact_125_old_OCons__path2, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,N2:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ N2) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N))) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N2) @ (((cons @ node) @ N2) @ Ns)) @ M)))))).
% 2.85/1.54 thf(fact_126_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.85/1.54 thf(fact_127_neq__NilE, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) => (~ ((! [X2:A,Xs2:(list @ A)]: ((L != (((cons @ A) @ X2) @ Xs2)))))))))).
% 2.85/1.54 thf(fact_128_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.85/1.54 thf(fact_129_revg_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [A4:A,As:(list @ A),B3:(list @ A)]: ((((P @ As) @ (((cons @ A) @ A4) @ B3)) => ((P @ (((cons @ A) @ A4) @ As)) @ B3)))) => ((P @ A0) @ A1)))))).
% 2.85/1.54 thf(fact_130_zipf_Oinduct, axiom, (! [A:$tType,C2:$tType,B:$tType,P:((A > (B > C2)) > ((list @ A) > ((list @ B) > $o))),A0:(A > (B > C2)),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > (B > C2))]: ((((P @ F2) @ (nil @ A)) @ (nil @ B)))) => ((! [F2:(A > (B > C2)),A4:A,As:(list @ A),B3:B,Bs:(list @ B)]: (((((P @ F2) @ As) @ Bs) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ (((cons @ B) @ B3) @ Bs))))) => ((! [A4:(A > (B > C2)),V2:A,Va:(list @ A)]: ((((P @ A4) @ (((cons @ A) @ V2) @ Va)) @ (nil @ B)))) => ((! [A4:(A > (B > C2)),V2:B,Va:(list @ B)]: ((((P @ A4) @ (nil @ A)) @ (((cons @ B) @ V2) @ Va)))) => (((P @ A0) @ A1) @ A22)))))))).
% 2.85/1.54 thf(fact_131_list_Oexhaust, axiom, (! [A:$tType,Y3:(list @ A)]: (((Y3 != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y3 != (((cons @ A) @ X212) @ X222)))))))))).
% 2.85/1.54 thf(fact_132_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X1) @ X23))))) => (P @ List)))))).
% 2.85/1.54 thf(fact_133_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y2:A,Ys2:(list @ A)]: ((Xs = (((cons @ A) @ Y2) @ Ys2)))))))).
% 2.85/1.54 thf(fact_134_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X2) @ Xs2)) @ (nil @ B)))) => ((! [Y4:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y4) @ Ys3)))) => ((! [X2:A,Xs2:(list @ A),Y4:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys3))))) => ((P @ Xs) @ Ys)))))))).
% 2.85/1.54 thf(fact_135_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X2:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((P @ Ys3) @ Xs2) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ Ys3)))) => ((P @ A0) @ A1)))))).
% 2.85/1.54 thf(fact_136_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Y4:A,Zs3:(list @ A)]: (((P @ Zs3) => ((P @ (((cons @ A) @ Y4) @ Zs3)) => (P @ (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Zs3))))))) => (P @ Xs))))))).
% 2.85/1.54 thf(fact_137_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X:(list @ A)]: (((! [X2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ Xs2)))) => (X = (nil @ A))))))))).
% 2.85/1.54 thf(fact_138_suffix__Cons, axiom, (! [A:$tType,Xs:(list @ A),Y3:A,Ys:(list @ A)]: (((((suffix @ A) @ Xs) @ (((cons @ A) @ Y3) @ Ys)) = ((Xs = (((cons @ A) @ Y3) @ Ys)) | (((suffix @ A) @ Xs) @ Ys)))))).
% 2.85/1.54 thf(fact_139_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys) => ((Xs = (((append @ A) @ Xs1) @ Zs)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs))))))).
% 2.85/1.54 thf(fact_140_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X2:A,Xs2:(list @ A)]: (((! [X213:A,X223:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X223)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X2) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 2.85/1.54 thf(fact_141_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X2:A,Xs2:(list @ A),Y4:A,Ys3:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y4) @ Ys3)) => (((P @ (((cons @ A) @ X2) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3)))))) => ((P @ A0) @ A1))))))).
% 2.85/1.54 thf(fact_142_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X2:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X2) @ Xs2)) @ Xss))))))))))).
% 2.85/1.54 thf(fact_143_suffix__ConsD, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.85/1.54 thf(fact_144_suffix__ConsI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Y3:A]: (((((suffix @ A) @ Xs) @ Ys) => (((suffix @ A) @ Xs) @ (((cons @ A) @ Y3) @ Ys)))))).
% 2.85/1.54 thf(fact_145_list__2pre__induct, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),W1:(list @ A),W2:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [E4:A,W12:(list @ A),W22:(list @ B)]: ((((P @ W12) @ W22) => ((P @ (((cons @ A) @ E4) @ W12)) @ W22)))) => ((! [E4:B,W13:(list @ A),W23:(list @ B)]: ((((P @ W13) @ W23) => ((P @ W13) @ (((cons @ B) @ E4) @ W23))))) => ((P @ W1) @ W2))))))).
% 2.85/1.54 thf(fact_146_suffix__ConsD2, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y3:A,Ys:(list @ A)]: (((((suffix @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y3) @ Ys)) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.85/1.54 thf(fact_147_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X2:A]: ((X != (((cons @ A) @ X2) @ (nil @ A))))) => (~ ((! [X2:A,Y4:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Xs2)))))))))))).
% 2.85/1.54 thf(fact_148_sorted__wrt_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P2:(A > (A > $o))]: (((P @ P2) @ (nil @ A)))) => ((! [P2:(A > (A > $o)),X2:A,Ys3:(list @ A)]: ((((P @ P2) @ Ys3) => ((P @ P2) @ (((cons @ A) @ X2) @ Ys3))))) => ((P @ A0) @ A1)))))).
% 2.85/1.54 thf(fact_149_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.85/1.54 thf(fact_150_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Y4:A,Xs2:(list @ A)]: ((((X2 = Y4) => (P @ (((cons @ A) @ X2) @ Xs2))) => (((X2 != Y4) => (P @ (((cons @ A) @ Y4) @ Xs2))) => (P @ (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Xs2))))))) => (P @ A0))))))).
% 2.85/1.54 thf(fact_151_list__induct__first2, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X1:A,X23:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((cons @ A) @ X1) @ (((cons @ A) @ X23) @ Xs2)))))) => (P @ Xs))))))).
% 2.85/1.54 thf(fact_152_list__match__lel__lel, axiom, (! [A:$tType,C1:(list @ A),Qs:A,C22:(list @ A),C12:(list @ A),Qs2:A,C23:(list @ A)]: ((((((append @ A) @ C1) @ (((cons @ A) @ Qs) @ C22)) = (((append @ A) @ C12) @ (((cons @ A) @ Qs2) @ C23))) => ((! [C21:(list @ A)]: (((C1 = (((append @ A) @ C12) @ (((cons @ A) @ Qs2) @ C21))) => (C23 != (((append @ A) @ C21) @ (((cons @ A) @ Qs) @ C22)))))) => (((C12 = C1) => ((Qs2 = Qs) => (C23 != C22))) => (~ ((! [C212:(list @ A)]: (((C12 = (((append @ A) @ C1) @ (((cons @ A) @ Qs) @ C212))) => (C22 != (((append @ A) @ C212) @ (((cons @ A) @ Qs2) @ C23)))))))))))))).
% 2.85/1.54 thf(fact_153_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F2:(A > B),X2:A]: (((P @ F2) @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [F2:(A > B),X2:A,Y4:A,Zs3:(list @ A)]: ((((P @ F2) @ (((cons @ A) @ Y4) @ Zs3)) => ((P @ F2) @ (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Zs3)))))) => ((! [A4:(A > B)]: (((P @ A4) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 2.85/1.54 thf(fact_154_successively_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P2:(A > (A > $o))]: (((P @ P2) @ (nil @ A)))) => ((! [P2:(A > (A > $o)),X2:A]: (((P @ P2) @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [P2:(A > (A > $o)),X2:A,Y4:A,Xs2:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ Y4) @ Xs2)) => ((P @ P2) @ (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 2.85/1.54 thf(fact_155_list__all__zip_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > (B > $o)) > ((list @ A) > ((list @ B) > $o))),A0:(A > (B > $o)),A1:(list @ A),A22:(list @ B)]: (((! [P2:(A > (B > $o))]: ((((P @ P2) @ (nil @ A)) @ (nil @ B)))) => ((! [P2:(A > (B > $o)),A4:A,As:(list @ A),B3:B,Bs:(list @ B)]: (((((P @ P2) @ As) @ Bs) => (((P @ P2) @ (((cons @ A) @ A4) @ As)) @ (((cons @ B) @ B3) @ Bs))))) => ((! [P2:(A > (B > $o)),V2:A,Va:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ V2) @ Va)) @ (nil @ B)))) => ((! [P2:(A > (B > $o)),V2:B,Va:(list @ B)]: ((((P @ P2) @ (nil @ A)) @ (((cons @ B) @ V2) @ Va)))) => (((P @ A0) @ A1) @ A22)))))))).
% 2.85/1.54 thf(fact_156_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X2) @ Xs2)))))) => (P @ Xs))))))).
% 2.85/1.54 thf(fact_157_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X_1:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X_1))) => ((! [F2:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A4)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.85/1.54 thf(fact_158_mergesort__by__rel__merge_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > ((list @ A) > $o))),A0:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: (((! [R:(A > (A > $o)),X2:A,Xs2:(list @ A),Y4:A,Ys3:(list @ A)]: (((((R @ X2) @ Y4) => (((P @ R) @ Xs2) @ (((cons @ A) @ Y4) @ Ys3))) => (((~ (((R @ X2) @ Y4))) => (((P @ R) @ (((cons @ A) @ X2) @ Xs2)) @ Ys3)) => (((P @ R) @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3)))))) => ((! [R:(A > (A > $o)),Xs2:(list @ A)]: ((((P @ R) @ Xs2) @ (nil @ A)))) => ((! [R:(A > (A > $o)),V2:A,Va:(list @ A)]: ((((P @ R) @ (nil @ A)) @ (((cons @ A) @ V2) @ Va)))) => (((P @ A0) @ A1) @ A22))))))).
% 2.85/1.54 thf(fact_159_mergesort__by__rel__merge__induct, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),R2:(A > (B > $o)),Xs:(list @ A),Ys:(list @ B)]: (((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ B)))) => ((! [X_1:(list @ B)]: (((P @ (nil @ A)) @ X_1))) => ((! [X2:A,Xs2:(list @ A),Y4:B,Ys3:(list @ B)]: ((((R2 @ X2) @ Y4) => (((P @ Xs2) @ (((cons @ B) @ Y4) @ Ys3)) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys3)))))) => ((! [X2:A,Xs2:(list @ A),Y4:B,Ys3:(list @ B)]: (((~ (((R2 @ X2) @ Y4))) => (((P @ (((cons @ A) @ X2) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys3)))))) => ((P @ Xs) @ Ys)))))))).
% 2.85/1.54 thf(fact_160_longest__common__prefix_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X2:A,Xs2:(list @ A),Y4:A,Ys3:(list @ A)]: ((((X2 = Y4) => ((P @ Xs2) @ Ys3)) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3))))) => ((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Uu:(list @ A)]: (((P @ Uu) @ (nil @ A)))) => ((P @ A0) @ A1))))))).
% 2.85/1.54 thf(fact_161_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A,Ys3:(list @ A)]: (((P @ Ys3) => (P @ (((cons @ A) @ X2) @ Ys3))))) => (P @ A0))))))))).
% 2.85/1.54 thf(fact_162_list_Osel_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((hd @ A) @ (((cons @ A) @ X21) @ X22)) = X21)))).
% 2.85/1.54 thf(fact_163_list_Osel_I3_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((tl @ A) @ (((cons @ A) @ X21) @ X22)) = X22)))).
% 2.85/1.54 thf(fact_164_list__tail__coinc, axiom, (! [A:$tType,N1:A,R1:(list @ A),N22:A,R22:(list @ A)]: ((((((cons @ A) @ N1) @ R1) = (((cons @ A) @ N22) @ R22)) => ((N1 = N22) & (R1 = R22)))))).
% 2.85/1.54 thf(fact_165_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.85/1.54 thf(fact_166_distinct__length__2__or__more, axiom, (! [A:$tType,A2:A,B2:A,Xs:(list @ A)]: ((((distinct @ A) @ (((cons @ A) @ A2) @ (((cons @ A) @ B2) @ Xs))) = ((A2 != B2) & (((distinct @ A) @ (((cons @ A) @ A2) @ Xs)) & ((distinct @ A) @ (((cons @ A) @ B2) @ Xs)))))))).
% 2.85/1.54 thf(fact_167_list_Oset__cases, axiom, (! [A:$tType,E:A,A2:(list @ A)]: (((((member @ A) @ E) @ ((set2 @ A) @ A2)) => ((! [Z2:(list @ A)]: ((A2 != (((cons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ A)]: (((A2 = (((cons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((set2 @ A) @ Z2)))))))))))))).
% 2.85/1.54 thf(fact_168_set__ConsD, axiom, (! [A:$tType,Y3:A,X:A,Xs:(list @ A)]: (((((member @ A) @ Y3) @ ((set2 @ A) @ (((cons @ A) @ X) @ Xs))) => ((Y3 = X) | (((member @ A) @ Y3) @ ((set2 @ A) @ Xs))))))).
% 2.85/1.54 thf(fact_169_list_Oset__intros_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((member @ A) @ X21) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22)))))).
% 2.85/1.54 thf(fact_170_list_Oset__intros_I2_J, axiom, (! [A:$tType,Y3:A,X22:(list @ A),X21:A]: (((((member @ A) @ Y3) @ ((set2 @ A) @ X22)) => (((member @ A) @ Y3) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22))))))).
% 2.85/1.54 thf(fact_171_list__append__eq__Cons__cases, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs) = (((cons @ A) @ X) @ Xs)) => (((Ys = (nil @ A)) => (Zs != (((cons @ A) @ X) @ Xs))) => (~ ((! [Ys4:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys4)) => ((((append @ A) @ Ys4) @ Zs) != Xs))))))))))).
% 2.85/1.54 thf(fact_172_list__Cons__eq__append__cases, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs)) => (((Ys = (nil @ A)) => (Zs != (((cons @ A) @ X) @ Xs))) => (~ ((! [Ys4:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys4)) => ((((append @ A) @ Ys4) @ Zs) != Xs))))))))))).
% 2.85/1.54 thf(fact_173_rev__nonempty__induct2_H, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Ys:(list @ B),P:((list @ A) > ((list @ B) > $o))]: (((Xs != (nil @ A)) => ((Ys != (nil @ B)) => ((! [X2:A,Y4:B]: (((P @ (((cons @ A) @ X2) @ (nil @ A))) @ (((cons @ B) @ Y4) @ (nil @ B))))) => ((! [X2:A,Xs2:(list @ A),Y4:B]: (((Xs2 != (nil @ A)) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))) @ (((cons @ B) @ Y4) @ (nil @ B)))))) => ((! [X2:A,Y4:B,Ys3:(list @ B)]: (((Ys3 != (nil @ B)) => ((P @ (((cons @ A) @ X2) @ (nil @ A))) @ (((append @ B) @ Ys3) @ (((cons @ B) @ Y4) @ (nil @ B))))))) => ((! [X2:A,Xs2:(list @ A),Y4:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((Xs2 != (nil @ A)) => ((Ys3 != (nil @ B)) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))) @ (((append @ B) @ Ys3) @ (((cons @ B) @ Y4) @ (nil @ B))))))))) => ((P @ Xs) @ Ys)))))))))).
% 2.85/1.54 thf(fact_174_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.85/1.54 thf(fact_175_append__eq__Cons__conv, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs) = (((cons @ A) @ X) @ Xs)) = (((Ys = (nil @ A)) & (Zs = (((cons @ A) @ X) @ Xs))) | (? [Ys5:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys5)) & ((((append @ A) @ Ys5) @ Zs) = Xs))))))))).
% 2.85/1.54 thf(fact_176_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs)) | (? [Ys5:(list @ A)]: ((((((cons @ A) @ X) @ Ys5) = Ys) & (Xs = (((append @ A) @ Ys5) @ Zs)))))))))).
% 2.85/1.54 thf(fact_177_neq__Nil__rev__conv, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) = (? [Xs3:(list @ A),X3:A]: ((L = (((append @ A) @ Xs3) @ (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.85/1.54 thf(fact_178_rev__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))) @ (nil @ B)))) => ((! [Y4:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((append @ B) @ Ys3) @ (((cons @ B) @ Y4) @ (nil @ B)))))) => ((! [X2:A,Xs2:(list @ A),Y4:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))) @ (((append @ B) @ Ys3) @ (((cons @ B) @ Y4) @ (nil @ B))))))) => ((P @ Xs) @ Ys)))))))).
% 2.85/1.54 thf(fact_179_neq__Nil__revE, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) => (~ ((! [Ll:(list @ A),E4:A]: ((L != (((append @ A) @ Ll) @ (((cons @ A) @ E4) @ (nil @ A)))))))))))).
% 2.85/1.54 thf(fact_180_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys3:(list @ A),Y4:A]: ((Xs != (((append @ A) @ Ys3) @ (((cons @ A) @ Y4) @ (nil @ A)))))))))))).
% 2.85/1.54 thf(fact_181_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.85/1.54 thf(fact_182_split__list, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys3:(list @ A),Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))))))))).
% 2.85/1.54 thf(fact_183_split__list__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys3:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs3))))))))))).
% 2.85/1.54 thf(fact_184_split__list__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys3:(list @ A),X2:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))))) & (P @ X2)))))))).
% 2.85/1.54 thf(fact_185_xy__in__set__cases, axiom, (! [A:$tType,X:A,L:(list @ A),Y3:A]: (((((member @ A) @ X) @ ((set2 @ A) @ L)) => ((((member @ A) @ Y3) @ ((set2 @ A) @ L)) => (((X = Y3) => (! [L12:(list @ A),L22:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ Y3) @ L22)))))) => (((X != Y3) => (! [L12:(list @ A),L22:(list @ A),L3:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ X) @ (((append @ A) @ L22) @ (((cons @ A) @ Y3) @ L3)))))))) => (~ (((X != Y3) => (! [L12:(list @ A),L22:(list @ A),L3:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ Y3) @ (((append @ A) @ L22) @ (((cons @ A) @ X) @ L3))))))))))))))))).
% 2.85/1.54 thf(fact_186_split__list__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys3:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys3))))))))))).
% 2.85/1.54 thf(fact_187_split__list__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys3:(list @ A),X2:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))))) => (~ ((P @ X2)))))))))))).
% 2.85/1.54 thf(fact_188_append__Cons__eq__iff, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Xs4:(list @ A),Ys6:(list @ A)]: (((~ ((((member @ A) @ X) @ ((set2 @ A) @ Xs)))) => ((~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys)))) => (((((append @ A) @ Xs) @ (((cons @ A) @ X) @ Ys)) = (((append @ A) @ Xs4) @ (((cons @ A) @ X) @ Ys6))) = ((Xs = Xs4) & (Ys = Ys6)))))))).
% 2.85/1.54 thf(fact_189_in__set__conv__decomp, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys2:(list @ A),Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs2))))))))).
% 2.85/1.54 thf(fact_190_in__set__list__format, axiom, (! [A:$tType,E:A,L:(list @ A)]: (((((member @ A) @ E) @ ((set2 @ A) @ L)) => (~ ((! [L12:(list @ A),L22:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ E) @ L22))))))))))).
% 2.85/1.54 thf(fact_191_split__list__last__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys3:(list @ A),X2:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))) & ((P @ X2) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Xa)))))))))))))).
% 2.85/1.54 thf(fact_192_split__list__first__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys3:(list @ A),X2:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))))) & ((P @ X2) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Xa)))))))))))))).
% 2.85/1.54 thf(fact_193_split__list__last__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys3:(list @ A),X2:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))) => ((P @ X2) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Xa)))))))))))))))))).
% 2.85/1.54 thf(fact_194_split__list__first__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys3:(list @ A),X2:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs3))))) => ((P @ X2) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Xa)))))))))))))))))).
% 2.85/1.54 thf(fact_195_in__set__conv__decomp__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys2:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs2))))))))))).
% 2.85/1.54 thf(fact_196_in__set__conv__decomp__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys2:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys2))))))))))).
% 2.85/1.54 thf(fact_197_split__list__last__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys2:(list @ A),X3:A,Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs2))) & ((P @ X3) & (! [Y2:A]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Zs2)) => (~ ((P @ Y2)))))))))))))).
% 2.85/1.54 thf(fact_198_split__list__first__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys2:(list @ A),X3:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs2))))) & ((P @ X3) & (! [Y2:A]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Y2)))))))))))))).
% 2.85/1.54 thf(fact_199_distinct__singleton, axiom, (! [A:$tType,X:A]: (((distinct @ A) @ (((cons @ A) @ X) @ (nil @ A)))))).
% 2.85/1.54 thf(fact_200_distinct_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((distinct @ A) @ (((cons @ A) @ X) @ Xs)) = ((~ ((((member @ A) @ X) @ ((set2 @ A) @ Xs)))) & ((distinct @ A) @ Xs)))))).
% 2.85/1.54 thf(fact_201_distinct__match, axiom, (! [A:$tType,Al:(list @ A),E:A,Bl:(list @ A),Al2:(list @ A),Bl2:(list @ A)]: ((((distinct @ A) @ (((append @ A) @ Al) @ (((cons @ A) @ E) @ Bl))) => (((((append @ A) @ Al) @ (((cons @ A) @ E) @ Bl)) = (((append @ A) @ Al2) @ (((cons @ A) @ E) @ Bl2))) = ((Al = Al2) & (Bl = Bl2))))))).
% 2.85/1.54 thf(fact_202_Nil__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((tl @ A) @ Xs)) = ((Xs = (nil @ A)) | (? [X3:A]: ((Xs = (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.85/1.54 thf(fact_203_tl__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((tl @ A) @ Xs) = (nil @ A)) = ((Xs = (nil @ A)) | (? [X3:A]: ((Xs = (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.85/1.54 thf(fact_204_tl__obtain__elem, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((tl @ A) @ Xs) = (nil @ A)) => (~ ((! [E4:A]: ((Xs != (((cons @ A) @ E4) @ (nil @ A)))))))))))).
% 2.85/1.54 thf(fact_205_not__distinct__decomp, axiom, (! [A:$tType,Ws:(list @ A)]: (((~ (((distinct @ A) @ Ws))) => (? [Xs2:(list @ A),Ys3:(list @ A),Zs3:(list @ A),Y4:A]: ((Ws = (((append @ A) @ Xs2) @ (((append @ A) @ (((cons @ A) @ Y4) @ (nil @ A))) @ (((append @ A) @ Ys3) @ (((append @ A) @ (((cons @ A) @ Y4) @ (nil @ A))) @ Zs3))))))))))).
% 2.85/1.54 thf(fact_206_not__distinct__conv__prefix, axiom, (! [A:$tType,As2:(list @ A)]: (((~ (((distinct @ A) @ As2))) = (? [Xs3:(list @ A),Y2:A,Ys2:(list @ A)]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Xs3)) & (((distinct @ A) @ Xs3) & (As2 = (((append @ A) @ Xs3) @ (((cons @ A) @ Y2) @ Ys2))))))))))).
% 2.85/1.54 thf(fact_207_not__suffix__induct, axiom, (! [A:$tType,Ps:(list @ A),Ls:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((~ ((((suffix @ A) @ Ps) @ Ls))) => ((! [X2:A,Xs2:(list @ A)]: (((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))) @ (nil @ A)))) => ((! [X2:A,Xs2:(list @ A),Y4:A,Ys3:(list @ A)]: (((X2 != Y4) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))) @ (((append @ A) @ Ys3) @ (((cons @ A) @ Y4) @ (nil @ A))))))) => ((! [X2:A,Xs2:(list @ A),Y4:A,Ys3:(list @ A)]: (((X2 = Y4) => ((~ ((((suffix @ A) @ Xs2) @ Ys3))) => (((P @ Xs2) @ Ys3) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))) @ (((append @ A) @ Ys3) @ (((cons @ A) @ Y4) @ (nil @ A))))))))) => ((P @ Ps) @ Ls)))))))).
% 2.85/1.54 thf(fact_208_not__suffix__cases, axiom, (! [A:$tType,Ps:(list @ A),Ls:(list @ A)]: (((~ ((((suffix @ A) @ Ps) @ Ls))) => (((Ps != (nil @ A)) => (Ls != (nil @ A))) => ((! [A4:A,As:(list @ A)]: (((Ps = (((append @ A) @ As) @ (((cons @ A) @ A4) @ (nil @ A)))) => (! [X2:A,Xs2:(list @ A)]: (((Ls = (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))) => ((X2 = A4) => (((suffix @ A) @ As) @ Xs2)))))))) => (~ ((! [A4:A]: (((? [As:(list @ A)]: ((Ps = (((append @ A) @ As) @ (((cons @ A) @ A4) @ (nil @ A)))))) => (! [X2:A]: (((? [Xs2:(list @ A)]: ((Ls = (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))))) => (X2 = A4))))))))))))))).
% 2.85/1.54 thf(fact_209_list_Oexhaust__sel, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => (List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))).
% 2.85/1.54 thf(fact_210_not__distinct__split__distinct, axiom, (! [A:$tType,Xs:(list @ A)]: (((~ (((distinct @ A) @ Xs))) => (~ ((! [Y4:A,Ys3:(list @ A)]: ((((distinct @ A) @ Ys3) => ((((member @ A) @ Y4) @ ((set2 @ A) @ Ys3)) => (! [Zs3:(list @ A)]: ((Xs != (((append @ A) @ Ys3) @ (((append @ A) @ (((cons @ A) @ Y4) @ (nil @ A))) @ Zs3))))))))))))))).
% 2.85/1.54 thf(fact_211_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs) @ Us)) & ((((append @ A) @ Us) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs) & (Ys = (((append @ A) @ Us) @ Ts)))))))))).
% 2.85/1.54 thf(fact_212_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs:(list @ A),Ys:(list @ A),Us2:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs) => ((Ys = (((append @ A) @ Xs1) @ Us2)) => ((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Us2))))))).
% 2.85/1.54 thf(fact_213_suffix__order_Odual__order_Oantisym, axiom, (! [A:$tType,B2:(list @ A),A2:(list @ A)]: (((((suffix @ A) @ B2) @ A2) => ((((suffix @ A) @ A2) @ B2) => (A2 = B2)))))).
% 2.85/1.54 thf(fact_214_suffix__order_Odual__order_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y5:(list @ A),Z:(list @ A)]: ((Y5 = Z))) = (^ [A5:(list @ A),B4:(list @ A)]: (((((suffix @ A) @ B4) @ A5) & (((suffix @ A) @ A5) @ B4)))))))).
% 2.85/1.54 thf(fact_215_suffix__order_Odual__order_Otrans, axiom, (! [A:$tType,B2:(list @ A),A2:(list @ A),C:(list @ A)]: (((((suffix @ A) @ B2) @ A2) => ((((suffix @ A) @ C) @ B2) => (((suffix @ A) @ C) @ A2)))))).
% 2.85/1.54 thf(fact_216_suffix__order_Oord__le__eq__trans, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((((suffix @ A) @ A2) @ B2) => ((B2 = C) => (((suffix @ A) @ A2) @ C)))))).
% 2.85/1.54 thf(fact_217_suffix__order_Oord__eq__le__trans, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((A2 = B2) => ((((suffix @ A) @ B2) @ C) => (((suffix @ A) @ A2) @ C)))))).
% 2.85/1.54 thf(fact_218_suffix__order_Oorder_Oantisym, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A)]: (((((suffix @ A) @ A2) @ B2) => ((((suffix @ A) @ B2) @ A2) => (A2 = B2)))))).
% 2.85/1.54 thf(fact_219_suffix__order_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y5:(list @ A),Z:(list @ A)]: ((Y5 = Z))) = (^ [A5:(list @ A),B4:(list @ A)]: (((((suffix @ A) @ A5) @ B4) & (((suffix @ A) @ B4) @ A5)))))))).
% 2.85/1.54 thf(fact_220_suffix__order_Oantisym__conv, axiom, (! [A:$tType,Y3:(list @ A),X:(list @ A)]: (((((suffix @ A) @ Y3) @ X) => ((((suffix @ A) @ X) @ Y3) = (X = Y3)))))).
% 2.85/1.54 thf(fact_221_suffix__order_Oorder__trans, axiom, (! [A:$tType,X:(list @ A),Y3:(list @ A),Z3:(list @ A)]: (((((suffix @ A) @ X) @ Y3) => ((((suffix @ A) @ Y3) @ Z3) => (((suffix @ A) @ X) @ Z3)))))).
% 2.85/1.54 thf(fact_222_suffix__order_Oorder_Otrans, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((((suffix @ A) @ A2) @ B2) => ((((suffix @ A) @ B2) @ C) => (((suffix @ A) @ A2) @ C)))))).
% 2.85/1.54 thf(fact_223_suffix__order_Oeq__refl, axiom, (! [A:$tType,X:(list @ A),Y3:(list @ A)]: (((X = Y3) => (((suffix @ A) @ X) @ Y3))))).
% 2.85/1.54 thf(fact_224_suffix__order_Oantisym, axiom, (! [A:$tType,X:(list @ A),Y3:(list @ A)]: (((((suffix @ A) @ X) @ Y3) => ((((suffix @ A) @ Y3) @ X) => (X = Y3)))))).
% 2.85/1.54 thf(fact_225_suffix__order_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y5:(list @ A),Z:(list @ A)]: ((Y5 = Z))) = (^ [X3:(list @ A),Y2:(list @ A)]: (((((suffix @ A) @ X3) @ Y2) & (((suffix @ A) @ Y2) @ X3)))))))).
% 2.85/1.54 thf(fact_226_suffix__same__cases, axiom, (! [A:$tType,Xs_1:(list @ A),Ys:(list @ A),Xs_2:(list @ A)]: (((((suffix @ A) @ Xs_1) @ Ys) => ((((suffix @ A) @ Xs_2) @ Ys) => ((((suffix @ A) @ Xs_1) @ Xs_2) | (((suffix @ A) @ Xs_2) @ Xs_1))))))).
% 2.85/1.54 thf(fact_227_finite__list, axiom, (! [A:$tType,A3:(set @ A)]: ((((finite_finite @ A) @ A3) => (? [Xs2:(list @ A)]: ((((set2 @ A) @ Xs2) = A3))))))).
% 2.85/1.54 thf(fact_228_append_Oleft__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A2) = A2)))).
% 2.85/1.54 thf(fact_229_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.85/1.54 thf(fact_230_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 2.85/1.54 thf(fact_231_distinct_Osimps_I1_J, axiom, (! [A:$tType]: (((distinct @ A) @ (nil @ A))))).
% 2.85/1.54 thf(fact_232_suffix__bot_Obot_Oextremum__uniqueI, axiom, (! [A:$tType,A2:(list @ A)]: (((((suffix @ A) @ A2) @ (nil @ A)) => (A2 = (nil @ A)))))).
% 2.85/1.54 thf(fact_233_suffix__bot_Obot_Oextremum, axiom, (! [A:$tType,A2:(list @ A)]: ((((suffix @ A) @ (nil @ A)) @ A2)))).
% 2.85/1.54 thf(fact_234_Nil__suffix, axiom, (! [A:$tType,Xs:(list @ A)]: ((((suffix @ A) @ (nil @ A)) @ Xs)))).
% 2.85/1.54 thf(fact_235_list_Osel_I2_J, axiom, (! [A:$tType]: ((((tl @ A) @ (nil @ A)) = (nil @ A))))).
% 2.85/1.54 thf(fact_236_suffix__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ Xs) @ Ys) => (((suffix @ A) @ Xs) @ (((append @ A) @ Zs) @ Ys)))))).
% 2.85/1.54 thf(fact_237_suffix__appendD, axiom, (! [A:$tType,Zs:(list @ A),Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Zs) @ Xs)) @ Ys) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.85/1.54 thf(fact_238_suffix__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)) = ((((suffix @ A) @ Xs) @ Zs) | (? [Xs5:(list @ A)]: (((Xs = (((append @ A) @ Xs5) @ Zs)) & (((suffix @ A) @ Xs5) @ Ys))))))))).
% 2.85/1.54 thf(fact_239_Sublist_Osuffix__def, axiom, (! [A:$tType]: (((suffix @ A) = (^ [Xs3:(list @ A),Ys2:(list @ A)]: ((? [Zs2:(list @ A)]: ((Ys2 = (((append @ A) @ Zs2) @ Xs3)))))))))).
% 2.85/1.54 thf(fact_240_suffixI, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Zs) @ Xs)) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.85/1.54 thf(fact_241_suffixE, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ Xs) @ Ys) => (~ ((! [Zs3:(list @ A)]: ((Ys != (((append @ A) @ Zs3) @ Xs)))))))))).
% 2.85/1.54 thf(fact_242_distinct__suffix, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((distinct @ A) @ Ys) => ((((suffix @ A) @ Xs) @ Ys) => ((distinct @ A) @ Xs)))))).
% 2.85/1.54 thf(fact_243_distinct__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((distinct @ A) @ Xs) => ((distinct @ A) @ ((tl @ A) @ Xs)))))).
% 2.85/1.54 thf(fact_244_suffix__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((suffix @ A) @ ((tl @ A) @ Xs)) @ Xs)))).
% 2.85/1.54 thf(fact_245_finite__distinct__list, axiom, (! [A:$tType,A3:(set @ A)]: ((((finite_finite @ A) @ A3) => (? [Xs2:(list @ A)]: (((((set2 @ A) @ Xs2) = A3) & ((distinct @ A) @ Xs2)))))))).
% 2.85/1.54 thf(fact_246_list_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(list @ A)]: (((A2 != (nil @ A)) => (((member @ A) @ ((hd @ A) @ A2)) @ ((set2 @ A) @ A2)))))).
% 2.85/1.54 thf(fact_247_hd__in__set, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((member @ A) @ ((hd @ A) @ Xs)) @ ((set2 @ A) @ Xs)))))).
% 2.85/1.54 thf(fact_248_list_Oset__sel_I2_J, axiom, (! [A:$tType,A2:(list @ A),X:A]: (((A2 != (nil @ A)) => ((((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ A2))) => (((member @ A) @ X) @ ((set2 @ A) @ A2))))))).
% 2.85/1.54 thf(fact_249_longest__common__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((? [Ps2:(list @ A),Xs6:(list @ A),Ys4:(list @ A)]: (((Xs = (((append @ A) @ Ps2) @ Xs6)) & ((Ys = (((append @ A) @ Ps2) @ Ys4)) & ((Xs6 = (nil @ A)) | ((Ys4 = (nil @ A)) | (((hd @ A) @ Xs6) != ((hd @ A) @ Ys4))))))))))).
% 2.85/1.54 thf(fact_250_hd__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((Xs = (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Ys))) & ((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Xs))))))).
% 2.85/1.54 thf(fact_251_list_Oexpand, axiom, (! [A:$tType,List:(list @ A),List2:(list @ A)]: ((((List = (nil @ A)) = (List2 = (nil @ A))) => (((List != (nil @ A)) => ((List2 != (nil @ A)) => ((((hd @ A) @ List) = ((hd @ A) @ List2)) & (((tl @ A) @ List) = ((tl @ A) @ List2))))) => (List = List2)))))).
% 2.85/1.54 thf(fact_252_not__hd__in__tl, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((X != ((hd @ A) @ Xs)) => ((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ Xs)))))))).
% 2.85/1.54 thf(fact_253_Misc_Odistinct__hd__tl, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((distinct @ A) @ Xs) => ((X = ((hd @ A) @ Xs)) => (~ ((((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ Xs)))))))))).
% 2.85/1.54 thf(fact_254_old_OEntry__unreachable, axiom, (! [G2:g]: (((invar @ G2) => (((((((graph_1822314308nEdges @ g) @ node) @ edgeD) @ inEdges) @ G2) @ (entry @ G2)) = (nil @ ((product_prod @ node) @ ((product_prod @ edgeD) @ node)))))))).
% 2.85/1.54 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 2.85/1.54 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: (((linorder @ A) => (ord @ A))))).
% 2.85/1.54 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.85/1.54 thf(tcon_Set_Oset___Orderings_Oord_1, axiom, (! [A6:$tType]: ((ord @ (set @ A6))))).
% 2.85/1.54 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.85/1.54 thf(tcon_HOL_Obool___Orderings_Oord_2, axiom, (ord @ $o)).
% 2.85/1.54 thf(tfree_0, hypothesis, (linorder @ node)).
% 2.85/1.54 thf(tfree_1, hypothesis, (linorder @ val)).
% 2.85/1.54 thf(conj_0, conjecture, (~ ((((member @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r)) @ ((set2 @ node) @ ((tl @ node) @ rs)))))).
% 2.85/1.54 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.cRKnHLkZP0/DTF2DTF20598.p
% 2.85/1.54 ------------------------
% 2.85/1.57 ---- Cleaned THF ---
% 2.85/1.57 thf(ty_t_Product__Type_Oprod,type,
% 2.85/1.57 product_prod: $tType > $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_Option_Ooption,type,
% 2.85/1.57 option: $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_List_Olist,type,
% 2.85/1.57 list: $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_Set_Oset,type,
% 2.85/1.57 set: $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_tf_edgeD,type,
% 2.85/1.57 edgeD: $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_tf_node,type,
% 2.85/1.57 node: $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_tf_val,type,
% 2.85/1.57 val: $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_tf_g,type,
% 2.85/1.57 g: $tType ).
% 2.85/1.57
% 2.85/1.57 thf(sy_cl_HOL_Otype,type,
% 2.85/1.57 type:
% 2.85/1.57 !>[A: $tType] : $o ).
% 2.85/1.57
% 2.85/1.57 thf(sy_cl_Orderings_Oord,type,
% 2.85/1.57 ord:
% 2.85/1.57 !>[A: $tType] : $o ).
% 2.85/1.57
% 2.85/1.57 thf(sy_cl_Orderings_Olinorder,type,
% 2.85/1.57 linorder:
% 2.85/1.57 !>[A: $tType] : $o ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Finite__Set_Ofinite,type,
% 2.85/1.57 finite_finite:
% 2.85/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Graph__path_Ograph__Entry_OEntryPath,type,
% 2.85/1.57 graph_2081878492ryPath:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > G > ( list @ Node ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Graph__path_Ograph__Entry_OisIdom,type,
% 2.85/1.57 graph_graph_isIdom:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > G > Node > Node > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Graph__path_Ograph__Entry__base_Odominates,type,
% 2.85/1.57 graph_709200220inates:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > G > Node > Node > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Graph__path_Ograph__path__base_OinEdges,type,
% 2.85/1.57 graph_1822314308nEdges:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ ( product_prod @ Node @ ( product_prod @ EdgeD @ Node ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Graph__path_Ograph__path__base_Opath2,type,
% 2.85/1.57 graph_1661282752_path2:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) > Node > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors,type,
% 2.85/1.57 graph_1201503639essors:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Oappend,type,
% 2.85/1.57 append:
% 2.85/1.57 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Odistinct,type,
% 2.85/1.57 distinct:
% 2.85/1.57 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Olist_OCons,type,
% 2.85/1.57 cons:
% 2.85/1.57 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Olist_ONil,type,
% 2.85/1.57 nil:
% 2.85/1.57 !>[A: $tType] : ( list @ A ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Olist_Ohd,type,
% 2.85/1.57 hd:
% 2.85/1.57 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Olist_Oset,type,
% 2.85/1.57 set2:
% 2.85/1.57 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Olist_Otl,type,
% 2.85/1.57 tl:
% 2.85/1.57 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Minimality_Ograph__Entry_Oreducible,type,
% 2.85/1.57 graph_reducible:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > G > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs,type,
% 2.85/1.57 sSA_CFG_SSA_allDefs:
% 2.85/1.57 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_SSA__CFG_OCFG__SSA__base_OdefAss,type,
% 2.85/1.57 sSA_CFG_SSA_defAss:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > Val > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs,type,
% 2.85/1.57 sSA_CFG_SSA_phiDefs:
% 2.85/1.57 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Node > ( set @ Val ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses,type,
% 2.85/1.57 sSA_CFG_SSA_phiUses:
% 2.85/1.57 !>[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 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode,type,
% 2.85/1.57 sSA_CF1081484811efNode:
% 2.85/1.57 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Node ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg,type,
% 2.85/1.57 sSA_CF1165125185phiArg:
% 2.85/1.57 !>[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 ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_SSA__CFG_OCFG__base_OdefAss_H,type,
% 2.85/1.57 sSA_CFG_defAss:
% 2.85/1.57 !>[G: $tType,Node: $tType,EdgeD: $tType,Var: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > ( G > Node ) > ( G > Node > ( set @ Var ) ) > G > Node > Var > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Set_OCollect,type,
% 2.85/1.57 collect:
% 2.85/1.57 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Sublist_Osuffix,type,
% 2.85/1.57 suffix:
% 2.85/1.57 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_member,type,
% 2.85/1.57 member:
% 2.85/1.57 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_Entry,type,
% 2.85/1.57 entry: g > node ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v__092_060alpha_062n,type,
% 2.85/1.57 alpha_n: g > ( list @ node ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 2.85/1.57 phi_r: val ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_defs,type,
% 2.85/1.57 defs: g > node > ( set @ val ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_g,type,
% 2.85/1.57 g2: g ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_inEdges_H,type,
% 2.85/1.57 inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_invar,type,
% 2.85/1.57 invar: g > $o ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_m,type,
% 2.85/1.57 m: node ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_ms,type,
% 2.85/1.57 ms: list @ node ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_n,type,
% 2.85/1.57 n: node ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_ns,type,
% 2.85/1.57 ns: list @ node ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_phis,type,
% 2.85/1.57 phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 2.85/1.57 pred_phi_r: node ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_r,type,
% 2.85/1.57 r: val ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_rs_H____,type,
% 2.85/1.57 rs: list @ node ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_rs____,type,
% 2.85/1.57 rs2: list @ node ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_s,type,
% 2.85/1.57 s: val ).
% 2.85/1.57
% 2.85/1.57 thf(fact_0_old_Opath2__hd,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( N
% 2.85/1.57 = ( hd @ node @ Ns ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_1_False,axiom,
% 2.85/1.57 r != phi_r ).
% 2.85/1.57
% 2.85/1.57 thf(fact_2_old_OEntry__in__graph,axiom,
% 2.85/1.57 ! [G2: g] : ( member @ node @ ( entry @ G2 ) @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_3_rs_H__props_I2_J,axiom,
% 2.85/1.57 graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs ).
% 2.85/1.57
% 2.85/1.57 thf(fact_4_rs_H__props_I1_J,axiom,
% 2.85/1.57 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 2.85/1.57
% 2.85/1.57 thf(fact_5_old_OEntryPath__distinct,axiom,
% 2.85/1.57 ! [G2: g,Ns: list @ node] :
% 2.85/1.57 ( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ Ns )
% 2.85/1.57 => ( distinct @ node @ Ns ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_6_old_O_092_060alpha_062n__distinct,axiom,
% 2.85/1.57 ! [G2: g] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( distinct @ node @ ( alpha_n @ G2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_7_rs_H__props_I3_J,axiom,
% 2.85/1.57 member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_8_assms_I10_J,axiom,
% 2.85/1.57 sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 2.85/1.57
% 2.85/1.57 thf(fact_9_allDefs__disjoint_H,axiom,
% 2.85/1.57 ! [N: node,G2: g,M: node,V: val] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 2.85/1.57 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ M ) )
% 2.85/1.57 => ( N = M ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_10_assms_I7_J,axiom,
% 2.85/1.57 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_11_defNode__eq,axiom,
% 2.85/1.57 ! [N: node,G2: g,V: val] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) )
% 2.85/1.57 => ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ G2 @ V )
% 2.85/1.57 = N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_12_rs_H__props_I4_J,axiom,
% 2.85/1.57 member @ node @ pred_phi_r @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_13_defs__in__allDefs,axiom,
% 2.85/1.57 ! [V: val,G2: g,N: node] :
% 2.85/1.57 ( ( member @ val @ V @ ( defs @ G2 @ N ) )
% 2.85/1.57 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_14_FormalSSA__Misc_Oin__set__tlD,axiom,
% 2.85/1.57 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.57 ( ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) )
% 2.85/1.57 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_15_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_16_old_Opath2__hd__in__ns,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( member @ node @ N @ ( set2 @ node @ Ns ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_17_old_Opath2__in___092_060alpha_062n,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node,L: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ( member @ node @ L @ ( set2 @ node @ Ns ) )
% 2.85/1.57 => ( member @ node @ L @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_18_old_Oinvar,axiom,
% 2.85/1.57 ! [G2: g] : ( invar @ G2 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_19_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_20_old_Opath2__last__in__ns,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( member @ node @ M @ ( set2 @ node @ Ns ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_21_old_Osuccessor__is__node,axiom,
% 2.85/1.57 ! [N: node,G2: g,N2: node] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 2.85/1.57 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( invar @ G2 )
% 2.85/1.57 => ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_22_old_Opredecessor__is__node,axiom,
% 2.85/1.57 ! [N: node,G2: g,N2: node] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 2.85/1.57 => ( ( invar @ G2 )
% 2.85/1.57 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_23_old_Opath2__forget__hd,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ Ns ) @ Ns @ M ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_24_old_OEntry__reachesE,axiom,
% 2.85/1.57 ! [N: node,G2: g] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( invar @ G2 )
% 2.85/1.57 => ~ ! [Ns2: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ N )
% 2.85/1.57 => ~ ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ Ns2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_25__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.85/1.57 ~ ! [Rs: list @ node,Pred_phi_r: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ Rs @ Pred_phi_r )
% 2.85/1.57 => ( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ Rs )
% 2.85/1.57 => ( ( member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ Pred_phi_r ) )
% 2.85/1.57 => ~ ( member @ node @ Pred_phi_r @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_26_old_OEntry__reaches,axiom,
% 2.85/1.57 ! [N: node,G2: g] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( invar @ G2 )
% 2.85/1.57 => ? [Ns2: list @ node] : ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_27_old_Oidom__ex,axiom,
% 2.85/1.57 ! [G2: g,N: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( N
% 2.85/1.57 != ( entry @ G2 ) )
% 2.85/1.57 => ? [X2: node] :
% 2.85/1.57 ( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ X2 )
% 2.85/1.57 & ! [Y: node] :
% 2.85/1.57 ( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ Y )
% 2.85/1.57 => ( Y = X2 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_28_FormalSSA__Misc_Odistinct__hd__tl,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A] :
% 2.85/1.57 ( ( distinct @ A @ Xs )
% 2.85/1.57 => ~ ( member @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_29_defAss_H__extend,axiom,
% 2.85/1.57 ! [G2: g,M: node,V: val,N: node,Ns: list @ node] :
% 2.85/1.57 ( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ M @ V )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ! [X2: node] :
% 2.85/1.57 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ns ) ) )
% 2.85/1.57 => ~ ( member @ val @ V @ ( defs @ G2 @ X2 ) ) )
% 2.85/1.57 => ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ N @ V ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_30_defAss_H__def,axiom,
% 2.85/1.57 ! [G2: g,M: node,V: val] :
% 2.85/1.57 ( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ M @ V )
% 2.85/1.57 = ( ! [Ns3: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns3 @ M )
% 2.85/1.57 => ? [X3: node] :
% 2.85/1.57 ( ( member @ node @ X3 @ ( set2 @ node @ Ns3 ) )
% 2.85/1.57 & ( member @ val @ V @ ( defs @ G2 @ X3 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_31_defAss_HI,axiom,
% 2.85/1.57 ! [G2: g,M: node,V: val] :
% 2.85/1.57 ( ! [Ns2: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ M )
% 2.85/1.57 => ? [X4: node] :
% 2.85/1.57 ( ( member @ node @ X4 @ ( set2 @ node @ Ns2 ) )
% 2.85/1.57 & ( member @ val @ V @ ( defs @ G2 @ X4 ) ) ) )
% 2.85/1.57 => ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ M @ V ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_32_defAss_HE,axiom,
% 2.85/1.57 ! [G2: g,M: node,V: val,Ns: list @ node] :
% 2.85/1.57 ( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ G2 @ M @ V )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns @ M )
% 2.85/1.57 => ~ ! [N3: node] :
% 2.85/1.57 ( ( member @ node @ N3 @ ( set2 @ node @ Ns ) )
% 2.85/1.57 => ~ ( member @ val @ V @ ( defs @ G2 @ N3 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_33_defAss__extend,axiom,
% 2.85/1.57 ! [G2: g,M: node,V: val,N: node,Ns: list @ node] :
% 2.85/1.57 ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ M @ V )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ! [X2: node] :
% 2.85/1.57 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ns ) ) )
% 2.85/1.57 => ~ ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X2 ) ) )
% 2.85/1.57 => ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ N @ V ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_34_assms_I8_J,axiom,
% 2.85/1.57 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_35_defAss__def,axiom,
% 2.85/1.57 ! [G2: g,M: node,V: val] :
% 2.85/1.57 ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ M @ V )
% 2.85/1.57 = ( ! [Ns3: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns3 @ M )
% 2.85/1.57 => ? [X3: node] :
% 2.85/1.57 ( ( member @ node @ X3 @ ( set2 @ node @ Ns3 ) )
% 2.85/1.57 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X3 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_36_defAssI,axiom,
% 2.85/1.57 ! [G2: g,M: node,V: val] :
% 2.85/1.57 ( ! [Ns2: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ M )
% 2.85/1.57 => ? [X4: node] :
% 2.85/1.57 ( ( member @ node @ X4 @ ( set2 @ node @ Ns2 ) )
% 2.85/1.57 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X4 ) ) ) )
% 2.85/1.57 => ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ M @ V ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_37_defAssD,axiom,
% 2.85/1.57 ! [G2: g,M: node,V: val,Ns: list @ node] :
% 2.85/1.57 ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ M @ V )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns @ M )
% 2.85/1.57 => ? [X2: node] :
% 2.85/1.57 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 2.85/1.57 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_38_phiDefs__in__allDefs,axiom,
% 2.85/1.57 ! [V: val,G2: g,N: node] :
% 2.85/1.57 ( ( member @ val @ V @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) )
% 2.85/1.57 => ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_39_defAss__dominating,axiom,
% 2.85/1.57 ! [N: node,G2: g,V: val] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G2 @ N @ V )
% 2.85/1.57 = ( ? [X3: node] :
% 2.85/1.57 ( ( member @ node @ X3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X3 @ N )
% 2.85/1.57 & ( member @ val @ V @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ X3 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_40_old_Osuccessor__in___092_060alpha_062n,axiom,
% 2.85/1.57 ! [G2: g,N: node] :
% 2.85/1.57 ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N )
% 2.85/1.57 != ( nil @ node ) )
% 2.85/1.57 => ( ( invar @ G2 )
% 2.85/1.57 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_41_phiUses__finite,axiom,
% 2.85/1.57 ! [N: node,G2: g] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( finite_finite @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_42_old_Opath2__split__last__prop,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ? [X4: node] :
% 2.85/1.57 ( ( member @ node @ X4 @ ( set2 @ node @ Ns ) )
% 2.85/1.57 & ( P @ X4 ) )
% 2.85/1.57 => ~ ! [N4: node,Ns4: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N4 @ Ns4 @ M )
% 2.85/1.57 => ( ( P @ N4 )
% 2.85/1.57 => ( ! [X4: node] :
% 2.85/1.57 ( ( member @ node @ X4 @ ( set2 @ node @ ( tl @ node @ Ns4 ) ) )
% 2.85/1.57 => ~ ( P @ X4 ) )
% 2.85/1.57 => ~ ( suffix @ node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_43_allDefs__finite,axiom,
% 2.85/1.57 ! [N: node,G2: g] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( finite_finite @ val @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ G2 @ N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_44_old_Opath2__not__Nil,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( Ns
% 2.85/1.57 != ( nil @ node ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_45_mem__Collect__eq,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,P: A > $o] :
% 2.85/1.57 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.85/1.57 = ( P @ A2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_46_Collect__mem__eq,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( collect @ A
% 2.85/1.57 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 2.85/1.57 = A3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_47_Collect__cong,axiom,
% 2.85/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.85/1.57 ( ! [X2: A] :
% 2.85/1.57 ( ( P @ X2 )
% 2.85/1.57 = ( Q @ X2 ) )
% 2.85/1.57 => ( ( collect @ A @ P )
% 2.85/1.57 = ( collect @ A @ Q ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_48_ext,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 2.85/1.57 ( ! [X2: A] :
% 2.85/1.57 ( ( F @ X2 )
% 2.85/1.57 = ( G2 @ X2 ) )
% 2.85/1.57 => ( F = G2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_49_old_Opath2__not__Nil2,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node] :
% 2.85/1.57 ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( nil @ node ) @ M ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_50_old_Opath2__app,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 2.85/1.57 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( tl @ node @ Ms ) ) @ L ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_51_defs__finite,axiom,
% 2.85/1.57 ! [G2: g,N: node] : ( finite_finite @ val @ ( defs @ G2 @ N ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_52_phiDefs__finite,axiom,
% 2.85/1.57 ! [G2: g,N: node] : ( finite_finite @ val @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ G2 @ N ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_53_strict__dom__trans_H,axiom,
% 2.85/1.57 ! [N: node,M: node,G2: g,M2: node] :
% 2.85/1.57 ( ( ( N != M )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M ) )
% 2.85/1.57 => ( ( ( M != M2 )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ M @ M2 ) )
% 2.85/1.57 => ( ( N != M2 )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_54_old_Ostrict__dom__trans,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node,M2: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( ( N != M )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M ) )
% 2.85/1.57 => ( ( ( M != M2 )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ M @ M2 ) )
% 2.85/1.57 => ( ( N != M2 )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_55_old_Odominates__trans,axiom,
% 2.85/1.57 ! [G2: g,N: node,N2: node,N5: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N2 @ N5 )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N5 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_56_old_Odominates__antitrans,axiom,
% 2.85/1.57 ! [G2: g,N_1: node,M: node,N_2: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N_1 @ M )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N_2 @ M )
% 2.85/1.57 => ( ~ ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N_1 @ N_2 )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N_2 @ N_1 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_57_old_Odominates__antisymm,axiom,
% 2.85/1.57 ! [G2: g,N: node,N2: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N2 @ N )
% 2.85/1.57 => ( N = N2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_58_dominates__trans_H,axiom,
% 2.85/1.57 ! [G2: g,N: node,N2: node,N5: node] :
% 2.85/1.57 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N2 @ N5 )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N5 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_59_dominates__antisymm_H,axiom,
% 2.85/1.57 ! [G2: g,N: node,N2: node] :
% 2.85/1.57 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N2 @ N )
% 2.85/1.57 => ( N = N2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_60_dominates__refl_H,axiom,
% 2.85/1.57 ! [N: node,G2: g] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_61_old_Odominates__path,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node] :
% 2.85/1.57 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 2.85/1.57 => ( ( invar @ G2 )
% 2.85/1.57 => ~ ! [Ns2: list @ node] :
% 2.85/1.57 ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns2 @ M ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_62_old_Odominates__mid,axiom,
% 2.85/1.57 ! [G2: g,N: node,X: node,M: node,Ns: list @ node] :
% 2.85/1.57 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ X )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X @ M )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ( invar @ G2 )
% 2.85/1.57 => ( member @ node @ X @ ( set2 @ node @ Ns ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_63_old_Odominates__def,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node] :
% 2.85/1.57 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 2.85/1.57 = ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 & ! [Ns3: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns3 @ M )
% 2.85/1.57 => ( member @ node @ N @ ( set2 @ node @ Ns3 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_64_old_OdominatesE,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node] :
% 2.85/1.57 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 2.85/1.57 => ~ ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ~ ! [Ns5: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns5 @ M )
% 2.85/1.57 => ( member @ node @ N @ ( set2 @ node @ Ns5 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_65_old_Odominates__unsnoc,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node,M2: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 2.85/1.57 => ( ( member @ node @ M2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M ) ) )
% 2.85/1.57 => ( ( N != M )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_66_non__dominated__predecessor,axiom,
% 2.85/1.57 ! [N: node,G2: g] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( N
% 2.85/1.57 != ( entry @ G2 ) )
% 2.85/1.57 => ~ ! [M3: node] :
% 2.85/1.57 ( ( member @ node @ M3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_67_old_OisIdom__def,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node] :
% 2.85/1.57 ( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 2.85/1.57 = ( ( M != N )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ M @ N )
% 2.85/1.57 & ! [X3: node] :
% 2.85/1.57 ( ( member @ node @ X3 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( ( X3 != N )
% 2.85/1.57 & ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X3 @ N ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X3 @ M ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_68_old_OEntryPath__suffix,axiom,
% 2.85/1.57 ! [G2: g,Ns: list @ node,Ns6: list @ node] :
% 2.85/1.57 ( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ Ns )
% 2.85/1.57 => ( ( suffix @ node @ Ns6 @ Ns )
% 2.85/1.57 => ( ( Ns6
% 2.85/1.57 != ( nil @ node ) )
% 2.85/1.57 => ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ Ns6 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_69_old_Odominates__unsnoc_H,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node,M2: node,Ms: list @ node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M2 @ Ms @ M )
% 2.85/1.57 => ( ! [X2: node] :
% 2.85/1.57 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ms ) ) )
% 2.85/1.57 => ( X2 != N ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_70_old_Odominates__extend,axiom,
% 2.85/1.57 ! [G2: g,N: node,M: node,M2: node,Ms: list @ node] :
% 2.85/1.57 ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M2 @ Ms @ M )
% 2.85/1.57 => ( ~ ( member @ node @ N @ ( set2 @ node @ ( tl @ node @ Ms ) ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_71_old_OEntry__no__predecessor,axiom,
% 2.85/1.57 ! [G2: g] :
% 2.85/1.57 ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( entry @ G2 ) )
% 2.85/1.57 = ( nil @ node ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_72_old_Odominates__refl,axiom,
% 2.85/1.57 ! [G2: g,N: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_73_old_OEntry__dominates,axiom,
% 2.85/1.57 ! [G2: g,N: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ ( entry @ G2 ) @ N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_74_old_OdominatesI,axiom,
% 2.85/1.57 ! [M: node,G2: g,N: node] :
% 2.85/1.57 ( ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ! [Ns2: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns2 @ M )
% 2.85/1.57 => ( member @ node @ N @ ( set2 @ node @ Ns2 ) ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ N @ M ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_75_old_OEntry__iff__unreachable,axiom,
% 2.85/1.57 ! [G2: g,N: node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N )
% 2.85/1.57 = ( nil @ node ) )
% 2.85/1.57 = ( N
% 2.85/1.57 = ( entry @ G2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_76_old_Oreducible__def,axiom,
% 2.85/1.57 ! [G2: g] :
% 2.85/1.57 ( ( graph_reducible @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 )
% 2.85/1.57 = ( ! [N6: node,Ns3: list @ node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N6 @ Ns3 @ N6 )
% 2.85/1.57 => ? [X3: node] :
% 2.85/1.57 ( ( member @ node @ X3 @ ( set2 @ node @ Ns3 ) )
% 2.85/1.57 & ! [Y2: node] :
% 2.85/1.57 ( ( member @ node @ Y2 @ ( set2 @ node @ Ns3 ) )
% 2.85/1.57 => ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ X3 @ Y2 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_77_in__hd__or__tl__conv,axiom,
% 2.85/1.57 ! [A: $tType,L: list @ A,X: A] :
% 2.85/1.57 ( ( L
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( ( X
% 2.85/1.57 = ( hd @ A @ L ) )
% 2.85/1.57 | ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ L ) ) ) )
% 2.85/1.57 = ( member @ A @ X @ ( set2 @ A @ L ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_78_old_Opath2__cases,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ( ( Ns
% 2.85/1.57 = ( cons @ node @ N @ ( nil @ node ) ) )
% 2.85/1.57 => ( M != N ) )
% 2.85/1.57 => ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) @ ( tl @ node @ Ns ) @ M )
% 2.85/1.57 => ~ ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_79_old_Opath2__snoc,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node,M2: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M2 ) ) )
% 2.85/1.57 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ M2 @ ( nil @ node ) ) ) @ M2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_80_old_Opath2__rev__induct,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( P @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) )
% 2.85/1.57 => ( ! [Ns2: list @ node,M4: node,M3: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns2 @ M4 )
% 2.85/1.57 => ( ( P @ N @ Ns2 @ M4 )
% 2.85/1.57 => ( ( member @ node @ M4 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M3 ) ) )
% 2.85/1.57 => ( P @ N @ ( append @ node @ Ns2 @ ( cons @ node @ M3 @ ( nil @ node ) ) ) @ M3 ) ) ) )
% 2.85/1.57 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_81_tl__append2,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( Xs
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( tl @ A @ ( append @ A @ Xs @ Ys ) )
% 2.85/1.57 = ( append @ A @ ( tl @ A @ Xs ) @ Ys ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_82_hd__append2,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( Xs
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.85/1.57 = ( hd @ A @ Xs ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_83_same__suffix__nil,axiom,
% 2.85/1.57 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.85/1.57 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ Xs )
% 2.85/1.57 = ( Ys
% 2.85/1.57 = ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_84_old_Opath2__induct,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ( ( invar @ G2 )
% 2.85/1.57 => ( P @ M @ ( cons @ node @ M @ ( nil @ node ) ) @ M ) )
% 2.85/1.57 => ( ! [Ns2: list @ node,N4: node,N3: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N3 @ Ns2 @ M )
% 2.85/1.57 => ( ( P @ N3 @ Ns2 @ M )
% 2.85/1.57 => ( ( member @ node @ N4 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N3 ) ) )
% 2.85/1.57 => ( P @ N4 @ ( cons @ node @ N4 @ Ns2 ) @ M ) ) ) )
% 2.85/1.57 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_85_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 2.85/1.57 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Y3: A] :
% 2.85/1.57 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.57 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ ( append @ A @ Ys @ ( cons @ A @ Y3 @ Xs ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_86_list_Oinject,axiom,
% 2.85/1.57 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.85/1.57 ( ( ( cons @ A @ X21 @ X22 )
% 2.85/1.57 = ( cons @ A @ Y21 @ Y22 ) )
% 2.85/1.57 = ( ( X21 = Y21 )
% 2.85/1.57 & ( X22 = Y22 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_87_same__append__eq,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.85/1.57 ( ( ( append @ A @ Xs @ Ys )
% 2.85/1.57 = ( append @ A @ Xs @ Zs ) )
% 2.85/1.57 = ( Ys = Zs ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_88_append__same__eq,axiom,
% 2.85/1.57 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.85/1.57 ( ( ( append @ A @ Ys @ Xs )
% 2.85/1.57 = ( append @ A @ Zs @ Xs ) )
% 2.85/1.57 = ( Ys = Zs ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_89_append__assoc,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.85/1.57 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 2.85/1.57 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_90_append_Oassoc,axiom,
% 2.85/1.57 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.85/1.57 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C )
% 2.85/1.57 = ( append @ A @ A2 @ ( append @ A @ B2 @ C ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_91_suffix__order_Odual__order_Orefl,axiom,
% 2.85/1.57 ! [A: $tType,A2: list @ A] : ( suffix @ A @ A2 @ A2 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_92_suffix__order_Oorder__refl,axiom,
% 2.85/1.57 ! [A: $tType,X: list @ A] : ( suffix @ A @ X @ X ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_93_old_Opath2__split_I2_J,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns6: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns6 ) ) @ M )
% 2.85/1.57 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns6 ) @ M ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_94_List_Ofinite__set,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A] : ( finite_finite @ A @ ( set2 @ A @ Xs ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_95_append_Oright__neutral,axiom,
% 2.85/1.57 ! [A: $tType,A2: list @ A] :
% 2.85/1.57 ( ( append @ A @ A2 @ ( nil @ A ) )
% 2.85/1.57 = A2 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_96_empty__append__eq__id,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( append @ A @ ( nil @ A ) )
% 2.85/1.57 = ( ^ [X3: list @ A] : X3 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_97_append__is__Nil__conv,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( ( append @ A @ Xs @ Ys )
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 = ( ( Xs
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 & ( Ys
% 2.85/1.57 = ( nil @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_98_Nil__is__append__conv,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( ( nil @ A )
% 2.85/1.57 = ( append @ A @ Xs @ Ys ) )
% 2.85/1.57 = ( ( Xs
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 & ( Ys
% 2.85/1.57 = ( nil @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_99_self__append__conv2,axiom,
% 2.85/1.57 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.85/1.57 ( ( Ys
% 2.85/1.57 = ( append @ A @ Xs @ Ys ) )
% 2.85/1.57 = ( Xs
% 2.85/1.57 = ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_100_append__self__conv2,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( ( append @ A @ Xs @ Ys )
% 2.85/1.57 = Ys )
% 2.85/1.57 = ( Xs
% 2.85/1.57 = ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_101_self__append__conv,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( Xs
% 2.85/1.57 = ( append @ A @ Xs @ Ys ) )
% 2.85/1.57 = ( Ys
% 2.85/1.57 = ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_102_append__self__conv,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( ( append @ A @ Xs @ Ys )
% 2.85/1.57 = Xs )
% 2.85/1.57 = ( Ys
% 2.85/1.57 = ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_103_append__Nil2,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A] :
% 2.85/1.57 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.85/1.57 = Xs ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_104_suffix__bot_Obot_Oextremum__unique,axiom,
% 2.85/1.57 ! [A: $tType,A2: list @ A] :
% 2.85/1.57 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 2.85/1.57 = ( A2
% 2.85/1.57 = ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_105_suffix__Nil,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A] :
% 2.85/1.57 ( ( suffix @ A @ Xs @ ( nil @ A ) )
% 2.85/1.57 = ( Xs
% 2.85/1.57 = ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_106_same__suffix__suffix,axiom,
% 2.85/1.57 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.85/1.57 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ ( append @ A @ Zs @ Xs ) )
% 2.85/1.57 = ( suffix @ A @ Ys @ Zs ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_107_old_Opath2__split_I1_J,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns6: list @ node,M: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns6 ) ) @ M )
% 2.85/1.57 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ ( nil @ node ) ) ) @ N2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_108_old_OEntry__loop,axiom,
% 2.85/1.57 ! [G2: g,Ns: list @ node] :
% 2.85/1.57 ( ( invar @ G2 )
% 2.85/1.57 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( entry @ G2 ) @ Ns @ ( entry @ G2 ) )
% 2.85/1.57 => ( Ns
% 2.85/1.57 = ( cons @ node @ ( entry @ G2 ) @ ( nil @ node ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_109_old_OEntryPath__triv,axiom,
% 2.85/1.57 ! [G2: g,N: node] : ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_110_append1__eq__conv,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y3: A] :
% 2.85/1.57 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.85/1.57 = ( append @ A @ Ys @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 2.85/1.57 = ( ( Xs = Ys )
% 2.85/1.57 & ( X = Y3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_111_list__ee__eq__leel_I1_J,axiom,
% 2.85/1.57 ! [A: $tType,E1: A,E2: A,L1: list @ A,E12: A,E22: A,L2: list @ A] :
% 2.85/1.57 ( ( ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) )
% 2.85/1.57 = ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) ) )
% 2.85/1.57 = ( ( L1
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 & ( E1 = E12 )
% 2.85/1.57 & ( E2 = E22 )
% 2.85/1.57 & ( L2
% 2.85/1.57 = ( nil @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_112_list__ee__eq__leel_I2_J,axiom,
% 2.85/1.57 ! [A: $tType,L1: list @ A,E12: A,E22: A,L2: list @ A,E1: A,E2: A] :
% 2.85/1.57 ( ( ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) )
% 2.85/1.57 = ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) ) )
% 2.85/1.57 = ( ( L1
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 & ( E1 = E12 )
% 2.85/1.57 & ( E2 = E22 )
% 2.85/1.57 & ( L2
% 2.85/1.57 = ( nil @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_113_list__se__match_I1_J,axiom,
% 2.85/1.57 ! [A: $tType,L1: list @ A,L2: list @ A,A2: A] :
% 2.85/1.57 ( ( L1
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( ( append @ A @ L1 @ L2 )
% 2.85/1.57 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.85/1.57 = ( ( L1
% 2.85/1.57 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.85/1.57 & ( L2
% 2.85/1.57 = ( nil @ A ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_114_list__se__match_I2_J,axiom,
% 2.85/1.57 ! [A: $tType,L2: list @ A,L1: list @ A,A2: A] :
% 2.85/1.57 ( ( L2
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( ( append @ A @ L1 @ L2 )
% 2.85/1.57 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.85/1.57 = ( ( L1
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 & ( L2
% 2.85/1.57 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_115_list__se__match_I3_J,axiom,
% 2.85/1.57 ! [A: $tType,L1: list @ A,A2: A,L2: list @ A] :
% 2.85/1.57 ( ( L1
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 2.85/1.57 = ( append @ A @ L1 @ L2 ) )
% 2.85/1.57 = ( ( L1
% 2.85/1.57 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.85/1.57 & ( L2
% 2.85/1.57 = ( nil @ A ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_116_list__se__match_I4_J,axiom,
% 2.85/1.57 ! [A: $tType,L2: list @ A,A2: A,L1: list @ A] :
% 2.85/1.57 ( ( L2
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 2.85/1.57 = ( append @ A @ L1 @ L2 ) )
% 2.85/1.57 = ( ( L1
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 & ( L2
% 2.85/1.57 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_117_list__e__eq__lel_I1_J,axiom,
% 2.85/1.57 ! [A: $tType,E: A,L1: list @ A,E3: A,L2: list @ A] :
% 2.85/1.57 ( ( ( cons @ A @ E @ ( nil @ A ) )
% 2.85/1.57 = ( append @ A @ L1 @ ( cons @ A @ E3 @ L2 ) ) )
% 2.85/1.57 = ( ( L1
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 & ( E3 = E )
% 2.85/1.57 & ( L2
% 2.85/1.57 = ( nil @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_118_list__e__eq__lel_I2_J,axiom,
% 2.85/1.57 ! [A: $tType,L1: list @ A,E3: A,L2: list @ A,E: A] :
% 2.85/1.57 ( ( ( append @ A @ L1 @ ( cons @ A @ E3 @ L2 ) )
% 2.85/1.57 = ( cons @ A @ E @ ( nil @ A ) ) )
% 2.85/1.57 = ( ( L1
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 & ( E3 = E )
% 2.85/1.57 & ( L2
% 2.85/1.57 = ( nil @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_119_snoc__suffix__snoc,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y3: A] :
% 2.85/1.57 ( ( suffix @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 2.85/1.57 = ( ( X = Y3 )
% 2.85/1.57 & ( suffix @ A @ Xs @ Ys ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_120_suffix__snoc,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y3: A] :
% 2.85/1.57 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 2.85/1.57 = ( ( Xs
% 2.85/1.57 = ( nil @ A ) )
% 2.85/1.57 | ? [Zs2: list @ A] :
% 2.85/1.57 ( ( Xs
% 2.85/1.57 = ( append @ A @ Zs2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 2.85/1.57 & ( suffix @ A @ Zs2 @ Ys ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_121_list_Ocollapse,axiom,
% 2.85/1.57 ! [A: $tType,List: list @ A] :
% 2.85/1.57 ( ( List
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 2.85/1.57 = List ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_122_hd__Cons__tl,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A] :
% 2.85/1.57 ( ( Xs
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 2.85/1.57 = Xs ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_123_rs__def,axiom,
% 2.85/1.57 ( rs2
% 2.85/1.57 = ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_124_old_Oempty__path2,axiom,
% 2.85/1.57 ! [N: node,G2: g] :
% 2.85/1.57 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.85/1.57 => ( ( invar @ G2 )
% 2.85/1.57 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_125_old_OCons__path2,axiom,
% 2.85/1.57 ! [G2: g,N: node,Ns: list @ node,M: node,N2: node] :
% 2.85/1.57 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.85/1.57 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 2.85/1.57 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns ) @ M ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_126_list_Odistinct_I1_J,axiom,
% 2.85/1.57 ! [A: $tType,X21: A,X22: list @ A] :
% 2.85/1.57 ( ( nil @ A )
% 2.85/1.57 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_127_neq__NilE,axiom,
% 2.85/1.57 ! [A: $tType,L: list @ A] :
% 2.85/1.57 ( ( L
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ~ ! [X2: A,Xs2: list @ A] :
% 2.85/1.57 ( L
% 2.85/1.57 != ( cons @ A @ X2 @ Xs2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_128_list_OdiscI,axiom,
% 2.85/1.57 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.85/1.57 ( ( List
% 2.85/1.57 = ( cons @ A @ X21 @ X22 ) )
% 2.85/1.57 => ( List
% 2.85/1.57 != ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_129_revg_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.85/1.57 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.85/1.57 => ( ! [A4: A,As: list @ A,B3: list @ A] :
% 2.85/1.57 ( ( P @ As @ ( cons @ A @ A4 @ B3 ) )
% 2.85/1.57 => ( P @ ( cons @ A @ A4 @ As ) @ B3 ) )
% 2.85/1.57 => ( P @ A0 @ A1 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_130_zipf_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,C2: $tType,B: $tType,P: ( A > B > C2 ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > C2,A1: list @ A,A22: list @ B] :
% 2.85/1.57 ( ! [F2: A > B > C2] : ( P @ F2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.85/1.57 => ( ! [F2: A > B > C2,A4: A,As: list @ A,B3: B,Bs: list @ B] :
% 2.85/1.57 ( ( P @ F2 @ As @ Bs )
% 2.85/1.57 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B @ B3 @ Bs ) ) )
% 2.85/1.57 => ( ! [A4: A > B > C2,V2: A,Va: list @ A] : ( P @ A4 @ ( cons @ A @ V2 @ Va ) @ ( nil @ B ) )
% 2.85/1.57 => ( ! [A4: A > B > C2,V2: B,Va: list @ B] : ( P @ A4 @ ( nil @ A ) @ ( cons @ B @ V2 @ Va ) )
% 2.85/1.57 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_131_list_Oexhaust,axiom,
% 2.85/1.57 ! [A: $tType,Y3: list @ A] :
% 2.85/1.57 ( ( Y3
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ~ ! [X212: A,X222: list @ A] :
% 2.85/1.57 ( Y3
% 2.85/1.57 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_132_list_Oinducts,axiom,
% 2.85/1.57 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.85/1.57 ( ( P @ ( nil @ A ) )
% 2.85/1.57 => ( ! [X1: A,X23: list @ A] :
% 2.85/1.57 ( ( P @ X23 )
% 2.85/1.57 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 2.85/1.57 => ( P @ List ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_133_neq__Nil__conv,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A] :
% 2.85/1.57 ( ( Xs
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 = ( ? [Y2: A,Ys2: list @ A] :
% 2.85/1.57 ( Xs
% 2.85/1.57 = ( cons @ A @ Y2 @ Ys2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_134_list__induct2_H,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.85/1.57 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.85/1.57 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B ) )
% 2.85/1.57 => ( ! [Y4: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys3 ) )
% 2.85/1.57 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 2.85/1.57 ( ( P @ Xs2 @ Ys3 )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) )
% 2.85/1.57 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_135_splice_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.85/1.57 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.85/1.57 => ( ! [X2: A,Xs2: list @ A,Ys3: list @ A] :
% 2.85/1.57 ( ( P @ Ys3 @ Xs2 )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ Ys3 ) )
% 2.85/1.57 => ( P @ A0 @ A1 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_136_induct__list012,axiom,
% 2.85/1.57 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.85/1.57 ( ( P @ ( nil @ A ) )
% 2.85/1.57 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.85/1.57 => ( ! [X2: A,Y4: A,Zs3: list @ A] :
% 2.85/1.57 ( ( P @ Zs3 )
% 2.85/1.57 => ( ( P @ ( cons @ A @ Y4 @ Zs3 ) )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Zs3 ) ) ) ) )
% 2.85/1.57 => ( P @ Xs ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_137_min__list_Ocases,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ord @ A )
% 2.85/1.57 => ! [X: list @ A] :
% 2.85/1.57 ( ! [X2: A,Xs2: list @ A] :
% 2.85/1.57 ( X
% 2.85/1.57 != ( cons @ A @ X2 @ Xs2 ) )
% 2.85/1.57 => ( X
% 2.85/1.57 = ( nil @ A ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_138_suffix__Cons,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Y3: A,Ys: list @ A] :
% 2.85/1.57 ( ( suffix @ A @ Xs @ ( cons @ A @ Y3 @ Ys ) )
% 2.85/1.57 = ( ( Xs
% 2.85/1.57 = ( cons @ A @ Y3 @ Ys ) )
% 2.85/1.57 | ( suffix @ A @ Xs @ Ys ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_139_Cons__eq__appendI,axiom,
% 2.85/1.57 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.85/1.57 ( ( ( cons @ A @ X @ Xs1 )
% 2.85/1.57 = Ys )
% 2.85/1.57 => ( ( Xs
% 2.85/1.57 = ( append @ A @ Xs1 @ Zs ) )
% 2.85/1.57 => ( ( cons @ A @ X @ Xs )
% 2.85/1.57 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_140_min__list_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( ord @ A )
% 2.85/1.57 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.85/1.57 ( ! [X2: A,Xs2: list @ A] :
% 2.85/1.57 ( ! [X213: A,X223: list @ A] :
% 2.85/1.57 ( ( Xs2
% 2.85/1.57 = ( cons @ A @ X213 @ X223 ) )
% 2.85/1.57 => ( P @ Xs2 ) )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.85/1.57 => ( ( P @ ( nil @ A ) )
% 2.85/1.57 => ( P @ A0 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_141_shuffles_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.85/1.57 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.85/1.57 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 2.85/1.57 => ( ! [X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 2.85/1.57 ( ( P @ Xs2 @ ( cons @ A @ Y4 @ Ys3 ) )
% 2.85/1.57 => ( ( P @ ( cons @ A @ X2 @ Xs2 ) @ Ys3 )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) )
% 2.85/1.57 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_142_transpose_Ocases,axiom,
% 2.85/1.57 ! [A: $tType,X: list @ ( list @ A )] :
% 2.85/1.57 ( ( X
% 2.85/1.57 != ( nil @ ( list @ A ) ) )
% 2.85/1.57 => ( ! [Xss: list @ ( list @ A )] :
% 2.85/1.57 ( X
% 2.85/1.57 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.85/1.57 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.85/1.57 ( X
% 2.85/1.57 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_143_suffix__ConsD,axiom,
% 2.85/1.57 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.85/1.57 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_144_suffix__ConsI,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y3: A] :
% 2.85/1.57 ( ( suffix @ A @ Xs @ Ys )
% 2.85/1.57 => ( suffix @ A @ Xs @ ( cons @ A @ Y3 @ Ys ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_145_list__2pre__induct,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,W1: list @ A,W2: list @ B] :
% 2.85/1.57 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.85/1.57 => ( ! [E4: A,W12: list @ A,W22: list @ B] :
% 2.85/1.57 ( ( P @ W12 @ W22 )
% 2.85/1.57 => ( P @ ( cons @ A @ E4 @ W12 ) @ W22 ) )
% 2.85/1.57 => ( ! [E4: B,W13: list @ A,W23: list @ B] :
% 2.85/1.57 ( ( P @ W13 @ W23 )
% 2.85/1.57 => ( P @ W13 @ ( cons @ B @ E4 @ W23 ) ) )
% 2.85/1.57 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_146_suffix__ConsD2,axiom,
% 2.85/1.57 ! [A: $tType,X: A,Xs: list @ A,Y3: A,Ys: list @ A] :
% 2.85/1.57 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y3 @ Ys ) )
% 2.85/1.57 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_147_remdups__adj_Ocases,axiom,
% 2.85/1.57 ! [A: $tType,X: list @ A] :
% 2.85/1.57 ( ( X
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ! [X2: A] :
% 2.85/1.57 ( X
% 2.85/1.57 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.85/1.57 => ~ ! [X2: A,Y4: A,Xs2: list @ A] :
% 2.85/1.57 ( X
% 2.85/1.57 != ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_148_sorted__wrt_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.85/1.57 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 2.85/1.57 => ( ! [P2: A > A > $o,X2: A,Ys3: list @ A] :
% 2.85/1.57 ( ( P @ P2 @ Ys3 )
% 2.85/1.57 => ( P @ P2 @ ( cons @ A @ X2 @ Ys3 ) ) )
% 2.85/1.57 => ( P @ A0 @ A1 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_149_append__Cons,axiom,
% 2.85/1.57 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.85/1.57 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.85/1.57 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_150_remdups__adj_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.85/1.57 ( ( P @ ( nil @ A ) )
% 2.85/1.57 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.85/1.57 => ( ! [X2: A,Y4: A,Xs2: list @ A] :
% 2.85/1.57 ( ( ( X2 = Y4 )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.85/1.57 => ( ( ( X2 != Y4 )
% 2.85/1.57 => ( P @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 2.85/1.57 => ( P @ A0 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_151_list__induct__first2,axiom,
% 2.85/1.57 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.85/1.57 ( ( P @ ( nil @ A ) )
% 2.85/1.57 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.85/1.57 => ( ! [X1: A,X23: A,Xs2: list @ A] :
% 2.85/1.57 ( ( P @ Xs2 )
% 2.85/1.57 => ( P @ ( cons @ A @ X1 @ ( cons @ A @ X23 @ Xs2 ) ) ) )
% 2.85/1.57 => ( P @ Xs ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_152_list__match__lel__lel,axiom,
% 2.85/1.57 ! [A: $tType,C1: list @ A,Qs: A,C22: list @ A,C12: list @ A,Qs2: A,C23: list @ A] :
% 2.85/1.57 ( ( ( append @ A @ C1 @ ( cons @ A @ Qs @ C22 ) )
% 2.85/1.57 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C23 ) ) )
% 2.85/1.57 => ( ! [C21: list @ A] :
% 2.85/1.57 ( ( C1
% 2.85/1.57 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C21 ) ) )
% 2.85/1.57 => ( C23
% 2.85/1.57 != ( append @ A @ C21 @ ( cons @ A @ Qs @ C22 ) ) ) )
% 2.85/1.57 => ( ( ( C12 = C1 )
% 2.85/1.57 => ( ( Qs2 = Qs )
% 2.85/1.57 => ( C23 != C22 ) ) )
% 2.85/1.57 => ~ ! [C212: list @ A] :
% 2.85/1.57 ( ( C12
% 2.85/1.57 = ( append @ A @ C1 @ ( cons @ A @ Qs @ C212 ) ) )
% 2.85/1.57 => ( C22
% 2.85/1.57 != ( append @ A @ C212 @ ( cons @ A @ Qs2 @ C23 ) ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_153_arg__min__list_Oinduct,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( linorder @ B )
% 2.85/1.57 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 2.85/1.57 ( ! [F2: A > B,X2: A] : ( P @ F2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.85/1.57 => ( ! [F2: A > B,X2: A,Y4: A,Zs3: list @ A] :
% 2.85/1.57 ( ( P @ F2 @ ( cons @ A @ Y4 @ Zs3 ) )
% 2.85/1.57 => ( P @ F2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Zs3 ) ) ) )
% 2.85/1.57 => ( ! [A4: A > B] : ( P @ A4 @ ( nil @ A ) )
% 2.85/1.57 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_154_successively_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.85/1.57 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 2.85/1.57 => ( ! [P2: A > A > $o,X2: A] : ( P @ P2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.85/1.57 => ( ! [P2: A > A > $o,X2: A,Y4: A,Xs2: list @ A] :
% 2.85/1.57 ( ( P @ P2 @ ( cons @ A @ Y4 @ Xs2 ) )
% 2.85/1.57 => ( P @ P2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) )
% 2.85/1.57 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_155_list__all__zip_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType,P: ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > $o,A1: list @ A,A22: list @ B] :
% 2.85/1.57 ( ! [P2: A > B > $o] : ( P @ P2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.85/1.57 => ( ! [P2: A > B > $o,A4: A,As: list @ A,B3: B,Bs: list @ B] :
% 2.85/1.57 ( ( P @ P2 @ As @ Bs )
% 2.85/1.57 => ( P @ P2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B @ B3 @ Bs ) ) )
% 2.85/1.57 => ( ! [P2: A > B > $o,V2: A,Va: list @ A] : ( P @ P2 @ ( cons @ A @ V2 @ Va ) @ ( nil @ B ) )
% 2.85/1.57 => ( ! [P2: A > B > $o,V2: B,Va: list @ B] : ( P @ P2 @ ( nil @ A ) @ ( cons @ B @ V2 @ Va ) )
% 2.85/1.57 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_156_list__nonempty__induct,axiom,
% 2.85/1.57 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.85/1.57 ( ( Xs
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.85/1.57 => ( ! [X2: A,Xs2: list @ A] :
% 2.85/1.57 ( ( Xs2
% 2.85/1.57 != ( nil @ A ) )
% 2.85/1.57 => ( ( P @ Xs2 )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 2.85/1.57 => ( P @ Xs ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_157_map__tailrec__rev_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.85/1.57 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 2.85/1.57 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.85/1.57 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 2.85/1.57 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.85/1.57 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_158_mergesort__by__rel__merge_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.85/1.57 ( ! [R: A > A > $o,X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 2.85/1.57 ( ( ( R @ X2 @ Y4 )
% 2.85/1.57 => ( P @ R @ Xs2 @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.85/1.57 => ( ( ~ ( R @ X2 @ Y4 )
% 2.85/1.57 => ( P @ R @ ( cons @ A @ X2 @ Xs2 ) @ Ys3 ) )
% 2.85/1.57 => ( P @ R @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) )
% 2.85/1.57 => ( ! [R: A > A > $o,Xs2: list @ A] : ( P @ R @ Xs2 @ ( nil @ A ) )
% 2.85/1.57 => ( ! [R: A > A > $o,V2: A,Va: list @ A] : ( P @ R @ ( nil @ A ) @ ( cons @ A @ V2 @ Va ) )
% 2.85/1.57 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_159_mergesort__by__rel__merge__induct,axiom,
% 2.85/1.57 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,R2: A > B > $o,Xs: list @ A,Ys: list @ B] :
% 2.85/1.57 ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ B ) )
% 2.85/1.57 => ( ! [X_1: list @ B] : ( P @ ( nil @ A ) @ X_1 )
% 2.85/1.57 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 2.85/1.57 ( ( R2 @ X2 @ Y4 )
% 2.85/1.57 => ( ( P @ Xs2 @ ( cons @ B @ Y4 @ Ys3 ) )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) ) )
% 2.85/1.57 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 2.85/1.57 ( ~ ( R2 @ X2 @ Y4 )
% 2.85/1.57 => ( ( P @ ( cons @ A @ X2 @ Xs2 ) @ Ys3 )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) ) )
% 2.85/1.57 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_160_longest__common__prefix_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.85/1.57 ( ! [X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 2.85/1.57 ( ( ( X2 = Y4 )
% 2.85/1.57 => ( P @ Xs2 @ Ys3 ) )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.85/1.57 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.85/1.57 => ( ! [Uu: list @ A] : ( P @ Uu @ ( nil @ A ) )
% 2.85/1.57 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_161_strict__sorted_Oinduct,axiom,
% 2.85/1.57 ! [A: $tType] :
% 2.85/1.57 ( ( linorder @ A )
% 2.85/1.57 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.85/1.57 ( ( P @ ( nil @ A ) )
% 2.85/1.57 => ( ! [X2: A,Ys3: list @ A] :
% 2.85/1.57 ( ( P @ Ys3 )
% 2.85/1.57 => ( P @ ( cons @ A @ X2 @ Ys3 ) ) )
% 2.85/1.57 => ( P @ A0 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_162_list_Osel_I1_J,axiom,
% 2.85/1.57 ! [A: $tType,X21: A,X22: list @ A] :
% 2.85/1.57 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 2.85/1.57 = X21 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_163_list_Osel_I3_J,axiom,
% 2.85/1.57 ! [A: $tType,X21: A,X22: list @ A] :
% 2.85/1.57 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 2.85/1.57 = X22 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_164_list__tail__coinc,axiom,
% 2.85/1.57 ! [A: $tType,N1: A,R1: list @ A,N22: A,R22: list @ A] :
% 2.85/1.57 ( ( ( cons @ A @ N1 @ R1 )
% 2.85/1.57 = ( cons @ A @ N22 @ R22 ) )
% 2.85/1.57 => ( ( N1 = N22 )
% 2.85/1.57 & ( R1 = R22 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_165_not__Cons__self2,axiom,
% 2.85/1.57 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.57 ( ( cons @ A @ X @ Xs )
% 2.85/1.57 != Xs ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_166_distinct__length__2__or__more,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,B2: A,Xs: list @ A] :
% 2.85/1.57 ( ( distinct @ A @ ( cons @ A @ A2 @ ( cons @ A @ B2 @ Xs ) ) )
% 2.85/1.57 = ( ( A2 != B2 )
% 2.85/1.57 & ( distinct @ A @ ( cons @ A @ A2 @ Xs ) )
% 2.85/1.57 & ( distinct @ A @ ( cons @ A @ B2 @ Xs ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_167_list_Oset__cases,axiom,
% 2.85/1.57 ! [A: $tType,E: A,A2: list @ A] :
% 2.85/1.57 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 2.85/1.58 => ( ! [Z2: list @ A] :
% 2.85/1.58 ( A2
% 2.85/1.58 != ( cons @ A @ E @ Z2 ) )
% 2.85/1.58 => ~ ! [Z1: A,Z2: list @ A] :
% 2.85/1.58 ( ( A2
% 2.85/1.58 = ( cons @ A @ Z1 @ Z2 ) )
% 2.85/1.58 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_168_set__ConsD,axiom,
% 2.85/1.58 ! [A: $tType,Y3: A,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( member @ A @ Y3 @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 2.85/1.58 => ( ( Y3 = X )
% 2.85/1.58 | ( member @ A @ Y3 @ ( set2 @ A @ Xs ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_169_list_Oset__intros_I1_J,axiom,
% 2.85/1.58 ! [A: $tType,X21: A,X22: list @ A] : ( member @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_170_list_Oset__intros_I2_J,axiom,
% 2.85/1.58 ! [A: $tType,Y3: A,X22: list @ A,X21: A] :
% 2.85/1.58 ( ( member @ A @ Y3 @ ( set2 @ A @ X22 ) )
% 2.85/1.58 => ( member @ A @ Y3 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_171_list__append__eq__Cons__cases,axiom,
% 2.85/1.58 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( ( append @ A @ Ys @ Zs )
% 2.85/1.58 = ( cons @ A @ X @ Xs ) )
% 2.85/1.58 => ( ( ( Ys
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 => ( Zs
% 2.85/1.58 != ( cons @ A @ X @ Xs ) ) )
% 2.85/1.58 => ~ ! [Ys4: list @ A] :
% 2.85/1.58 ( ( Ys
% 2.85/1.58 = ( cons @ A @ X @ Ys4 ) )
% 2.85/1.58 => ( ( append @ A @ Ys4 @ Zs )
% 2.85/1.58 != Xs ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_172_list__Cons__eq__append__cases,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.85/1.58 ( ( ( cons @ A @ X @ Xs )
% 2.85/1.58 = ( append @ A @ Ys @ Zs ) )
% 2.85/1.58 => ( ( ( Ys
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 => ( Zs
% 2.85/1.58 != ( cons @ A @ X @ Xs ) ) )
% 2.85/1.58 => ~ ! [Ys4: list @ A] :
% 2.85/1.58 ( ( Ys
% 2.85/1.58 = ( cons @ A @ X @ Ys4 ) )
% 2.85/1.58 => ( ( append @ A @ Ys4 @ Zs )
% 2.85/1.58 != Xs ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_173_rev__nonempty__induct2_H,axiom,
% 2.85/1.58 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( Ys
% 2.85/1.58 != ( nil @ B ) )
% 2.85/1.58 => ( ! [X2: A,Y4: B] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) @ ( cons @ B @ Y4 @ ( nil @ B ) ) )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A,Y4: B] :
% 2.85/1.58 ( ( Xs2
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) )
% 2.85/1.58 => ( ! [X2: A,Y4: B,Ys3: list @ B] :
% 2.85/1.58 ( ( Ys3
% 2.85/1.58 != ( nil @ B ) )
% 2.85/1.58 => ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) ) )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 2.85/1.58 ( ( P @ Xs2 @ Ys3 )
% 2.85/1.58 => ( ( Xs2
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( Ys3
% 2.85/1.58 != ( nil @ B ) )
% 2.85/1.58 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) ) ) ) )
% 2.85/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_174_rev__nonempty__induct,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A] :
% 2.85/1.58 ( ( Xs2
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( P @ Xs2 )
% 2.85/1.58 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ) )
% 2.85/1.58 => ( P @ Xs ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_175_append__eq__Cons__conv,axiom,
% 2.85/1.58 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( ( append @ A @ Ys @ Zs )
% 2.85/1.58 = ( cons @ A @ X @ Xs ) )
% 2.85/1.58 = ( ( ( Ys
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 & ( Zs
% 2.85/1.58 = ( cons @ A @ X @ Xs ) ) )
% 2.85/1.58 | ? [Ys5: list @ A] :
% 2.85/1.58 ( ( Ys
% 2.85/1.58 = ( cons @ A @ X @ Ys5 ) )
% 2.85/1.58 & ( ( append @ A @ Ys5 @ Zs )
% 2.85/1.58 = Xs ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_176_Cons__eq__append__conv,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.85/1.58 ( ( ( cons @ A @ X @ Xs )
% 2.85/1.58 = ( append @ A @ Ys @ Zs ) )
% 2.85/1.58 = ( ( ( Ys
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 & ( ( cons @ A @ X @ Xs )
% 2.85/1.58 = Zs ) )
% 2.85/1.58 | ? [Ys5: list @ A] :
% 2.85/1.58 ( ( ( cons @ A @ X @ Ys5 )
% 2.85/1.58 = Ys )
% 2.85/1.58 & ( Xs
% 2.85/1.58 = ( append @ A @ Ys5 @ Zs ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_177_neq__Nil__rev__conv,axiom,
% 2.85/1.58 ! [A: $tType,L: list @ A] :
% 2.85/1.58 ( ( L
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 = ( ? [Xs3: list @ A,X3: A] :
% 2.85/1.58 ( L
% 2.85/1.58 = ( append @ A @ Xs3 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_178_rev__induct2_H,axiom,
% 2.85/1.58 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.85/1.58 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( nil @ B ) )
% 2.85/1.58 => ( ! [Y4: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 2.85/1.58 ( ( P @ Xs2 @ Ys3 )
% 2.85/1.58 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y4 @ ( nil @ B ) ) ) ) )
% 2.85/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_179_neq__Nil__revE,axiom,
% 2.85/1.58 ! [A: $tType,L: list @ A] :
% 2.85/1.58 ( ( L
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ~ ! [Ll: list @ A,E4: A] :
% 2.85/1.58 ( L
% 2.85/1.58 != ( append @ A @ Ll @ ( cons @ A @ E4 @ ( nil @ A ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_180_rev__exhaust,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ~ ! [Ys3: list @ A,Y4: A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 != ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_181_rev__induct,axiom,
% 2.85/1.58 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.85/1.58 ( ( P @ ( nil @ A ) )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A] :
% 2.85/1.58 ( ( P @ Xs2 )
% 2.85/1.58 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) )
% 2.85/1.58 => ( P @ Xs ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_182_split__list,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 => ? [Ys3: list @ A,Zs3: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_183_split__list__last,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 => ? [Ys3: list @ A,Zs3: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.85/1.58 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_184_split__list__prop,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.85/1.58 ( ? [X4: A] :
% 2.85/1.58 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( P @ X4 ) )
% 2.85/1.58 => ? [Ys3: list @ A,X2: A] :
% 2.85/1.58 ( ? [Zs3: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 2.85/1.58 & ( P @ X2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_185_xy__in__set__cases,axiom,
% 2.85/1.58 ! [A: $tType,X: A,L: list @ A,Y3: A] :
% 2.85/1.58 ( ( member @ A @ X @ ( set2 @ A @ L ) )
% 2.85/1.58 => ( ( member @ A @ Y3 @ ( set2 @ A @ L ) )
% 2.85/1.58 => ( ( ( X = Y3 )
% 2.85/1.58 => ! [L12: list @ A,L22: list @ A] :
% 2.85/1.58 ( L
% 2.85/1.58 != ( append @ A @ L12 @ ( cons @ A @ Y3 @ L22 ) ) ) )
% 2.85/1.58 => ( ( ( X != Y3 )
% 2.85/1.58 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 2.85/1.58 ( L
% 2.85/1.58 != ( append @ A @ L12 @ ( cons @ A @ X @ ( append @ A @ L22 @ ( cons @ A @ Y3 @ L3 ) ) ) ) ) )
% 2.85/1.58 => ~ ( ( X != Y3 )
% 2.85/1.58 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 2.85/1.58 ( L
% 2.85/1.58 != ( append @ A @ L12 @ ( cons @ A @ Y3 @ ( append @ A @ L22 @ ( cons @ A @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_186_split__list__first,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 => ? [Ys3: list @ A,Zs3: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.85/1.58 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_187_split__list__propE,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.85/1.58 ( ? [X4: A] :
% 2.85/1.58 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( P @ X4 ) )
% 2.85/1.58 => ~ ! [Ys3: list @ A,X2: A] :
% 2.85/1.58 ( ? [Zs3: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 2.85/1.58 => ~ ( P @ X2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_188_append__Cons__eq__iff,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Xs4: list @ A,Ys6: list @ A] :
% 2.85/1.58 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 => ( ~ ( member @ A @ X @ ( set2 @ A @ Ys ) )
% 2.85/1.58 => ( ( ( append @ A @ Xs @ ( cons @ A @ X @ Ys ) )
% 2.85/1.58 = ( append @ A @ Xs4 @ ( cons @ A @ X @ Ys6 ) ) )
% 2.85/1.58 = ( ( Xs = Xs4 )
% 2.85/1.58 & ( Ys = Ys6 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_189_in__set__conv__decomp,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 = ( ? [Ys2: list @ A,Zs2: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_190_in__set__list__format,axiom,
% 2.85/1.58 ! [A: $tType,E: A,L: list @ A] :
% 2.85/1.58 ( ( member @ A @ E @ ( set2 @ A @ L ) )
% 2.85/1.58 => ~ ! [L12: list @ A,L22: list @ A] :
% 2.85/1.58 ( L
% 2.85/1.58 != ( append @ A @ L12 @ ( cons @ A @ E @ L22 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_191_split__list__last__prop,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.85/1.58 ( ? [X4: A] :
% 2.85/1.58 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( P @ X4 ) )
% 2.85/1.58 => ? [Ys3: list @ A,X2: A,Zs3: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 2.85/1.58 & ( P @ X2 )
% 2.85/1.58 & ! [Xa: A] :
% 2.85/1.58 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 2.85/1.58 => ~ ( P @ Xa ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_192_split__list__first__prop,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.85/1.58 ( ? [X4: A] :
% 2.85/1.58 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( P @ X4 ) )
% 2.85/1.58 => ? [Ys3: list @ A,X2: A] :
% 2.85/1.58 ( ? [Zs3: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 2.85/1.58 & ( P @ X2 )
% 2.85/1.58 & ! [Xa: A] :
% 2.85/1.58 ( ( member @ A @ Xa @ ( set2 @ A @ Ys3 ) )
% 2.85/1.58 => ~ ( P @ Xa ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_193_split__list__last__propE,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.85/1.58 ( ? [X4: A] :
% 2.85/1.58 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( P @ X4 ) )
% 2.85/1.58 => ~ ! [Ys3: list @ A,X2: A,Zs3: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 2.85/1.58 => ( ( P @ X2 )
% 2.85/1.58 => ~ ! [Xa: A] :
% 2.85/1.58 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 2.85/1.58 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_194_split__list__first__propE,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.85/1.58 ( ? [X4: A] :
% 2.85/1.58 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( P @ X4 ) )
% 2.85/1.58 => ~ ! [Ys3: list @ A,X2: A] :
% 2.85/1.58 ( ? [Zs3: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs3 ) ) )
% 2.85/1.58 => ( ( P @ X2 )
% 2.85/1.58 => ~ ! [Xa: A] :
% 2.85/1.58 ( ( member @ A @ Xa @ ( set2 @ A @ Ys3 ) )
% 2.85/1.58 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_195_in__set__conv__decomp__last,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 = ( ? [Ys2: list @ A,Zs2: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.85/1.58 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_196_in__set__conv__decomp__first,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 = ( ? [Ys2: list @ A,Zs2: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.85/1.58 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_197_split__list__last__prop__iff,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.85/1.58 ( ( ? [X3: A] :
% 2.85/1.58 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( P @ X3 ) ) )
% 2.85/1.58 = ( ? [Ys2: list @ A,X3: A,Zs2: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 2.85/1.58 & ( P @ X3 )
% 2.85/1.58 & ! [Y2: A] :
% 2.85/1.58 ( ( member @ A @ Y2 @ ( set2 @ A @ Zs2 ) )
% 2.85/1.58 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_198_split__list__first__prop__iff,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.85/1.58 ( ( ? [X3: A] :
% 2.85/1.58 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( P @ X3 ) ) )
% 2.85/1.58 = ( ? [Ys2: list @ A,X3: A] :
% 2.85/1.58 ( ? [Zs2: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 2.85/1.58 & ( P @ X3 )
% 2.85/1.58 & ! [Y2: A] :
% 2.85/1.58 ( ( member @ A @ Y2 @ ( set2 @ A @ Ys2 ) )
% 2.85/1.58 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_199_distinct__singleton,axiom,
% 2.85/1.58 ! [A: $tType,X: A] : ( distinct @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_200_distinct_Osimps_I2_J,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( distinct @ A @ ( cons @ A @ X @ Xs ) )
% 2.85/1.58 = ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 & ( distinct @ A @ Xs ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_201_distinct__match,axiom,
% 2.85/1.58 ! [A: $tType,Al: list @ A,E: A,Bl: list @ A,Al2: list @ A,Bl2: list @ A] :
% 2.85/1.58 ( ( distinct @ A @ ( append @ A @ Al @ ( cons @ A @ E @ Bl ) ) )
% 2.85/1.58 => ( ( ( append @ A @ Al @ ( cons @ A @ E @ Bl ) )
% 2.85/1.58 = ( append @ A @ Al2 @ ( cons @ A @ E @ Bl2 ) ) )
% 2.85/1.58 = ( ( Al = Al2 )
% 2.85/1.58 & ( Bl = Bl2 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_202_Nil__tl,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] :
% 2.85/1.58 ( ( ( nil @ A )
% 2.85/1.58 = ( tl @ A @ Xs ) )
% 2.85/1.58 = ( ( Xs
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 | ? [X3: A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_203_tl__Nil,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] :
% 2.85/1.58 ( ( ( tl @ A @ Xs )
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 = ( ( Xs
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 | ? [X3: A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_204_tl__obtain__elem,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( ( tl @ A @ Xs )
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 => ~ ! [E4: A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 != ( cons @ A @ E4 @ ( nil @ A ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_205_not__distinct__decomp,axiom,
% 2.85/1.58 ! [A: $tType,Ws: list @ A] :
% 2.85/1.58 ( ~ ( distinct @ A @ Ws )
% 2.85/1.58 => ? [Xs2: list @ A,Ys3: list @ A,Zs3: list @ A,Y4: A] :
% 2.85/1.58 ( Ws
% 2.85/1.58 = ( append @ A @ Xs2 @ ( append @ A @ ( cons @ A @ Y4 @ ( nil @ A ) ) @ ( append @ A @ Ys3 @ ( append @ A @ ( cons @ A @ Y4 @ ( nil @ A ) ) @ Zs3 ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_206_not__distinct__conv__prefix,axiom,
% 2.85/1.58 ! [A: $tType,As2: list @ A] :
% 2.85/1.58 ( ( ~ ( distinct @ A @ As2 ) )
% 2.85/1.58 = ( ? [Xs3: list @ A,Y2: A,Ys2: list @ A] :
% 2.85/1.58 ( ( member @ A @ Y2 @ ( set2 @ A @ Xs3 ) )
% 2.85/1.58 & ( distinct @ A @ Xs3 )
% 2.85/1.58 & ( As2
% 2.85/1.58 = ( append @ A @ Xs3 @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_207_not__suffix__induct,axiom,
% 2.85/1.58 ! [A: $tType,Ps: list @ A,Ls: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.85/1.58 ( ~ ( suffix @ A @ Ps @ Ls )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( nil @ A ) )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 2.85/1.58 ( ( X2 != Y4 )
% 2.85/1.58 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) )
% 2.85/1.58 => ( ! [X2: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 2.85/1.58 ( ( X2 = Y4 )
% 2.85/1.58 => ( ~ ( suffix @ A @ Xs2 @ Ys3 )
% 2.85/1.58 => ( ( P @ Xs2 @ Ys3 )
% 2.85/1.58 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) @ ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ) )
% 2.85/1.58 => ( P @ Ps @ Ls ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_208_not__suffix__cases,axiom,
% 2.85/1.58 ! [A: $tType,Ps: list @ A,Ls: list @ A] :
% 2.85/1.58 ( ~ ( suffix @ A @ Ps @ Ls )
% 2.85/1.58 => ( ( ( Ps
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( Ls
% 2.85/1.58 != ( nil @ A ) ) )
% 2.85/1.58 => ( ! [A4: A,As: list @ A] :
% 2.85/1.58 ( ( Ps
% 2.85/1.58 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 2.85/1.58 => ! [X2: A,Xs2: list @ A] :
% 2.85/1.58 ( ( Ls
% 2.85/1.58 = ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 2.85/1.58 => ( ( X2 = A4 )
% 2.85/1.58 => ( suffix @ A @ As @ Xs2 ) ) ) )
% 2.85/1.58 => ~ ! [A4: A] :
% 2.85/1.58 ( ? [As: list @ A] :
% 2.85/1.58 ( Ps
% 2.85/1.58 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 2.85/1.58 => ! [X2: A] :
% 2.85/1.58 ( ? [Xs2: list @ A] :
% 2.85/1.58 ( Ls
% 2.85/1.58 = ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) )
% 2.85/1.58 => ( X2 = A4 ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_209_list_Oexhaust__sel,axiom,
% 2.85/1.58 ! [A: $tType,List: list @ A] :
% 2.85/1.58 ( ( List
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( List
% 2.85/1.58 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_210_not__distinct__split__distinct,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] :
% 2.85/1.58 ( ~ ( distinct @ A @ Xs )
% 2.85/1.58 => ~ ! [Y4: A,Ys3: list @ A] :
% 2.85/1.58 ( ( distinct @ A @ Ys3 )
% 2.85/1.58 => ( ( member @ A @ Y4 @ ( set2 @ A @ Ys3 ) )
% 2.85/1.58 => ! [Zs3: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 != ( append @ A @ Ys3 @ ( append @ A @ ( cons @ A @ Y4 @ ( nil @ A ) ) @ Zs3 ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_211_append__eq__append__conv2,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 2.85/1.58 ( ( ( append @ A @ Xs @ Ys )
% 2.85/1.58 = ( append @ A @ Zs @ Ts ) )
% 2.85/1.58 = ( ? [Us: list @ A] :
% 2.85/1.58 ( ( ( Xs
% 2.85/1.58 = ( append @ A @ Zs @ Us ) )
% 2.85/1.58 & ( ( append @ A @ Us @ Ys )
% 2.85/1.58 = Ts ) )
% 2.85/1.58 | ( ( ( append @ A @ Xs @ Us )
% 2.85/1.58 = Zs )
% 2.85/1.58 & ( Ys
% 2.85/1.58 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_212_append__eq__appendI,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us2: list @ A] :
% 2.85/1.58 ( ( ( append @ A @ Xs @ Xs1 )
% 2.85/1.58 = Zs )
% 2.85/1.58 => ( ( Ys
% 2.85/1.58 = ( append @ A @ Xs1 @ Us2 ) )
% 2.85/1.58 => ( ( append @ A @ Xs @ Ys )
% 2.85/1.58 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_213_suffix__order_Odual__order_Oantisym,axiom,
% 2.85/1.58 ! [A: $tType,B2: list @ A,A2: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ B2 @ A2 )
% 2.85/1.58 => ( ( suffix @ A @ A2 @ B2 )
% 2.85/1.58 => ( A2 = B2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_214_suffix__order_Odual__order_Oeq__iff,axiom,
% 2.85/1.58 ! [A: $tType] :
% 2.85/1.58 ( ( ^ [Y5: list @ A,Z: list @ A] : ( Y5 = Z ) )
% 2.85/1.58 = ( ^ [A5: list @ A,B4: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ B4 @ A5 )
% 2.85/1.58 & ( suffix @ A @ A5 @ B4 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_215_suffix__order_Odual__order_Otrans,axiom,
% 2.85/1.58 ! [A: $tType,B2: list @ A,A2: list @ A,C: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ B2 @ A2 )
% 2.85/1.58 => ( ( suffix @ A @ C @ B2 )
% 2.85/1.58 => ( suffix @ A @ C @ A2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_216_suffix__order_Oord__le__eq__trans,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ A2 @ B2 )
% 2.85/1.58 => ( ( B2 = C )
% 2.85/1.58 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_217_suffix__order_Oord__eq__le__trans,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.85/1.58 ( ( A2 = B2 )
% 2.85/1.58 => ( ( suffix @ A @ B2 @ C )
% 2.85/1.58 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_218_suffix__order_Oorder_Oantisym,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A,B2: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ A2 @ B2 )
% 2.85/1.58 => ( ( suffix @ A @ B2 @ A2 )
% 2.85/1.58 => ( A2 = B2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_219_suffix__order_Oorder_Oeq__iff,axiom,
% 2.85/1.58 ! [A: $tType] :
% 2.85/1.58 ( ( ^ [Y5: list @ A,Z: list @ A] : ( Y5 = Z ) )
% 2.85/1.58 = ( ^ [A5: list @ A,B4: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ A5 @ B4 )
% 2.85/1.58 & ( suffix @ A @ B4 @ A5 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_220_suffix__order_Oantisym__conv,axiom,
% 2.85/1.58 ! [A: $tType,Y3: list @ A,X: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ Y3 @ X )
% 2.85/1.58 => ( ( suffix @ A @ X @ Y3 )
% 2.85/1.58 = ( X = Y3 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_221_suffix__order_Oorder__trans,axiom,
% 2.85/1.58 ! [A: $tType,X: list @ A,Y3: list @ A,Z3: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ X @ Y3 )
% 2.85/1.58 => ( ( suffix @ A @ Y3 @ Z3 )
% 2.85/1.58 => ( suffix @ A @ X @ Z3 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_222_suffix__order_Oorder_Otrans,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ A2 @ B2 )
% 2.85/1.58 => ( ( suffix @ A @ B2 @ C )
% 2.85/1.58 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_223_suffix__order_Oeq__refl,axiom,
% 2.85/1.58 ! [A: $tType,X: list @ A,Y3: list @ A] :
% 2.85/1.58 ( ( X = Y3 )
% 2.85/1.58 => ( suffix @ A @ X @ Y3 ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_224_suffix__order_Oantisym,axiom,
% 2.85/1.58 ! [A: $tType,X: list @ A,Y3: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ X @ Y3 )
% 2.85/1.58 => ( ( suffix @ A @ Y3 @ X )
% 2.85/1.58 => ( X = Y3 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_225_suffix__order_Oeq__iff,axiom,
% 2.85/1.58 ! [A: $tType] :
% 2.85/1.58 ( ( ^ [Y5: list @ A,Z: list @ A] : ( Y5 = Z ) )
% 2.85/1.58 = ( ^ [X3: list @ A,Y2: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ X3 @ Y2 )
% 2.85/1.58 & ( suffix @ A @ Y2 @ X3 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_226_suffix__same__cases,axiom,
% 2.85/1.58 ! [A: $tType,Xs_1: list @ A,Ys: list @ A,Xs_2: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ Xs_1 @ Ys )
% 2.85/1.58 => ( ( suffix @ A @ Xs_2 @ Ys )
% 2.85/1.58 => ( ( suffix @ A @ Xs_1 @ Xs_2 )
% 2.85/1.58 | ( suffix @ A @ Xs_2 @ Xs_1 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_227_finite__list,axiom,
% 2.85/1.58 ! [A: $tType,A3: set @ A] :
% 2.85/1.58 ( ( finite_finite @ A @ A3 )
% 2.85/1.58 => ? [Xs2: list @ A] :
% 2.85/1.58 ( ( set2 @ A @ Xs2 )
% 2.85/1.58 = A3 ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_228_append_Oleft__neutral,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A] :
% 2.85/1.58 ( ( append @ A @ ( nil @ A ) @ A2 )
% 2.85/1.58 = A2 ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_229_append__Nil,axiom,
% 2.85/1.58 ! [A: $tType,Ys: list @ A] :
% 2.85/1.58 ( ( append @ A @ ( nil @ A ) @ Ys )
% 2.85/1.58 = Ys ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_230_eq__Nil__appendI,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.58 ( ( Xs = Ys )
% 2.85/1.58 => ( Xs
% 2.85/1.58 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_231_distinct_Osimps_I1_J,axiom,
% 2.85/1.58 ! [A: $tType] : ( distinct @ A @ ( nil @ A ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_232_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 2.85/1.58 => ( A2
% 2.85/1.58 = ( nil @ A ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_233_suffix__bot_Obot_Oextremum,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A] : ( suffix @ A @ ( nil @ A ) @ A2 ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_234_Nil__suffix,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( nil @ A ) @ Xs ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_235_list_Osel_I2_J,axiom,
% 2.85/1.58 ! [A: $tType] :
% 2.85/1.58 ( ( tl @ A @ ( nil @ A ) )
% 2.85/1.58 = ( nil @ A ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_236_suffix__appendI,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ Xs @ Ys )
% 2.85/1.58 => ( suffix @ A @ Xs @ ( append @ A @ Zs @ Ys ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_237_suffix__appendD,axiom,
% 2.85/1.58 ! [A: $tType,Zs: list @ A,Xs: list @ A,Ys: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ ( append @ A @ Zs @ Xs ) @ Ys )
% 2.85/1.58 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_238_suffix__append,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ Zs ) )
% 2.85/1.58 = ( ( suffix @ A @ Xs @ Zs )
% 2.85/1.58 | ? [Xs5: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Xs5 @ Zs ) )
% 2.85/1.58 & ( suffix @ A @ Xs5 @ Ys ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_239_Sublist_Osuffix__def,axiom,
% 2.85/1.58 ! [A: $tType] :
% 2.85/1.58 ( ( suffix @ A )
% 2.85/1.58 = ( ^ [Xs3: list @ A,Ys2: list @ A] :
% 2.85/1.58 ? [Zs2: list @ A] :
% 2.85/1.58 ( Ys2
% 2.85/1.58 = ( append @ A @ Zs2 @ Xs3 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_240_suffixI,axiom,
% 2.85/1.58 ! [A: $tType,Ys: list @ A,Zs: list @ A,Xs: list @ A] :
% 2.85/1.58 ( ( Ys
% 2.85/1.58 = ( append @ A @ Zs @ Xs ) )
% 2.85/1.58 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_241_suffixE,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.58 ( ( suffix @ A @ Xs @ Ys )
% 2.85/1.58 => ~ ! [Zs3: list @ A] :
% 2.85/1.58 ( Ys
% 2.85/1.58 != ( append @ A @ Zs3 @ Xs ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_242_distinct__suffix,axiom,
% 2.85/1.58 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.85/1.58 ( ( distinct @ A @ Ys )
% 2.85/1.58 => ( ( suffix @ A @ Xs @ Ys )
% 2.85/1.58 => ( distinct @ A @ Xs ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_243_distinct__tl,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] :
% 2.85/1.58 ( ( distinct @ A @ Xs )
% 2.85/1.58 => ( distinct @ A @ ( tl @ A @ Xs ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_244_suffix__tl,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( tl @ A @ Xs ) @ Xs ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_245_finite__distinct__list,axiom,
% 2.85/1.58 ! [A: $tType,A3: set @ A] :
% 2.85/1.58 ( ( finite_finite @ A @ A3 )
% 2.85/1.58 => ? [Xs2: list @ A] :
% 2.85/1.58 ( ( ( set2 @ A @ Xs2 )
% 2.85/1.58 = A3 )
% 2.85/1.58 & ( distinct @ A @ Xs2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_246_list_Oset__sel_I1_J,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A] :
% 2.85/1.58 ( ( A2
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( member @ A @ ( hd @ A @ A2 ) @ ( set2 @ A @ A2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_247_hd__in__set,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( member @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ Xs ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_248_list_Oset__sel_I2_J,axiom,
% 2.85/1.58 ! [A: $tType,A2: list @ A,X: A] :
% 2.85/1.58 ( ( A2
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ A2 ) ) )
% 2.85/1.58 => ( member @ A @ X @ ( set2 @ A @ A2 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_249_longest__common__prefix,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.58 ? [Ps2: list @ A,Xs6: list @ A,Ys4: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 = ( append @ A @ Ps2 @ Xs6 ) )
% 2.85/1.58 & ( Ys
% 2.85/1.58 = ( append @ A @ Ps2 @ Ys4 ) )
% 2.85/1.58 & ( ( Xs6
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 | ( Ys4
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 | ( ( hd @ A @ Xs6 )
% 2.85/1.58 != ( hd @ A @ Ys4 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_250_hd__append,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.85/1.58 ( ( ( Xs
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.85/1.58 = ( hd @ A @ Ys ) ) )
% 2.85/1.58 & ( ( Xs
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.85/1.58 = ( hd @ A @ Xs ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_251_list_Oexpand,axiom,
% 2.85/1.58 ! [A: $tType,List: list @ A,List2: list @ A] :
% 2.85/1.58 ( ( ( List
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 = ( List2
% 2.85/1.58 = ( nil @ A ) ) )
% 2.85/1.58 => ( ( ( List
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( List2
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( ( hd @ A @ List )
% 2.85/1.58 = ( hd @ A @ List2 ) )
% 2.85/1.58 & ( ( tl @ A @ List )
% 2.85/1.58 = ( tl @ A @ List2 ) ) ) ) )
% 2.85/1.58 => ( List = List2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_252_not__hd__in__tl,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( X
% 2.85/1.58 != ( hd @ A @ Xs ) )
% 2.85/1.58 => ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.85/1.58 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_253_Misc_Odistinct__hd__tl,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,X: A] :
% 2.85/1.58 ( ( distinct @ A @ Xs )
% 2.85/1.58 => ( ( X
% 2.85/1.58 = ( hd @ A @ Xs ) )
% 2.85/1.58 => ~ ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_254_old_OEntry__unreachable,axiom,
% 2.85/1.58 ! [G2: g] :
% 2.85/1.58 ( ( invar @ G2 )
% 2.85/1.58 => ( ( graph_1822314308nEdges @ g @ node @ edgeD @ inEdges @ G2 @ ( entry @ G2 ) )
% 2.85/1.58 = ( nil @ ( product_prod @ node @ ( product_prod @ edgeD @ node ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.85/1.58 ! [A: $tType] :
% 2.85/1.58 ( ( linorder @ A )
% 2.85/1.58 => ( type @ A ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 2.85/1.58 ! [A: $tType] :
% 2.85/1.58 ( ( linorder @ A )
% 2.85/1.58 => ( ord @ A ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_fun___Orderings_Oord,axiom,
% 2.85/1.58 ! [A6: $tType,A7: $tType] :
% 2.85/1.58 ( ( ord @ A7 )
% 2.85/1.58 => ( ord @ ( A6 > A7 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_Set_Oset___Orderings_Oord_1,axiom,
% 2.85/1.58 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.85/1.58 linorder @ $o ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_HOL_Obool___Orderings_Oord_2,axiom,
% 2.85/1.58 ord @ $o ).
% 2.85/1.58
% 2.85/1.58 thf(tfree_0,hypothesis,
% 2.85/1.58 linorder @ node ).
% 2.85/1.58
% 2.85/1.58 thf(tfree_1,hypothesis,
% 2.85/1.58 linorder @ val ).
% 2.85/1.58
% 2.85/1.58 thf(conj_0,conjecture,
% 2.85/1.58 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ) ).
% 2.85/1.58 ------------------------
% 2.95/1.60 % (20790)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/183Mi)
% 2.95/1.60 % (20796)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/18Mi)
% 2.95/1.60 % (20794)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_20598 for (2999ds/2Mi)
% 2.95/1.61 % (20794)Instruction limit reached!
% 2.95/1.61 % (20794)------------------------------
% 2.95/1.61 % (20794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (20794)Termination reason: Unknown
% 2.95/1.61 % (20794)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (20794)Memory used [KB]: 1407
% 2.95/1.61 % (20794)Time elapsed: 0.003 s
% 2.95/1.61 % (20794)Instructions burned: 4 (million)
% 2.95/1.61 % (20794)------------------------------
% 2.95/1.61 % (20794)------------------------------
% 2.95/1.61 % (20795)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_20598 for (2999ds/275Mi)
% 2.95/1.61 % (20793)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/2Mi)
% 2.95/1.61 % (20793)Instruction limit reached!
% 2.95/1.61 % (20793)------------------------------
% 2.95/1.61 % (20793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (20793)Termination reason: Unknown
% 2.95/1.61 % (20793)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (20793)Memory used [KB]: 1407
% 2.95/1.61 % (20793)Time elapsed: 0.002 s
% 2.95/1.61 % (20793)Instructions burned: 2 (million)
% 2.95/1.61 % (20793)------------------------------
% 2.95/1.61 % (20793)------------------------------
% 2.95/1.62 % (20796)Instruction limit reached!
% 2.95/1.62 % (20796)------------------------------
% 2.95/1.62 % (20796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (20796)Termination reason: Unknown
% 2.95/1.62 % (20796)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (20796)Memory used [KB]: 1535
% 2.95/1.62 % (20796)Time elapsed: 0.010 s
% 2.95/1.62 % (20796)Instructions burned: 20 (million)
% 2.95/1.62 % (20796)------------------------------
% 2.95/1.62 % (20796)------------------------------
% 2.95/1.62 % (20797)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/3Mi)
% 2.95/1.62 % (20797)Instruction limit reached!
% 2.95/1.62 % (20797)------------------------------
% 2.95/1.62 % (20797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (20797)Termination reason: Unknown
% 2.95/1.62 % (20797)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (20797)Memory used [KB]: 1407
% 2.95/1.62 % (20797)Time elapsed: 0.003 s
% 2.95/1.62 % (20797)Instructions burned: 3 (million)
% 2.95/1.62 % (20797)------------------------------
% 2.95/1.62 % (20797)------------------------------
% 2.95/1.62 % (20791)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_20598 for (2999ds/4Mi)
% 2.95/1.62 % (20791)Instruction limit reached!
% 2.95/1.62 % (20791)------------------------------
% 2.95/1.62 % (20791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (20791)Termination reason: Unknown
% 2.95/1.62 % (20791)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (20791)Memory used [KB]: 1407
% 2.95/1.62 % (20791)Time elapsed: 0.004 s
% 2.95/1.62 % (20791)Instructions burned: 4 (million)
% 2.95/1.62 % (20791)------------------------------
% 2.95/1.62 % (20791)------------------------------
% 2.95/1.62 % (20792)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_20598 for (2999ds/27Mi)
% 2.95/1.63 % (20799)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_20598 for (2999ds/15Mi)
% 2.95/1.63 % (20799)Instruction limit reached!
% 2.95/1.63 % (20799)------------------------------
% 2.95/1.63 % (20799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (20799)Termination reason: Unknown
% 2.95/1.63 % (20799)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (20799)Memory used [KB]: 1535
% 2.95/1.63 % (20799)Time elapsed: 0.006 s
% 2.95/1.63 % (20799)Instructions burned: 15 (million)
% 2.95/1.63 % (20799)------------------------------
% 2.95/1.63 % (20799)------------------------------
% 2.95/1.63 % (20798)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_20598 for (2999ds/37Mi)
% 2.95/1.64 % (20800)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_20598 for (2999ds/3Mi)
% 2.95/1.64 % (20800)Instruction limit reached!
% 2.95/1.64 % (20800)------------------------------
% 2.95/1.64 % (20800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (20800)Termination reason: Unknown
% 2.95/1.64 % (20800)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (20800)Memory used [KB]: 1407
% 2.95/1.64 % (20800)Time elapsed: 0.004 s
% 2.95/1.64 % (20800)Instructions burned: 5 (million)
% 2.95/1.64 % (20800)------------------------------
% 2.95/1.64 % (20800)------------------------------
% 2.95/1.64 % (20792)Instruction limit reached!
% 2.95/1.64 % (20792)------------------------------
% 2.95/1.64 % (20792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (20792)Termination reason: Unknown
% 2.95/1.64 % (20792)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (20792)Memory used [KB]: 1791
% 2.95/1.64 % (20792)Time elapsed: 0.016 s
% 2.95/1.64 % (20792)Instructions burned: 27 (million)
% 2.95/1.64 % (20792)------------------------------
% 2.95/1.64 % (20792)------------------------------
% 2.95/1.64 % (20801)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_20598 for (2999ds/1041Mi)
% 2.95/1.64 % (20802)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/7Mi)
% 2.95/1.64 % (20802)Instruction limit reached!
% 2.95/1.64 % (20802)------------------------------
% 2.95/1.64 % (20802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (20802)Termination reason: Unknown
% 2.95/1.64 % (20802)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (20802)Memory used [KB]: 1407
% 2.95/1.64 % (20802)Time elapsed: 0.004 s
% 2.95/1.64 % (20802)Instructions burned: 9 (million)
% 2.95/1.64 % (20802)------------------------------
% 2.95/1.64 % (20802)------------------------------
% 2.95/1.65 % (20798)Instruction limit reached!
% 2.95/1.65 % (20798)------------------------------
% 2.95/1.65 % (20798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (20798)Termination reason: Unknown
% 2.95/1.65 % (20798)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (20798)Memory used [KB]: 2174
% 2.95/1.65 % (20798)Time elapsed: 0.015 s
% 2.95/1.65 % (20798)Instructions burned: 39 (million)
% 2.95/1.65 % (20798)------------------------------
% 2.95/1.65 % (20798)------------------------------
% 2.95/1.65 % (20803)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/16Mi)
% 2.95/1.65 % (20804)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_20598 for (2999ds/3Mi)
% 2.95/1.65 % (20804)Instruction limit reached!
% 2.95/1.65 % (20804)------------------------------
% 2.95/1.65 % (20804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (20804)Termination reason: Unknown
% 2.95/1.65 % (20804)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (20804)Memory used [KB]: 1407
% 2.95/1.65 % (20804)Time elapsed: 0.002 s
% 2.95/1.65 % (20804)Instructions burned: 3 (million)
% 2.95/1.65 % (20804)------------------------------
% 2.95/1.65 % (20804)------------------------------
% 2.95/1.65 % (20805)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_20598 for (2999ds/3Mi)
% 2.95/1.65 % (20805)Instruction limit reached!
% 2.95/1.65 % (20805)------------------------------
% 2.95/1.65 % (20805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (20805)Termination reason: Unknown
% 2.95/1.65 % (20805)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (20805)Memory used [KB]: 1407
% 2.95/1.65 % (20805)Time elapsed: 0.002 s
% 2.95/1.65 % (20805)Instructions burned: 3 (million)
% 2.95/1.65 % (20805)------------------------------
% 2.95/1.65 % (20805)------------------------------
% 2.95/1.65 % (20803)Instruction limit reached!
% 2.95/1.65 % (20803)------------------------------
% 2.95/1.65 % (20803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (20803)Termination reason: Unknown
% 2.95/1.65 % (20803)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (20803)Memory used [KB]: 1535
% 2.95/1.65 % (20803)Time elapsed: 0.008 s
% 2.95/1.65 % (20803)Instructions burned: 18 (million)
% 2.95/1.65 % (20803)------------------------------
% 2.95/1.65 % (20803)------------------------------
% 2.95/1.65 % (20790)Instruction limit reached!
% 2.95/1.65 % (20790)------------------------------
% 2.95/1.65 % (20790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (20790)Termination reason: Unknown
% 2.95/1.65 % (20790)Termination phase: Saturation
% 2.95/1.65
% 2.95/1.65 % (20790)Memory used [KB]: 7164
% 2.95/1.65 % (20790)Time elapsed: 0.055 s
% 2.95/1.65 % (20790)Instructions burned: 184 (million)
% 2.95/1.65 % (20790)------------------------------
% 2.95/1.65 % (20790)------------------------------
% 2.95/1.66 % (20806)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/7Mi)
% 2.95/1.66 % (20806)Instruction limit reached!
% 2.95/1.66 % (20806)------------------------------
% 2.95/1.66 % (20806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.66 % (20806)Termination reason: Unknown
% 2.95/1.66 % (20806)Termination phase: shuffling
% 2.95/1.66
% 2.95/1.66 % (20806)Memory used [KB]: 1535
% 2.95/1.66 % (20806)Time elapsed: 0.005 s
% 2.95/1.66 % (20806)Instructions burned: 9 (million)
% 2.95/1.66 % (20806)------------------------------
% 2.95/1.66 % (20806)------------------------------
% 2.95/1.66 % (20807)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/3Mi)
% 2.95/1.66 % (20807)Instruction limit reached!
% 2.95/1.66 % (20807)------------------------------
% 2.95/1.66 % (20807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.66 % (20807)Termination reason: Unknown
% 2.95/1.66 % (20807)Termination phase: shuffling
% 2.95/1.66
% 2.95/1.66 % (20807)Memory used [KB]: 1407
% 2.95/1.66 % (20807)Time elapsed: 0.002 s
% 2.95/1.66 % (20807)Instructions burned: 3 (million)
% 2.95/1.66 % (20807)------------------------------
% 2.95/1.66 % (20807)------------------------------
% 2.95/1.66 % (20808)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/4Mi)
% 2.95/1.66 % (20809)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/18Mi)
% 2.95/1.66 % (20810)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/710Mi)
% 2.95/1.67 % (20808)Instruction limit reached!
% 2.95/1.67 % (20808)------------------------------
% 2.95/1.67 % (20808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.67 % (20808)Termination reason: Unknown
% 2.95/1.67 % (20808)Termination phase: shuffling
% 2.95/1.67
% 2.95/1.67 % (20808)Memory used [KB]: 1407
% 2.95/1.67 % (20808)Time elapsed: 0.003 s
% 2.95/1.67 % (20808)Instructions burned: 6 (million)
% 2.95/1.67 % (20808)------------------------------
% 2.95/1.67 % (20808)------------------------------
% 2.95/1.67 % (20809)Instruction limit reached!
% 2.95/1.67 % (20809)------------------------------
% 2.95/1.67 % (20809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.67 % (20809)Termination reason: Unknown
% 2.95/1.67 % (20809)Termination phase: shuffling
% 2.95/1.67
% 2.95/1.67 % (20809)Memory used [KB]: 1535
% 2.95/1.67 % (20809)Time elapsed: 0.007 s
% 2.95/1.67 % (20809)Instructions burned: 19 (million)
% 2.95/1.67 % (20809)------------------------------
% 2.95/1.67 % (20809)------------------------------
% 2.95/1.67 % (20811)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/6Mi)
% 2.95/1.67 % (20811)Instruction limit reached!
% 2.95/1.67 % (20811)------------------------------
% 2.95/1.67 % (20811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.67 % (20811)Termination reason: Unknown
% 2.95/1.67 % (20811)Termination phase: shuffling
% 2.95/1.67
% 2.95/1.67 % (20811)Memory used [KB]: 1407
% 2.95/1.67 % (20811)Time elapsed: 0.003 s
% 2.95/1.67 % (20811)Instructions burned: 6 (million)
% 2.95/1.67 % (20811)------------------------------
% 2.95/1.67 % (20811)------------------------------
% 2.95/1.68 % (20813)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/21Mi)
% 2.95/1.68 % (20812)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/902Mi)
% 2.95/1.68 % (20814)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/5Mi)
% 2.95/1.68 % (20813)Instruction limit reached!
% 2.95/1.68 % (20813)------------------------------
% 2.95/1.68 % (20813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.68 % (20813)Termination reason: Unknown
% 2.95/1.68 % (20813)Termination phase: shuffling
% 2.95/1.68
% 2.95/1.68 % (20813)Memory used [KB]: 1663
% 2.95/1.68 % (20813)Time elapsed: 0.009 s
% 2.95/1.68 % (20813)Instructions burned: 24 (million)
% 2.95/1.68 % (20813)------------------------------
% 2.95/1.68 % (20813)------------------------------
% 2.95/1.68 % (20814)Instruction limit reached!
% 2.95/1.68 % (20814)------------------------------
% 2.95/1.68 % (20814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.68 % (20814)Termination reason: Unknown
% 2.95/1.68 % (20814)Termination phase: shuffling
% 2.95/1.68
% 2.95/1.68 % (20814)Memory used [KB]: 1535
% 2.95/1.68 % (20814)Time elapsed: 0.003 s
% 2.95/1.68 % (20814)Instructions burned: 7 (million)
% 2.95/1.68 % (20814)------------------------------
% 2.95/1.68 % (20814)------------------------------
% 2.95/1.68 % (20817)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/6Mi)
% 2.95/1.69 % (20817)Instruction limit reached!
% 2.95/1.69 % (20817)------------------------------
% 2.95/1.69 % (20817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.69 % (20817)Termination reason: Unknown
% 2.95/1.69 % (20817)Termination phase: shuffling
% 2.95/1.69
% 2.95/1.69 % (20817)Memory used [KB]: 1535
% 2.95/1.69 % (20817)Time elapsed: 0.004 s
% 2.95/1.69 % (20817)Instructions burned: 7 (million)
% 2.95/1.69 % (20817)------------------------------
% 2.95/1.69 % (20817)------------------------------
% 2.95/1.69 % (20821)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/377Mi)
% 2.95/1.69 % (20822)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/779Mi)
% 2.95/1.70 % (20823)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_20598 for (2999ds/19Mi)
% 2.95/1.70 % (20823)Instruction limit reached!
% 2.95/1.70 % (20823)------------------------------
% 2.95/1.70 % (20823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.70 % (20823)Termination reason: Unknown
% 2.95/1.70 % (20823)Termination phase: shuffling
% 2.95/1.70
% 2.95/1.70 % (20823)Memory used [KB]: 1791
% 2.95/1.70 % (20823)Time elapsed: 0.008 s
% 2.95/1.70 % (20823)Instructions burned: 21 (million)
% 2.95/1.70 % (20823)------------------------------
% 2.95/1.70 % (20823)------------------------------
% 2.95/1.71 % (20795)Instruction limit reached!
% 2.95/1.71 % (20795)------------------------------
% 2.95/1.71 % (20795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.71 % (20795)Termination reason: Unknown
% 2.95/1.71 % (20795)Termination phase: Saturation
% 2.95/1.71
% 2.95/1.71 % (20795)Memory used [KB]: 7803
% 2.95/1.71 % (20795)Time elapsed: 0.096 s
% 2.95/1.71 % (20795)Instructions burned: 275 (million)
% 2.95/1.71 % (20795)------------------------------
% 2.95/1.71 % (20795)------------------------------
% 2.95/1.71 % (20824)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20598 for (2998ds/879Mi)
% 2.95/1.71 % (20825)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20598 for (2998ds/17Mi)
% 2.95/1.72 % (20825)Instruction limit reached!
% 2.95/1.72 % (20825)------------------------------
% 2.95/1.72 % (20825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.72 % (20825)Termination reason: Unknown
% 2.95/1.72 % (20825)Termination phase: shuffling
% 2.95/1.72
% 2.95/1.72 % (20825)Memory used [KB]: 1535
% 2.95/1.72 % (20825)Time elapsed: 0.007 s
% 2.95/1.72 % (20825)Instructions burned: 19 (million)
% 2.95/1.72 % (20825)------------------------------
% 2.95/1.72 % (20825)------------------------------
% 2.95/1.73 % (20828)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20598 for (2998ds/3Mi)
% 2.95/1.73 % (20828)Instruction limit reached!
% 2.95/1.73 % (20828)------------------------------
% 2.95/1.73 % (20828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.73 % (20828)Termination reason: Unknown
% 2.95/1.73 % (20828)Termination phase: shuffling
% 2.95/1.73
% 2.95/1.73 % (20828)Memory used [KB]: 1407
% 2.95/1.73 % (20828)Time elapsed: 0.003 s
% 2.95/1.73 % (20828)Instructions burned: 3 (million)
% 2.95/1.73 % (20828)------------------------------
% 2.95/1.73 % (20828)------------------------------
% 2.95/1.75 % (20836)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20598 for (2998ds/30Mi)
% 2.95/1.76 % (20836)Instruction limit reached!
% 2.95/1.76 % (20836)------------------------------
% 2.95/1.76 % (20836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.76 % (20836)Termination reason: Unknown
% 2.95/1.76 % (20836)Termination phase: shuffling
% 2.95/1.76
% 2.95/1.76 % (20836)Memory used [KB]: 1791
% 2.95/1.76 % (20836)Time elapsed: 0.016 s
% 2.95/1.76 % (20836)Instructions burned: 30 (million)
% 2.95/1.76 % (20836)------------------------------
% 2.95/1.76 % (20836)------------------------------
% 2.95/1.78 % (20843)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20598 for (2998ds/127Mi)
% 2.95/1.83 % (20843)Instruction limit reached!
% 2.95/1.83 % (20843)------------------------------
% 2.95/1.83 % (20843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.83 % (20843)Termination reason: Unknown
% 2.95/1.83 % (20843)Termination phase: Property scanning
% 2.95/1.83
% 2.95/1.83 % (20843)Memory used [KB]: 2558
% 2.95/1.83 % (20843)Time elapsed: 0.050 s
% 2.95/1.83 % (20843)Instructions burned: 127 (million)
% 2.95/1.83 % (20843)------------------------------
% 2.95/1.83 % (20843)------------------------------
% 2.95/1.84 % (20821)Instruction limit reached!
% 2.95/1.84 % (20821)------------------------------
% 2.95/1.84 % (20821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.84 % (20821)Termination reason: Unknown
% 2.95/1.84 % (20821)Termination phase: Saturation
% 2.95/1.84
% 2.95/1.84 % (20821)Memory used [KB]: 8443
% 2.95/1.84 % (20821)Time elapsed: 0.145 s
% 2.95/1.84 % (20821)Instructions burned: 378 (million)
% 2.95/1.84 % (20821)------------------------------
% 2.95/1.84 % (20821)------------------------------
% 2.95/1.84 % (20856)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20598 for (2997ds/100Mi)
% 2.95/1.85 % (20857)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_20598 for (2997ds/3Mi)
% 2.95/1.85 % (20857)Instruction limit reached!
% 2.95/1.85 % (20857)------------------------------
% 2.95/1.85 % (20857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.85 % (20857)Termination reason: Unknown
% 2.95/1.85 % (20857)Termination phase: shuffling
% 2.95/1.85
% 2.95/1.85 % (20857)Memory used [KB]: 1407
% 2.95/1.85 % (20857)Time elapsed: 0.002 s
% 2.95/1.85 % (20857)Instructions burned: 3 (million)
% 2.95/1.85 % (20857)------------------------------
% 2.95/1.85 % (20857)------------------------------
% 2.95/1.86 % (20858)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_20598 for (2997ds/20Mi)
% 2.95/1.86 % (20858)Instruction limit reached!
% 2.95/1.86 % (20858)------------------------------
% 2.95/1.86 % (20858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.86 % (20858)Termination reason: Unknown
% 2.95/1.86 % (20858)Termination phase: shuffling
% 2.95/1.86
% 2.95/1.86 % (20858)Memory used [KB]: 1535
% 2.95/1.86 % (20858)Time elapsed: 0.008 s
% 2.95/1.86 % (20858)Instructions burned: 22 (million)
% 2.95/1.86 % (20858)------------------------------
% 2.95/1.86 % (20858)------------------------------
% 2.95/1.86 % (20856)Instruction limit reached!
% 2.95/1.86 % (20856)------------------------------
% 2.95/1.86 % (20856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.86 % (20856)Termination reason: Unknown
% 2.95/1.86 % (20856)Termination phase: Preprocessing 1
% 2.95/1.86
% 2.95/1.86 % (20856)Memory used [KB]: 2430
% 2.95/1.86 % (20856)Time elapsed: 0.028 s
% 2.95/1.86 % (20856)Instructions burned: 101 (million)
% 2.95/1.86 % (20856)------------------------------
% 2.95/1.86 % (20856)------------------------------
% 2.95/1.87 % (20859)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_20598 for (2997ds/86Mi)
% 2.95/1.87 % (20860)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_20598 for (2997ds/107Mi)
% 2.95/1.90 % (20859)Instruction limit reached!
% 2.95/1.90 % (20859)------------------------------
% 2.95/1.90 % (20859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.90 % (20859)Termination reason: Unknown
% 2.95/1.90 % (20859)Termination phase: Preprocessing 3
% 2.95/1.90
% 2.95/1.90 % (20859)Memory used [KB]: 2302
% 2.95/1.90 % (20859)Time elapsed: 0.027 s
% 2.95/1.90 % (20859)Instructions burned: 87 (million)
% 2.95/1.90 % (20859)------------------------------
% 2.95/1.90 % (20859)------------------------------
% 2.95/1.90 % (20810)Instruction limit reached!
% 2.95/1.90 % (20810)------------------------------
% 2.95/1.90 % (20810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.90 % (20810)Termination reason: Unknown
% 2.95/1.90 % (20810)Termination phase: Saturation
% 2.95/1.90
% 2.95/1.90 % (20810)Memory used [KB]: 8571
% 2.95/1.90 % (20810)Time elapsed: 0.240 s
% 2.95/1.90 % (20810)Instructions burned: 712 (million)
% 2.95/1.90 % (20810)------------------------------
% 2.95/1.90 % (20810)------------------------------
% 2.95/1.91 % (20860)Instruction limit reached!
% 2.95/1.91 % (20860)------------------------------
% 2.95/1.91 % (20860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.91 % (20860)Termination reason: Unknown
% 2.95/1.91 % (20860)Termination phase: Preprocessing 3
% 2.95/1.91
% 2.95/1.91 % (20860)Memory used [KB]: 2558
% 2.95/1.91 % (20860)Time elapsed: 0.033 s
% 2.95/1.91 % (20860)Instructions burned: 108 (million)
% 2.95/1.91 % (20860)------------------------------
% 2.95/1.91 % (20860)------------------------------
% 2.95/1.91 % (20861)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/39Mi)
% 2.95/1.91 % (20862)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/448Mi)
% 2.95/1.92 % (20863)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/46Mi)
% 2.95/1.92 % (20861)Instruction limit reached!
% 2.95/1.92 % (20861)------------------------------
% 2.95/1.92 % (20861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.92 % (20861)Termination reason: Unknown
% 2.95/1.92 % (20861)Termination phase: shuffling
% 2.95/1.92
% 2.95/1.92 % (20861)Memory used [KB]: 2174
% 2.95/1.92 % (20861)Time elapsed: 0.012 s
% 2.95/1.92 % (20861)Instructions burned: 40 (million)
% 2.95/1.92 % (20861)------------------------------
% 2.95/1.92 % (20861)------------------------------
% 2.95/1.93 % (20864)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/98Mi)
% 2.95/1.93 % (20863)Instruction limit reached!
% 2.95/1.93 % (20863)------------------------------
% 2.95/1.93 % (20863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.93 % (20863)Termination reason: Unknown
% 2.95/1.93 % (20863)Termination phase: shuffling
% 2.95/1.93
% 2.95/1.93 % (20863)Memory used [KB]: 1918
% 2.95/1.93 % (20863)Time elapsed: 0.016 s
% 2.95/1.93 % (20863)Instructions burned: 48 (million)
% 2.95/1.93 % (20863)------------------------------
% 2.95/1.93 % (20863)------------------------------
% 2.95/1.94 % (20865)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/507Mi)
% 2.95/1.95 % (20812)Instruction limit reached!
% 2.95/1.95 % (20812)------------------------------
% 2.95/1.95 % (20812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.95 % (20812)Termination reason: Unknown
% 2.95/1.95 % (20812)Termination phase: Saturation
% 2.95/1.95
% 2.95/1.95 % (20812)Memory used [KB]: 8443
% 2.95/1.95 % (20812)Time elapsed: 0.272 s
% 2.95/1.95 % (20812)Instructions burned: 902 (million)
% 2.95/1.95 % (20812)------------------------------
% 2.95/1.95 % (20812)------------------------------
% 2.95/1.95 % (20822)Instruction limit reached!
% 2.95/1.95 % (20822)------------------------------
% 2.95/1.95 % (20822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.95 % (20822)Termination reason: Unknown
% 2.95/1.95 % (20822)Termination phase: Saturation
% 2.95/1.95
% 2.95/1.95 % (20822)Memory used [KB]: 9722
% 2.95/1.95 % (20822)Time elapsed: 0.261 s
% 2.95/1.95 % (20822)Instructions burned: 779 (million)
% 2.95/1.95 % (20822)------------------------------
% 2.95/1.95 % (20822)------------------------------
% 2.95/1.95 % (20864)Instruction limit reached!
% 2.95/1.95 % (20864)------------------------------
% 2.95/1.95 % (20864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.95 % (20864)Termination reason: Unknown
% 2.95/1.95 % (20864)Termination phase: Preprocessing 1
% 2.95/1.95
% 2.95/1.95 % (20864)Memory used [KB]: 2430
% 2.95/1.95 % (20864)Time elapsed: 0.027 s
% 2.95/1.95 % (20864)Instructions burned: 99 (million)
% 2.95/1.95 % (20864)------------------------------
% 2.95/1.95 % (20864)------------------------------
% 2.95/1.96 % (20866)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/149Mi)
% 2.95/1.96 % (20867)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/39Mi)
% 2.95/1.96 % (20869)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/6Mi)
% 2.95/1.97 % (20869)Instruction limit reached!
% 2.95/1.97 % (20869)------------------------------
% 2.95/1.97 % (20869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.97 % (20869)Termination reason: Unknown
% 2.95/1.97 % (20869)Termination phase: shuffling
% 2.95/1.97
% 2.95/1.97 % (20869)Memory used [KB]: 1407
% 2.95/1.97 % (20869)Time elapsed: 0.003 s
% 2.95/1.97 % (20869)Instructions burned: 6 (million)
% 2.95/1.97 % (20869)------------------------------
% 2.95/1.97 % (20869)------------------------------
% 2.95/1.98 % (20875)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/1087Mi)
% 2.95/1.98 % (20867)Instruction limit reached!
% 2.95/1.98 % (20867)------------------------------
% 2.95/1.98 % (20867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.98 % (20867)Termination reason: Unknown
% 2.95/1.98 % (20867)Termination phase: shuffling
% 2.95/1.98
% 2.95/1.98 % (20867)Memory used [KB]: 1791
% 2.95/1.98 % (20867)Time elapsed: 0.014 s
% 2.95/1.98 % (20867)Instructions burned: 39 (million)
% 2.95/1.98 % (20867)------------------------------
% 2.95/1.98 % (20867)------------------------------
% 2.95/1.98 % (20881)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20598 for (2996ds/47Mi)
% 2.95/2.00 % (20866)Instruction limit reached!
% 2.95/2.00 % (20866)------------------------------
% 2.95/2.00 % (20866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.00 % (20866)Termination reason: Unknown
% 2.95/2.00 % (20866)Termination phase: Property scanning
% 2.95/2.00
% 2.95/2.00 % (20866)Memory used [KB]: 2686
% 2.95/2.00 % (20866)Time elapsed: 0.045 s
% 2.95/2.00 % (20866)Instructions burned: 152 (million)
% 2.95/2.00 % (20866)------------------------------
% 2.95/2.00 % (20866)------------------------------
% 2.95/2.00 % (20881)Instruction limit reached!
% 2.95/2.00 % (20881)------------------------------
% 2.95/2.00 % (20881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.00 % (20881)Termination reason: Unknown
% 2.95/2.00 % (20881)Termination phase: shuffling
% 2.95/2.00
% 2.95/2.00 % (20881)Memory used [KB]: 1918
% 2.95/2.00 % (20881)Time elapsed: 0.017 s
% 2.95/2.00 % (20881)Instructions burned: 48 (million)
% 2.95/2.00 % (20881)------------------------------
% 2.95/2.00 % (20881)------------------------------
% 2.95/2.01 % (20892)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/44Mi)
% 2.95/2.01 % (20893)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/432Mi)
% 5.76/2.02 % (20892)Instruction limit reached!
% 5.76/2.02 % (20892)------------------------------
% 5.76/2.02 % (20892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.02 % (20892)Termination reason: Unknown
% 5.76/2.02 % (20892)Termination phase: shuffling
% 5.76/2.02
% 5.76/2.02 % (20892)Memory used [KB]: 2174
% 5.76/2.02 % (20892)Time elapsed: 0.014 s
% 5.76/2.02 % (20892)Instructions burned: 47 (million)
% 5.76/2.02 % (20892)------------------------------
% 5.76/2.02 % (20892)------------------------------
% 5.76/2.03 % (20902)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/62Mi)
% 5.76/2.03 % (20824)Instruction limit reached!
% 5.76/2.03 % (20824)------------------------------
% 5.76/2.03 % (20824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.03 % (20824)Termination reason: Unknown
% 5.76/2.03 % (20824)Termination phase: Saturation
% 5.76/2.03
% 5.76/2.03 % (20824)Memory used [KB]: 8571
% 5.76/2.03 % (20824)Time elapsed: 0.323 s
% 5.76/2.03 % (20824)Instructions burned: 882 (million)
% 5.76/2.03 % (20824)------------------------------
% 5.76/2.03 % (20824)------------------------------
% 5.76/2.04 % (20862)Instruction limit reached!
% 5.76/2.04 % (20862)------------------------------
% 5.76/2.04 % (20862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.04 % (20862)Termination reason: Unknown
% 5.76/2.04 % (20862)Termination phase: Saturation
% 5.76/2.04
% 5.76/2.04 % (20862)Memory used [KB]: 8955
% 5.76/2.04 % (20862)Time elapsed: 0.126 s
% 5.76/2.04 % (20862)Instructions burned: 449 (million)
% 5.76/2.04 % (20862)------------------------------
% 5.76/2.04 % (20862)------------------------------
% 5.76/2.04 % (20911)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/31Mi)
% 5.76/2.05 % (20913)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/96Mi)
% 5.76/2.05 % (20902)Instruction limit reached!
% 5.76/2.05 % (20902)------------------------------
% 5.76/2.05 % (20902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.05 % (20902)Termination reason: Unknown
% 5.76/2.05 % (20902)Termination phase: Property scanning
% 5.76/2.05
% 5.76/2.05 % (20902)Memory used [KB]: 2302
% 5.76/2.05 % (20902)Time elapsed: 0.019 s
% 5.76/2.05 % (20902)Instructions burned: 64 (million)
% 5.76/2.05 % (20902)------------------------------
% 5.76/2.05 % (20902)------------------------------
% 5.76/2.06 % (20911)Instruction limit reached!
% 5.76/2.06 % (20911)------------------------------
% 5.76/2.06 % (20911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.06 % (20911)Termination reason: Unknown
% 5.76/2.06 % (20911)Termination phase: shuffling
% 5.76/2.06
% 5.76/2.06 % (20911)Memory used [KB]: 1791
% 5.76/2.06 % (20911)Time elapsed: 0.012 s
% 5.76/2.06 % (20911)Instructions burned: 33 (million)
% 5.76/2.06 % (20911)------------------------------
% 5.76/2.06 % (20911)------------------------------
% 5.76/2.06 % (20917)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/453Mi)
% 5.76/2.06 % (20801)Instruction limit reached!
% 5.76/2.06 % (20801)------------------------------
% 5.76/2.06 % (20801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.06 % (20801)Termination reason: Unknown
% 5.76/2.06 % (20801)Termination phase: Saturation
% 5.76/2.06
% 5.76/2.06 % (20801)Memory used [KB]: 10234
% 5.76/2.06 % (20801)Time elapsed: 0.425 s
% 5.76/2.06 % (20801)Instructions burned: 1042 (million)
% 5.76/2.06 % (20801)------------------------------
% 5.76/2.06 % (20801)------------------------------
% 5.76/2.06 % (20920)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/71Mi)
% 5.76/2.07 % (20925)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/83Mi)
% 5.76/2.08 % (20913)Instruction limit reached!
% 5.76/2.08 % (20913)------------------------------
% 5.76/2.08 % (20913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.08 % (20913)Termination reason: Unknown
% 5.76/2.08 % (20913)Termination phase: Clausification
% 5.76/2.08
% 5.76/2.08 % (20913)Memory used [KB]: 2558
% 5.76/2.08 % (20913)Time elapsed: 0.031 s
% 5.76/2.08 % (20913)Instructions burned: 97 (million)
% 5.76/2.08 % (20913)------------------------------
% 5.76/2.08 % (20913)------------------------------
% 5.76/2.09 % (20920)Instruction limit reached!
% 5.76/2.09 % (20920)------------------------------
% 5.76/2.09 % (20920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.09 % (20920)Termination reason: Unknown
% 5.76/2.09 % (20920)Termination phase: Preprocessing 1
% 5.76/2.09
% 5.76/2.09 % (20920)Memory used [KB]: 2046
% 5.76/2.09 % (20920)Time elapsed: 0.023 s
% 5.76/2.09 % (20920)Instructions burned: 73 (million)
% 5.76/2.09 % (20920)------------------------------
% 5.76/2.09 % (20920)------------------------------
% 5.76/2.09 % (20932)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_20598 for (2995ds/11Mi)
% 5.76/2.09 % (20932)Instruction limit reached!
% 5.76/2.09 % (20932)------------------------------
% 5.76/2.09 % (20932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.09 % (20932)Termination reason: Unknown
% 5.76/2.09 % (20932)Termination phase: shuffling
% 5.76/2.09
% 5.76/2.09 % (20932)Memory used [KB]: 1663
% 5.76/2.09 % (20932)Time elapsed: 0.004 s
% 5.76/2.09 % (20932)Instructions burned: 11 (million)
% 5.76/2.09 % (20932)------------------------------
% 5.76/2.09 % (20932)------------------------------
% 5.76/2.09 % (20865)Instruction limit reached!
% 5.76/2.09 % (20865)------------------------------
% 5.76/2.09 % (20865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.09 % (20865)Termination reason: Unknown
% 5.76/2.09 % (20865)Termination phase: Saturation
% 5.76/2.09
% 5.76/2.09 % (20865)Memory used [KB]: 8827
% 5.76/2.09 % (20865)Time elapsed: 0.152 s
% 5.76/2.09 % (20865)Instructions burned: 510 (million)
% 5.76/2.09 % (20865)------------------------------
% 5.76/2.09 % (20865)------------------------------
% 5.76/2.10 % (20936)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/41Mi)
% 5.76/2.10 % (20925)Instruction limit reached!
% 5.76/2.10 % (20925)------------------------------
% 5.76/2.10 % (20925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.10 % (20925)Termination reason: Unknown
% 5.76/2.10 % (20925)Termination phase: SInE selection
% 5.76/2.10
% 5.76/2.10 % (20925)Memory used [KB]: 1918
% 5.76/2.10 % (20925)Time elapsed: 0.026 s
% 5.76/2.10 % (20925)Instructions burned: 85 (million)
% 5.76/2.10 % (20925)------------------------------
% 5.76/2.10 % (20925)------------------------------
% 5.76/2.10 % (20938)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/6Mi)
% 5.76/2.10 % (20939)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/150Mi)
% 5.76/2.10 % (20938)Instruction limit reached!
% 5.76/2.10 % (20938)------------------------------
% 5.76/2.10 % (20938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.10 % (20938)Termination reason: Unknown
% 5.76/2.10 % (20938)Termination phase: shuffling
% 5.76/2.10
% 5.76/2.10 % (20938)Memory used [KB]: 1407
% 5.76/2.10 % (20938)Time elapsed: 0.003 s
% 5.76/2.10 % (20938)Instructions burned: 6 (million)
% 5.76/2.10 % (20938)------------------------------
% 5.76/2.10 % (20938)------------------------------
% 5.76/2.11 % (20936)Instruction limit reached!
% 5.76/2.11 % (20936)------------------------------
% 5.76/2.11 % (20936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.11 % (20936)Termination reason: Unknown
% 5.76/2.11 % (20936)Termination phase: shuffling
% 5.76/2.11
% 5.76/2.11 % (20936)Memory used [KB]: 2174
% 5.76/2.11 % (20936)Time elapsed: 0.013 s
% 5.76/2.11 % (20936)Instructions burned: 43 (million)
% 5.76/2.11 % (20936)------------------------------
% 5.76/2.11 % (20936)------------------------------
% 5.76/2.11 % (20941)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/343Mi)
% 5.76/2.11 % (20942)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/109Mi)
% 6.31/2.12 % (20946)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/253Mi)
% 6.31/2.14 % (20893)Instruction limit reached!
% 6.31/2.14 % (20893)------------------------------
% 6.31/2.14 % (20893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.14 % (20893)Termination reason: Unknown
% 6.31/2.14 % (20893)Termination phase: Saturation
% 6.31/2.14
% 6.31/2.14 % (20893)Memory used [KB]: 3837
% 6.31/2.14 % (20893)Time elapsed: 0.128 s
% 6.31/2.14 % (20893)Instructions burned: 433 (million)
% 6.31/2.14 % (20893)------------------------------
% 6.31/2.14 % (20893)------------------------------
% 6.31/2.14 % (20942)Instruction limit reached!
% 6.31/2.14 % (20942)------------------------------
% 6.31/2.14 % (20942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.14 % (20942)Termination reason: Unknown
% 6.31/2.14 % (20942)Termination phase: Preprocessing 3
% 6.31/2.14
% 6.31/2.14 % (20942)Memory used [KB]: 2558
% 6.31/2.14 % (20942)Time elapsed: 0.034 s
% 6.31/2.14 % (20942)Instructions burned: 110 (million)
% 6.31/2.14 % (20942)------------------------------
% 6.31/2.14 % (20942)------------------------------
% 6.31/2.14 % (20939)Instruction limit reached!
% 6.31/2.14 % (20939)------------------------------
% 6.31/2.14 % (20939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.14 % (20939)Termination reason: Unknown
% 6.31/2.14 % (20939)Termination phase: Function definition elimination
% 6.31/2.14
% 6.31/2.14 % (20939)Memory used [KB]: 2814
% 6.31/2.14 % (20939)Time elapsed: 0.044 s
% 6.31/2.14 % (20939)Instructions burned: 150 (million)
% 6.31/2.14 % (20939)------------------------------
% 6.31/2.14 % (20939)------------------------------
% 6.31/2.15 % (20957)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/140Mi)
% 6.31/2.15 % (20964)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/614Mi)
% 6.31/2.15 % (20965)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/202Mi)
% 6.31/2.18 % (20917)Instruction limit reached!
% 6.31/2.18 % (20917)------------------------------
% 6.31/2.18 % (20917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.18 % (20917)Termination reason: Unknown
% 6.31/2.18 % (20917)Termination phase: Saturation
% 6.31/2.18
% 6.31/2.18 % (20917)Memory used [KB]: 7931
% 6.31/2.18 % (20917)Time elapsed: 0.125 s
% 6.31/2.18 % (20917)Instructions burned: 455 (million)
% 6.31/2.18 % (20917)------------------------------
% 6.31/2.18 % (20917)------------------------------
% 6.31/2.19 % (20957)Instruction limit reached!
% 6.31/2.19 % (20957)------------------------------
% 6.31/2.19 % (20957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.19 % (20957)Termination reason: Unknown
% 6.31/2.19 % (20957)Termination phase: Saturation
% 6.31/2.19
% 6.31/2.19 % (20957)Memory used [KB]: 7036
% 6.31/2.19 % (20957)Time elapsed: 0.043 s
% 6.31/2.19 % (20957)Instructions burned: 140 (million)
% 6.31/2.19 % (20957)------------------------------
% 6.31/2.19 % (20957)------------------------------
% 6.31/2.19 % (20946)Instruction limit reached!
% 6.31/2.19 % (20946)------------------------------
% 6.31/2.19 % (20946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.19 % (20946)Termination reason: Unknown
% 6.31/2.19 % (20946)Termination phase: Saturation
% 6.31/2.19
% 6.31/2.19 % (20946)Memory used [KB]: 3709
% 6.31/2.19 % (20946)Time elapsed: 0.074 s
% 6.31/2.19 % (20946)Instructions burned: 253 (million)
% 6.31/2.19 % (20946)------------------------------
% 6.31/2.19 % (20946)------------------------------
% 6.31/2.19 % (20981)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/339Mi)
% 6.89/2.20 % (20987)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/283Mi)
% 6.89/2.20 % (20989)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_20598 for (2994ds/134Mi)
% 6.89/2.21 % (20941)Instruction limit reached!
% 6.89/2.21 % (20941)------------------------------
% 6.89/2.21 % (20941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.21 % (20941)Termination reason: Unknown
% 6.89/2.21 % (20941)Termination phase: Saturation
% 6.89/2.21
% 6.89/2.21 % (20941)Memory used [KB]: 7803
% 6.89/2.21 % (20941)Time elapsed: 0.102 s
% 6.89/2.21 % (20941)Instructions burned: 343 (million)
% 6.89/2.21 % (20941)------------------------------
% 6.89/2.21 % (20941)------------------------------
% 6.89/2.21 % (20965)Instruction limit reached!
% 6.89/2.21 % (20965)------------------------------
% 6.89/2.21 % (20965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.21 % (20965)Termination reason: Unknown
% 6.89/2.21 % (20965)Termination phase: Saturation
% 6.89/2.21
% 6.89/2.21 % (20965)Memory used [KB]: 7675
% 6.89/2.21 % (20965)Time elapsed: 0.060 s
% 6.89/2.21 % (20965)Instructions burned: 205 (million)
% 6.89/2.21 % (20965)------------------------------
% 6.89/2.21 % (20965)------------------------------
% 6.89/2.22 % (21001)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_20598 for (2993ds/298Mi)
% 6.89/2.22 % (21004)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_20598 for (2993ds/192Mi)
% 6.89/2.24 % (20989)Instruction limit reached!
% 6.89/2.24 % (20989)------------------------------
% 6.89/2.24 % (20989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.24 % (20989)Termination reason: Unknown
% 6.89/2.24 % (20989)Termination phase: Function definition elimination
% 6.89/2.24
% 6.89/2.24 % (20989)Memory used [KB]: 2686
% 6.89/2.24 % (20989)Time elapsed: 0.040 s
% 6.89/2.24 % (20989)Instructions burned: 134 (million)
% 6.89/2.24 % (20989)------------------------------
% 6.89/2.24 % (20989)------------------------------
% 6.89/2.25 % (21015)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_20598 for (2993ds/258Mi)
% 6.89/2.28 % (21004)Instruction limit reached!
% 6.89/2.28 % (21004)------------------------------
% 6.89/2.28 % (21004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.28 % (21004)Termination reason: Unknown
% 6.89/2.28 % (21004)Termination phase: Saturation
% 6.89/2.28
% 6.89/2.28 % (21004)Memory used [KB]: 2942
% 6.89/2.28 % (21004)Time elapsed: 0.056 s
% 6.89/2.28 % (21004)Instructions burned: 194 (million)
% 6.89/2.28 % (21004)------------------------------
% 6.89/2.28 % (21004)------------------------------
% 6.89/2.28 % (20987)Instruction limit reached!
% 6.89/2.28 % (20987)------------------------------
% 6.89/2.28 % (20987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.28 % (20987)Termination reason: Unknown
% 6.89/2.28 % (20987)Termination phase: Saturation
% 6.89/2.28
% 6.89/2.28 % (20987)Memory used [KB]: 7547
% 6.89/2.28 % (20987)Time elapsed: 0.081 s
% 6.89/2.28 % (20987)Instructions burned: 285 (million)
% 6.89/2.28 % (20987)------------------------------
% 6.89/2.28 % (20987)------------------------------
% 6.89/2.29 % (21032)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_20598 for (2993ds/90Mi)
% 6.89/2.29 % (21034)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_20598 for (2993ds/231Mi)
% 6.89/2.29 % (20981)Instruction limit reached!
% 6.89/2.29 % (20981)------------------------------
% 6.89/2.29 % (20981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.29 % (20981)Termination reason: Unknown
% 6.89/2.29 % (20981)Termination phase: Saturation
% 6.89/2.29
% 6.89/2.29 % (20981)Memory used [KB]: 7675
% 6.89/2.29 % (20981)Time elapsed: 0.097 s
% 6.89/2.29 % (20981)Instructions burned: 340 (million)
% 6.89/2.29 % (20981)------------------------------
% 6.89/2.29 % (20981)------------------------------
% 7.47/2.30 % (21038)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_20598 for (2993ds/458Mi)
% 7.47/2.30 % (21001)Instruction limit reached!
% 7.47/2.30 % (21001)------------------------------
% 7.47/2.30 % (21001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.30 % (21001)Termination reason: Unknown
% 7.47/2.30 % (21001)Termination phase: Saturation
% 7.47/2.30
% 7.47/2.30 % (21001)Memory used [KB]: 7675
% 7.47/2.30 % (21001)Time elapsed: 0.081 s
% 7.47/2.30 % (21001)Instructions burned: 299 (million)
% 7.47/2.30 % (21001)------------------------------
% 7.47/2.30 % (21001)------------------------------
% 7.47/2.31 % (21043)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_20598 for (2992ds/31Mi)
% 7.47/2.31 % (20875)Instruction limit reached!
% 7.47/2.31 % (20875)------------------------------
% 7.47/2.31 % (20875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.31 % (20875)Termination reason: Unknown
% 7.47/2.31 % (20875)Termination phase: Saturation
% 7.47/2.31
% 7.47/2.31 % (20875)Memory used [KB]: 9210
% 7.47/2.31 % (20875)Time elapsed: 0.339 s
% 7.47/2.31 % (20875)Instructions burned: 1087 (million)
% 7.47/2.31 % (20875)------------------------------
% 7.47/2.31 % (20875)------------------------------
% 7.47/2.31 % (21032)Instruction limit reached!
% 7.47/2.31 % (21032)------------------------------
% 7.47/2.31 % (21032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.31 % (21032)Termination reason: Unknown
% 7.47/2.31 % (21032)Termination phase: Preprocessing 3
% 7.47/2.31
% 7.47/2.31 % (21032)Memory used [KB]: 2430
% 7.47/2.31 % (21032)Time elapsed: 0.029 s
% 7.47/2.31 % (21032)Instructions burned: 91 (million)
% 7.47/2.31 % (21032)------------------------------
% 7.47/2.31 % (21032)------------------------------
% 7.47/2.32 % (21043)Instruction limit reached!
% 7.47/2.32 % (21043)------------------------------
% 7.47/2.32 % (21043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.32 % (21043)Termination reason: Unknown
% 7.47/2.32 % (21043)Termination phase: shuffling
% 7.47/2.32
% 7.47/2.32 % (21043)Memory used [KB]: 1791
% 7.47/2.32 % (21043)Time elapsed: 0.012 s
% 7.47/2.32 % (21043)Instructions burned: 33 (million)
% 7.47/2.32 % (21043)------------------------------
% 7.47/2.32 % (21043)------------------------------
% 7.47/2.32 % (21015)Instruction limit reached!
% 7.47/2.32 % (21015)------------------------------
% 7.47/2.32 % (21015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.32 % (21015)Termination reason: Unknown
% 7.47/2.32 % (21015)Termination phase: Saturation
% 7.47/2.32
% 7.47/2.32 % (21015)Memory used [KB]: 3326
% 7.47/2.32 % (21015)Time elapsed: 0.075 s
% 7.47/2.32 % (21015)Instructions burned: 259 (million)
% 7.47/2.32 % (21015)------------------------------
% 7.47/2.32 % (21015)------------------------------
% 7.47/2.32 % (21048)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_20598 for (2992ds/297Mi)
% 7.47/2.32 % (21049)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_20598 for (2992ds/987Mi)
% 7.47/2.33 % (21052)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_20598 for (2992ds/182Mi)
% 7.47/2.33 % (21054)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_20598 for (2992ds/182Mi)
% 7.47/2.33 % (20964)Instruction limit reached!
% 7.47/2.33 % (20964)------------------------------
% 7.47/2.33 % (20964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.33 % (20964)Termination reason: Unknown
% 7.47/2.33 % (20964)Termination phase: Saturation
% 7.47/2.33
% 7.47/2.33 % (20964)Memory used [KB]: 8827
% 7.47/2.33 % (20964)Time elapsed: 0.180 s
% 7.47/2.33 % (20964)Instructions burned: 614 (million)
% 7.47/2.33 % (20964)------------------------------
% 7.47/2.33 % (20964)------------------------------
% 7.47/2.34 % (21058)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_20598 for (2992ds/154Mi)
% 7.47/2.35 % (21034)Instruction limit reached!
% 7.47/2.35 % (21034)------------------------------
% 7.47/2.35 % (21034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.35 % (21034)Termination reason: Unknown
% 7.47/2.35 % (21034)Termination phase: Saturation
% 7.47/2.35
% 7.47/2.35 % (21034)Memory used [KB]: 7164
% 7.47/2.35 % (21034)Time elapsed: 0.063 s
% 7.47/2.35 % (21034)Instructions burned: 231 (million)
% 7.47/2.35 % (21034)------------------------------
% 7.47/2.35 % (21034)------------------------------
% 7.47/2.36 % (21065)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_20598 for (2992ds/79Mi)
% 7.47/2.38 % (21052)Instruction limit reached!
% 7.47/2.38 % (21052)------------------------------
% 7.47/2.38 % (21052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.38 % (21052)Termination reason: Unknown
% 7.47/2.38 % (21052)Termination phase: Property scanning
% 7.47/2.38
% 7.47/2.38 % (21052)Memory used [KB]: 2686
% 7.47/2.38 % (21052)Time elapsed: 0.051 s
% 7.47/2.38 % (21052)Instructions burned: 182 (million)
% 7.47/2.38 % (21052)------------------------------
% 7.47/2.38 % (21052)------------------------------
% 7.47/2.38 % (21058)Instruction limit reached!
% 7.47/2.38 % (21058)------------------------------
% 7.47/2.38 % (21058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.38 % (21058)Termination reason: Unknown
% 7.47/2.38 % (21058)Termination phase: Function definition elimination
% 7.47/2.38
% 7.47/2.38 % (21058)Memory used [KB]: 2558
% 7.47/2.38 % (21058)Time elapsed: 0.042 s
% 7.47/2.38 % (21058)Instructions burned: 155 (million)
% 7.47/2.38 % (21058)------------------------------
% 7.47/2.38 % (21058)------------------------------
% 7.47/2.38 % (21054)Instruction limit reached!
% 7.47/2.38 % (21054)------------------------------
% 7.47/2.38 % (21054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.38 % (21054)Termination reason: Unknown
% 7.47/2.38 % (21054)Termination phase: Property scanning
% 7.47/2.38
% 7.47/2.38 % (21054)Memory used [KB]: 2814
% 7.47/2.38 % (21054)Time elapsed: 0.052 s
% 7.47/2.38 % (21054)Instructions burned: 183 (million)
% 7.47/2.38 % (21054)------------------------------
% 7.47/2.38 % (21054)------------------------------
% 7.47/2.38 % (21065)Instruction limit reached!
% 7.47/2.38 % (21065)------------------------------
% 7.47/2.38 % (21065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.38 % (21065)Termination reason: Unknown
% 7.47/2.38 % (21065)Termination phase: Preprocessing 3
% 7.47/2.38
% 7.47/2.38 % (21065)Memory used [KB]: 2174
% 7.47/2.38 % (21065)Time elapsed: 0.025 s
% 7.47/2.38 % (21065)Instructions burned: 80 (million)
% 7.47/2.38 % (21065)------------------------------
% 7.47/2.38 % (21065)------------------------------
% 7.47/2.39 % (21076)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/216Mi)
% 7.47/2.39 % (21078)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/114Mi)
% 7.47/2.39 % (21079)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/922Mi)
% 7.47/2.39 % (21080)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/182Mi)
% 8.20/2.40 % (21048)Instruction limit reached!
% 8.20/2.40 % (21048)------------------------------
% 8.20/2.40 % (21048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.40 % (21048)Termination reason: Unknown
% 8.20/2.40 % (21048)Termination phase: Saturation
% 8.20/2.40
% 8.20/2.40 % (21048)Memory used [KB]: 7675
% 8.20/2.40 % (21048)Time elapsed: 0.083 s
% 8.20/2.40 % (21048)Instructions burned: 297 (million)
% 8.20/2.40 % (21048)------------------------------
% 8.20/2.40 % (21048)------------------------------
% 8.20/2.41 % (21085)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/164Mi)
% 8.20/2.43 % (21078)Instruction limit reached!
% 8.20/2.43 % (21078)------------------------------
% 8.20/2.43 % (21078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.43 % (21078)Termination reason: Unknown
% 8.20/2.43 % (21078)Termination phase: Property scanning
% 8.20/2.43
% 8.20/2.43 % (21078)Memory used [KB]: 2558
% 8.20/2.43 % (21078)Time elapsed: 0.035 s
% 8.20/2.43 % (21078)Instructions burned: 114 (million)
% 8.20/2.43 % (21078)------------------------------
% 8.20/2.43 % (21078)------------------------------
% 8.20/2.43 % (21038)Instruction limit reached!
% 8.20/2.43 % (21038)------------------------------
% 8.20/2.43 % (21038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.43 % (21038)Termination reason: Unknown
% 8.20/2.43 % (21038)Termination phase: Saturation
% 8.20/2.43
% 8.20/2.43 % (21038)Memory used [KB]: 8571
% 8.20/2.43 % (21038)Time elapsed: 0.136 s
% 8.20/2.43 % (21038)Instructions burned: 458 (million)
% 8.20/2.43 % (21038)------------------------------
% 8.20/2.43 % (21038)------------------------------
% 8.20/2.44 % (21093)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/50Mi)
% 8.20/2.44 % (21080)Instruction limit reached!
% 8.20/2.44 % (21080)------------------------------
% 8.20/2.44 % (21080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.44 % (21080)Termination reason: Unknown
% 8.20/2.44 % (21080)Termination phase: Property scanning
% 8.20/2.44
% 8.20/2.44 % (21080)Memory used [KB]: 2558
% 8.20/2.44 % (21080)Time elapsed: 0.049 s
% 8.20/2.44 % (21080)Instructions burned: 182 (million)
% 8.20/2.44 % (21080)------------------------------
% 8.20/2.44 % (21080)------------------------------
% 8.20/2.44 % (21097)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/368Mi)
% 8.20/2.45 % (21076)Instruction limit reached!
% 8.20/2.45 % (21076)------------------------------
% 8.20/2.45 % (21076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.45 % (21076)Termination reason: Unknown
% 8.20/2.45 % (21076)Termination phase: Saturation
% 8.20/2.45
% 8.20/2.45 % (21076)Memory used [KB]: 7291
% 8.20/2.45 % (21076)Time elapsed: 0.059 s
% 8.20/2.45 % (21076)Instructions burned: 216 (million)
% 8.20/2.45 % (21076)------------------------------
% 8.20/2.45 % (21076)------------------------------
% 8.20/2.45 % (21101)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/1021Mi)
% 8.20/2.45 % (21093)Instruction limit reached!
% 8.20/2.45 % (21093)------------------------------
% 8.20/2.45 % (21093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.45 % (21093)Termination reason: Unknown
% 8.20/2.45 % (21093)Termination phase: shuffling
% 8.20/2.45
% 8.20/2.45 % (21093)Memory used [KB]: 2302
% 8.20/2.45 % (21093)Time elapsed: 0.016 s
% 8.20/2.45 % (21093)Instructions burned: 53 (million)
% 8.20/2.45 % (21093)------------------------------
% 8.20/2.45 % (21093)------------------------------
% 8.20/2.46 % (21102)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/267Mi)
% 8.20/2.46 % (21085)Instruction limit reached!
% 8.20/2.46 % (21085)------------------------------
% 8.20/2.46 % (21085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.46 % (21085)Termination reason: Unknown
% 8.20/2.46 % (21085)Termination phase: Saturation
% 8.20/2.46
% 8.20/2.46 % (21085)Memory used [KB]: 2430
% 8.20/2.46 % (21085)Time elapsed: 0.046 s
% 8.20/2.46 % (21085)Instructions burned: 167 (million)
% 8.20/2.46 % (21085)------------------------------
% 8.20/2.46 % (21085)------------------------------
% 8.20/2.46 % (21105)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/204Mi)
% 8.20/2.47 % (21107)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/26Mi)
% 8.20/2.48 % (21107)Instruction limit reached!
% 8.20/2.48 % (21107)------------------------------
% 8.20/2.48 % (21107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.48 % (21107)Termination reason: Unknown
% 8.20/2.48 % (21107)Termination phase: shuffling
% 8.20/2.48
% 8.20/2.48 % (21107)Memory used [KB]: 1918
% 8.20/2.48 % (21107)Time elapsed: 0.009 s
% 8.20/2.48 % (21107)Instructions burned: 29 (million)
% 8.20/2.48 % (21107)------------------------------
% 8.20/2.48 % (21107)------------------------------
% 8.20/2.49 % (21117)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_20598 for (2991ds/53Mi)
% 8.70/2.50 % (21117)Instruction limit reached!
% 8.70/2.50 % (21117)------------------------------
% 8.70/2.50 % (21117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.50 % (21117)Termination reason: Unknown
% 8.70/2.50 % (21117)Termination phase: shuffling
% 8.70/2.50
% 8.70/2.50 % (21117)Memory used [KB]: 2302
% 8.70/2.50 % (21117)Time elapsed: 0.016 s
% 8.70/2.50 % (21117)Instructions burned: 55 (million)
% 8.70/2.50 % (21117)------------------------------
% 8.70/2.50 % (21117)------------------------------
% 8.70/2.51 % (21135)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_20598 for (2990ds/4436Mi)
% 8.70/2.52 % (21105)Instruction limit reached!
% 8.70/2.52 % (21105)------------------------------
% 8.70/2.52 % (21105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.52 % (21105)Termination reason: Unknown
% 8.70/2.52 % (21105)Termination phase: Saturation
% 8.70/2.52
% 8.70/2.52 % (21105)Memory used [KB]: 7164
% 8.70/2.52 % (21105)Time elapsed: 0.058 s
% 8.70/2.52 % (21105)Instructions burned: 204 (million)
% 8.70/2.52 % (21105)------------------------------
% 8.70/2.52 % (21105)------------------------------
% 8.70/2.53 % (21145)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_20598 for (2990ds/1539Mi)
% 8.70/2.53 % (21102)Instruction limit reached!
% 8.70/2.53 % (21102)------------------------------
% 8.70/2.53 % (21102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.53 % (21102)Termination reason: Unknown
% 8.70/2.53 % (21102)Termination phase: Saturation
% 8.70/2.53
% 8.70/2.53 % (21102)Memory used [KB]: 7419
% 8.70/2.53 % (21102)Time elapsed: 0.075 s
% 8.70/2.53 % (21102)Instructions burned: 267 (million)
% 8.70/2.53 % (21102)------------------------------
% 8.70/2.53 % (21102)------------------------------
% 8.70/2.54 % (21150)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_20598 for (2990ds/408Mi)
% 8.70/2.55 % (21097)Instruction limit reached!
% 8.70/2.55 % (21097)------------------------------
% 8.70/2.55 % (21097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.55 % (21097)Termination reason: Unknown
% 8.70/2.55 % (21097)Termination phase: Saturation
% 8.70/2.55
% 8.70/2.55 % (21097)Memory used [KB]: 8315
% 8.70/2.55 % (21097)Time elapsed: 0.110 s
% 8.70/2.55 % (21097)Instructions burned: 370 (million)
% 8.70/2.55 % (21097)------------------------------
% 8.70/2.55 % (21097)------------------------------
% 8.70/2.56 % (21153)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_20598 for (2990ds/5205Mi)
% 9.00/2.62 % (21049)Instruction limit reached!
% 9.00/2.62 % (21049)------------------------------
% 9.00/2.62 % (21049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.00/2.62 % (21049)Termination reason: Unknown
% 9.00/2.62 % (21049)Termination phase: Saturation
% 9.00/2.62
% 9.00/2.62 % (21049)Memory used [KB]: 8955
% 9.00/2.62 % (21049)Time elapsed: 0.294 s
% 9.00/2.62 % (21049)Instructions burned: 989 (million)
% 9.00/2.62 % (21049)------------------------------
% 9.00/2.62 % (21049)------------------------------
% 9.00/2.63 % (21154)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_20598 for (2989ds/1913Mi)
% 9.00/2.66 % (21150)Instruction limit reached!
% 9.00/2.66 % (21150)------------------------------
% 9.00/2.66 % (21150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.00/2.66 % (21150)Termination reason: Unknown
% 9.00/2.66 % (21150)Termination phase: Saturation
% 9.00/2.66
% 9.00/2.66 % (21150)Memory used [KB]: 8699
% 9.00/2.66 % (21150)Time elapsed: 0.119 s
% 9.00/2.66 % (21150)Instructions burned: 408 (million)
% 9.00/2.66 % (21150)------------------------------
% 9.00/2.66 % (21150)------------------------------
% 9.00/2.67 % (21155)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_20598 for (2989ds/4350Mi)
% 9.00/2.68 % (21079)Instruction limit reached!
% 9.00/2.68 % (21079)------------------------------
% 9.00/2.68 % (21079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.00/2.68 % (21079)Termination reason: Unknown
% 9.00/2.68 % (21079)Termination phase: Saturation
% 9.00/2.68
% 9.00/2.68 % (21079)Memory used [KB]: 8827
% 9.00/2.68 % (21079)Time elapsed: 0.287 s
% 9.00/2.68 % (21079)Instructions burned: 924 (million)
% 9.00/2.68 % (21079)------------------------------
% 9.00/2.68 % (21079)------------------------------
% 9.00/2.69 % (21156)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_20598 for (2989ds/68Mi)
% 9.72/2.71 % (21156)Instruction limit reached!
% 9.72/2.71 % (21156)------------------------------
% 9.72/2.71 % (21156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.71 % (21156)Termination reason: Unknown
% 9.72/2.71 % (21156)Termination phase: SInE selection
% 9.72/2.71
% 9.72/2.71 % (21156)Memory used [KB]: 1918
% 9.72/2.71 % (21156)Time elapsed: 0.022 s
% 9.72/2.71 % (21156)Instructions burned: 71 (million)
% 9.72/2.71 % (21156)------------------------------
% 9.72/2.71 % (21156)------------------------------
% 9.72/2.72 % (21157)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_20598 for (2988ds/358Mi)
% 9.72/2.76 % (21101)Instruction limit reached!
% 9.72/2.76 % (21101)------------------------------
% 9.72/2.76 % (21101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.76 % (21101)Termination reason: Unknown
% 9.72/2.76 % (21101)Termination phase: Saturation
% 9.72/2.76
% 9.72/2.76 % (21101)Memory used [KB]: 8955
% 9.72/2.76 % (21101)Time elapsed: 0.315 s
% 9.72/2.76 % (21101)Instructions burned: 1022 (million)
% 9.72/2.76 % (21101)------------------------------
% 9.72/2.76 % (21101)------------------------------
% 9.72/2.77 % (21158)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_20598 for (2988ds/31Mi)
% 9.72/2.78 % (21158)Instruction limit reached!
% 9.72/2.78 % (21158)------------------------------
% 9.72/2.78 % (21158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.78 % (21158)Termination reason: Unknown
% 9.72/2.78 % (21158)Termination phase: shuffling
% 9.72/2.78
% 9.72/2.78 % (21158)Memory used [KB]: 1791
% 9.72/2.78 % (21158)Time elapsed: 0.011 s
% 9.72/2.78 % (21158)Instructions burned: 31 (million)
% 9.72/2.78 % (21158)------------------------------
% 9.72/2.78 % (21158)------------------------------
% 9.72/2.79 % (21159)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_20598 for (2988ds/279Mi)
% 10.10/2.83 % (21157)Instruction limit reached!
% 10.10/2.83 % (21157)------------------------------
% 10.10/2.83 % (21157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.10/2.83 % (21157)Termination reason: Unknown
% 10.10/2.83 % (21157)Termination phase: Saturation
% 10.10/2.83
% 10.10/2.83 % (21157)Memory used [KB]: 7803
% 10.10/2.83 % (21157)Time elapsed: 0.108 s
% 10.10/2.83 % (21157)Instructions burned: 359 (million)
% 10.10/2.83 % (21157)------------------------------
% 10.10/2.83 % (21157)------------------------------
% 10.10/2.83 % (21160)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_20598 for (2987ds/258Mi)
% 10.10/2.87 % (21159)Instruction limit reached!
% 10.10/2.87 % (21159)------------------------------
% 10.10/2.87 % (21159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.10/2.87 % (21159)Termination reason: Unknown
% 10.10/2.87 % (21159)Termination phase: Saturation
% 10.10/2.87
% 10.10/2.87 % (21159)Memory used [KB]: 7675
% 10.10/2.87 % (21159)Time elapsed: 0.075 s
% 10.10/2.87 % (21159)Instructions burned: 280 (million)
% 10.10/2.87 % (21159)------------------------------
% 10.10/2.87 % (21159)------------------------------
% 10.10/2.88 % (21161)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_20598 for (2987ds/26Mi)
% 10.10/2.88 % (21161)Instruction limit reached!
% 10.10/2.88 % (21161)------------------------------
% 10.10/2.88 % (21161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.10/2.88 % (21161)Termination reason: Unknown
% 10.10/2.88 % (21161)Termination phase: shuffling
% 10.10/2.88
% 10.10/2.88 % (21161)Memory used [KB]: 1918
% 10.10/2.88 % (21161)Time elapsed: 0.009 s
% 10.10/2.88 % (21161)Instructions burned: 27 (million)
% 10.10/2.88 % (21161)------------------------------
% 10.10/2.88 % (21161)------------------------------
% 10.10/2.89 % (21162)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_20598 for (2987ds/995Mi)
% 10.32/2.91 % (21160)Instruction limit reached!
% 10.32/2.91 % (21160)------------------------------
% 10.32/2.91 % (21160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.91 % (21160)Termination reason: Unknown
% 10.32/2.91 % (21160)Termination phase: Saturation
% 10.32/2.91
% 10.32/2.91 % (21160)Memory used [KB]: 7547
% 10.32/2.91 % (21160)Time elapsed: 0.074 s
% 10.32/2.91 % (21160)Instructions burned: 258 (million)
% 10.32/2.91 % (21160)------------------------------
% 10.32/2.91 % (21160)------------------------------
% 10.32/2.92 % (21163)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_20598 for (2986ds/373Mi)
% 10.32/2.99 % (21145)Instruction limit reached!
% 10.32/2.99 % (21145)------------------------------
% 10.32/2.99 % (21145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.99 % (21145)Termination reason: Unknown
% 10.32/2.99 % (21145)Termination phase: Saturation
% 10.32/2.99
% 10.32/2.99 % (21145)Memory used [KB]: 11129
% 10.32/2.99 % (21145)Time elapsed: 0.464 s
% 10.32/2.99 % (21145)Instructions burned: 1541 (million)
% 10.32/2.99 % (21145)------------------------------
% 10.32/2.99 % (21145)------------------------------
% 10.32/3.00 % (21164)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_20598 for (2986ds/253Mi)
% 12.87/3.03 % (21163)Instruction limit reached!
% 12.87/3.03 % (21163)------------------------------
% 12.87/3.03 % (21163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.87/3.03 % (21163)Termination reason: Unknown
% 12.87/3.03 % (21163)Termination phase: Saturation
% 12.87/3.03
% 12.87/3.03 % (21163)Memory used [KB]: 8187
% 12.87/3.03 % (21163)Time elapsed: 0.133 s
% 12.87/3.03 % (21163)Instructions burned: 375 (million)
% 12.87/3.03 % (21163)------------------------------
% 12.87/3.03 % (21163)------------------------------
% 12.87/3.04 % (21165)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_20598 for (2985ds/832Mi)
% 12.87/3.07 % (21164)Instruction limit reached!
% 12.87/3.07 % (21164)------------------------------
% 12.87/3.07 % (21164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.87/3.07 % (21164)Termination reason: Unknown
% 12.87/3.07 % (21164)Termination phase: Saturation
% 12.87/3.07
% 12.87/3.07 % (21164)Memory used [KB]: 7419
% 12.87/3.07 % (21164)Time elapsed: 0.068 s
% 12.87/3.07 % (21164)Instructions burned: 255 (million)
% 12.87/3.07 % (21164)------------------------------
% 12.87/3.07 % (21164)------------------------------
% 12.87/3.08 % (21166)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_20598 for (2985ds/668Mi)
% 13.43/3.18 % (21162)Instruction limit reached!
% 13.43/3.18 % (21162)------------------------------
% 13.43/3.18 % (21162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.43/3.18 % (21162)Termination reason: Unknown
% 13.43/3.18 % (21162)Termination phase: Saturation
% 13.43/3.18
% 13.43/3.18 % (21162)Memory used [KB]: 9083
% 13.43/3.18 % (21162)Time elapsed: 0.288 s
% 13.43/3.18 % (21162)Instructions burned: 995 (million)
% 13.43/3.18 % (21162)------------------------------
% 13.43/3.18 % (21162)------------------------------
% 13.43/3.19 % (21167)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_20598 for (2983ds/40Mi)
% 13.81/3.20 % (21167)Instruction limit reached!
% 13.81/3.20 % (21167)------------------------------
% 13.81/3.20 % (21167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.20 % (21167)Termination reason: Unknown
% 13.81/3.20 % (21167)Termination phase: shuffling
% 13.81/3.20
% 13.81/3.20 % (21167)Memory used [KB]: 2174
% 13.81/3.20 % (21167)Time elapsed: 0.013 s
% 13.81/3.20 % (21167)Instructions burned: 43 (million)
% 13.81/3.20 % (21167)------------------------------
% 13.81/3.20 % (21167)------------------------------
% 13.81/3.21 % (21154)Instruction limit reached!
% 13.81/3.21 % (21154)------------------------------
% 13.81/3.21 % (21154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.21 % (21154)Termination reason: Unknown
% 13.81/3.21 % (21154)Termination phase: Saturation
% 13.81/3.21
% 13.81/3.21 % (21154)Memory used [KB]: 4861
% 13.81/3.21 % (21154)Time elapsed: 0.584 s
% 13.81/3.21 % (21154)Instructions burned: 1913 (million)
% 13.81/3.21 % (21154)------------------------------
% 13.81/3.21 % (21154)------------------------------
% 13.81/3.21 % (21168)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_20598 for (2983ds/294Mi)
% 13.81/3.22 % (21169)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_20598 for (2983ds/187Mi)
% 13.81/3.26 % (21166)Instruction limit reached!
% 13.81/3.26 % (21166)------------------------------
% 13.81/3.26 % (21166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.26 % (21166)Termination reason: Unknown
% 13.81/3.26 % (21166)Termination phase: Saturation
% 13.81/3.26
% 13.81/3.26 % (21166)Memory used [KB]: 13304
% 13.81/3.26 % (21166)Time elapsed: 0.189 s
% 13.81/3.26 % (21166)Instructions burned: 670 (million)
% 13.81/3.26 % (21166)------------------------------
% 13.81/3.26 % (21166)------------------------------
% 13.81/3.27 % (21169)Instruction limit reached!
% 13.81/3.27 % (21169)------------------------------
% 13.81/3.27 % (21169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.27 % (21169)Termination reason: Unknown
% 13.81/3.27 % (21169)Termination phase: Saturation
% 13.81/3.27
% 13.81/3.27 % (21169)Memory used [KB]: 7291
% 13.81/3.27 % (21169)Time elapsed: 0.053 s
% 13.81/3.27 % (21169)Instructions burned: 187 (million)
% 13.81/3.27 % (21169)------------------------------
% 13.81/3.27 % (21169)------------------------------
% 13.81/3.27 % (21170)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_20598 for (2983ds/371Mi)
% 13.81/3.28 % (21171)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_20598 for (2983ds/1827Mi)
% 13.81/3.28 % (21165)Instruction limit reached!
% 13.81/3.28 % (21165)------------------------------
% 13.81/3.28 % (21165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.28 % (21165)Termination reason: Unknown
% 13.81/3.28 % (21165)Termination phase: Saturation
% 13.81/3.28
% 13.81/3.28 % (21165)Memory used [KB]: 10106
% 13.81/3.28 % (21165)Time elapsed: 0.245 s
% 13.81/3.28 % (21165)Instructions burned: 833 (million)
% 13.81/3.28 % (21165)------------------------------
% 13.81/3.28 % (21165)------------------------------
% 13.81/3.29 % (21172)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_20598 for (2983ds/70Mi)
% 13.81/3.29 % (21168)Instruction limit reached!
% 13.81/3.29 % (21168)------------------------------
% 13.81/3.29 % (21168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.29 % (21168)Termination reason: Unknown
% 13.81/3.29 % (21168)Termination phase: Saturation
% 13.81/3.29
% 13.81/3.29 % (21168)Memory used [KB]: 7547
% 13.81/3.29 % (21168)Time elapsed: 0.082 s
% 13.81/3.29 % (21168)Instructions burned: 294 (million)
% 13.81/3.29 % (21168)------------------------------
% 13.81/3.29 % (21168)------------------------------
% 14.76/3.30 % (21173)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_20598 for (2982ds/316Mi)
% 14.76/3.31 % (21172)Instruction limit reached!
% 14.76/3.31 % (21172)------------------------------
% 14.76/3.31 % (21172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.76/3.31 % (21172)Termination reason: Unknown
% 14.76/3.31 % (21172)Termination phase: Property scanning
% 14.76/3.31
% 14.76/3.31 % (21172)Memory used [KB]: 2302
% 14.76/3.31 % (21172)Time elapsed: 0.020 s
% 14.76/3.31 % (21172)Instructions burned: 71 (million)
% 14.76/3.31 % (21172)------------------------------
% 14.76/3.31 % (21172)------------------------------
% 14.76/3.32 % (21174)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_20598 for (2982ds/932Mi)
% 14.76/3.39 % (21170)Instruction limit reached!
% 14.76/3.39 % (21170)------------------------------
% 14.76/3.39 % (21170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.76/3.39 % (21170)Termination reason: Unknown
% 14.76/3.39 % (21170)Termination phase: Saturation
% 14.76/3.39
% 14.76/3.39 % (21170)Memory used [KB]: 8187
% 14.76/3.39 % (21170)Time elapsed: 0.113 s
% 14.76/3.39 % (21170)Instructions burned: 373 (million)
% 14.76/3.39 % (21170)------------------------------
% 14.76/3.39 % (21170)------------------------------
% 14.76/3.39 % (21173)Instruction limit reached!
% 14.76/3.39 % (21173)------------------------------
% 14.76/3.39 % (21173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.76/3.39 % (21173)Termination reason: Unknown
% 14.76/3.39 % (21173)Termination phase: Saturation
% 14.76/3.39
% 14.76/3.39 % (21173)Memory used [KB]: 7675
% 14.76/3.39 % (21173)Time elapsed: 0.087 s
% 14.76/3.39 % (21173)Instructions burned: 316 (million)
% 14.76/3.39 % (21173)------------------------------
% 14.76/3.39 % (21173)------------------------------
% 14.76/3.40 % (21175)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_20598 for (2981ds/4714Mi)
% 15.29/3.40 % (21176)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_20598 for (2981ds/8250Mi)
% 15.59/3.58 % (21174)Instruction limit reached!
% 15.59/3.58 % (21174)------------------------------
% 15.59/3.58 % (21174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.59/3.58 % (21174)Termination reason: Unknown
% 15.59/3.58 % (21174)Termination phase: Saturation
% 15.59/3.58
% 15.59/3.58 % (21174)Memory used [KB]: 9722
% 15.59/3.58 % (21174)Time elapsed: 0.263 s
% 15.59/3.58 % (21174)Instructions burned: 933 (million)
% 15.59/3.58 % (21174)------------------------------
% 15.59/3.58 % (21174)------------------------------
% 15.59/3.59 % (21177)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_20598 for (2980ds/770Mi)
% 16.76/3.83 % (21177)Instruction limit reached!
% 16.76/3.83 % (21177)------------------------------
% 16.76/3.83 % (21177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.76/3.83 % (21177)Termination reason: Unknown
% 16.76/3.83 % (21177)Termination phase: Saturation
% 16.76/3.83
% 16.76/3.83 % (21177)Memory used [KB]: 8443
% 16.76/3.83 % (21177)Time elapsed: 0.234 s
% 16.76/3.83 % (21177)Instructions burned: 772 (million)
% 16.76/3.83 % (21177)------------------------------
% 16.76/3.83 % (21177)------------------------------
% 16.76/3.84 % (21178)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_20598 for (2977ds/794Mi)
% 16.76/3.85 % (21171)Instruction limit reached!
% 16.76/3.85 % (21171)------------------------------
% 16.76/3.85 % (21171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.76/3.85 % (21171)Termination reason: Unknown
% 16.76/3.85 % (21171)Termination phase: Saturation
% 16.76/3.85
% 16.76/3.85 % (21171)Memory used [KB]: 10234
% 16.76/3.85 % (21171)Time elapsed: 0.566 s
% 16.76/3.85 % (21171)Instructions burned: 1829 (million)
% 16.76/3.85 % (21171)------------------------------
% 16.76/3.85 % (21171)------------------------------
% 16.76/3.86 % (21179)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_20598 for (2977ds/464Mi)
% 16.76/3.87 % (21135)Instruction limit reached!
% 16.76/3.87 % (21135)------------------------------
% 16.76/3.87 % (21135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.76/3.87 % (21135)Termination reason: Unknown
% 16.76/3.87 % (21135)Termination phase: Saturation
% 16.76/3.87
% 16.76/3.87 % (21135)Memory used [KB]: 13048
% 16.76/3.87 % (21135)Time elapsed: 1.361 s
% 16.76/3.87 % (21135)Instructions burned: 4438 (million)
% 16.76/3.87 % (21135)------------------------------
% 16.76/3.87 % (21135)------------------------------
% 16.76/3.88 % (21180)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_20598 for (2977ds/1376Mi)
% 17.87/3.93 % (21155)Instruction limit reached!
% 17.87/3.93 % (21155)------------------------------
% 17.87/3.93 % (21155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.93 % (21155)Termination reason: Unknown
% 17.87/3.93 % (21155)Termination phase: Saturation
% 17.87/3.93
% 17.87/3.93 % (21155)Memory used [KB]: 12665
% 17.87/3.93 % (21155)Time elapsed: 1.261 s
% 17.87/3.93 % (21155)Instructions burned: 4353 (million)
% 17.87/3.93 % (21155)------------------------------
% 17.87/3.93 % (21155)------------------------------
% 17.87/3.94 % (21181)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_20598 for (2976ds/906Mi)
% 17.87/4.00 % (21179)Instruction limit reached!
% 17.87/4.00 % (21179)------------------------------
% 17.87/4.00 % (21179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/4.00 % (21179)Termination reason: Unknown
% 17.87/4.00 % (21179)Termination phase: Saturation
% 17.87/4.00
% 17.87/4.00 % (21179)Memory used [KB]: 8315
% 17.87/4.00 % (21179)Time elapsed: 0.142 s
% 17.87/4.00 % (21179)Instructions burned: 464 (million)
% 17.87/4.00 % (21179)------------------------------
% 17.87/4.00 % (21179)------------------------------
% 17.87/4.01 % (21182)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_20598 for (2975ds/434Mi)
% 19.85/4.08 % (21178)Instruction limit reached!
% 19.85/4.08 % (21178)------------------------------
% 19.85/4.08 % (21178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.08 % (21178)Termination reason: Unknown
% 19.85/4.08 % (21178)Termination phase: Saturation
% 19.85/4.08
% 19.85/4.08 % (21178)Memory used [KB]: 5628
% 19.85/4.08 % (21178)Time elapsed: 0.242 s
% 19.85/4.08 % (21178)Instructions burned: 794 (million)
% 19.85/4.08 % (21178)------------------------------
% 19.85/4.08 % (21178)------------------------------
% 19.85/4.08 % (21153)Instruction limit reached!
% 19.85/4.08 % (21153)------------------------------
% 19.85/4.08 % (21153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.08 % (21153)Termination reason: Unknown
% 19.85/4.08 % (21153)Termination phase: Saturation
% 19.85/4.08
% 19.85/4.08 % (21153)Memory used [KB]: 14839
% 19.85/4.08 % (21153)Time elapsed: 1.524 s
% 19.85/4.08 % (21153)Instructions burned: 5208 (million)
% 19.85/4.08 % (21153)------------------------------
% 19.85/4.08 % (21153)------------------------------
% 19.85/4.09 % (21183)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_20598 for (2975ds/865Mi)
% 19.85/4.10 % (21184)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_20598 for (2975ds/593Mi)
% 20.42/4.13 % (21182)Instruction limit reached!
% 20.42/4.13 % (21182)------------------------------
% 20.42/4.13 % (21182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.42/4.13 % (21182)Termination reason: Unknown
% 20.42/4.13 % (21182)Termination phase: Saturation
% 20.42/4.13
% 20.42/4.13 % (21182)Memory used [KB]: 8443
% 20.42/4.13 % (21182)Time elapsed: 0.125 s
% 20.42/4.13 % (21182)Instructions burned: 434 (million)
% 20.42/4.13 % (21182)------------------------------
% 20.42/4.13 % (21182)------------------------------
% 20.42/4.14 % (21185)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_20598 for (2974ds/443Mi)
% 20.85/4.25 % (21181)Instruction limit reached!
% 20.85/4.25 % (21181)------------------------------
% 20.85/4.25 % (21181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.25 % (21181)Termination reason: Unknown
% 20.85/4.25 % (21181)Termination phase: Saturation
% 20.85/4.25
% 20.85/4.25 % (21181)Memory used [KB]: 12665
% 20.85/4.25 % (21181)Time elapsed: 0.315 s
% 20.85/4.25 % (21181)Instructions burned: 908 (million)
% 20.85/4.25 % (21181)------------------------------
% 20.85/4.25 % (21181)------------------------------
% 20.85/4.26 % (21184)Instruction limit reached!
% 20.85/4.26 % (21184)------------------------------
% 20.85/4.26 % (21184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.26 % (21184)Termination reason: Unknown
% 20.85/4.26 % (21184)Termination phase: Saturation
% 20.85/4.26
% 20.85/4.26 % (21184)Memory used [KB]: 9594
% 20.85/4.26 % (21184)Time elapsed: 0.166 s
% 20.85/4.26 % (21184)Instructions burned: 594 (million)
% 20.85/4.26 % (21184)------------------------------
% 20.85/4.26 % (21184)------------------------------
% 20.85/4.26 % (21186)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_20598 for (2973ds/594Mi)
% 20.85/4.27 % (21187)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_20598 for (2973ds/327Mi)
% 20.85/4.27 % (21185)Instruction limit reached!
% 20.85/4.27 % (21185)------------------------------
% 20.85/4.27 % (21185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.27 % (21185)Termination reason: Unknown
% 20.85/4.27 % (21185)Termination phase: Saturation
% 20.85/4.27
% 20.85/4.27 % (21185)Memory used [KB]: 8571
% 20.85/4.27 % (21185)Time elapsed: 0.134 s
% 20.85/4.27 % (21185)Instructions burned: 445 (million)
% 20.85/4.27 % (21185)------------------------------
% 20.85/4.27 % (21185)------------------------------
% 20.85/4.28 % (21188)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_20598 for (2972ds/5411Mi)
% 20.85/4.29 % (21180)Instruction limit reached!
% 20.85/4.29 % (21180)------------------------------
% 20.85/4.29 % (21180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.29 % (21180)Termination reason: Unknown
% 20.85/4.29 % (21180)Termination phase: Saturation
% 20.85/4.29
% 20.85/4.29 % (21180)Memory used [KB]: 14072
% 20.85/4.29 % (21180)Time elapsed: 0.414 s
% 20.85/4.29 % (21180)Instructions burned: 1377 (million)
% 20.85/4.29 % (21180)------------------------------
% 20.85/4.29 % (21180)------------------------------
% 21.53/4.30 % (21189)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_20598 for (2972ds/1762Mi)
% 21.53/4.34 % (21183)Instruction limit reached!
% 21.53/4.34 % (21183)------------------------------
% 21.53/4.34 % (21183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.53/4.34 % (21183)Termination reason: Unknown
% 21.53/4.34 % (21183)Termination phase: Saturation
% 21.53/4.34
% 21.53/4.34 % (21183)Memory used [KB]: 9338
% 21.53/4.34 % (21183)Time elapsed: 0.256 s
% 21.53/4.34 % (21183)Instructions burned: 867 (million)
% 21.53/4.34 % (21183)------------------------------
% 21.53/4.34 % (21183)------------------------------
% 21.53/4.35 % (21190)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_20598 for (2972ds/96Mi)
% 21.53/4.37 % (21187)Instruction limit reached!
% 21.53/4.37 % (21187)------------------------------
% 21.53/4.37 % (21187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.53/4.37 % (21187)Termination reason: Unknown
% 21.53/4.37 % (21187)Termination phase: Saturation
% 21.53/4.37
% 21.53/4.37 % (21187)Memory used [KB]: 8059
% 21.53/4.37 % (21187)Time elapsed: 0.098 s
% 21.53/4.37 % (21187)Instructions burned: 327 (million)
% 21.53/4.37 % (21187)------------------------------
% 21.53/4.37 % (21187)------------------------------
% 21.53/4.38 % (21191)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_20598 for (2972ds/503Mi)
% 21.53/4.38 % (21190)Instruction limit reached!
% 21.53/4.38 % (21190)------------------------------
% 21.53/4.38 % (21190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.53/4.38 % (21190)Termination reason: Unknown
% 21.53/4.38 % (21190)Termination phase: Preprocessing 1
% 21.53/4.38
% 21.53/4.38 % (21190)Memory used [KB]: 2430
% 21.53/4.38 % (21190)Time elapsed: 0.027 s
% 21.53/4.38 % (21190)Instructions burned: 98 (million)
% 21.53/4.38 % (21190)------------------------------
% 21.53/4.38 % (21190)------------------------------
% 21.53/4.39 % (21192)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_20598 for (2971ds/90Mi)
% 22.13/4.41 % (21192)Instruction limit reached!
% 22.13/4.41 % (21192)------------------------------
% 22.13/4.41 % (21192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.13/4.41 % (21192)Termination reason: Unknown
% 22.13/4.41 % (21192)Termination phase: Preprocessing 3
% 22.13/4.41
% 22.13/4.41 % (21192)Memory used [KB]: 2430
% 22.13/4.41 % (21192)Time elapsed: 0.028 s
% 22.13/4.41 % (21192)Instructions burned: 91 (million)
% 22.13/4.41 % (21192)------------------------------
% 22.13/4.41 % (21192)------------------------------
% 22.13/4.42 % (21193)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_20598 for (2971ds/593Mi)
% 22.13/4.44 % (21186)Instruction limit reached!
% 22.13/4.44 % (21186)------------------------------
% 22.13/4.44 % (21186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.13/4.44 % (21186)Termination reason: Unknown
% 22.13/4.44 % (21186)Termination phase: Saturation
% 22.13/4.44
% 22.13/4.44 % (21186)Memory used [KB]: 8443
% 22.13/4.44 % (21186)Time elapsed: 0.183 s
% 22.13/4.44 % (21186)Instructions burned: 595 (million)
% 22.13/4.44 % (21186)------------------------------
% 22.13/4.44 % (21186)------------------------------
% 22.13/4.45 % (21194)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_20598 for (2971ds/1512Mi)
% 22.56/4.52 % (21191)Instruction limit reached!
% 22.56/4.52 % (21191)------------------------------
% 22.56/4.52 % (21191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.56/4.52 % (21191)Termination reason: Unknown
% 22.56/4.52 % (21191)Termination phase: Saturation
% 22.56/4.52
% 22.56/4.52 % (21191)Memory used [KB]: 8699
% 22.56/4.52 % (21191)Time elapsed: 0.142 s
% 22.56/4.52 % (21191)Instructions burned: 503 (million)
% 22.56/4.52 % (21191)------------------------------
% 22.56/4.52 % (21191)------------------------------
% 22.56/4.53 % (21195)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_20598 for (2970ds/569Mi)
% 22.92/4.60 % (21193)Instruction limit reached!
% 22.92/4.60 % (21193)------------------------------
% 22.92/4.60 % (21193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.92/4.60 % (21193)Termination reason: Unknown
% 22.92/4.60 % (21193)Termination phase: Saturation
% 22.92/4.60
% 22.92/4.60 % (21193)Memory used [KB]: 8827
% 22.92/4.60 % (21193)Time elapsed: 0.179 s
% 22.92/4.60 % (21193)Instructions burned: 593 (million)
% 22.92/4.60 % (21193)------------------------------
% 22.92/4.60 % (21193)------------------------------
% 22.92/4.61 % (21196)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_20598 for (2969ds/501Mi)
% 22.92/4.63 % (21175)Instruction limit reached!
% 22.92/4.63 % (21175)------------------------------
% 22.92/4.63 % (21175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.92/4.63 % (21175)Termination reason: Unknown
% 22.92/4.63 % (21175)Termination phase: Saturation
% 22.92/4.63
% 22.92/4.63 % (21175)Memory used [KB]: 13304
% 22.92/4.63 % (21175)Time elapsed: 1.239 s
% 22.92/4.63 % (21175)Instructions burned: 4717 (million)
% 22.92/4.63 % (21175)------------------------------
% 22.92/4.63 % (21175)------------------------------
% 22.92/4.64 % (21197)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_20598 for (2969ds/562Mi)
% 22.92/4.69 % (21195)Instruction limit reached!
% 22.92/4.69 % (21195)------------------------------
% 22.92/4.69 % (21195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.92/4.69 % (21195)Termination reason: Unknown
% 22.92/4.69 % (21195)Termination phase: Saturation
% 22.92/4.69
% 22.92/4.69 % (21195)Memory used [KB]: 8571
% 22.92/4.69 % (21195)Time elapsed: 0.163 s
% 22.92/4.69 % (21195)Instructions burned: 571 (million)
% 22.92/4.69 % (21195)------------------------------
% 22.92/4.69 % (21195)------------------------------
% 23.43/4.70 % (21198)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_20598 for (2968ds/406Mi)
% 23.43/4.75 % (21196)Instruction limit reached!
% 23.43/4.75 % (21196)------------------------------
% 23.43/4.75 % (21196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.43/4.75 % (21196)Termination reason: Unknown
% 23.43/4.75 % (21196)Termination phase: Saturation
% 23.43/4.75
% 23.43/4.75 % (21196)Memory used [KB]: 9466
% 23.43/4.75 % (21196)Time elapsed: 0.144 s
% 23.43/4.75 % (21196)Instructions burned: 502 (million)
% 23.43/4.75 % (21196)------------------------------
% 23.43/4.75 % (21196)------------------------------
% 23.43/4.76 % (21199)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_20598 for (2968ds/582Mi)
% 23.43/4.78 % (21189)Instruction limit reached!
% 23.43/4.78 % (21189)------------------------------
% 23.43/4.78 % (21189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.43/4.78 % (21189)Termination reason: Unknown
% 23.43/4.78 % (21189)Termination phase: Saturation
% 23.43/4.78
% 23.43/4.78 % (21189)Memory used [KB]: 9722
% 23.43/4.78 % (21189)Time elapsed: 0.480 s
% 23.43/4.78 % (21189)Instructions burned: 1763 (million)
% 23.43/4.78 % (21189)------------------------------
% 23.43/4.78 % (21189)------------------------------
% 23.43/4.79 % (21200)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_20598 for (2967ds/456Mi)
% 24.18/4.80 % (21197)Instruction limit reached!
% 24.18/4.80 % (21197)------------------------------
% 24.18/4.80 % (21197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.18/4.80 % (21197)Termination reason: Unknown
% 24.18/4.80 % (21197)Termination phase: Saturation
% 24.18/4.80
% 24.18/4.80 % (21197)Memory used [KB]: 8699
% 24.18/4.80 % (21197)Time elapsed: 0.162 s
% 24.18/4.80 % (21197)Instructions burned: 562 (million)
% 24.18/4.80 % (21197)------------------------------
% 24.18/4.80 % (21197)------------------------------
% 24.18/4.81 % (21201)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_20598 for (2967ds/393Mi)
% 24.18/4.82 % (21198)Instruction limit reached!
% 24.18/4.82 % (21198)------------------------------
% 24.18/4.82 % (21198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.18/4.82 % (21198)Termination reason: Unknown
% 24.18/4.82 % (21198)Termination phase: Saturation
% 24.18/4.82
% 24.18/4.82 % (21198)Memory used [KB]: 8187
% 24.18/4.82 % (21198)Time elapsed: 0.122 s
% 24.18/4.82 % (21198)Instructions burned: 407 (million)
% 24.18/4.82 % (21198)------------------------------
% 24.18/4.82 % (21198)------------------------------
% 24.18/4.83 % (21202)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_20598 for (2967ds/1335Mi)
% 24.18/4.90 % (21194)Instruction limit reached!
% 24.18/4.90 % (21194)------------------------------
% 24.18/4.90 % (21194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.18/4.90 % (21194)Termination reason: Unknown
% 24.18/4.90 % (21194)Termination phase: Saturation
% 24.18/4.90
% 24.18/4.90 % (21194)Memory used [KB]: 9083
% 24.18/4.90 % (21194)Time elapsed: 0.443 s
% 24.18/4.90 % (21194)Instructions burned: 1513 (million)
% 24.18/4.90 % (21194)------------------------------
% 24.18/4.90 % (21194)------------------------------
% 25.03/4.90 % (21203)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_20598 for (2966ds/3373Mi)
% 25.03/4.92 % (21201)Instruction limit reached!
% 25.03/4.92 % (21201)------------------------------
% 25.03/4.92 % (21201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.03/4.92 % (21201)Termination reason: Unknown
% 25.03/4.92 % (21201)Termination phase: Saturation
% 25.03/4.92
% 25.03/4.92 % (21201)Memory used [KB]: 7547
% 25.03/4.92 % (21201)Time elapsed: 0.108 s
% 25.03/4.92 % (21201)Instructions burned: 394 (million)
% 25.03/4.92 % (21201)------------------------------
% 25.03/4.92 % (21201)------------------------------
% 25.03/4.93 % (21200)Instruction limit reached!
% 25.03/4.93 % (21200)------------------------------
% 25.03/4.93 % (21200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.03/4.93 % (21200)Termination reason: Unknown
% 25.03/4.93 % (21200)Termination phase: Saturation
% 25.03/4.93
% 25.03/4.93 % (21200)Memory used [KB]: 8955
% 25.03/4.93 % (21200)Time elapsed: 0.134 s
% 25.03/4.93 % (21200)Instructions burned: 457 (million)
% 25.03/4.93 % (21200)------------------------------
% 25.03/4.93 % (21200)------------------------------
% 25.03/4.93 % (21204)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_20598 for (2966ds/474Mi)
% 25.03/4.94 % (21205)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_20598 for (2966ds/157Mi)
% 25.03/4.94 % (21199)Instruction limit reached!
% 25.03/4.94 % (21199)------------------------------
% 25.03/4.94 % (21199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.03/4.94 % (21199)Termination reason: Unknown
% 25.03/4.94 % (21199)Termination phase: Saturation
% 25.03/4.94
% 25.03/4.94 % (21199)Memory used [KB]: 8827
% 25.03/4.94 % (21199)Time elapsed: 0.178 s
% 25.03/4.94 % (21199)Instructions burned: 584 (million)
% 25.03/4.94 % (21199)------------------------------
% 25.03/4.94 % (21199)------------------------------
% 25.03/4.95 % (21206)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_20598 for (2966ds/590Mi)
% 25.03/4.98 % (21205)Instruction limit reached!
% 25.03/4.98 % (21205)------------------------------
% 25.03/4.98 % (21205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.03/4.98 % (21205)Termination reason: Unknown
% 25.03/4.98 % (21205)Termination phase: Property scanning
% 25.03/4.98
% 25.03/4.98 % (21205)Memory used [KB]: 2430
% 25.03/4.98 % (21205)Time elapsed: 0.043 s
% 25.03/4.98 % (21205)Instructions burned: 159 (million)
% 25.03/4.98 % (21205)------------------------------
% 25.03/4.98 % (21205)------------------------------
% 25.03/4.99 % (21207)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_20598 for (2966ds/104Mi)
% 25.03/5.02 % (21207)Instruction limit reached!
% 25.03/5.02 % (21207)------------------------------
% 25.03/5.02 % (21207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.03/5.02 % (21207)Termination reason: Unknown
% 25.03/5.02 % (21207)Termination phase: Property scanning
% 25.03/5.02
% 25.03/5.02 % (21207)Memory used [KB]: 2558
% 25.03/5.02 % (21207)Time elapsed: 0.032 s
% 25.03/5.02 % (21207)Instructions burned: 106 (million)
% 25.03/5.02 % (21207)------------------------------
% 25.03/5.02 % (21207)------------------------------
% 26.91/5.03 % (21208)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_20598 for (2965ds/414Mi)
% 26.91/5.07 % (21204)Instruction limit reached!
% 26.91/5.07 % (21204)------------------------------
% 26.91/5.07 % (21204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.91/5.07 % (21204)Termination reason: Unknown
% 26.91/5.07 % (21204)Termination phase: Saturation
% 26.91/5.07
% 26.91/5.07 % (21204)Memory used [KB]: 8443
% 26.91/5.07 % (21204)Time elapsed: 0.136 s
% 26.91/5.07 % (21204)Instructions burned: 474 (million)
% 26.91/5.07 % (21204)------------------------------
% 26.91/5.07 % (21204)------------------------------
% 26.91/5.08 % (21209)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_20598 for (2965ds/715Mi)
% 26.91/5.12 % (21206)Instruction limit reached!
% 26.91/5.12 % (21206)------------------------------
% 26.91/5.12 % (21206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.91/5.12 % (21206)Termination reason: Unknown
% 26.91/5.12 % (21206)Termination phase: Saturation
% 26.91/5.12
% 26.91/5.12 % (21206)Memory used [KB]: 8955
% 26.91/5.12 % (21206)Time elapsed: 0.169 s
% 26.91/5.12 % (21206)Instructions burned: 592 (million)
% 26.91/5.12 % (21206)------------------------------
% 26.91/5.12 % (21206)------------------------------
% 27.48/5.13 % (21210)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_20598 for (2964ds/961Mi)
% 27.48/5.14 % (21208)Instruction limit reached!
% 27.48/5.14 % (21208)------------------------------
% 27.48/5.14 % (21208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.48/5.14 % (21208)Termination reason: Unknown
% 27.48/5.14 % (21208)Termination phase: Saturation
% 27.48/5.14
% 27.48/5.14 % (21208)Memory used [KB]: 7803
% 27.48/5.14 % (21208)Time elapsed: 0.138 s
% 27.48/5.14 % (21208)Instructions burned: 415 (million)
% 27.48/5.14 % (21208)------------------------------
% 27.48/5.14 % (21208)------------------------------
% 27.48/5.15 % (21211)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_20598 for (2964ds/1213Mi)
% 27.89/5.22 % (21202)Instruction limit reached!
% 27.89/5.22 % (21202)------------------------------
% 27.89/5.22 % (21202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.89/5.22 % (21202)Termination reason: Unknown
% 27.89/5.22 % (21202)Termination phase: Saturation
% 27.89/5.22
% 27.89/5.22 % (21202)Memory used [KB]: 9466
% 27.89/5.22 % (21202)Time elapsed: 0.391 s
% 27.89/5.22 % (21202)Instructions burned: 1337 (million)
% 27.89/5.22 % (21202)------------------------------
% 27.89/5.22 % (21202)------------------------------
% 27.89/5.23 % (21212)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_20598 for (2963ds/1979Mi)
% 27.89/5.29 % (21209)Instruction limit reached!
% 27.89/5.29 % (21209)------------------------------
% 27.89/5.29 % (21209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.89/5.29 % (21209)Termination reason: Unknown
% 27.89/5.29 % (21209)Termination phase: Saturation
% 27.89/5.29
% 27.89/5.29 % (21209)Memory used [KB]: 4349
% 27.89/5.29 % (21209)Time elapsed: 0.246 s
% 27.89/5.29 % (21209)Instructions burned: 716 (million)
% 27.89/5.29 % (21209)------------------------------
% 27.89/5.29 % (21209)------------------------------
% 28.45/5.30 % (21213)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_20598 for (2962ds/481Mi)
% 28.75/5.41 % (21210)Instruction limit reached!
% 28.75/5.41 % (21210)------------------------------
% 28.75/5.41 % (21210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.75/5.41 % (21210)Termination reason: Unknown
% 28.75/5.41 % (21210)Termination phase: Saturation
% 28.75/5.41
% 28.75/5.41 % (21210)Memory used [KB]: 8315
% 28.75/5.41 % (21210)Time elapsed: 0.311 s
% 28.75/5.41 % (21210)Instructions burned: 961 (million)
% 28.75/5.41 % (21210)------------------------------
% 28.75/5.41 % (21210)------------------------------
% 28.75/5.42 % (21214)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_20598 for (2961ds/783Mi)
% 28.75/5.44 % (21213)Instruction limit reached!
% 28.75/5.44 % (21213)------------------------------
% 28.75/5.44 % (21213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.75/5.44 % (21213)Termination reason: Unknown
% 28.75/5.44 % (21213)Termination phase: Saturation
% 28.75/5.44
% 28.75/5.44 % (21213)Memory used [KB]: 8059
% 28.75/5.44 % (21213)Time elapsed: 0.141 s
% 28.75/5.44 % (21213)Instructions burned: 481 (million)
% 28.75/5.44 % (21213)------------------------------
% 28.75/5.44 % (21213)------------------------------
% 28.75/5.45 % (21215)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_20598 for (2961ds/432Mi)
% 29.50/5.52 % (21211)Instruction limit reached!
% 29.50/5.52 % (21211)------------------------------
% 29.50/5.52 % (21211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.50/5.52 % (21211)Termination reason: Unknown
% 29.50/5.52 % (21211)Termination phase: Saturation
% 29.50/5.52
% 29.50/5.52 % (21211)Memory used [KB]: 9466
% 29.50/5.52 % (21211)Time elapsed: 0.373 s
% 29.50/5.52 % (21211)Instructions burned: 1213 (million)
% 29.50/5.52 % (21211)------------------------------
% 29.50/5.52 % (21211)------------------------------
% 29.50/5.53 % (21216)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_20598 for (2960ds/1670Mi)
% 29.50/5.58 % (21215)Instruction limit reached!
% 29.50/5.58 % (21215)------------------------------
% 29.50/5.58 % (21215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.50/5.58 % (21215)Termination reason: Unknown
% 29.50/5.58 % (21215)Termination phase: Saturation
% 29.50/5.58
% 29.50/5.58 % (21215)Memory used [KB]: 7931
% 29.50/5.58 % (21215)Time elapsed: 0.132 s
% 29.50/5.58 % (21215)Instructions burned: 434 (million)
% 29.50/5.58 % (21215)------------------------------
% 29.50/5.58 % (21215)------------------------------
% 29.50/5.59 % (21217)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_20598 for (2959ds/90Mi)
% 30.33/5.62 % (21217)Instruction limit reached!
% 30.33/5.62 % (21217)------------------------------
% 30.33/5.62 % (21217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.33/5.62 % (21217)Termination reason: Unknown
% 30.33/5.62 % (21217)Termination phase: Preprocessing 3
% 30.33/5.62
% 30.33/5.62 % (21217)Memory used [KB]: 2302
% 30.33/5.62 % (21217)Time elapsed: 0.028 s
% 30.33/5.62 % (21217)Instructions burned: 90 (million)
% 30.33/5.62 % (21217)------------------------------
% 30.33/5.62 % (21217)------------------------------
% 30.33/5.63 % (21218)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_20598 for (2959ds/346Mi)
% 30.33/5.66 % (21214)Instruction limit reached!
% 30.33/5.66 % (21214)------------------------------
% 30.33/5.66 % (21214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.33/5.66 % (21214)Termination reason: Unknown
% 30.33/5.66 % (21214)Termination phase: Saturation
% 30.33/5.66
% 30.33/5.66 % (21214)Memory used [KB]: 8571
% 30.33/5.66 % (21214)Time elapsed: 0.238 s
% 30.33/5.66 % (21214)Instructions burned: 786 (million)
% 30.33/5.66 % (21214)------------------------------
% 30.33/5.66 % (21214)------------------------------
% 30.33/5.67 % (21219)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_20598 for (2959ds/401Mi)
% 30.91/5.73 % (21218)Instruction limit reached!
% 30.91/5.73 % (21218)------------------------------
% 30.91/5.73 % (21218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/5.73 % (21218)Termination reason: Unknown
% 30.91/5.73 % (21218)Termination phase: Saturation
% 30.91/5.73
% 30.91/5.73 % (21218)Memory used [KB]: 7675
% 30.91/5.73 % (21218)Time elapsed: 0.100 s
% 30.91/5.73 % (21218)Instructions burned: 348 (million)
% 30.91/5.73 % (21218)------------------------------
% 30.91/5.73 % (21218)------------------------------
% 30.91/5.74 % (21220)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_20598 for (2958ds/6454Mi)
% 30.91/5.78 % (21219)Instruction limit reached!
% 30.91/5.78 % (21219)------------------------------
% 30.91/5.78 % (21219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/5.78 % (21219)Termination reason: Unknown
% 30.91/5.78 % (21219)Termination phase: Saturation
% 30.91/5.78
% 30.91/5.78 % (21219)Memory used [KB]: 8571
% 30.91/5.78 % (21219)Time elapsed: 0.109 s
% 30.91/5.78 % (21219)Instructions burned: 403 (million)
% 30.91/5.78 % (21219)------------------------------
% 30.91/5.78 % (21219)------------------------------
% 30.91/5.78 % (21176)Instruction limit reached!
% 30.91/5.78 % (21176)------------------------------
% 30.91/5.78 % (21176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/5.78 % (21176)Termination reason: Unknown
% 30.91/5.78 % (21176)Termination phase: Saturation
% 30.91/5.78
% 30.91/5.78 % (21176)Memory used [KB]: 13048
% 30.91/5.78 % (21176)Time elapsed: 2.382 s
% 30.91/5.78 % (21176)Instructions burned: 8251 (million)
% 30.91/5.78 % (21176)------------------------------
% 30.91/5.78 % (21176)------------------------------
% 30.91/5.79 % (21212)Instruction limit reached!
% 30.91/5.79 % (21212)------------------------------
% 30.91/5.79 % (21212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/5.79 % (21212)Termination reason: Unknown
% 30.91/5.79 % (21212)Termination phase: Saturation
% 30.91/5.79
% 30.91/5.79 % (21212)Memory used [KB]: 8699
% 30.91/5.79 % (21212)Time elapsed: 0.559 s
% 30.91/5.79 % (21212)Instructions burned: 1979 (million)
% 30.91/5.79 % (21212)------------------------------
% 30.91/5.79 % (21212)------------------------------
% 30.91/5.79 % (21221)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_20598 for (2957ds/283Mi)
% 30.91/5.79 % (21222)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_20598 for (2957ds/865Mi)
% 32.00/5.80 % (21223)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_20598 for (2957ds/4528Mi)
% 32.00/5.82 % (21188)Instruction limit reached!
% 32.00/5.82 % (21188)------------------------------
% 32.00/5.82 % (21188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.00/5.82 % (21188)Termination reason: Unknown
% 32.00/5.82 % (21188)Termination phase: Saturation
% 32.00/5.82
% 32.00/5.82 % (21188)Memory used [KB]: 10362
% 32.00/5.82 % (21188)Time elapsed: 1.542 s
% 32.00/5.82 % (21188)Instructions burned: 5413 (million)
% 32.00/5.82 % (21188)------------------------------
% 32.00/5.82 % (21188)------------------------------
% 32.00/5.83 % (21224)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_20598 for (2957ds/1001Mi)
% 32.00/5.87 % (21221)Instruction limit reached!
% 32.00/5.87 % (21221)------------------------------
% 32.00/5.87 % (21221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.00/5.87 % (21221)Termination reason: Unknown
% 32.00/5.87 % (21221)Termination phase: Saturation
% 32.00/5.87
% 32.00/5.87 % (21221)Memory used [KB]: 7803
% 32.00/5.87 % (21221)Time elapsed: 0.085 s
% 32.00/5.87 % (21221)Instructions burned: 285 (million)
% 32.00/5.87 % (21221)------------------------------
% 32.00/5.87 % (21221)------------------------------
% 32.00/5.88 % (21225)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_20598 for (2957ds/102Mi)
% 32.00/5.88 % (21203)Instruction limit reached!
% 32.00/5.88 % (21203)------------------------------
% 32.00/5.88 % (21203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.00/5.88 % (21203)Termination reason: Unknown
% 32.00/5.88 % (21203)Termination phase: Saturation
% 32.00/5.88
% 32.00/5.88 % (21203)Memory used [KB]: 11897
% 32.00/5.88 % (21203)Time elapsed: 0.979 s
% 32.00/5.88 % (21203)Instructions burned: 3373 (million)
% 32.00/5.88 % (21203)------------------------------
% 32.00/5.88 % (21203)------------------------------
% 32.00/5.89 % (21226)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_20598 for (2956ds/952Mi)
% 32.24/5.91 % (21225)Instruction limit reached!
% 32.24/5.91 % (21225)------------------------------
% 32.24/5.91 % (21225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.24/5.91 % (21225)Termination reason: Unknown
% 32.24/5.91 % (21225)Termination phase: Preprocessing 1
% 32.24/5.91
% 32.24/5.91 % (21225)Memory used [KB]: 2430
% 32.24/5.91 % (21225)Time elapsed: 0.028 s
% 32.24/5.91 % (21225)Instructions burned: 102 (million)
% 32.24/5.91 % (21225)------------------------------
% 32.24/5.91 % (21225)------------------------------
% 32.24/5.92 % (21227)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_20598 for (2956ds/578Mi)
% 32.24/6.02 % (21216)Instruction limit reached!
% 32.24/6.02 % (21216)------------------------------
% 32.24/6.02 % (21216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.24/6.02 % (21216)Termination reason: Unknown
% 32.24/6.02 % (21216)Termination phase: Saturation
% 32.24/6.02
% 32.24/6.02 % (21216)Memory used [KB]: 11513
% 32.24/6.02 % (21216)Time elapsed: 0.486 s
% 32.24/6.02 % (21216)Instructions burned: 1671 (million)
% 32.24/6.02 % (21216)------------------------------
% 32.24/6.02 % (21216)------------------------------
% 33.43/6.03 % (21228)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_20598 for (2955ds/643Mi)
% 33.43/6.05 % (21222)Instruction limit reached!
% 33.43/6.05 % (21222)------------------------------
% 33.43/6.05 % (21222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.43/6.05 % (21222)Termination reason: Unknown
% 33.43/6.05 % (21222)Termination phase: Saturation
% 33.43/6.05
% 33.43/6.05 % (21222)Memory used [KB]: 9978
% 33.43/6.05 % (21222)Time elapsed: 0.266 s
% 33.43/6.05 % (21222)Instructions burned: 866 (million)
% 33.43/6.05 % (21222)------------------------------
% 33.43/6.05 % (21222)------------------------------
% 33.43/6.06 % (21229)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_20598 for (2955ds/865Mi)
% 33.43/6.08 % (21227)Instruction limit reached!
% 33.43/6.08 % (21227)------------------------------
% 33.43/6.08 % (21227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.43/6.08 % (21227)Termination reason: Unknown
% 33.43/6.08 % (21227)Termination phase: Saturation
% 33.43/6.08
% 33.43/6.08 % (21227)Memory used [KB]: 9210
% 33.43/6.08 % (21227)Time elapsed: 0.167 s
% 33.43/6.08 % (21227)Instructions burned: 578 (million)
% 33.43/6.08 % (21227)------------------------------
% 33.43/6.08 % (21227)------------------------------
% 33.43/6.09 % (21230)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_20598 for (2954ds/1174Mi)
% 34.46/6.13 % (21224)Instruction limit reached!
% 34.46/6.13 % (21224)------------------------------
% 34.46/6.13 % (21224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.46/6.13 % (21224)Termination reason: Unknown
% 34.46/6.13 % (21224)Termination phase: Saturation
% 34.46/6.13
% 34.46/6.13 % (21224)Memory used [KB]: 10362
% 34.46/6.13 % (21224)Time elapsed: 0.294 s
% 34.46/6.13 % (21224)Instructions burned: 1001 (million)
% 34.46/6.13 % (21224)------------------------------
% 34.46/6.13 % (21224)------------------------------
% 34.46/6.14 % (21231)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_20598 for (2954ds/644Mi)
% 34.46/6.18 % (21226)Instruction limit reached!
% 34.46/6.18 % (21226)------------------------------
% 34.46/6.18 % (21226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.46/6.18 % (21226)Termination reason: Unknown
% 34.46/6.18 % (21226)Termination phase: Saturation
% 34.46/6.18
% 34.46/6.18 % (21226)Memory used [KB]: 10106
% 34.46/6.18 % (21226)Time elapsed: 0.292 s
% 34.46/6.18 % (21226)Instructions burned: 953 (million)
% 34.46/6.18 % (21226)------------------------------
% 34.46/6.18 % (21226)------------------------------
% 34.46/6.19 % (21232)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_20598 for (2953ds/1201Mi)
% 34.68/6.22 % (21228)Instruction limit reached!
% 34.68/6.22 % (21228)------------------------------
% 34.68/6.22 % (21228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.22 % (21228)Termination reason: Unknown
% 34.68/6.22 % (21228)Termination phase: Saturation
% 34.68/6.22
% 34.68/6.22 % (21228)Memory used [KB]: 9594
% 34.68/6.22 % (21228)Time elapsed: 0.183 s
% 34.68/6.22 % (21228)Instructions burned: 645 (million)
% 34.68/6.22 % (21228)------------------------------
% 34.68/6.22 % (21228)------------------------------
% 34.68/6.23 % (21233)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_20598 for (2953ds/1046Mi)
% 34.68/6.29 % (21229)Refutation not found, non-redundant clauses discarded% (21229)------------------------------
% 34.68/6.29 % (21229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.29 % (21229)Termination reason: Refutation not found, non-redundant clauses discarded
% 34.68/6.29
% 34.68/6.29 % (21229)Memory used [KB]: 8827
% 34.68/6.29 % (21229)Time elapsed: 0.224 s
% 34.68/6.29 % (21229)Instructions burned: 736 (million)
% 34.68/6.29 % (21229)------------------------------
% 34.68/6.29 % (21229)------------------------------
% 35.31/6.30 % (21234)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_20598 for (2952ds/222Mi)
% 35.31/6.33 % (21231)Instruction limit reached!
% 35.31/6.33 % (21231)------------------------------
% 35.31/6.33 % (21231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.31/6.33 % (21231)Termination reason: Unknown
% 35.31/6.33 % (21231)Termination phase: Saturation
% 35.31/6.33
% 35.31/6.33 % (21231)Memory used [KB]: 10234
% 35.31/6.33 % (21231)Time elapsed: 0.194 s
% 35.31/6.33 % (21231)Instructions burned: 646 (million)
% 35.31/6.33 % (21231)------------------------------
% 35.31/6.33 % (21231)------------------------------
% 35.31/6.34 % (21235)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_20598 for (2952ds/68Mi)
% 35.31/6.36 % (21234)Instruction limit reached!
% 35.31/6.36 % (21234)------------------------------
% 35.31/6.36 % (21234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.31/6.36 % (21234)Termination reason: Unknown
% 35.31/6.36 % (21234)Termination phase: Saturation
% 35.31/6.36
% 35.31/6.36 % (21234)Memory used [KB]: 7291
% 35.31/6.36 % (21234)Time elapsed: 0.059 s
% 35.31/6.36 % (21234)Instructions burned: 224 (million)
% 35.31/6.36 % (21234)------------------------------
% 35.31/6.36 % (21234)------------------------------
% 35.31/6.36 % (21235)Instruction limit reached!
% 35.31/6.36 % (21235)------------------------------
% 35.31/6.36 % (21235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.31/6.36 % (21235)Termination reason: Unknown
% 35.31/6.36 % (21235)Termination phase: SInE selection
% 35.31/6.36
% 35.31/6.36 % (21235)Memory used [KB]: 1918
% 35.31/6.36 % (21235)Time elapsed: 0.022 s
% 35.31/6.36 % (21235)Instructions burned: 71 (million)
% 35.31/6.36 % (21235)------------------------------
% 35.31/6.36 % (21235)------------------------------
% 35.31/6.37 % (21236)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_20598 for (2952ds/454Mi)
% 35.31/6.37 % (21237)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_20598 for (2952ds/360Mi)
% 35.82/6.45 % (21230)Instruction limit reached!
% 35.82/6.45 % (21230)------------------------------
% 35.82/6.45 % (21230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.82/6.45 % (21230)Termination reason: Unknown
% 35.82/6.45 % (21230)Termination phase: Saturation
% 35.82/6.45
% 35.82/6.45 % (21230)Memory used [KB]: 9978
% 35.82/6.45 % (21230)Time elapsed: 0.357 s
% 35.82/6.45 % (21230)Instructions burned: 1175 (million)
% 35.82/6.45 % (21230)------------------------------
% 35.82/6.45 % (21230)------------------------------
% 35.82/6.46 % (21238)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_20598 for (2951ds/157Mi)
% 35.82/6.47 % (21237)Instruction limit reached!
% 35.82/6.47 % (21237)------------------------------
% 35.82/6.47 % (21237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.82/6.47 % (21237)Termination reason: Unknown
% 35.82/6.47 % (21237)Termination phase: Saturation
% 35.82/6.47
% 35.82/6.47 % (21237)Memory used [KB]: 7803
% 35.82/6.47 % (21237)Time elapsed: 0.101 s
% 35.82/6.47 % (21237)Instructions burned: 362 (million)
% 35.82/6.47 % (21237)------------------------------
% 35.82/6.47 % (21237)------------------------------
% 35.82/6.48 % (21239)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_20598 for (2951ds/5061Mi)
% 35.82/6.50 % (21236)Instruction limit reached!
% 35.82/6.50 % (21236)------------------------------
% 35.82/6.50 % (21236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.82/6.50 % (21236)Termination reason: Unknown
% 35.82/6.50 % (21236)Termination phase: Saturation
% 35.82/6.50
% 35.82/6.50 % (21236)Memory used [KB]: 13176
% 35.82/6.50 % (21236)Time elapsed: 0.131 s
% 35.82/6.50 % (21236)Instructions burned: 455 (million)
% 35.82/6.50 % (21236)------------------------------
% 35.82/6.50 % (21236)------------------------------
% 36.64/6.50 % (21238)Instruction limit reached!
% 36.64/6.50 % (21238)------------------------------
% 36.64/6.50 % (21238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.64/6.50 % (21238)Termination reason: Unknown
% 36.64/6.50 % (21238)Termination phase: Property scanning
% 36.64/6.50
% 36.64/6.50 % (21238)Memory used [KB]: 2558
% 36.64/6.50 % (21238)Time elapsed: 0.043 s
% 36.64/6.50 % (21238)Instructions burned: 160 (million)
% 36.64/6.50 % (21238)------------------------------
% 36.64/6.50 % (21238)------------------------------
% 36.64/6.51 % (21240)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_20598 for (2950ds/2401Mi)
% 36.64/6.51 % (21241)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_20598 for (2950ds/5798Mi)
% 36.64/6.52 % (21232)Instruction limit reached!
% 36.64/6.52 % (21232)------------------------------
% 36.64/6.52 % (21232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.64/6.52 % (21232)Termination reason: Unknown
% 36.64/6.52 % (21232)Termination phase: Saturation
% 36.64/6.52
% 36.64/6.52 % (21232)Memory used [KB]: 10106
% 36.64/6.52 % (21232)Time elapsed: 0.332 s
% 36.64/6.52 % (21232)Instructions burned: 1201 (million)
% 36.64/6.52 % (21232)------------------------------
% 36.64/6.52 % (21232)------------------------------
% 36.64/6.53 % (21233)Instruction limit reached!
% 36.64/6.53 % (21233)------------------------------
% 36.64/6.53 % (21233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.64/6.53 % (21233)Termination reason: Unknown
% 36.64/6.53 % (21233)Termination phase: Saturation
% 36.64/6.53
% 36.64/6.53 % (21233)Memory used [KB]: 9210
% 36.64/6.53 % (21233)Time elapsed: 0.302 s
% 36.64/6.53 % (21233)Instructions burned: 1049 (million)
% 36.64/6.53 % (21233)------------------------------
% 36.64/6.53 % (21233)------------------------------
% 36.64/6.53 % (21242)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_20598 for (2950ds/346Mi)
% 36.64/6.54 % (21243)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_20598 for (2950ds/1321Mi)
% 37.54/6.63 % (21242)Instruction limit reached!
% 37.54/6.63 % (21242)------------------------------
% 37.54/6.63 % (21242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.54/6.63 % (21242)Termination reason: Unknown
% 37.54/6.63 % (21242)Termination phase: Saturation
% 37.54/6.63
% 37.54/6.63 % (21242)Memory used [KB]: 7675
% 37.54/6.63 % (21242)Time elapsed: 0.100 s
% 37.54/6.63 % (21242)Instructions burned: 346 (million)
% 37.54/6.63 % (21242)------------------------------
% 37.54/6.63 % (21242)------------------------------
% 37.54/6.64 % (21244)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_20598 for (2949ds/1312Mi)
% 38.25/6.91 % (21243)Instruction limit reached!
% 38.25/6.91 % (21243)------------------------------
% 38.25/6.91 % (21243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.25/6.91 % (21243)Termination reason: Unknown
% 38.25/6.91 % (21243)Termination phase: Saturation
% 38.25/6.91
% 38.25/6.91 % (21243)Memory used [KB]: 6012
% 38.25/6.91 % (21243)Time elapsed: 0.373 s
% 38.25/6.91 % (21243)Instructions burned: 1322 (million)
% 38.25/6.91 % (21243)------------------------------
% 38.25/6.91 % (21243)------------------------------
% 38.25/6.92 % (21245)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_20598 for (2946ds/672Mi)
% 40.93/7.03 % (21244)Instruction limit reached!
% 40.93/7.03 % (21244)------------------------------
% 40.93/7.03 % (21244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.93/7.03 % (21244)Termination reason: Unknown
% 40.93/7.03 % (21244)Termination phase: Saturation
% 40.93/7.03
% 40.93/7.03 % (21244)Memory used [KB]: 9850
% 40.93/7.03 % (21244)Time elapsed: 0.385 s
% 40.93/7.03 % (21244)Instructions burned: 1312 (million)
% 40.93/7.03 % (21244)------------------------------
% 40.93/7.03 % (21244)------------------------------
% 40.93/7.04 % (21246)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_20598 for (2945ds/1897Mi)
% 40.93/7.07 % (21223)Instruction limit reached!
% 40.93/7.07 % (21223)------------------------------
% 40.93/7.07 % (21223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.93/7.07 % (21223)Termination reason: Unknown
% 40.93/7.07 % (21223)Termination phase: Saturation
% 40.93/7.07
% 40.93/7.07 % (21223)Memory used [KB]: 8315
% 40.93/7.07 % (21223)Time elapsed: 1.278 s
% 40.93/7.07 % (21223)Instructions burned: 4528 (million)
% 40.93/7.07 % (21223)------------------------------
% 40.93/7.07 % (21223)------------------------------
% 40.93/7.08 % (21247)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_20598 for (2945ds/1202Mi)
% 40.93/7.12 % (21245)Instruction limit reached!
% 40.93/7.12 % (21245)------------------------------
% 40.93/7.12 % (21245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.93/7.12 % (21245)Termination reason: Unknown
% 40.93/7.12 % (21245)Termination phase: Saturation
% 40.93/7.12
% 40.93/7.12 % (21245)Memory used [KB]: 8827
% 40.93/7.12 % (21245)Time elapsed: 0.204 s
% 40.93/7.12 % (21245)Instructions burned: 674 (million)
% 40.93/7.12 % (21245)------------------------------
% 40.93/7.12 % (21245)------------------------------
% 41.52/7.13 % (21248)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_20598 for (2944ds/1493Mi)
% 41.52/7.18 % (21240)Instruction limit reached!
% 41.52/7.18 % (21240)------------------------------
% 41.52/7.18 % (21240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.52/7.18 % (21240)Termination reason: Unknown
% 41.52/7.18 % (21240)Termination phase: Saturation
% 41.52/7.18
% 41.52/7.18 % (21240)Memory used [KB]: 6396
% 41.52/7.18 % (21240)Time elapsed: 0.680 s
% 41.52/7.18 % (21240)Instructions burned: 2402 (million)
% 41.52/7.18 % (21240)------------------------------
% 41.52/7.18 % (21240)------------------------------
% 41.52/7.19 % (21249)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_20598 for (2943ds/7679Mi)
% 42.42/7.45 % (21247)Instruction limit reached!
% 42.42/7.45 % (21247)------------------------------
% 42.42/7.45 % (21247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.42/7.45 % (21247)Termination reason: Unknown
% 42.42/7.45 % (21247)Termination phase: Saturation
% 42.42/7.45
% 42.42/7.45 % (21247)Memory used [KB]: 5884
% 42.42/7.45 % (21247)Time elapsed: 0.369 s
% 42.42/7.45 % (21247)Instructions burned: 1203 (million)
% 42.42/7.45 % (21247)------------------------------
% 42.42/7.45 % (21247)------------------------------
% 42.42/7.46 % (21250)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_20598 for (2941ds/340Mi)
% 43.11/7.54 % (21248)Instruction limit reached!
% 43.11/7.54 % (21248)------------------------------
% 43.11/7.54 % (21248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.11/7.54 % (21248)Termination reason: Unknown
% 43.11/7.54 % (21248)Termination phase: Saturation
% 43.11/7.54
% 43.11/7.54 % (21248)Memory used [KB]: 7931
% 43.11/7.54 % (21248)Time elapsed: 0.415 s
% 43.11/7.54 % (21248)Instructions burned: 1495 (million)
% 43.11/7.54 % (21248)------------------------------
% 43.11/7.54 % (21248)------------------------------
% 43.11/7.55 % (21251)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_20598 for (2940ds/3672Mi)
% 43.11/7.56 % (21250)Instruction limit reached!
% 43.11/7.56 % (21250)------------------------------
% 43.11/7.56 % (21250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.11/7.56 % (21250)Termination reason: Unknown
% 43.11/7.56 % (21250)Termination phase: Saturation
% 43.11/7.56
% 43.11/7.56 % (21250)Memory used [KB]: 8827
% 43.11/7.56 % (21250)Time elapsed: 0.100 s
% 43.11/7.56 % (21250)Instructions burned: 340 (million)
% 43.11/7.56 % (21250)------------------------------
% 43.11/7.56 % (21250)------------------------------
% 43.11/7.57 % (21252)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_20598 for (2940ds/1535Mi)
% 43.93/7.62 % (21246)Instruction limit reached!
% 43.93/7.62 % (21246)------------------------------
% 43.93/7.62 % (21246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.93/7.62 % (21246)Termination reason: Unknown
% 43.93/7.62 % (21246)Termination phase: Saturation
% 43.93/7.62
% 43.93/7.62 % (21246)Memory used [KB]: 11129
% 43.93/7.62 % (21246)Time elapsed: 0.579 s
% 43.93/7.62 % (21246)Instructions burned: 1898 (million)
% 43.93/7.62 % (21246)------------------------------
% 43.93/7.62 % (21246)------------------------------
% 43.93/7.63 % (21253)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_20598 for (2939ds/4637Mi)
% 43.93/7.63 % (21220)Instruction limit reached!
% 43.93/7.63 % (21220)------------------------------
% 43.93/7.63 % (21220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.93/7.63 % (21220)Termination reason: Unknown
% 43.93/7.63 % (21220)Termination phase: Saturation
% 43.93/7.63
% 43.93/7.63 % (21220)Memory used [KB]: 14583
% 43.93/7.63 % (21220)Time elapsed: 1.893 s
% 43.93/7.63 % (21220)Instructions burned: 6455 (million)
% 43.93/7.63 % (21220)------------------------------
% 43.93/7.63 % (21220)------------------------------
% 43.93/7.64 % (21254)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_20598 for (2939ds/3174Mi)
% 45.17/8.02 % (21239)Instruction limit reached!
% 45.17/8.02 % (21239)------------------------------
% 45.17/8.02 % (21239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.17/8.02 % (21239)Termination reason: Unknown
% 45.17/8.02 % (21239)Termination phase: Saturation
% 45.17/8.02
% 45.17/8.02 % (21239)Memory used [KB]: 14328
% 45.17/8.02 % (21239)Time elapsed: 1.545 s
% 45.17/8.02 % (21239)Instructions burned: 5061 (million)
% 45.17/8.02 % (21239)------------------------------
% 45.17/8.02 % (21239)------------------------------
% 47.97/8.03 % (21252)Instruction limit reached!
% 47.97/8.03 % (21252)------------------------------
% 47.97/8.03 % (21252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.97/8.03 % (21252)Termination reason: Unknown
% 47.97/8.03 % (21252)Termination phase: Saturation
% 47.97/8.03
% 47.97/8.03 % (21252)Memory used [KB]: 12153
% 47.97/8.03 % (21252)Time elapsed: 0.464 s
% 47.97/8.03 % (21252)Instructions burned: 1537 (million)
% 47.97/8.03 % (21252)------------------------------
% 47.97/8.03 % (21252)------------------------------
% 47.97/8.04 % (21255)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_20598 for (2935ds/307Mi)
% 47.97/8.04 % (21256)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_20598 for (2935ds/3619Mi)
% 47.97/8.12 % (21255)Instruction limit reached!
% 47.97/8.12 % (21255)------------------------------
% 47.97/8.12 % (21255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.97/8.12 % (21255)Termination reason: Unknown
% 47.97/8.12 % (21255)Termination phase: Saturation
% 47.97/8.12
% 47.97/8.12 % (21255)Memory used [KB]: 7419
% 47.97/8.12 % (21255)Time elapsed: 0.083 s
% 47.97/8.12 % (21255)Instructions burned: 307 (million)
% 47.97/8.12 % (21255)------------------------------
% 47.97/8.12 % (21255)------------------------------
% 48.60/8.13 % (21257)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_20598 for (2934ds/2325Mi)
% 48.97/8.28 % (21241)Instruction limit reached!
% 48.97/8.28 % (21241)------------------------------
% 48.97/8.28 % (21241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.97/8.28 % (21241)Termination reason: Unknown
% 48.97/8.28 % (21241)Termination phase: Saturation
% 48.97/8.28
% 48.97/8.28 % (21241)Memory used [KB]: 10618
% 48.97/8.28 % (21241)Time elapsed: 1.766 s
% 48.97/8.28 % (21241)Instructions burned: 5799 (million)
% 48.97/8.28 % (21241)------------------------------
% 48.97/8.28 % (21241)------------------------------
% 48.97/8.29 % (21258)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_20598 for (2933ds/2341Mi)
% 48.97/8.29 % (21251)Instruction limit reached!
% 48.97/8.29 % (21251)------------------------------
% 48.97/8.29 % (21251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.97/8.29 % (21251)Termination reason: Unknown
% 48.97/8.29 % (21251)Termination phase: Saturation
% 48.97/8.29
% 48.97/8.29 % (21251)Memory used [KB]: 8827
% 48.97/8.29 % (21251)Time elapsed: 0.736 s
% 48.97/8.29 % (21251)Instructions burned: 3675 (million)
% 48.97/8.29 % (21251)------------------------------
% 48.97/8.29 % (21251)------------------------------
% 49.46/8.30 % (21259)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_20598 for (2932ds/7257Mi)
% 50.05/8.59 % (21254)First to succeed.
% 50.05/8.60 % (21254)Refutation found. Thanks to Tanya!
% 50.05/8.60 % SZS status Theorem for DTF2THF_20598
% 50.05/8.60 % SZS output start Proof for DTF2THF_20598
% 50.05/8.60 thf(type_def_5, type, set: ($tType) > $tType).
% 50.05/8.60 thf(type_def_7, type, list: ($tType) > $tType).
% 50.05/8.60 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 50.05/8.60 thf(type_def_9, type, option: ($tType) > $tType).
% 50.05/8.60 thf(type_def_10, type, g: $tType).
% 50.05/8.60 thf(type_def_11, type, node: $tType).
% 50.05/8.60 thf(type_def_12, type, val: $tType).
% 50.05/8.60 thf(type_def_13, type, edgeD: $tType).
% 50.05/8.60 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 50.05/8.60 thf(func_def_1, type, option: ($tType) > $tType).
% 50.05/8.60 thf(func_def_2, type, list: ($tType) > $tType).
% 50.05/8.60 thf(func_def_3, type, set: ($tType) > $tType).
% 50.05/8.60 thf(func_def_4, type, edgeD: $tType).
% 50.05/8.60 thf(func_def_5, type, node: $tType).
% 50.05/8.60 thf(func_def_6, type, val: $tType).
% 50.05/8.60 thf(func_def_7, type, g: $tType).
% 50.05/8.60 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 50.05/8.60 thf(func_def_9, type, ord: !>[X0: $tType]:($o)).
% 50.05/8.60 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 50.05/8.60 thf(func_def_11, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 50.05/8.60 thf(func_def_12, type, graph_2081878492ryPath: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1) > X0 > list @ X1 > $o)).
% 50.05/8.60 thf(func_def_13, type, graph_graph_isIdom: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1) > X0 > X1 > X1 > $o)).
% 50.05/8.60 thf(func_def_14, type, graph_709200220inates: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1) > X0 > X1 > X1 > $o)).
% 50.05/8.60 thf(func_def_15, type, graph_1822314308nEdges: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ product_prod @ X1 @ product_prod @ X2 @ X1)).
% 50.05/8.60 thf(func_def_16, type, graph_1661282752_path2: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1 > X1 > $o)).
% 50.05/8.60 thf(func_def_17, type, graph_1201503639essors: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1)).
% 50.05/8.60 thf(func_def_18, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_19, type, distinct: !>[X0: $tType]:(list @ X0 > $o)).
% 50.05/8.60 thf(func_def_20, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_21, type, nil: !>[X0: $tType]:(list @ X0)).
% 50.05/8.60 thf(func_def_22, type, hd: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_23, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 50.05/8.60 thf(func_def_24, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_25, type, graph_reducible: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1) > X0 > $o)).
% 50.05/8.60 thf(func_def_26, 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)).
% 50.05/8.60 thf(func_def_27, type, sSA_CFG_SSA_defAss: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > X1 > X3 > $o)).
% 50.05/8.60 thf(func_def_28, type, sSA_CFG_SSA_phiDefs: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X1 > set @ X2)).
% 50.05/8.60 thf(func_def_29, 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)).
% 50.05/8.60 thf(func_def_30, 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)).
% 50.05/8.60 thf(func_def_31, 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)).
% 50.05/8.60 thf(func_def_32, type, sSA_CFG_defAss: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1) > (X0 > X1 > set @ X3) > X0 > X1 > X3 > $o)).
% 50.05/8.60 thf(func_def_33, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 50.05/8.60 thf(func_def_34, type, suffix: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 50.05/8.60 thf(func_def_35, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 50.05/8.60 thf(func_def_36, type, entry: g > node).
% 50.05/8.60 thf(func_def_37, type, alpha_n: g > list @ node).
% 50.05/8.60 thf(func_def_38, type, phi_r: val).
% 50.05/8.60 thf(func_def_39, type, defs: g > node > set @ val).
% 50.05/8.60 thf(func_def_40, type, g2: g).
% 50.05/8.60 thf(func_def_41, type, inEdges: g > node > list @ product_prod @ node @ edgeD).
% 50.05/8.60 thf(func_def_42, type, invar: g > $o).
% 50.05/8.60 thf(func_def_43, type, m: node).
% 50.05/8.60 thf(func_def_44, type, ms: list @ node).
% 50.05/8.60 thf(func_def_45, type, n: node).
% 50.05/8.60 thf(func_def_46, type, ns: list @ node).
% 50.05/8.60 thf(func_def_47, type, phis: g > product_prod @ node @ val > option @ list @ val).
% 50.05/8.60 thf(func_def_48, type, pred_phi_r: node).
% 50.05/8.60 thf(func_def_49, type, r: val).
% 50.05/8.60 thf(func_def_50, type, rs: list @ node).
% 50.05/8.60 thf(func_def_51, type, rs2: list @ node).
% 50.05/8.60 thf(func_def_52, type, s: val).
% 50.05/8.60 thf(func_def_68, type, sP0: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_69, type, sP1: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 50.05/8.60 thf(func_def_70, type, sP2: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > $o)).
% 50.05/8.60 thf(func_def_71, type, sP3: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > (X1 > X0 > $o) > $o)).
% 50.05/8.60 thf(func_def_72, type, sK4: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_73, type, sK5: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_74, type, sK6: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_75, type, sK7: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_76, type, sK8: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_77, type, sK9: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_78, type, sK10: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_79, type, sK11: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_80, type, sK12: list @ node > node > node).
% 50.05/8.60 thf(func_def_81, type, sK13: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_82, type, sK14: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_83, type, sK15: g > node > node).
% 50.05/8.60 thf(func_def_84, type, sK16: g > node > list @ node).
% 50.05/8.60 thf(func_def_85, type, sK17: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_86, type, sK18: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_87, type, sK19: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_88, type, sK20: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_89, type, sK21: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_90, type, sK22: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_91, type, sK23: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_92, type, sK24: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_93, type, sK25: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_94, type, sK26: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_95, type, sK27: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_96, type, sK28: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_97, type, sK29: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_98, type, sK30: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_99, type, sK31: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_100, type, sK32: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_101, type, sK33: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_102, type, sK34: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_103, type, sK35: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_104, type, sK36: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_105, type, sK37: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_106, type, sK38: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_107, type, sK39: (node > list @ node > node > $o) > node > g > list @ node).
% 50.05/8.60 thf(func_def_108, type, sK40: (node > list @ node > node > $o) > node > g > node).
% 50.05/8.60 thf(func_def_109, type, sK41: (node > list @ node > node > $o) > node > g > node).
% 50.05/8.60 thf(func_def_110, type, sK42: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_111, type, sK43: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_112, type, sK44: list @ node > val > g > node).
% 50.05/8.60 thf(func_def_113, type, sK45: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_114, type, sK46: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_115, type, sK47: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_116, type, sK48: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_117, type, sK49: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_118, type, sK50: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_119, type, sK51: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_120, type, sK52: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_121, type, sK53: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 50.05/8.60 thf(func_def_122, type, sK54: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_123, type, sK55: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_124, type, sK56: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_125, type, sK57: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_126, type, sK58: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 50.05/8.60 thf(func_def_127, type, sK59: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_128, type, sK60: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_129, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 50.05/8.60 thf(func_def_130, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_131, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_132, type, sK64: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 50.05/8.60 thf(func_def_133, type, sK65: val > node > g > list @ node).
% 50.05/8.60 thf(func_def_134, type, sK66: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_135, type, sK67: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_136, type, sK68: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_137, type, sK69: !>[X0: $tType]:(set @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_138, type, sK70: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_139, type, sK71: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_140, type, sK72: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_141, type, sK73: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_142, type, sK74: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_143, type, sK75: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_144, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 50.05/8.60 thf(func_def_145, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X2)).
% 50.05/8.60 thf(func_def_146, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X2)).
% 50.05/8.60 thf(func_def_147, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 50.05/8.60 thf(func_def_148, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 50.05/8.60 thf(func_def_149, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0)).
% 50.05/8.60 thf(func_def_150, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_151, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X2)).
% 50.05/8.60 thf(func_def_152, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X2)).
% 50.05/8.60 thf(func_def_153, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 50.05/8.60 thf(func_def_154, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0)).
% 50.05/8.60 thf(func_def_155, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_156, type, sK88: list @ node > val > g > node).
% 50.05/8.60 thf(func_def_157, type, sK89: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_158, type, sK90: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_159, type, sK91: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 50.05/8.60 thf(func_def_160, type, sK92: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_161, type, sK93: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 50.05/8.60 thf(func_def_162, type, sK94: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 50.05/8.60 thf(func_def_163, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_164, type, sK96: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_165, type, sK97: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_166, type, sK98: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_167, type, sK99: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_168, type, sK100: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_169, type, sK101: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_170, type, sK102: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_171, type, sK103: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_172, type, sK104: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_173, type, sK105: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_174, type, sK106: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_175, type, sK107: (node > $o) > node > list @ node > g > node).
% 50.05/8.60 thf(func_def_176, type, sK108: (node > $o) > node > list @ node > g > list @ node).
% 50.05/8.60 thf(func_def_177, type, sK109: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_178, type, sK110: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_179, type, sK111: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_180, type, sK112: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_181, type, sK113: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_182, type, sK114: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_183, type, sK115: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_184, type, sK116: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_185, type, sK117: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_186, type, sK118: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_187, type, sK119: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_188, type, sK120: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_189, type, sK121: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_190, type, sK122: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_191, type, sK123: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_192, type, sK124: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_193, type, sK125: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > X1)).
% 50.05/8.60 thf(func_def_194, type, sK126: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_195, type, sK127: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_196, type, sK128: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_197, type, sK129: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_198, type, sK130: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_199, type, sK131: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_200, type, sK132: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_201, type, sK133: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_202, type, sK134: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_203, type, sK135: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_204, type, sK136: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_205, type, sK137: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > (X1 > X0 > $o) > X1)).
% 50.05/8.60 thf(func_def_206, type, sK138: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > (X1 > X0 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_207, type, sK139: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > (X1 > X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_208, type, sK140: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > (X1 > X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_209, type, sK141: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_210, type, sK142: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_211, type, sK143: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_212, type, sK144: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_213, type, sK145: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_214, type, sK146: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_215, type, sK147: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_216, type, sK148: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_217, type, sK149: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_218, type, sK150: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_219, type, sK151: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_220, type, sK152: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_221, type, sK153: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_222, type, sK154: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_223, type, sK155: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_224, type, sK156: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_225, type, sK157: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_226, type, sK158: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_227, type, sK159: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_228, type, sK160: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_229, type, sK161: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_230, type, sK162: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_231, type, sK163: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_232, type, sK164: list @ node > val > g > node).
% 50.05/8.60 thf(func_def_233, type, sK165: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_234, type, sK166: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_235, type, sK167: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_236, type, sK168: (node > list @ node > node > $o) > node > g > list @ node).
% 50.05/8.60 thf(func_def_237, type, sK169: (node > list @ node > node > $o) > node > g > node).
% 50.05/8.60 thf(func_def_238, type, sK170: (node > list @ node > node > $o) > node > g > node).
% 50.05/8.60 thf(func_def_239, type, sK171: g > node > list @ node).
% 50.05/8.60 thf(func_def_240, type, sK172: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_241, type, sK173: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_242, type, sK174: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_243, type, sK175: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_244, type, sK176: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_245, type, sK177: list @ node > val > g > node).
% 50.05/8.60 thf(func_def_246, type, sK178: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_247, type, sK179: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_248, type, sK180: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_249, type, sK181: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_250, type, sK182: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_251, type, sK183: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_252, type, sK184: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_253, type, sK185: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_254, type, sK186: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_255, type, sK187: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_256, type, sK188: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_257, type, sK189: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_258, type, sK190: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_259, type, sK191: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_260, type, sK192: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 50.05/8.60 thf(func_def_261, type, sK193: !>[X0: $tType]:(set @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_262, type, sK194: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_263, type, sK195: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_264, type, sK196: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_265, type, sK197: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 50.05/8.60 thf(func_def_266, type, sK198: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_267, type, sK199: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_268, type, sK200: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_269, type, sK201: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 50.05/8.60 thf(func_def_270, type, sK202: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 50.05/8.60 thf(func_def_271, type, sK203: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_272, type, sK204: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_273, type, sK205: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 50.05/8.60 thf(func_def_274, type, sK206: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 50.05/8.60 thf(func_def_275, type, sK207: node > g > node > list @ node).
% 50.05/8.60 thf(func_def_276, type, sK208: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_277, type, sK209: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_278, type, sK210: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_279, type, sK211: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_280, type, sK212: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_281, type, sK213: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_282, type, sK214: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_283, type, sK215: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_284, type, sK216: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_285, type, sK217: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_286, type, sK218: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_287, type, sK219: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_288, type, sK220: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_289, type, sK221: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_290, type, sK222: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_291, type, sK223: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_292, type, sK224: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_293, type, sK225: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 50.05/8.60 thf(func_def_294, type, sK226: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_295, type, sK227: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_296, type, sK228: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_297, type, sK229: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_298, type, sK230: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_299, type, sK231: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_300, type, sK232: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_301, type, sK233: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_302, type, sK234: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_303, type, sK235: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_304, type, sK236: !>[X0: $tType]:(list @ X0 > X0 > X0)).
% 50.05/8.60 thf(func_def_305, type, sK237: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_306, type, sK238: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_307, type, sK239: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_308, type, sK240: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_309, type, sK241: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 50.05/8.60 thf(func_def_310, type, sK242: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_311, type, sK243: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 50.05/8.60 thf(func_def_312, type, sK244: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 50.05/8.60 thf(func_def_313, type, sK245: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_314, type, sK246: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_315, type, sK247: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_316, type, sK248: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_317, type, sK249: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_318, type, sK250: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_319, type, sK251: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_320, type, sK252: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_321, type, sK253: node > node > g > list @ node).
% 50.05/8.60 thf(func_def_322, type, sK254: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_323, type, sK255: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_324, type, sK256: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_325, type, sK257: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_326, type, sK258: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_327, type, sK259: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_328, type, sK260: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_329, type, sK261: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_330, type, sK262: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_331, type, sK263: val > node > g > list @ node).
% 50.05/8.60 thf(func_def_332, type, sK264: list @ node).
% 50.05/8.60 thf(func_def_333, type, sK265: node).
% 50.05/8.60 thf(func_def_335, type, sK267: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_336, type, sK268: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_337, type, sK269: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_338, type, sK270: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_339, type, sK271: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_340, type, sK272: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 50.05/8.60 thf(func_def_341, type, sK273: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_342, type, sK274: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_343, type, sK275: node > g > node > node).
% 50.05/8.60 thf(func_def_344, type, sK276: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_345, type, sK277: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_346, type, sK278: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 50.05/8.60 thf(func_def_347, type, sK279: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_348, type, sK280: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_349, type, sK281: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 50.05/8.60 thf(func_def_350, type, sK282: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_351, type, sK283: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_352, type, sK284: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_353, type, sK285: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_354, type, sK286: g > list @ node).
% 50.05/8.60 thf(func_def_355, type, sK287: g > node).
% 50.05/8.60 thf(func_def_356, type, sK288: node > g > node).
% 50.05/8.60 thf(func_def_357, type, sK289: list @ node > g > node).
% 50.05/8.60 thf(func_def_358, type, sK290: node > g > node > list @ node).
% 50.05/8.60 thf(func_def_359, type, sK291: node > g > val > list @ node).
% 50.05/8.60 thf(func_def_360, type, sK292: list @ node > g > val > node).
% 50.05/8.60 thf(func_def_361, type, sK293: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_362, type, sK294: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_363, type, sK295: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_364, type, sK296: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_365, type, sK297: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_366, type, sK298: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_367, type, sK299: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_368, type, sK300: !>[X0: $tType]:(X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_369, type, sK301: !>[X0: $tType]:(list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_370, type, sK302: !>[X0: $tType]:(list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_371, type, sK303: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_372, type, sK304: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_373, type, sK305: !>[X0: $tType]:(list @ X0 > list @ X0 > X0 > list @ X0)).
% 50.05/8.60 thf(func_def_374, type, sK306: g > val > node > node).
% 50.05/8.60 thf(func_def_375, type, sK307: val > list @ node > g > node).
% 50.05/8.60 thf(func_def_376, type, sK308: node > g > val > list @ node).
% 50.05/8.60 thf(func_def_377, type, sK309: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 50.05/8.60 thf(func_def_378, type, sK310: !>[X0: $tType]:(list @ X0 > X0)).
% 50.05/8.60 thf(func_def_379, type, ph311: !>[X0: $tType]:(X0)).
% 50.05/8.60 thf(f6619,plain,(
% 50.05/8.60 $false),
% 50.05/8.60 inference(subsumption_resolution,[status(thm)],[f6610,f5934])).
% 50.05/8.60 thf(f5934,plain,(
% 50.05/8.60 ((distinct @ node @ rs) = $true)),
% 50.05/8.60 inference(trivial_inequality_removal,[status(thm)],[f5932])).
% 50.05/8.60 thf(f5932,plain,(
% 50.05/8.60 ((distinct @ node @ rs) = $true) | ($true != $true)),
% 50.05/8.60 inference(superposition,[status(thm)],[f1335,f1343])).
% 50.05/8.60 thf(f1343,plain,(
% 50.05/8.60 ((graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs) = $true)),
% 50.05/8.60 inference(cnf_transformation,[status(thm)],[f436])).
% 50.05/8.60 thf(f436,plain,(
% 50.05/8.60 ((graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs) = $true)),
% 50.05/8.60 inference(fool_elimination,[status(thm)],[f435])).
% 50.05/8.60 thf(f435,plain,(
% 50.05/8.60 (graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs)),
% 50.05/8.60 inference(rectify,[status(thm)],[f4])).
% 50.05/8.60 thf(f4,axiom,(
% 50.05/8.60 (graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs)),
% 50.05/8.60 file('/export/starexec/sandbox/tmp/tmp.cRKnHLkZP0/DTF2THF_20598.p',fact_3_rs_H__props_I2_J)).
% 50.05/8.60 thf(f1335,plain,(
% 50.05/8.60 ( ! [X0 : g,X1 : list @ node] : (($true != (graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1)) | ($true = (distinct @ node @ X1))) )),
% 50.05/8.60 inference(cnf_transformation,[status(thm)],[f924])).
% 50.05/8.60 thf(f924,plain,(
% 50.05/8.60 ! [X0 : g,X1 : list @ node] : (($true = (distinct @ node @ X1)) | ($true != (graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1)))),
% 50.05/8.60 inference(ennf_transformation,[status(thm)],[f322])).
% 50.05/8.60 thf(f322,plain,(
% 50.05/8.60 ! [X0 : g,X1 : list @ node] : (($true = (graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1)) => ($true = (distinct @ node @ X1)))),
% 50.05/8.60 inference(fool_elimination,[status(thm)],[f321])).
% 50.05/8.60 thf(f321,plain,(
% 50.05/8.60 ! [X0 : g,X1 : list @ node] : ((graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1) => (distinct @ node @ X1))),
% 50.05/8.60 inference(rectify,[status(thm)],[f6])).
% 50.05/8.60 thf(f6,axiom,(
% 50.05/8.60 ! [X6 : g,X8 : list @ node] : ((graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ X6 @ X8) => (distinct @ node @ X8))),
% 50.05/8.60 file('/export/starexec/sandbox/tmp/tmp.cRKnHLkZP0/DTF2THF_20598.p',fact_5_old_OEntryPath__distinct)).
% 50.05/8.60 thf(f6610,plain,(
% 50.05/8.60 ((distinct @ node @ rs) != $true)),
% 50.05/8.60 inference(trivial_inequality_removal,[status(thm)],[f6587])).
% 50.05/8.60 thf(f6587,plain,(
% 50.05/8.60 ($true != $true) | ((distinct @ node @ rs) != $true)),
% 50.05/8.60 inference(superposition,[status(thm)],[f1688,f6567])).
% 50.05/8.60 thf(f6567,plain,(
% 50.05/8.60 ($true = (member @ node @ (hd @ node @ rs) @ (set2 @ node @ (tl @ node @ rs))))),
% 50.05/8.60 inference(backward_demodulation,[status(thm)],[f1309,f6565])).
% 50.05/8.60 thf(f6565,plain,(
% 50.05/8.60 ((sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) = (hd @ node @ rs))),
% 50.05/8.60 inference(trivial_inequality_removal,[status(thm)],[f6561])).
% 50.05/8.60 thf(f6561,plain,(
% 50.05/8.60 ($true != $true) | ((sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) = (hd @ node @ rs))),
% 50.05/8.60 inference(superposition,[status(thm)],[f1668,f1604])).
% 50.05/8.60 thf(f1604,plain,(
% 50.05/8.60 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r) = $true)),
% 50.05/8.60 inference(cnf_transformation,[status(thm)],[f598])).
% 50.05/8.60 thf(f598,plain,(
% 50.05/8.60 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r) = $true)),
% 50.05/8.60 inference(fool_elimination,[status(thm)],[f597])).
% 50.05/8.60 thf(f597,plain,(
% 50.05/8.60 (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r)),
% 50.05/8.60 inference(rectify,[status(thm)],[f5])).
% 50.05/8.60 thf(f5,axiom,(
% 50.05/8.60 (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r)),
% 50.05/8.60 file('/export/starexec/sandbox/tmp/tmp.cRKnHLkZP0/DTF2THF_20598.p',fact_4_rs_H__props_I1_J)).
% 50.05/8.60 thf(f1668,plain,(
% 50.05/8.60 ( ! [X2 : list @ node,X3 : node,X0 : g,X1 : node] : (($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3)) | ((hd @ node @ X2) = X1)) )),
% 50.05/8.60 inference(cnf_transformation,[status(thm)],[f801])).
% 50.05/8.60 thf(f801,plain,(
% 50.05/8.60 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node] : (($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3)) | ((hd @ node @ X2) = X1))),
% 50.05/8.60 inference(ennf_transformation,[status(thm)],[f654])).
% 50.05/8.60 thf(f654,plain,(
% 50.05/8.60 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node] : (($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3)) => ((hd @ node @ X2) = X1))),
% 50.05/8.60 inference(fool_elimination,[status(thm)],[f653])).
% 50.05/8.60 thf(f653,plain,(
% 50.05/8.60 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node] : ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3) => ((hd @ node @ X2) = X1))),
% 50.05/8.60 inference(rectify,[status(thm)],[f1])).
% 50.05/8.60 thf(f1,axiom,(
% 50.05/8.60 ! [X6 : g,X7 : node,X8 : list @ node,X9 : node] : ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X6 @ X7 @ X8 @ X9) => ((hd @ node @ X8) = X7))),
% 50.05/8.60 file('/export/starexec/sandbox/tmp/tmp.cRKnHLkZP0/DTF2THF_20598.p',fact_0_old_Opath2__hd)).
% 50.05/8.60 thf(f1309,plain,(
% 50.05/8.60 ((member @ node @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ (set2 @ node @ (tl @ node @ rs))) = $true)),
% 50.05/8.60 inference(cnf_transformation,[status(thm)],[f713])).
% 50.05/8.60 thf(f713,plain,(
% 50.05/8.60 ((member @ node @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ (set2 @ node @ (tl @ node @ rs))) = $true)),
% 50.05/8.60 inference(flattening,[status(thm)],[f478])).
% 50.05/8.60 thf(f478,plain,(
% 50.05/8.60 ~~((member @ node @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ (set2 @ node @ (tl @ node @ rs))) = $true)),
% 50.05/8.60 inference(fool_elimination,[status(thm)],[f477])).
% 50.05/8.60 thf(f477,plain,(
% 50.05/8.60 ~~(member @ node @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ (set2 @ node @ (tl @ node @ rs)))),
% 50.05/8.60 inference(rectify,[status(thm)],[f265])).
% 50.05/8.60 thf(f265,negated_conjecture,(
% 50.05/8.60 ~~(member @ node @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ (set2 @ node @ (tl @ node @ rs)))),
% 50.05/8.60 inference(negated_conjecture,[status(cth)],[f264])).
% 50.05/8.60 thf(f264,conjecture,(
% 50.05/8.60 ~(member @ node @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ (set2 @ node @ (tl @ node @ rs)))),
% 50.05/8.60 file('/export/starexec/sandbox/tmp/tmp.cRKnHLkZP0/DTF2THF_20598.p',conj_0)).
% 50.05/8.60 thf(f1688,plain,(
% 50.05/8.60 ( ! [X0 : $tType,X1 : list @ X0] : (($true != (member @ X0 @ (hd @ X0 @ X1) @ (set2 @ X0 @ (tl @ X0 @ X1)))) | ($true != (distinct @ X0 @ X1))) )),
% 50.05/8.60 inference(equality_resolution,[status(thm)],[f1330])).
% 50.05/8.60 thf(f1330,plain,(
% 50.05/8.60 ( ! [X0 : $tType,X2 : X0,X1 : list @ X0] : (((hd @ X0 @ X1) != X2) | ((member @ X0 @ X2 @ (set2 @ X0 @ (tl @ X0 @ X1))) != $true) | ($true != (distinct @ X0 @ X1))) )),
% 50.05/8.60 inference(cnf_transformation,[status(thm)],[f822])).
% 50.05/8.60 thf(f822,plain,(
% 50.05/8.60 ! [X0 : $tType,X1 : list @ X0,X2 : X0] : (((hd @ X0 @ X1) != X2) | ((member @ X0 @ X2 @ (set2 @ X0 @ (tl @ X0 @ X1))) != $true) | ($true != (distinct @ X0 @ X1)))),
% 50.05/8.60 inference(flattening,[status(thm)],[f821])).
% 50.05/8.60 thf(f821,plain,(
% 50.05/8.60 ! [X0 : $tType,X1 : list @ X0,X2 : X0] : ((((member @ X0 @ X2 @ (set2 @ X0 @ (tl @ X0 @ X1))) != $true) | ((hd @ X0 @ X1) != X2)) | ($true != (distinct @ X0 @ X1)))),
% 50.05/8.60 inference(ennf_transformation,[status(thm)],[f733])).
% 50.05/8.60 thf(f733,plain,(
% 50.05/8.60 ! [X0 : $tType,X1 : list @ X0,X2 : X0] : (($true = (distinct @ X0 @ X1)) => (((hd @ X0 @ X1) = X2) => ((member @ X0 @ X2 @ (set2 @ X0 @ (tl @ X0 @ X1))) != $true)))),
% 50.05/8.60 inference(flattening,[status(thm)],[f386])).
% 50.05/8.60 thf(f386,plain,(
% 50.05/8.60 ! [X0 : $tType,X1 : list @ X0,X2 : X0] : (($true = (distinct @ X0 @ X1)) => (((hd @ X0 @ X1) = X2) => ~((member @ X0 @ X2 @ (set2 @ X0 @ (tl @ X0 @ X1))) = $true)))),
% 50.05/8.60 inference(fool_elimination,[status(thm)],[f385])).
% 50.05/8.60 thf(f385,plain,(
% 50.05/8.60 ! [X0 : $tType,X1 : list @ X0,X2 : X0] : ((distinct @ X0 @ X1) => (((hd @ X0 @ X1) = X2) => ~(member @ X0 @ X2 @ (set2 @ X0 @ (tl @ X0 @ X1)))))),
% 50.05/8.60 inference(rectify,[status(thm)],[f254])).
% 50.05/8.60 thf(f254,axiom,(
% 50.05/8.60 ! [X0 : $tType,X12 : list @ X0,X11 : X0] : ((distinct @ X0 @ X12) => (((hd @ X0 @ X12) = X11) => ~(member @ X0 @ X11 @ (set2 @ X0 @ (tl @ X0 @ X12)))))),
% 50.05/8.60 file('/export/starexec/sandbox/tmp/tmp.cRKnHLkZP0/DTF2THF_20598.p',fact_253_Misc_Odistinct__hd__tl)).
% 50.05/8.60 % SZS output end Proof for DTF2THF_20598
% 50.05/8.60 % (21254)------------------------------
% 50.05/8.60 % (21254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.05/8.60 % (21254)Termination reason: Refutation
% 50.05/8.60
% 50.05/8.60 % (21254)Memory used [KB]: 13176
% 50.05/8.60 % (21254)Time elapsed: 0.953 s
% 50.05/8.60 % (21254)Instructions burned: 3082 (million)
% 50.05/8.60 % (21254)------------------------------
% 50.05/8.60 % (21254)------------------------------
% 50.05/8.60 % (20789)Success in time 7.017 s
%------------------------------------------------------------------------------