%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP082^2 : 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 : n015.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 08:55:24 AM UTC 2026
% Result : Theorem 2.82s 1.78s
% Output : Refutation 2.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP082^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n015.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 08:26:01 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP082^2 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer Irreducible problem prob_559__6628256_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : Irreducible/prob_559__6628256_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 315 ( 104 unt; 51 typ; 0 def)
% 0.20/0.46 % Number of atoms : 779 ( 365 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 14 ( 2 avg)
% 0.20/0.46 % Number of connectives : 5240 ( 161 ~; 16 |; 66 &;4591 @)
% 0.20/0.46 % ( 0 <=>; 406 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 29 ( 10 avg)
% 0.20/0.46 % Number of types : 5 ( 4 usr)
% 0.20/0.46 % Number of type conns : 232 ( 232 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 48 ( 47 usr; 16 con; 0-12 aty)
% 0.20/0.46 % Number of variables : 1147 ( 16 ^;1034 !; 60 ?;1147 :)
% 0.20/0.46 % ( 37 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.46 % SPC : TH1_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:27:26.217
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (8)
% 0.20/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.20/0.46 product_prod: $tType > $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Option_Ooption,type,
% 0.20/0.46 option: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_List_Olist,type,
% 0.20/0.46 list: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Set_Oset,type,
% 0.20/0.46 set: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_tf_edgeD,type,
% 0.20/0.46 edgeD: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_tf_node,type,
% 0.20/0.46 node: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_tf_val,type,
% 0.20/0.46 val: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_tf_g,type,
% 0.20/0.46 g: $tType ).
% 0.20/0.46
% 0.20/0.46 % Explicit typings (43)
% 0.20/0.46 thf(sy_cl_HOL_Otype,type,
% 0.20/0.46 type:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.20/0.46 ord:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.46 linorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Graph__path_Ograph__path__base_Opath,type,
% 0.20/0.46 graph_1146196722h_path:
% 0.20/0.46 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > ( list @ Node ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Graph__path_Ograph__path__base_Opath2,type,
% 0.20/0.46 graph_1661282752_path2:
% 0.20/0.46 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) > Node > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors,type,
% 0.20/0.46 graph_1201503639essors:
% 0.20/0.46 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oappend,type,
% 0.20/0.46 append:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Obutlast,type,
% 0.20/0.46 butlast:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_OCons,type,
% 0.20/0.46 cons:
% 0.20/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.20/0.46 nil:
% 0.20/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_Ohd,type,
% 0.20/0.46 hd:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_Oset,type,
% 0.20/0.46 set2:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_Otl,type,
% 0.20/0.46 tl:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Minimality_Ograph__path_OpathsConverge,type,
% 0.20/0.46 graph_pathsConverge:
% 0.20/0.46 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) > Node > ( list @ Node ) > Node > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.20/0.46 ord_less_eq:
% 0.20/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses,type,
% 0.20/0.46 sSA_CFG_SSA_phiUses:
% 0.20/0.46 !>[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 ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode,type,
% 0.20/0.46 sSA_CF1081484811efNode:
% 0.20/0.46 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Node ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg,type,
% 0.20/0.46 sSA_CF1165125185phiArg:
% 0.20/0.46 !>[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 ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect,type,
% 0.20/0.46 collect:
% 0.20/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Sublist_Oprefix,type,
% 0.20/0.46 prefix:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Sublist_Osuffix,type,
% 0.20/0.46 suffix:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member,type,
% 0.20/0.46 member:
% 0.20/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060alpha_062n,type,
% 0.20/0.46 alpha_n: g > ( list @ node ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 0.20/0.46 phi_r: val ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_defs,type,
% 0.20/0.46 defs: g > node > ( set @ val ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_g,type,
% 0.20/0.46 g2: g ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_i____,type,
% 0.20/0.46 i: node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_inEdges_H,type,
% 0.20/0.46 inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_invar,type,
% 0.20/0.46 invar: g > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_m,type,
% 0.20/0.46 m: node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_ms,type,
% 0.20/0.46 ms: list @ node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_ms_H____,type,
% 0.20/0.46 ms2: list @ node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_n,type,
% 0.20/0.46 n: node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_ns,type,
% 0.20/0.46 ns: list @ node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_phis,type,
% 0.20/0.46 phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 0.20/0.46 pred_phi_r: node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_r,type,
% 0.20/0.46 r: val ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_ri____,type,
% 0.20/0.46 ri: list @ node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_rs_H____,type,
% 0.20/0.46 rs: list @ node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_rs_H__rest____,type,
% 0.20/0.46 rs_rest: list @ node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_rs____,type,
% 0.20/0.46 rs2: list @ node ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_s,type,
% 0.20/0.46 s: val ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_tmp____,type,
% 0.20/0.46 tmp: list @ node ).
% 0.20/0.46
% 0.20/0.46 % Relevant facts (255)
% 0.20/0.46 thf(fact_0_m__i__differ_I2_J,axiom,
% 0.20/0.46 m != i ).
% 0.20/0.46
% 0.20/0.46 % m_i_differ(2)
% 0.20/0.46 thf(fact_1_rs_H__rest__def,axiom,
% 0.20/0.46 ( rs
% 0.20/0.46 = ( append @ node @ tmp @ ( cons @ node @ i @ rs_rest ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rs'_rest_def
% 0.20/0.46 thf(fact_2_old_Oinvar,axiom,
% 0.20/0.46 ! [G2: g] : ( invar @ G2 ) ).
% 0.20/0.46
% 0.20/0.46 % old.invar
% 0.20/0.46 thf(fact_3_old_Opath2__split_I2_J,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns2: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns2 ) ) @ M )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns2 ) @ M ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_split(2)
% 0.20/0.46 thf(fact_4_False,axiom,
% 0.20/0.46 r != phi_r ).
% 0.20/0.46
% 0.20/0.46 % False
% 0.20/0.46 thf(fact_5_rs_H__props_I1_J,axiom,
% 0.20/0.46 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 ).
% 0.20/0.46
% 0.20/0.46 % rs'_props(1)
% 0.20/0.46 thf(fact_6_ms_H__props_I1_J,axiom,
% 0.20/0.46 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 0.20/0.46
% 0.20/0.46 % ms'_props(1)
% 0.20/0.46 thf(fact_7_rs_H__rest__prop,axiom,
% 0.20/0.46 ( rs
% 0.20/0.46 = ( append @ node @ ri @ rs_rest ) ) ).
% 0.20/0.46
% 0.20/0.46 % rs'_rest_prop
% 0.20/0.46 thf(fact_8_rs_H__props_I3_J,axiom,
% 0.20/0.46 member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 0.20/0.46
% 0.20/0.46 % rs'_props(3)
% 0.20/0.46 thf(fact_9_old_Opath2__not__Nil,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( Ns
% 0.20/0.46 != ( nil @ node ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_not_Nil
% 0.20/0.46 thf(fact_10_old_Opath2__not__Nil2,axiom,
% 0.20/0.46 ! [G2: g,N: node,M: node] :
% 0.20/0.46 ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( nil @ node ) @ M ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_not_Nil2
% 0.20/0.46 thf(fact_11_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_hd_in_\<alpha>n
% 0.20/0.46 thf(fact_12_old_Opath2__hd__in__ns,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( member @ node @ N @ ( set2 @ node @ Ns ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_hd_in_ns
% 0.20/0.46 thf(fact_13_old_Opath2__in___092_060alpha_062n,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,L: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( member @ node @ L @ ( set2 @ node @ Ns ) )
% 0.20/0.46 => ( member @ node @ L @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_in_\<alpha>n
% 0.20/0.46 thf(fact_14_old_Opath2__last__in__ns,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( member @ node @ M @ ( set2 @ node @ Ns ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_last_in_ns
% 0.20/0.46 thf(fact_15_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_tl_in_\<alpha>n
% 0.20/0.46 thf(fact_16_old_Opath2__forget__hd,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ Ns ) @ Ns @ M ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_forget_hd
% 0.20/0.46 thf(fact_17_old_Opath2__hd,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( N
% 0.20/0.46 = ( hd @ node @ Ns ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_hd
% 0.20/0.46 thf(fact_18__092_060open_062ri_A_061_Atmp_A_064_A_091i_093_092_060close_062,axiom,
% 0.20/0.46 ( ri
% 0.20/0.46 = ( append @ node @ tmp @ ( cons @ node @ i @ ( nil @ node ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>ri = tmp @ [i]\<close>
% 0.20/0.46 thf(fact_19__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H__rest_O_Ars_H_A_061_Ari_A_064_Ars_H__rest_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.46 ~ ! [Rs_rest: list @ node] :
% 0.20/0.46 ( rs
% 0.20/0.46 != ( append @ node @ ri @ Rs_rest ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>\<And>thesis. (\<And>rs'_rest. rs' = ri @ rs'_rest \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.46 thf(fact_20_ri__props_I2_J,axiom,
% 0.20/0.46 member @ node @ i @ ( set2 @ node @ ms ) ).
% 0.20/0.46
% 0.20/0.46 % ri_props(2)
% 0.20/0.46 thf(fact_21_m__i__differ_I1_J,axiom,
% 0.20/0.46 ( i
% 0.20/0.46 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 0.20/0.46
% 0.20/0.46 % m_i_differ(1)
% 0.20/0.46 thf(fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tmp_O_Ari_A_061_Atmp_A_064_A_091i_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.46 ~ ! [Tmp: list @ node] :
% 0.20/0.46 ( ri
% 0.20/0.46 != ( append @ node @ Tmp @ ( cons @ node @ i @ ( nil @ node ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>\<And>thesis. (\<And>tmp. ri = tmp @ [i] \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.46 thf(fact_23_ri__props_I1_J,axiom,
% 0.20/0.46 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 0.20/0.46
% 0.20/0.46 % ri_props(1)
% 0.20/0.46 thf(fact_24_old_Opath2__split_I1_J,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns2: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns2 ) ) @ M )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ ( nil @ node ) ) ) @ N2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_split(1)
% 0.20/0.46 thf(fact_25__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 0.20/0.46 ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 0.20/0.46 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>defNode g \<phi>\<^sub>r \<noteq> defNode g r\<close>
% 0.20/0.46 thf(fact_26__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.46 ( ( i
% 0.20/0.46 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.20/0.46 => ( ( ( i
% 0.20/0.46 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.20/0.46 => ( m != i ) )
% 0.20/0.46 => ~ ( ( i
% 0.20/0.46 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.20/0.46 => ( m = i ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>\<And>thesis. \<lbrakk>i = defNode g \<phi>\<^sub>r \<Longrightarrow> thesis; \<lbrakk>i \<noteq> defNode g \<phi>\<^sub>r; m = i\<rbrakk> \<Longrightarrow> thesis; \<lbrakk>i \<noteq> defNode g \<phi>\<^sub>r; m \<noteq> i\<rbrakk> \<Longrightarrow> thesis\<rbrakk> \<Longrightarrow> thesis\<close>
% 0.20/0.46 thf(fact_27_old_Oempty__path2,axiom,
% 0.20/0.46 ! [N: node,G2: g] :
% 0.20/0.46 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.20/0.46 => ( ( invar @ G2 )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.empty_path2
% 0.20/0.46 thf(fact_28_ms_H__props_I3_J,axiom,
% 0.20/0.46 ~ ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ ms2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ms'_props(3)
% 0.20/0.46 thf(fact_29_assms_I10_J,axiom,
% 0.20/0.46 sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 0.20/0.46
% 0.20/0.46 % assms(10)
% 0.20/0.46 thf(fact_30_rs_H__props_I4_J,axiom,
% 0.20/0.46 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 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rs'_props(4)
% 0.20/0.46 thf(fact_31_assms_I7_J,axiom,
% 0.20/0.46 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 0.20/0.46
% 0.20/0.46 % assms(7)
% 0.20/0.46 thf(fact_32_rs__props_I1_J,axiom,
% 0.20/0.46 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 0.20/0.46
% 0.20/0.46 % rs_props(1)
% 0.20/0.46 thf(fact_33_rs__def,axiom,
% 0.20/0.46 ( rs2
% 0.20/0.46 = ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rs_def
% 0.20/0.46 thf(fact_34_assms_I8_J,axiom,
% 0.20/0.46 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 0.20/0.46
% 0.20/0.46 % assms(8)
% 0.20/0.46 thf(fact_35_rs_H__loopfree,axiom,
% 0.20/0.46 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rs'_loopfree
% 0.20/0.46 thf(fact_36_hd__append2,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( hd @ A @ Xs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % hd_append2
% 0.20/0.46 thf(fact_37_append1__eq__conv,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.20/0.46 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.20/0.46 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.20/0.46 = ( ( Xs = Ys )
% 0.20/0.46 & ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append1_eq_conv
% 0.20/0.46 thf(fact_38_list__ee__eq__leel_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,E1: A,E2: A,L1: list @ A,E12: A,E22: A,L2: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) )
% 0.20/0.46 = ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) ) )
% 0.20/0.46 = ( ( L1
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( E1 = E12 )
% 0.20/0.46 & ( E2 = E22 )
% 0.20/0.46 & ( L2
% 0.20/0.46 = ( nil @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_ee_eq_leel(1)
% 0.20/0.46 thf(fact_39_list__ee__eq__leel_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,L1: list @ A,E12: A,E22: A,L2: list @ A,E1: A,E2: A] :
% 0.20/0.46 ( ( ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) )
% 0.20/0.46 = ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) ) )
% 0.20/0.46 = ( ( L1
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( E1 = E12 )
% 0.20/0.46 & ( E2 = E22 )
% 0.20/0.46 & ( L2
% 0.20/0.46 = ( nil @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_ee_eq_leel(2)
% 0.20/0.46 thf(fact_40_list__se__match_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,L1: list @ A,L2: list @ A,A2: A] :
% 0.20/0.46 ( ( L1
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ( append @ A @ L1 @ L2 )
% 0.20/0.46 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.20/0.46 = ( ( L1
% 0.20/0.46 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.20/0.46 & ( L2
% 0.20/0.46 = ( nil @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_se_match(1)
% 0.20/0.46 thf(fact_41_ri__props_I3_J,axiom,
% 0.20/0.46 ! [X2: node] :
% 0.20/0.46 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ ri ) ) )
% 0.20/0.46 => ~ ( member @ node @ X2 @ ( set2 @ node @ ms ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ri_props(3)
% 0.20/0.46 thf(fact_42_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Y: A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ ( append @ A @ Ys @ ( cons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.elem_set_implies_elem_tl_app_cons
% 0.20/0.46 thf(fact_43_list_Oinject,axiom,
% 0.20/0.46 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ X21 @ X22 )
% 0.20/0.46 = ( cons @ A @ Y21 @ Y22 ) )
% 0.20/0.46 = ( ( X21 = Y21 )
% 0.20/0.46 & ( X22 = Y22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.inject
% 0.20/0.46 thf(fact_44_same__append__eq,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.20/0.46 = ( append @ A @ Xs @ Zs ) )
% 0.20/0.46 = ( Ys = Zs ) ) ).
% 0.20/0.46
% 0.20/0.46 % same_append_eq
% 0.20/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.20/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.20/0.46 = ( P @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A: $tType,A3: set @ A] :
% 0.20/0.46 ( ( collect @ A
% 0.20/0.46 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.20/0.46 = A3 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_47_Collect__cong,axiom,
% 0.20/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.20/0.46 ( ! [X4: A] :
% 0.20/0.46 ( ( P @ X4 )
% 0.20/0.46 = ( Q @ X4 ) )
% 0.20/0.46 => ( ( collect @ A @ P )
% 0.20/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_cong
% 0.20/0.46 thf(fact_48_ext,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.20/0.46 ( ! [X4: A] :
% 0.20/0.46 ( ( F @ X4 )
% 0.20/0.46 = ( G2 @ X4 ) )
% 0.20/0.46 => ( F = G2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % ext
% 0.20/0.46 thf(fact_49_append__same__eq,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Ys @ Xs )
% 0.20/0.46 = ( append @ A @ Zs @ Xs ) )
% 0.20/0.46 = ( Ys = Zs ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_same_eq
% 0.20/0.46 thf(fact_50_append__assoc,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 0.20/0.46 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_assoc
% 0.20/0.46 thf(fact_51_append_Oassoc,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.20/0.46 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C )
% 0.20/0.46 = ( append @ A @ A2 @ ( append @ A @ B2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append.assoc
% 0.20/0.46 thf(fact_52_old_Opredecessor__is__node,axiom,
% 0.20/0.46 ! [N: node,G2: g,N2: node] :
% 0.20/0.46 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 0.20/0.46 => ( ( invar @ G2 )
% 0.20/0.46 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.predecessor_is_node
% 0.20/0.46 thf(fact_53_old_Osuccessor__is__node,axiom,
% 0.20/0.46 ! [N: node,G2: g,N2: node] :
% 0.20/0.46 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 0.20/0.46 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.20/0.46 => ( ( invar @ G2 )
% 0.20/0.46 => ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.successor_is_node
% 0.20/0.46 thf(fact_54_old_Osuccessor__in___092_060alpha_062n,axiom,
% 0.20/0.46 ! [G2: g,N: node] :
% 0.20/0.46 ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N )
% 0.20/0.46 != ( nil @ node ) )
% 0.20/0.46 => ( ( invar @ G2 )
% 0.20/0.46 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.successor_in_\<alpha>n
% 0.20/0.46 thf(fact_55_old_Opath2__app_H,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ ( butlast @ node @ Ns ) @ Ms ) @ L ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_app'
% 0.20/0.46 thf(fact_56_old_Opath2__app,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( tl @ node @ Ms ) ) @ L ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_app
% 0.20/0.46 thf(fact_57_append_Oright__neutral,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] :
% 0.20/0.46 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % append.right_neutral
% 0.20/0.46 thf(fact_58_empty__append__eq__id,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( append @ A @ ( nil @ A ) )
% 0.20/0.46 = ( ^ [X3: list @ A] : X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % empty_append_eq_id
% 0.20/0.46 thf(fact_59_append__is__Nil__conv,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 = ( ( Xs
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( Ys
% 0.20/0.46 = ( nil @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_is_Nil_conv
% 0.20/0.46 thf(fact_60_Nil__is__append__conv,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( ( nil @ A )
% 0.20/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( ( Xs
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( Ys
% 0.20/0.46 = ( nil @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Nil_is_append_conv
% 0.20/0.46 thf(fact_61_self__append__conv2,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.20/0.46 ( ( Ys
% 0.20/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( Xs
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % self_append_conv2
% 0.20/0.46 thf(fact_62_append__self__conv2,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.20/0.46 = Ys )
% 0.20/0.46 = ( Xs
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_self_conv2
% 0.20/0.46 thf(fact_63_self__append__conv,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( Ys
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % self_append_conv
% 0.20/0.46 thf(fact_64_append__self__conv,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.20/0.46 = Xs )
% 0.20/0.46 = ( Ys
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_self_conv
% 0.20/0.46 thf(fact_65_append__Nil2,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.20/0.46 = Xs ) ).
% 0.20/0.46
% 0.20/0.46 % append_Nil2
% 0.20/0.46 thf(fact_66_old_Opath2__split__ex_H,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 0.20/0.46 => ~ ! [Ns_1: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns_1 @ X )
% 0.20/0.46 => ! [Ns_2: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_2 @ M )
% 0.20/0.46 => ( Ns
% 0.20/0.46 != ( append @ node @ ( butlast @ node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_split_ex'
% 0.20/0.46 thf(fact_67_old_Opath2__induct,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( ( invar @ G2 )
% 0.20/0.46 => ( P @ M @ ( cons @ node @ M @ ( nil @ node ) ) @ M ) )
% 0.20/0.46 => ( ! [Ns3: list @ node,N3: node,N4: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N4 @ Ns3 @ M )
% 0.20/0.46 => ( ( P @ N4 @ Ns3 @ M )
% 0.20/0.46 => ( ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N4 ) ) )
% 0.20/0.46 => ( P @ N3 @ ( cons @ node @ N3 @ Ns3 ) @ M ) ) ) )
% 0.20/0.46 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_induct
% 0.20/0.46 thf(fact_68_old_Opath2__split__ex,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 0.20/0.46 => ~ ! [Ns_1: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns_1 @ X )
% 0.20/0.46 => ! [Ns_2: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_2 @ M )
% 0.20/0.46 => ( ( Ns
% 0.20/0.46 = ( append @ node @ Ns_1 @ ( tl @ node @ Ns_2 ) ) )
% 0.20/0.46 => ( Ns
% 0.20/0.46 != ( append @ node @ ( butlast @ node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_split_ex
% 0.20/0.46 thf(fact_69_old_Opath2__rev__induct,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.20/0.46 => ( P @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) )
% 0.20/0.46 => ( ! [Ns3: list @ node,M2: node,M3: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns3 @ M2 )
% 0.20/0.46 => ( ( P @ N @ Ns3 @ M2 )
% 0.20/0.46 => ( ( member @ node @ M2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M3 ) ) )
% 0.20/0.46 => ( P @ N @ ( append @ node @ Ns3 @ ( cons @ node @ M3 @ ( nil @ node ) ) ) @ M3 ) ) ) )
% 0.20/0.46 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_rev_induct
% 0.20/0.46 thf(fact_70_old_Opath2__snoc,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,M4: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M4 ) ) )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ M4 @ ( nil @ node ) ) ) @ M4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_snoc
% 0.20/0.46 thf(fact_71_list__e__eq__lel_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,L1: list @ A,E: A,L2: list @ A,E3: A] :
% 0.20/0.46 ( ( ( append @ A @ L1 @ ( cons @ A @ E @ L2 ) )
% 0.20/0.46 = ( cons @ A @ E3 @ ( nil @ A ) ) )
% 0.20/0.46 = ( ( L1
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( E = E3 )
% 0.20/0.46 & ( L2
% 0.20/0.46 = ( nil @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_e_eq_lel(2)
% 0.20/0.46 thf(fact_72_list__e__eq__lel_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,E3: A,L1: list @ A,E: A,L2: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ E3 @ ( nil @ A ) )
% 0.20/0.46 = ( append @ A @ L1 @ ( cons @ A @ E @ L2 ) ) )
% 0.20/0.46 = ( ( L1
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( E = E3 )
% 0.20/0.46 & ( L2
% 0.20/0.46 = ( nil @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_e_eq_lel(1)
% 0.20/0.46 thf(fact_73_list__se__match_I4_J,axiom,
% 0.20/0.46 ! [A: $tType,L2: list @ A,A2: A,L1: list @ A] :
% 0.20/0.46 ( ( L2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 0.20/0.46 = ( append @ A @ L1 @ L2 ) )
% 0.20/0.46 = ( ( L1
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( L2
% 0.20/0.46 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_se_match(4)
% 0.20/0.46 thf(fact_74_list__se__match_I3_J,axiom,
% 0.20/0.46 ! [A: $tType,L1: list @ A,A2: A,L2: list @ A] :
% 0.20/0.46 ( ( L1
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 0.20/0.46 = ( append @ A @ L1 @ L2 ) )
% 0.20/0.46 = ( ( L1
% 0.20/0.46 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.20/0.46 & ( L2
% 0.20/0.46 = ( nil @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_se_match(3)
% 0.20/0.46 thf(fact_75_list__se__match_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,L2: list @ A,L1: list @ A,A2: A] :
% 0.20/0.46 ( ( L2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ( append @ A @ L1 @ L2 )
% 0.20/0.46 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.20/0.46 = ( ( L1
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( L2
% 0.20/0.46 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_se_match(2)
% 0.20/0.46 thf(fact_76_tl__append2,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( tl @ A @ ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( append @ A @ ( tl @ A @ Xs ) @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % tl_append2
% 0.20/0.46 thf(fact_77_old_Opath2__cases,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( ( Ns
% 0.20/0.46 = ( cons @ node @ N @ ( nil @ node ) ) )
% 0.20/0.46 => ( M != N ) )
% 0.20/0.46 => ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) @ ( tl @ node @ Ns ) @ M )
% 0.20/0.46 => ~ ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_cases
% 0.20/0.46 thf(fact_78_rs__props_I3_J,axiom,
% 0.20/0.46 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rs_props(3)
% 0.20/0.46 thf(fact_79_butlast__snoc,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.20/0.46 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.20/0.46 = Xs ) ).
% 0.20/0.46
% 0.20/0.46 % butlast_snoc
% 0.20/0.46 thf(fact_80_list_Ocollapse,axiom,
% 0.20/0.46 ! [A: $tType,List: list @ A] :
% 0.20/0.46 ( ( List
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 0.20/0.46 = List ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.collapse
% 0.20/0.46 thf(fact_81_hd__Cons__tl,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 0.20/0.46 = Xs ) ) ).
% 0.20/0.46
% 0.20/0.46 % hd_Cons_tl
% 0.20/0.46 thf(fact_82_in__hd__or__tl__conv,axiom,
% 0.20/0.46 ! [A: $tType,L: list @ A,X: A] :
% 0.20/0.46 ( ( L
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ( X
% 0.20/0.46 = ( hd @ A @ L ) )
% 0.20/0.46 | ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ L ) ) ) )
% 0.20/0.46 = ( member @ A @ X @ ( set2 @ A @ L ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_hd_or_tl_conv
% 0.20/0.46 thf(fact_83_ri__props_I4_J,axiom,
% 0.20/0.46 prefix @ node @ ri @ rs2 ).
% 0.20/0.46
% 0.20/0.46 % ri_props(4)
% 0.20/0.46 thf(fact_84_ms_H__props_I2_J,axiom,
% 0.20/0.46 prefix @ node @ ms2 @ ms ).
% 0.20/0.46
% 0.20/0.46 % ms'_props(2)
% 0.20/0.46 thf(fact_85_old_OCons__path2,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,N2: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns ) @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.Cons_path2
% 0.20/0.46 thf(fact_86_butlast__tl,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 0.20/0.46 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % butlast_tl
% 0.20/0.46 thf(fact_87_butlast_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( butlast @ A @ ( nil @ A ) )
% 0.20/0.46 = ( nil @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % butlast.simps(1)
% 0.20/0.46 thf(fact_88_list_Osel_I3_J,axiom,
% 0.20/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.20/0.46 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.20/0.46 = X22 ) ).
% 0.20/0.46
% 0.20/0.46 % list.sel(3)
% 0.20/0.46 thf(fact_89_in__set__butlastD,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.20/0.46 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_set_butlastD
% 0.20/0.46 thf(fact_90_list_Osel_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( tl @ A @ ( nil @ A ) )
% 0.20/0.46 = ( nil @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.sel(2)
% 0.20/0.46 thf(fact_91_butlast_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.20/0.46 ( ( ( Xs
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.20/0.46 = ( nil @ A ) ) )
% 0.20/0.46 & ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.20/0.46 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % butlast.simps(2)
% 0.20/0.46 thf(fact_92_tl__obtain__elem,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ( tl @ A @ Xs )
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 => ~ ! [E4: A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 != ( cons @ A @ E4 @ ( nil @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % tl_obtain_elem
% 0.20/0.46 thf(fact_93_tl__Nil,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( ( tl @ A @ Xs )
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 = ( ( Xs
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 | ? [X3: A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % tl_Nil
% 0.20/0.46 thf(fact_94_Nil__tl,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( ( nil @ A )
% 0.20/0.46 = ( tl @ A @ Xs ) )
% 0.20/0.46 = ( ( Xs
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 | ? [X3: A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Nil_tl
% 0.20/0.46 thf(fact_95_butlast__append,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.20/0.46 ( ( ( Ys
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( butlast @ A @ Xs ) ) )
% 0.20/0.46 & ( ( Ys
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % butlast_append
% 0.20/0.46 thf(fact_96_list_Oset__sel_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A,X: A] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ A2 ) ) )
% 0.20/0.46 => ( member @ A @ X @ ( set2 @ A @ A2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.set_sel(2)
% 0.20/0.46 thf(fact_97_in__set__butlast__appendI,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.20/0.46 | ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 0.20/0.46 => ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_set_butlast_appendI
% 0.20/0.46 thf(fact_98_list_Oexpand,axiom,
% 0.20/0.46 ! [A: $tType,List: list @ A,List2: list @ A] :
% 0.20/0.46 ( ( ( List
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 = ( List2
% 0.20/0.46 = ( nil @ A ) ) )
% 0.20/0.46 => ( ( ( List
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( List2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ( hd @ A @ List )
% 0.20/0.46 = ( hd @ A @ List2 ) )
% 0.20/0.46 & ( ( tl @ A @ List )
% 0.20/0.46 = ( tl @ A @ List2 ) ) ) ) )
% 0.20/0.46 => ( List = List2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.expand
% 0.20/0.46 thf(fact_99_not__hd__in__tl,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 != ( hd @ A @ Xs ) )
% 0.20/0.46 => ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_hd_in_tl
% 0.20/0.46 thf(fact_100_butlast__eq__cons__conv,axiom,
% 0.20/0.46 ! [A: $tType,L: list @ A,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( ( butlast @ A @ L )
% 0.20/0.46 = ( cons @ A @ X @ Xs ) )
% 0.20/0.46 = ( ? [Xl: A] :
% 0.20/0.46 ( L
% 0.20/0.46 = ( cons @ A @ X @ ( append @ A @ Xs @ ( cons @ A @ Xl @ ( nil @ A ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % butlast_eq_cons_conv
% 0.20/0.46 thf(fact_101_butlast__eq__consE,axiom,
% 0.20/0.46 ! [A: $tType,L: list @ A,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( ( butlast @ A @ L )
% 0.20/0.46 = ( cons @ A @ X @ Xs ) )
% 0.20/0.46 => ~ ! [Xl2: A] :
% 0.20/0.46 ( L
% 0.20/0.46 != ( cons @ A @ X @ ( append @ A @ Xs @ ( cons @ A @ Xl2 @ ( nil @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % butlast_eq_consE
% 0.20/0.46 thf(fact_102_list_Oexhaust__sel,axiom,
% 0.20/0.46 ! [A: $tType,List: list @ A] :
% 0.20/0.46 ( ( List
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( List
% 0.20/0.46 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.exhaust_sel
% 0.20/0.46 thf(fact_103_not__Cons__self2,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( cons @ A @ X @ Xs )
% 0.20/0.46 != Xs ) ).
% 0.20/0.46
% 0.20/0.46 % not_Cons_self2
% 0.20/0.46 thf(fact_104_list__tail__coinc,axiom,
% 0.20/0.46 ! [A: $tType,N1: A,R1: list @ A,N22: A,R2: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ N1 @ R1 )
% 0.20/0.46 = ( cons @ A @ N22 @ R2 ) )
% 0.20/0.46 => ( ( N1 = N22 )
% 0.20/0.46 & ( R1 = R2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_tail_coinc
% 0.20/0.46 thf(fact_105_append__eq__append__conv2,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.20/0.46 = ( append @ A @ Zs @ Ts ) )
% 0.20/0.46 = ( ? [Us: list @ A] :
% 0.20/0.46 ( ( ( Xs
% 0.20/0.46 = ( append @ A @ Zs @ Us ) )
% 0.20/0.46 & ( ( append @ A @ Us @ Ys )
% 0.20/0.46 = Ts ) )
% 0.20/0.46 | ( ( ( append @ A @ Xs @ Us )
% 0.20/0.46 = Zs )
% 0.20/0.46 & ( Ys
% 0.20/0.46 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_eq_append_conv2
% 0.20/0.46 thf(fact_106_append__eq__appendI,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us2: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Xs @ Xs1 )
% 0.20/0.46 = Zs )
% 0.20/0.46 => ( ( Ys
% 0.20/0.46 = ( append @ A @ Xs1 @ Us2 ) )
% 0.20/0.46 => ( ( append @ A @ Xs @ Ys )
% 0.20/0.46 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_eq_appendI
% 0.20/0.46 thf(fact_107_list_Odistinct_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.20/0.46 ( ( nil @ A )
% 0.20/0.46 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.distinct(1)
% 0.20/0.46 thf(fact_108_neq__NilE,axiom,
% 0.20/0.46 ! [A: $tType,L: list @ A] :
% 0.20/0.46 ( ( L
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ~ ! [X4: A,Xs2: list @ A] :
% 0.20/0.46 ( L
% 0.20/0.46 != ( cons @ A @ X4 @ Xs2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % neq_NilE
% 0.20/0.46 thf(fact_109_list_OdiscI,axiom,
% 0.20/0.46 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.20/0.46 ( ( List
% 0.20/0.46 = ( cons @ A @ X21 @ X22 ) )
% 0.20/0.46 => ( List
% 0.20/0.46 != ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.discI
% 0.20/0.46 thf(fact_110_revg_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.20/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.20/0.46 => ( ! [A4: A,As: list @ A,B3: list @ A] :
% 0.20/0.46 ( ( P @ As @ ( cons @ A @ A4 @ B3 ) )
% 0.20/0.46 => ( P @ ( cons @ A @ A4 @ As ) @ B3 ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % revg.induct
% 0.20/0.46 thf(fact_111_zipf_Oinduct,axiom,
% 0.20/0.46 ! [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] :
% 0.20/0.46 ( ! [F2: A > B > C2] : ( P @ F2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [F2: A > B > C2,A4: A,As: list @ A,B3: B,Bs: list @ B] :
% 0.20/0.46 ( ( P @ F2 @ As @ Bs )
% 0.20/0.46 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B @ B3 @ Bs ) ) )
% 0.20/0.46 => ( ! [A4: A > B > C2,V: A,Va: list @ A] : ( P @ A4 @ ( cons @ A @ V @ Va ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [A4: A > B > C2,V: B,Va: list @ B] : ( P @ A4 @ ( nil @ A ) @ ( cons @ B @ V @ Va ) )
% 0.20/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % zipf.induct
% 0.20/0.46 thf(fact_112_list_Oexhaust,axiom,
% 0.20/0.46 ! [A: $tType,Y: list @ A] :
% 0.20/0.46 ( ( Y
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ~ ! [X212: A,X222: list @ A] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.exhaust
% 0.20/0.46 thf(fact_113_list_Oinducts,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X1: A,X23: list @ A] :
% 0.20/0.46 ( ( P @ X23 )
% 0.20/0.46 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 0.20/0.46 => ( P @ List ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.inducts
% 0.20/0.46 thf(fact_114_neq__Nil__conv,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 = ( ? [Y2: A,Ys2: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( cons @ A @ Y2 @ Ys2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % neq_Nil_conv
% 0.20/0.46 thf(fact_115_list__induct2_H,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.20/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.20/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
% 0.20/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_induct2'
% 0.20/0.46 thf(fact_116_splice_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.20/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.20/0.46 ( ( P @ Ys3 @ Xs2 )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splice.induct
% 0.20/0.46 thf(fact_117_induct__list012,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [X4: A,Y3: A,Zs2: list @ A] :
% 0.20/0.46 ( ( P @ Zs2 )
% 0.20/0.46 => ( ( P @ ( cons @ A @ Y3 @ Zs2 ) )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs2 ) ) ) ) )
% 0.20/0.46 => ( P @ Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % induct_list012
% 0.20/0.46 thf(fact_118_min__list_Ocases,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A )
% 0.20/0.46 => ! [X: list @ A] :
% 0.20/0.46 ( ! [X4: A,Xs2: list @ A] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( cons @ A @ X4 @ Xs2 ) )
% 0.20/0.46 => ( X
% 0.20/0.46 = ( nil @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % min_list.cases
% 0.20/0.46 thf(fact_119_min__list_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A )
% 0.20/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.20/0.46 ( ! [X4: A,Xs2: list @ A] :
% 0.20/0.46 ( ! [X213: A,X223: list @ A] :
% 0.20/0.46 ( ( Xs2
% 0.20/0.46 = ( cons @ A @ X213 @ X223 ) )
% 0.20/0.46 => ( P @ Xs2 ) )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 0.20/0.46 => ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % min_list.induct
% 0.20/0.46 thf(fact_120_shuffles_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.20/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.20/0.46 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.20/0.46 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
% 0.20/0.46 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % shuffles.induct
% 0.20/0.46 thf(fact_121_list__2pre__induct,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,W1: list @ A,W2: list @ B] :
% 0.20/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [E4: A,W12: list @ A,W22: list @ B] :
% 0.20/0.46 ( ( P @ W12 @ W22 )
% 0.20/0.46 => ( P @ ( cons @ A @ E4 @ W12 ) @ W22 ) )
% 0.20/0.46 => ( ! [E4: B,W13: list @ A,W23: list @ B] :
% 0.20/0.46 ( ( P @ W13 @ W23 )
% 0.20/0.46 => ( P @ W13 @ ( cons @ B @ E4 @ W23 ) ) )
% 0.20/0.46 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_2pre_induct
% 0.20/0.46 thf(fact_122_remdups__adj_Ocases,axiom,
% 0.20/0.46 ! [A: $tType,X: list @ A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.20/0.46 => ~ ! [X4: A,Y3: A,Xs2: list @ A] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % remdups_adj.cases
% 0.20/0.46 thf(fact_123_sorted__wrt_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.20/0.46 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.20/0.46 => ( ! [P2: A > A > $o,X4: A,Ys3: list @ A] :
% 0.20/0.46 ( ( P @ P2 @ Ys3 )
% 0.20/0.46 => ( P @ P2 @ ( cons @ A @ X4 @ Ys3 ) ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sorted_wrt.induct
% 0.20/0.46 thf(fact_124_remdups__adj_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [X4: A,Y3: A,Xs2: list @ A] :
% 0.20/0.46 ( ( ( X4 = Y3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 0.20/0.46 => ( ( ( X4 != Y3 )
% 0.20/0.46 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % remdups_adj.induct
% 0.20/0.46 thf(fact_125_list__induct__first2,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [X1: A,X23: A,Xs2: list @ A] :
% 0.20/0.46 ( ( P @ Xs2 )
% 0.20/0.46 => ( P @ ( cons @ A @ X1 @ ( cons @ A @ X23 @ Xs2 ) ) ) )
% 0.20/0.46 => ( P @ Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_induct_first2
% 0.20/0.46 thf(fact_126_arg__min__list_Oinduct,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType] :
% 0.20/0.46 ( ( linorder @ B )
% 0.20/0.46 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.20/0.46 ( ! [F2: A > B,X4: A] : ( P @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [F2: A > B,X4: A,Y3: A,Zs2: list @ A] :
% 0.20/0.46 ( ( P @ F2 @ ( cons @ A @ Y3 @ Zs2 ) )
% 0.20/0.46 => ( P @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs2 ) ) ) )
% 0.20/0.46 => ( ! [A4: A > B] : ( P @ A4 @ ( nil @ A ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % arg_min_list.induct
% 0.20/0.46 thf(fact_127_successively_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.20/0.46 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.20/0.46 => ( ! [P2: A > A > $o,X4: A] : ( P @ P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [P2: A > A > $o,X4: A,Y3: A,Xs2: list @ A] :
% 0.20/0.46 ( ( P @ P2 @ ( cons @ A @ Y3 @ Xs2 ) )
% 0.20/0.46 => ( P @ P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % successively.induct
% 0.20/0.46 thf(fact_128_list__all__zip_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,P: ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > $o,A1: list @ A,A22: list @ B] :
% 0.20/0.46 ( ! [P2: A > B > $o] : ( P @ P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [P2: A > B > $o,A4: A,As: list @ A,B3: B,Bs: list @ B] :
% 0.20/0.46 ( ( P @ P2 @ As @ Bs )
% 0.20/0.46 => ( P @ P2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B @ B3 @ Bs ) ) )
% 0.20/0.46 => ( ! [P2: A > B > $o,V: A,Va: list @ A] : ( P @ P2 @ ( cons @ A @ V @ Va ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [P2: A > B > $o,V: B,Va: list @ B] : ( P @ P2 @ ( nil @ A ) @ ( cons @ B @ V @ Va ) )
% 0.20/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_all_zip.induct
% 0.20/0.46 thf(fact_129_list__nonempty__induct,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A] :
% 0.20/0.46 ( ( Xs2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( P @ Xs2 )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 0.20/0.46 => ( P @ Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_nonempty_induct
% 0.20/0.46 thf(fact_130_map__tailrec__rev_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.20/0.46 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 0.20/0.46 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.20/0.46 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 0.20/0.46 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.20/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % map_tailrec_rev.induct
% 0.20/0.46 thf(fact_131_mergesort__by__rel__merge_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.20/0.46 ( ! [R: A > A > $o,X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.20/0.46 ( ( ( R @ X4 @ Y3 )
% 0.20/0.46 => ( P @ R @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 0.20/0.46 => ( ( ~ ( R @ X4 @ Y3 )
% 0.20/0.46 => ( P @ R @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 ) )
% 0.20/0.46 => ( P @ R @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 0.20/0.46 => ( ! [R: A > A > $o,Xs2: list @ A] : ( P @ R @ Xs2 @ ( nil @ A ) )
% 0.20/0.46 => ( ! [R: A > A > $o,V: A,Va: list @ A] : ( P @ R @ ( nil @ A ) @ ( cons @ A @ V @ Va ) )
% 0.20/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mergesort_by_rel_merge.induct
% 0.20/0.46 thf(fact_132_mergesort__by__rel__merge__induct,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,R3: A > B > $o,Xs: list @ A,Ys: list @ B] :
% 0.20/0.46 ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ B ) )
% 0.20/0.46 => ( ! [X_1: list @ B] : ( P @ ( nil @ A ) @ X_1 )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.20/0.46 ( ( R3 @ X4 @ Y3 )
% 0.20/0.46 => ( ( P @ Xs2 @ ( cons @ B @ Y3 @ Ys3 ) )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.20/0.46 ( ~ ( R3 @ X4 @ Y3 )
% 0.20/0.46 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) )
% 0.20/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mergesort_by_rel_merge_induct
% 0.20/0.46 thf(fact_133_strict__sorted_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A )
% 0.20/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A,Ys3: list @ A] :
% 0.20/0.46 ( ( P @ Ys3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ Ys3 ) ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % strict_sorted.induct
% 0.20/0.46 thf(fact_134_transpose_Ocases,axiom,
% 0.20/0.46 ! [A: $tType,X: list @ ( list @ A )] :
% 0.20/0.46 ( ( X
% 0.20/0.46 != ( nil @ ( list @ A ) ) )
% 0.20/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.20/0.46 => ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % transpose.cases
% 0.20/0.46 thf(fact_135_list_Oset__intros_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,Y: A,X22: list @ A,X21: A] :
% 0.20/0.46 ( ( member @ A @ Y @ ( set2 @ A @ X22 ) )
% 0.20/0.46 => ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.set_intros(2)
% 0.20/0.46 thf(fact_136_list_Oset__intros_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,X21: A,X22: list @ A] : ( member @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.set_intros(1)
% 0.20/0.46 thf(fact_137_set__ConsD,axiom,
% 0.20/0.46 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 0.20/0.46 => ( ( Y = X )
% 0.20/0.46 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % set_ConsD
% 0.20/0.46 thf(fact_138_list_Oset__cases,axiom,
% 0.20/0.46 ! [A: $tType,E3: A,A2: list @ A] :
% 0.20/0.46 ( ( member @ A @ E3 @ ( set2 @ A @ A2 ) )
% 0.20/0.46 => ( ! [Z2: list @ A] :
% 0.20/0.46 ( A2
% 0.20/0.46 != ( cons @ A @ E3 @ Z2 ) )
% 0.20/0.46 => ~ ! [Z1: A,Z2: list @ A] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( cons @ A @ Z1 @ Z2 ) )
% 0.20/0.46 => ~ ( member @ A @ E3 @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.set_cases
% 0.20/0.46 thf(fact_139_Cons__eq__appendI,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ X @ Xs1 )
% 0.20/0.46 = Ys )
% 0.20/0.46 => ( ( Xs
% 0.20/0.46 = ( append @ A @ Xs1 @ Zs ) )
% 0.20/0.46 => ( ( cons @ A @ X @ Xs )
% 0.20/0.46 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Cons_eq_appendI
% 0.20/0.46 thf(fact_140_append__Cons,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.20/0.46 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_Cons
% 0.20/0.46 thf(fact_141_list__match__lel__lel,axiom,
% 0.20/0.46 ! [A: $tType,C1: list @ A,Qs: A,C22: list @ A,C12: list @ A,Qs2: A,C23: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ C1 @ ( cons @ A @ Qs @ C22 ) )
% 0.20/0.46 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C23 ) ) )
% 0.20/0.46 => ( ! [C21: list @ A] :
% 0.20/0.46 ( ( C1
% 0.20/0.46 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C21 ) ) )
% 0.20/0.46 => ( C23
% 0.20/0.46 != ( append @ A @ C21 @ ( cons @ A @ Qs @ C22 ) ) ) )
% 0.20/0.46 => ( ( ( C12 = C1 )
% 0.20/0.46 => ( ( Qs2 = Qs )
% 0.20/0.46 => ( C23 != C22 ) ) )
% 0.20/0.46 => ~ ! [C212: list @ A] :
% 0.20/0.46 ( ( C12
% 0.20/0.46 = ( append @ A @ C1 @ ( cons @ A @ Qs @ C212 ) ) )
% 0.20/0.46 => ( C22
% 0.20/0.46 != ( append @ A @ C212 @ ( cons @ A @ Qs2 @ C23 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_match_lel_lel
% 0.20/0.46 thf(fact_142_append_Oleft__neutral,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] :
% 0.20/0.46 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % append.left_neutral
% 0.20/0.46 thf(fact_143_append__Nil,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A] :
% 0.20/0.46 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.20/0.46 = Ys ) ).
% 0.20/0.46
% 0.20/0.46 % append_Nil
% 0.20/0.46 thf(fact_144_eq__Nil__appendI,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( Xs = Ys )
% 0.20/0.46 => ( Xs
% 0.20/0.46 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_Nil_appendI
% 0.20/0.46 thf(fact_145_list_Osel_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.20/0.46 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.20/0.46 = X21 ) ).
% 0.20/0.46
% 0.20/0.46 % list.sel(1)
% 0.20/0.46 thf(fact_146_rev__induct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A] :
% 0.20/0.46 ( ( P @ Xs2 )
% 0.20/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 0.20/0.46 => ( P @ Xs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rev_induct
% 0.20/0.46 thf(fact_147_rev__exhaust,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ~ ! [Ys3: list @ A,Y3: A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 != ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rev_exhaust
% 0.20/0.46 thf(fact_148_neq__Nil__revE,axiom,
% 0.20/0.46 ! [A: $tType,L: list @ A] :
% 0.20/0.46 ( ( L
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ~ ! [Ll: list @ A,E4: A] :
% 0.20/0.46 ( L
% 0.20/0.46 != ( append @ A @ Ll @ ( cons @ A @ E4 @ ( nil @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % neq_Nil_revE
% 0.20/0.46 thf(fact_149_rev__induct2_H,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.20/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.20/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.20/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) ) )
% 0.20/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rev_induct2'
% 0.20/0.46 thf(fact_150_neq__Nil__rev__conv,axiom,
% 0.20/0.46 ! [A: $tType,L: list @ A] :
% 0.20/0.46 ( ( L
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 = ( ? [Xs3: list @ A,X3: A] :
% 0.20/0.46 ( L
% 0.20/0.46 = ( append @ A @ Xs3 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % neq_Nil_rev_conv
% 0.20/0.46 thf(fact_151_Cons__eq__append__conv,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ X @ Xs )
% 0.20/0.46 = ( append @ A @ Ys @ Zs ) )
% 0.20/0.46 = ( ( ( Ys
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( ( cons @ A @ X @ Xs )
% 0.20/0.46 = Zs ) )
% 0.20/0.46 | ? [Ys4: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ X @ Ys4 )
% 0.20/0.46 = Ys )
% 0.20/0.46 & ( Xs
% 0.20/0.46 = ( append @ A @ Ys4 @ Zs ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Cons_eq_append_conv
% 0.20/0.46 thf(fact_152_append__eq__Cons__conv,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Ys @ Zs )
% 0.20/0.46 = ( cons @ A @ X @ Xs ) )
% 0.20/0.46 = ( ( ( Ys
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( Zs
% 0.20/0.46 = ( cons @ A @ X @ Xs ) ) )
% 0.20/0.46 | ? [Ys4: list @ A] :
% 0.20/0.46 ( ( Ys
% 0.20/0.46 = ( cons @ A @ X @ Ys4 ) )
% 0.20/0.46 & ( ( append @ A @ Ys4 @ Zs )
% 0.20/0.46 = Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_eq_Cons_conv
% 0.20/0.46 thf(fact_153_rev__nonempty__induct,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A] :
% 0.20/0.46 ( ( Xs2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( P @ Xs2 )
% 0.20/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 0.20/0.46 => ( P @ Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rev_nonempty_induct
% 0.20/0.46 thf(fact_154_rev__nonempty__induct2_H,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( Ys
% 0.20/0.46 != ( nil @ B ) )
% 0.20/0.46 => ( ! [X4: A,Y3: B] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) @ ( cons @ B @ Y3 @ ( nil @ B ) ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: B] :
% 0.20/0.46 ( ( Xs2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) )
% 0.20/0.46 => ( ! [X4: A,Y3: B,Ys3: list @ B] :
% 0.20/0.46 ( ( Ys3
% 0.20/0.46 != ( nil @ B ) )
% 0.20/0.46 => ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.20/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.20/0.46 => ( ( Xs2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( Ys3
% 0.20/0.46 != ( nil @ B ) )
% 0.20/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) ) ) ) )
% 0.20/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % rev_nonempty_induct2'
% 0.20/0.46 thf(fact_155_list__Cons__eq__append__cases,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ X @ Xs )
% 0.20/0.46 = ( append @ A @ Ys @ Zs ) )
% 0.20/0.46 => ( ( ( Ys
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 => ( Zs
% 0.20/0.46 != ( cons @ A @ X @ Xs ) ) )
% 0.20/0.46 => ~ ! [Ys5: list @ A] :
% 0.20/0.46 ( ( Ys
% 0.20/0.46 = ( cons @ A @ X @ Ys5 ) )
% 0.20/0.46 => ( ( append @ A @ Ys5 @ Zs )
% 0.20/0.46 != Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_Cons_eq_append_cases
% 0.20/0.46 thf(fact_156_list__append__eq__Cons__cases,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( ( append @ A @ Ys @ Zs )
% 0.20/0.46 = ( cons @ A @ X @ Xs ) )
% 0.20/0.46 => ( ( ( Ys
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 => ( Zs
% 0.20/0.46 != ( cons @ A @ X @ Xs ) ) )
% 0.20/0.46 => ~ ! [Ys5: list @ A] :
% 0.20/0.46 ( ( Ys
% 0.20/0.46 = ( cons @ A @ X @ Ys5 ) )
% 0.20/0.46 => ( ( append @ A @ Ys5 @ Zs )
% 0.20/0.46 != Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_append_eq_Cons_cases
% 0.20/0.46 thf(fact_157_split__list,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 => ? [Ys3: list @ A,Zs2: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list
% 0.20/0.46 thf(fact_158_split__list__last,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 => ? [Ys3: list @ A,Zs2: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.20/0.46 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_last
% 0.20/0.46 thf(fact_159_split__list__prop,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.20/0.46 ( ? [X2: A] :
% 0.20/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 => ? [Ys3: list @ A,X4: A] :
% 0.20/0.46 ( ? [Zs2: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.20/0.46 & ( P @ X4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_prop
% 0.20/0.46 thf(fact_160_xy__in__set__cases,axiom,
% 0.20/0.46 ! [A: $tType,X: A,L: list @ A,Y: A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ L ) )
% 0.20/0.46 => ( ( member @ A @ Y @ ( set2 @ A @ L ) )
% 0.20/0.46 => ( ( ( X = Y )
% 0.20/0.46 => ! [L12: list @ A,L22: list @ A] :
% 0.20/0.46 ( L
% 0.20/0.46 != ( append @ A @ L12 @ ( cons @ A @ Y @ L22 ) ) ) )
% 0.20/0.46 => ( ( ( X != Y )
% 0.20/0.46 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 0.20/0.46 ( L
% 0.20/0.46 != ( append @ A @ L12 @ ( cons @ A @ X @ ( append @ A @ L22 @ ( cons @ A @ Y @ L3 ) ) ) ) ) )
% 0.20/0.46 => ~ ( ( X != Y )
% 0.20/0.46 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 0.20/0.46 ( L
% 0.20/0.46 != ( append @ A @ L12 @ ( cons @ A @ Y @ ( append @ A @ L22 @ ( cons @ A @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % xy_in_set_cases
% 0.20/0.46 thf(fact_161_split__list__first,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 => ? [Ys3: list @ A,Zs2: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.20/0.46 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_first
% 0.20/0.46 thf(fact_162_split__list__propE,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.20/0.46 ( ? [X2: A] :
% 0.20/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 => ~ ! [Ys3: list @ A,X4: A] :
% 0.20/0.46 ( ? [Zs2: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.20/0.46 => ~ ( P @ X4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_propE
% 0.20/0.46 thf(fact_163_append__Cons__eq__iff,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Xs4: list @ A,Ys6: list @ A] :
% 0.20/0.46 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 => ( ~ ( member @ A @ X @ ( set2 @ A @ Ys ) )
% 0.20/0.46 => ( ( ( append @ A @ Xs @ ( cons @ A @ X @ Ys ) )
% 0.20/0.46 = ( append @ A @ Xs4 @ ( cons @ A @ X @ Ys6 ) ) )
% 0.20/0.46 = ( ( Xs = Xs4 )
% 0.20/0.46 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % append_Cons_eq_iff
% 0.20/0.46 thf(fact_164_in__set__conv__decomp,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 = ( ? [Ys2: list @ A,Zs3: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_set_conv_decomp
% 0.20/0.46 thf(fact_165_in__set__list__format,axiom,
% 0.20/0.46 ! [A: $tType,E3: A,L: list @ A] :
% 0.20/0.46 ( ( member @ A @ E3 @ ( set2 @ A @ L ) )
% 0.20/0.46 => ~ ! [L12: list @ A,L22: list @ A] :
% 0.20/0.46 ( L
% 0.20/0.46 != ( append @ A @ L12 @ ( cons @ A @ E3 @ L22 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_set_list_format
% 0.20/0.46 thf(fact_166_split__list__last__prop,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.20/0.46 ( ? [X2: A] :
% 0.20/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 => ? [Ys3: list @ A,X4: A,Zs2: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.20/0.46 & ( P @ X4 )
% 0.20/0.46 & ! [Xa: A] :
% 0.20/0.46 ( ( member @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 0.20/0.46 => ~ ( P @ Xa ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_last_prop
% 0.20/0.46 thf(fact_167_split__list__first__prop,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.20/0.46 ( ? [X2: A] :
% 0.20/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 => ? [Ys3: list @ A,X4: A] :
% 0.20/0.46 ( ? [Zs2: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.20/0.46 & ( P @ X4 )
% 0.20/0.46 & ! [Xa: A] :
% 0.20/0.46 ( ( member @ A @ Xa @ ( set2 @ A @ Ys3 ) )
% 0.20/0.46 => ~ ( P @ Xa ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_first_prop
% 0.20/0.46 thf(fact_168_split__list__last__propE,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.20/0.46 ( ? [X2: A] :
% 0.20/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 => ~ ! [Ys3: list @ A,X4: A,Zs2: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.20/0.46 => ( ( P @ X4 )
% 0.20/0.46 => ~ ! [Xa: A] :
% 0.20/0.46 ( ( member @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 0.20/0.46 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_last_propE
% 0.20/0.46 thf(fact_169_split__list__first__propE,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.20/0.46 ( ? [X2: A] :
% 0.20/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 => ~ ! [Ys3: list @ A,X4: A] :
% 0.20/0.46 ( ? [Zs2: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.20/0.46 => ( ( P @ X4 )
% 0.20/0.46 => ~ ! [Xa: A] :
% 0.20/0.46 ( ( member @ A @ Xa @ ( set2 @ A @ Ys3 ) )
% 0.20/0.46 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_first_propE
% 0.20/0.46 thf(fact_170_in__set__conv__decomp__last,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 = ( ? [Ys2: list @ A,Zs3: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.20/0.46 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_set_conv_decomp_last
% 0.20/0.46 thf(fact_171_in__set__conv__decomp__first,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.20/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.20/0.46 = ( ? [Ys2: list @ A,Zs3: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.20/0.46 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_set_conv_decomp_first
% 0.20/0.46 thf(fact_172_split__list__last__prop__iff,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.20/0.46 ( ( ? [X3: A] :
% 0.20/0.46 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 & ( P @ X3 ) ) )
% 0.20/0.46 = ( ? [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.20/0.46 & ( P @ X3 )
% 0.20/0.46 & ! [Y2: A] :
% 0.20/0.46 ( ( member @ A @ Y2 @ ( set2 @ A @ Zs3 ) )
% 0.20/0.46 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_last_prop_iff
% 0.20/0.46 thf(fact_173_split__list__first__prop__iff,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.20/0.46 ( ( ? [X3: A] :
% 0.20/0.46 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 & ( P @ X3 ) ) )
% 0.20/0.46 = ( ? [Ys2: list @ A,X3: A] :
% 0.20/0.46 ( ? [Zs3: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.20/0.46 & ( P @ X3 )
% 0.20/0.46 & ! [Y2: A] :
% 0.20/0.46 ( ( member @ A @ Y2 @ ( set2 @ A @ Ys2 ) )
% 0.20/0.46 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % split_list_first_prop_iff
% 0.20/0.46 thf(fact_174_hd__in__set,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( member @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ Xs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % hd_in_set
% 0.20/0.46 thf(fact_175_list_Oset__sel_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( member @ A @ ( hd @ A @ A2 ) @ ( set2 @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.set_sel(1)
% 0.20/0.46 thf(fact_176_longest__common__prefix,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ? [Ps: list @ A,Xs5: list @ A,Ys5: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Ps @ Xs5 ) )
% 0.20/0.46 & ( Ys
% 0.20/0.46 = ( append @ A @ Ps @ Ys5 ) )
% 0.20/0.46 & ( ( Xs5
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 | ( Ys5
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 | ( ( hd @ A @ Xs5 )
% 0.20/0.46 != ( hd @ A @ Ys5 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % longest_common_prefix
% 0.20/0.46 thf(fact_177_hd__append,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( ( Xs
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( hd @ A @ Ys ) ) )
% 0.20/0.46 & ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.20/0.46 = ( hd @ A @ Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % hd_append
% 0.20/0.46 thf(fact_178__092_060open_062old_OpathsConverge_Ag_Am_Ams_H_An_A_Ins_A_064_Atl_Ari_J_Ai_092_060close_062,axiom,
% 0.20/0.46 graph_pathsConverge @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ n @ ( append @ node @ ns @ ( tl @ node @ ri ) ) @ i ).
% 0.20/0.46
% 0.20/0.46 % \<open>old.pathsConverge g m ms' n (ns @ tl ri) i\<close>
% 0.20/0.46 thf(fact_179__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.46 ~ ! [I: node,Ri: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 0.20/0.46 => ( ( member @ node @ I @ ( set2 @ node @ ms ) )
% 0.20/0.46 => ( ! [X2: node] :
% 0.20/0.46 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ Ri ) ) )
% 0.20/0.46 => ~ ( member @ node @ X2 @ ( set2 @ node @ ms ) ) )
% 0.20/0.46 => ~ ( prefix @ node @ Ri @ rs2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>\<And>thesis. (\<And>i ri. \<lbrakk>g \<turnstile> defNode g r-ri\<rightarrow>i; i \<in> set ms; \<forall>n\<in>set (butlast ri). n \<notin> set ms; prefix ri rs\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.46 thf(fact_180__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.46 ~ ! [Ms2: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 0.20/0.46 => ( ( prefix @ node @ Ms2 @ ms )
% 0.20/0.46 => ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ Ms2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>\<And>thesis. (\<And>ms'. \<lbrakk>g \<turnstile> m-ms'\<rightarrow>i; prefix ms' ms; i \<notin> set (butlast ms')\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.46 thf(fact_181_old_Opath2__simple__loop,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,N2: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ N )
% 0.20/0.46 => ( ( member @ node @ N2 @ ( set2 @ node @ Ns ) )
% 0.20/0.46 => ~ ! [Ns4: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns4 @ N )
% 0.20/0.46 => ( ( member @ node @ N2 @ ( set2 @ node @ Ns4 ) )
% 0.20/0.46 => ( ~ ( member @ node @ N @ ( set2 @ node @ ( tl @ node @ ( butlast @ node @ Ns4 ) ) ) )
% 0.20/0.46 => ~ ( ord_less_eq @ ( set @ node ) @ ( set2 @ node @ Ns4 ) @ ( set2 @ node @ Ns ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_simple_loop
% 0.20/0.46 thf(fact_182_old_Opath_Ocases,axiom,
% 0.20/0.46 ! [G2: g,A2: list @ node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ A2 )
% 0.20/0.46 => ( ! [N4: node] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( cons @ node @ N4 @ ( nil @ node ) ) )
% 0.20/0.46 => ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.20/0.46 => ~ ( invar @ G2 ) ) )
% 0.20/0.46 => ~ ! [Ns3: list @ node,N3: node] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( cons @ node @ N3 @ Ns3 ) )
% 0.20/0.46 => ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns3 )
% 0.20/0.46 => ~ ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns3 ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path.cases
% 0.20/0.46 thf(fact_183_old_Opath_Oinducts,axiom,
% 0.20/0.46 ! [G2: g,X: list @ node,P: ( list @ node ) > $o] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X )
% 0.20/0.46 => ( ! [N4: node] :
% 0.20/0.46 ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.20/0.46 => ( ( invar @ G2 )
% 0.20/0.46 => ( P @ ( cons @ node @ N4 @ ( nil @ node ) ) ) ) )
% 0.20/0.46 => ( ! [Ns3: list @ node,N3: node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns3 )
% 0.20/0.46 => ( ( P @ Ns3 )
% 0.20/0.46 => ( ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns3 ) ) ) )
% 0.20/0.46 => ( P @ ( cons @ node @ N3 @ Ns3 ) ) ) ) )
% 0.20/0.46 => ( P @ X ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path.inducts
% 0.20/0.46 thf(fact_184_old_Opath_Osimps,axiom,
% 0.20/0.46 ! [G2: g,A2: list @ node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ A2 )
% 0.20/0.46 = ( ? [N5: node] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( cons @ node @ N5 @ ( nil @ node ) ) )
% 0.20/0.46 & ( member @ node @ N5 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.20/0.46 & ( invar @ G2 ) )
% 0.20/0.46 | ? [Ns5: list @ node,N6: node] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( cons @ node @ N6 @ Ns5 ) )
% 0.20/0.46 & ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns5 )
% 0.20/0.46 & ( member @ node @ N6 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns5 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path.simps
% 0.20/0.46 thf(fact_185_old_Opath__snoc,axiom,
% 0.20/0.46 ! [G2: g,Ns: list @ node,N: node,M: node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ N @ ( nil @ node ) ) ) )
% 0.20/0.46 => ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M ) ) )
% 0.20/0.46 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ N @ ( cons @ node @ M @ ( nil @ node ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path_snoc
% 0.20/0.46 thf(fact_186_ri__rs_H__prefix,axiom,
% 0.20/0.46 prefix @ node @ ri @ rs ).
% 0.20/0.46
% 0.20/0.46 % ri_rs'_prefix
% 0.20/0.46 thf(fact_187_old_Opath__not__Nil,axiom,
% 0.20/0.46 ! [G2: g,Ns: list @ node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 0.20/0.46 => ( Ns
% 0.20/0.46 != ( nil @ node ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path_not_Nil
% 0.20/0.46 thf(fact_188_old_Opath__hd,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ Ns ) )
% 0.20/0.46 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path_hd
% 0.20/0.46 thf(fact_189_old_Opath__split_I2_J,axiom,
% 0.20/0.46 ! [G2: g,Ns: list @ node,M: node,Ns2: list @ node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ Ns2 ) ) )
% 0.20/0.46 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ M @ Ns2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path_split(2)
% 0.20/0.46 thf(fact_190_old_Oempty__path,axiom,
% 0.20/0.46 ! [N: node,G2: g] :
% 0.20/0.46 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.20/0.46 => ( ( invar @ G2 )
% 0.20/0.46 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.empty_path
% 0.20/0.46 thf(fact_191_old_Opath__split_I1_J,axiom,
% 0.20/0.46 ! [G2: g,Ns: list @ node,M: node,Ns2: list @ node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ Ns2 ) ) )
% 0.20/0.46 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ ( nil @ node ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path_split(1)
% 0.20/0.46 thf(fact_192_old_Opath2__split__first__prop,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ? [X2: node] :
% 0.20/0.46 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 => ~ ! [M2: node,Ns4: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns4 @ M2 )
% 0.20/0.46 => ( ( P @ M2 )
% 0.20/0.46 => ( ! [X2: node] :
% 0.20/0.46 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ Ns4 ) ) )
% 0.20/0.46 => ~ ( P @ X2 ) )
% 0.20/0.46 => ~ ( prefix @ node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_split_first_prop
% 0.20/0.46 thf(fact_193_old_Opath2__prefix__ex,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,M4: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( member @ node @ M4 @ ( set2 @ node @ Ns ) )
% 0.20/0.46 => ~ ! [Ns4: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns4 @ M4 )
% 0.20/0.46 => ( ( prefix @ node @ Ns4 @ Ns )
% 0.20/0.46 => ( member @ node @ M4 @ ( set2 @ node @ ( butlast @ node @ Ns4 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_prefix_ex
% 0.20/0.46 thf(fact_194_old_OCons__path,axiom,
% 0.20/0.46 ! [G2: g,Ns: list @ node,N2: node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 0.20/0.46 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns ) ) ) )
% 0.20/0.46 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ns ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.Cons_path
% 0.20/0.46 thf(fact_195_old_Opath2__prefix,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,Ns2: list @ node,M4: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( prefix @ node @ ( append @ node @ Ns2 @ ( cons @ node @ M4 @ ( nil @ node ) ) ) @ Ns )
% 0.20/0.46 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns2 @ ( cons @ node @ M4 @ ( nil @ node ) ) ) @ M4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_prefix
% 0.20/0.46 thf(fact_196_old_Opath__invar,axiom,
% 0.20/0.46 ! [G2: g,Ns: list @ node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 0.20/0.46 => ( invar @ G2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path_invar
% 0.20/0.46 thf(fact_197_old_Opath__in___092_060alpha_062n,axiom,
% 0.20/0.46 ! [G2: g,Ns: list @ node,N: node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 0.20/0.46 => ( ( member @ node @ N @ ( set2 @ node @ Ns ) )
% 0.20/0.46 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path_in_\<alpha>n
% 0.20/0.46 thf(fact_198_old_Opath__by__tail,axiom,
% 0.20/0.46 ! [G2: g,N: node,N2: node,Ns: list @ node,Ms: list @ node] :
% 0.20/0.46 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( cons @ node @ N2 @ Ns ) ) )
% 0.20/0.46 => ( ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ns ) )
% 0.20/0.46 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ms ) ) )
% 0.20/0.46 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( cons @ node @ N2 @ Ms ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path_by_tail
% 0.20/0.46 thf(fact_199_subset__Collect__conv,axiom,
% 0.20/0.46 ! [A: $tType,S: set @ A,P: A > $o] :
% 0.20/0.46 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 0.20/0.46 = ( ! [X3: A] :
% 0.20/0.46 ( ( member @ A @ X3 @ S )
% 0.20/0.46 => ( P @ X3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_Collect_conv
% 0.20/0.46 thf(fact_200_ord__eq__le__eq__trans,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A )
% 0.20/0.46 => ! [A2: A,B2: A,C: A,D: A] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.20/0.46 => ( ( C = D )
% 0.20/0.46 => ( ord_less_eq @ A @ A2 @ D ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_eq_trans
% 0.20/0.46 thf(fact_201_subset__code_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,B4: set @ A] :
% 0.20/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ B4 )
% 0.20/0.46 = ( ! [X3: A] :
% 0.20/0.46 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.20/0.46 => ( member @ A @ X3 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_code(1)
% 0.20/0.46 thf(fact_202_set__subset__Cons,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,X: A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % set_subset_Cons
% 0.20/0.46 thf(fact_203_tl__subset,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,A3: set @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A3 )
% 0.20/0.46 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( tl @ A @ Xs ) ) @ A3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % tl_subset
% 0.20/0.46 thf(fact_204_butlast__subset,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,A3: set @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A3 )
% 0.20/0.46 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( butlast @ A @ Xs ) ) @ A3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % butlast_subset
% 0.20/0.46 thf(fact_205_prefix__snoc,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 0.20/0.46 ( ( prefix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.20/0.46 = ( ( Xs
% 0.20/0.46 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.20/0.46 | ( prefix @ A @ Xs @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % prefix_snoc
% 0.20/0.46 thf(fact_206_old_Opath2__split__first__last,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 0.20/0.46 => ~ ! [Ns_1: list @ node,Ns_3: list @ node,Ns_2: list @ node] :
% 0.20/0.46 ( ( Ns
% 0.20/0.46 = ( append @ node @ Ns_1 @ ( append @ node @ Ns_3 @ Ns_2 ) ) )
% 0.20/0.46 => ( ( prefix @ node @ ( append @ node @ Ns_1 @ ( cons @ node @ X @ ( nil @ node ) ) ) @ Ns )
% 0.20/0.46 => ( ( suffix @ node @ ( cons @ node @ X @ Ns_2 ) @ Ns )
% 0.20/0.46 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns_1 @ ( cons @ node @ X @ ( nil @ node ) ) ) @ X )
% 0.20/0.46 => ( ~ ( member @ node @ X @ ( set2 @ node @ Ns_1 ) )
% 0.20/0.46 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_3 @ X )
% 0.20/0.46 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ ( cons @ node @ X @ Ns_2 ) @ M )
% 0.20/0.46 => ( member @ node @ X @ ( set2 @ node @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_split_first_last
% 0.20/0.46 thf(fact_207_same__prefix__nil,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( prefix @ A @ ( append @ A @ Xs @ Ys ) @ Xs )
% 0.20/0.46 = ( Ys
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % same_prefix_nil
% 0.20/0.46 thf(fact_208_prefix__order_Odual__order_Orefl,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] : ( prefix @ A @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % prefix_order.dual_order.refl
% 0.20/0.46 thf(fact_209_prefix__order_Oorder__refl,axiom,
% 0.20/0.46 ! [A: $tType,X: list @ A] : ( prefix @ A @ X @ X ) ).
% 0.20/0.46
% 0.20/0.46 % prefix_order.order_refl
% 0.20/0.46 thf(fact_210_suffix__order_Odual__order_Orefl,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] : ( suffix @ A @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.dual_order.refl
% 0.20/0.46 thf(fact_211_suffix__order_Oorder__refl,axiom,
% 0.20/0.46 ! [A: $tType,X: list @ A] : ( suffix @ A @ X @ X ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.order_refl
% 0.20/0.46 thf(fact_212_Cons__prefix__Cons,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.20/0.46 ( ( prefix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.20/0.46 = ( ( X = Y )
% 0.20/0.46 & ( prefix @ A @ Xs @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Cons_prefix_Cons
% 0.20/0.46 thf(fact_213_prefix__code_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] : ( prefix @ A @ ( nil @ A ) @ Xs ) ).
% 0.20/0.46
% 0.20/0.46 % prefix_code(1)
% 0.20/0.46 thf(fact_214_prefix__Nil,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( prefix @ A @ Xs @ ( nil @ A ) )
% 0.20/0.46 = ( Xs
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % prefix_Nil
% 0.20/0.46 thf(fact_215_prefix__bot_Obot_Oextremum__unique,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] :
% 0.20/0.46 ( ( prefix @ A @ A2 @ ( nil @ A ) )
% 0.20/0.46 = ( A2
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % prefix_bot.bot.extremum_unique
% 0.20/0.46 thf(fact_216_suffix__bot_Obot_Oextremum__unique,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 0.20/0.46 = ( A2
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_bot.bot.extremum_unique
% 0.20/0.46 thf(fact_217_suffix__Nil,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ Xs @ ( nil @ A ) )
% 0.20/0.46 = ( Xs
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_Nil
% 0.20/0.46 thf(fact_218_same__prefix__prefix,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( prefix @ A @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs ) )
% 0.20/0.46 = ( prefix @ A @ Ys @ Zs ) ) ).
% 0.20/0.46
% 0.20/0.46 % same_prefix_prefix
% 0.20/0.46 thf(fact_219_same__suffix__suffix,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ ( append @ A @ Zs @ Xs ) )
% 0.20/0.46 = ( suffix @ A @ Ys @ Zs ) ) ).
% 0.20/0.46
% 0.20/0.46 % same_suffix_suffix
% 0.20/0.46 thf(fact_220_old_Opath2__split__last__prop,axiom,
% 0.20/0.46 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.20/0.46 => ( ? [X2: node] :
% 0.20/0.46 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 => ~ ! [N3: node,Ns4: list @ node] :
% 0.20/0.46 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N3 @ Ns4 @ M )
% 0.20/0.46 => ( ( P @ N3 )
% 0.20/0.46 => ( ! [X2: node] :
% 0.20/0.46 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ns4 ) ) )
% 0.20/0.46 => ~ ( P @ X2 ) )
% 0.20/0.46 => ~ ( suffix @ node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.path2_split_last_prop
% 0.20/0.46 thf(fact_221_same__suffix__nil,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ Xs )
% 0.20/0.46 = ( Ys
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % same_suffix_nil
% 0.20/0.46 thf(fact_222_snoc__suffix__snoc,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.20/0.46 ( ( suffix @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.20/0.46 = ( ( X = Y )
% 0.20/0.46 & ( suffix @ A @ Xs @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % snoc_suffix_snoc
% 0.20/0.46 thf(fact_223_suffix__snoc,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 0.20/0.46 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.20/0.46 = ( ( Xs
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 | ? [Zs3: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Zs3 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.20/0.46 & ( suffix @ A @ Zs3 @ Ys ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_snoc
% 0.20/0.46 thf(fact_224_suffix__tl,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( tl @ A @ Xs ) @ Xs ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_tl
% 0.20/0.46 thf(fact_225_suffix__Cons,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ Xs @ ( cons @ A @ Y @ Ys ) )
% 0.20/0.46 = ( ( Xs
% 0.20/0.46 = ( cons @ A @ Y @ Ys ) )
% 0.20/0.46 | ( suffix @ A @ Xs @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_Cons
% 0.20/0.46 thf(fact_226_suffix__ConsD,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.20/0.46 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_ConsD
% 0.20/0.46 thf(fact_227_suffix__ConsI,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 0.20/0.46 ( ( suffix @ A @ Xs @ Ys )
% 0.20/0.46 => ( suffix @ A @ Xs @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_ConsI
% 0.20/0.46 thf(fact_228_suffix__ConsD2,axiom,
% 0.20/0.46 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.20/0.46 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_ConsD2
% 0.20/0.46 thf(fact_229_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 0.20/0.46 => ( A2
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_bot.bot.extremum_uniqueI
% 0.20/0.46 thf(fact_230_suffix__bot_Obot_Oextremum,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A] : ( suffix @ A @ ( nil @ A ) @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_bot.bot.extremum
% 0.20/0.46 thf(fact_231_Nil__suffix,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( nil @ A ) @ Xs ) ).
% 0.20/0.46
% 0.20/0.46 % Nil_suffix
% 0.20/0.46 thf(fact_232_set__mono__suffix,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ Xs @ Ys )
% 0.20/0.46 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % set_mono_suffix
% 0.20/0.46 thf(fact_233_not__suffix__cases,axiom,
% 0.20/0.46 ! [A: $tType,Ps2: list @ A,Ls: list @ A] :
% 0.20/0.46 ( ~ ( suffix @ A @ Ps2 @ Ls )
% 0.20/0.46 => ( ( ( Ps2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( Ls
% 0.20/0.46 != ( nil @ A ) ) )
% 0.20/0.46 => ( ! [A4: A,As: list @ A] :
% 0.20/0.46 ( ( Ps2
% 0.20/0.46 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 0.20/0.46 => ! [X4: A,Xs2: list @ A] :
% 0.20/0.46 ( ( Ls
% 0.20/0.46 = ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 0.20/0.46 => ( ( X4 = A4 )
% 0.20/0.46 => ( suffix @ A @ As @ Xs2 ) ) ) )
% 0.20/0.46 => ~ ! [A4: A] :
% 0.20/0.46 ( ? [As: list @ A] :
% 0.20/0.46 ( Ps2
% 0.20/0.46 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 0.20/0.46 => ! [X4: A] :
% 0.20/0.46 ( ? [Xs2: list @ A] :
% 0.20/0.46 ( Ls
% 0.20/0.46 = ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 0.20/0.46 => ( X4 = A4 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_suffix_cases
% 0.20/0.46 thf(fact_234_not__suffix__induct,axiom,
% 0.20/0.46 ! [A: $tType,Ps2: list @ A,Ls: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.20/0.46 ( ~ ( suffix @ A @ Ps2 @ Ls )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.20/0.46 ( ( X4 != Y3 )
% 0.20/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) )
% 0.20/0.46 => ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.20/0.46 ( ( X4 = Y3 )
% 0.20/0.46 => ( ~ ( suffix @ A @ Xs2 @ Ys3 )
% 0.20/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.20/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ) )
% 0.20/0.46 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_suffix_induct
% 0.20/0.46 thf(fact_235_suffix__order_Odual__order_Oantisym,axiom,
% 0.20/0.46 ! [A: $tType,B2: list @ A,A2: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ B2 @ A2 )
% 0.20/0.46 => ( ( suffix @ A @ A2 @ B2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.dual_order.antisym
% 0.20/0.46 thf(fact_236_suffix__order_Odual__order_Oeq__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [A5: list @ A,B5: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ B5 @ A5 )
% 0.20/0.46 & ( suffix @ A @ A5 @ B5 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.dual_order.eq_iff
% 0.20/0.46 thf(fact_237_suffix__order_Odual__order_Otrans,axiom,
% 0.20/0.46 ! [A: $tType,B2: list @ A,A2: list @ A,C: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ B2 @ A2 )
% 0.20/0.46 => ( ( suffix @ A @ C @ B2 )
% 0.20/0.46 => ( suffix @ A @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.dual_order.trans
% 0.20/0.46 thf(fact_238_suffix__order_Oord__le__eq__trans,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ A2 @ B2 )
% 0.20/0.46 => ( ( B2 = C )
% 0.20/0.46 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.ord_le_eq_trans
% 0.20/0.46 thf(fact_239_suffix__order_Oord__eq__le__trans,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ( suffix @ A @ B2 @ C )
% 0.20/0.46 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.ord_eq_le_trans
% 0.20/0.46 thf(fact_240_suffix__order_Oorder_Oantisym,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A,B2: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ A2 @ B2 )
% 0.20/0.46 => ( ( suffix @ A @ B2 @ A2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.order.antisym
% 0.20/0.46 thf(fact_241_suffix__order_Oorder_Oeq__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [A5: list @ A,B5: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ A5 @ B5 )
% 0.20/0.46 & ( suffix @ A @ B5 @ A5 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.order.eq_iff
% 0.20/0.46 thf(fact_242_suffix__order_Oantisym__conv,axiom,
% 0.20/0.46 ! [A: $tType,Y: list @ A,X: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ Y @ X )
% 0.20/0.46 => ( ( suffix @ A @ X @ Y )
% 0.20/0.46 = ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.antisym_conv
% 0.20/0.46 thf(fact_243_suffix__order_Oorder__trans,axiom,
% 0.20/0.46 ! [A: $tType,X: list @ A,Y: list @ A,Z3: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ X @ Y )
% 0.20/0.46 => ( ( suffix @ A @ Y @ Z3 )
% 0.20/0.46 => ( suffix @ A @ X @ Z3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.order_trans
% 0.20/0.46 thf(fact_244_suffix__order_Oorder_Otrans,axiom,
% 0.20/0.46 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ A2 @ B2 )
% 0.20/0.46 => ( ( suffix @ A @ B2 @ C )
% 0.20/0.46 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.order.trans
% 0.20/0.46 thf(fact_245_suffix__order_Oeq__refl,axiom,
% 0.20/0.46 ! [A: $tType,X: list @ A,Y: list @ A] :
% 0.20/0.46 ( ( X = Y )
% 0.20/0.46 => ( suffix @ A @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.eq_refl
% 0.20/0.46 thf(fact_246_suffix__order_Oantisym,axiom,
% 0.20/0.46 ! [A: $tType,X: list @ A,Y: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ X @ Y )
% 0.20/0.46 => ( ( suffix @ A @ Y @ X )
% 0.20/0.46 => ( X = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.antisym
% 0.20/0.46 thf(fact_247_suffix__order_Oeq__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [X3: list @ A,Y2: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ X3 @ Y2 )
% 0.20/0.46 & ( suffix @ A @ Y2 @ X3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_order.eq_iff
% 0.20/0.46 thf(fact_248_suffix__same__cases,axiom,
% 0.20/0.46 ! [A: $tType,Xs_1: list @ A,Ys: list @ A,Xs_2: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ Xs_1 @ Ys )
% 0.20/0.46 => ( ( suffix @ A @ Xs_2 @ Ys )
% 0.20/0.46 => ( ( suffix @ A @ Xs_1 @ Xs_2 )
% 0.20/0.46 | ( suffix @ A @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_same_cases
% 0.20/0.46 thf(fact_249_suffixE,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ Xs @ Ys )
% 0.20/0.46 => ~ ! [Zs2: list @ A] :
% 0.20/0.46 ( Ys
% 0.20/0.46 != ( append @ A @ Zs2 @ Xs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffixE
% 0.20/0.46 thf(fact_250_suffixI,axiom,
% 0.20/0.46 ! [A: $tType,Ys: list @ A,Zs: list @ A,Xs: list @ A] :
% 0.20/0.46 ( ( Ys
% 0.20/0.46 = ( append @ A @ Zs @ Xs ) )
% 0.20/0.46 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffixI
% 0.20/0.46 thf(fact_251_Sublist_Osuffix__def,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( suffix @ A )
% 0.20/0.46 = ( ^ [Xs3: list @ A,Ys2: list @ A] :
% 0.20/0.46 ? [Zs3: list @ A] :
% 0.20/0.46 ( Ys2
% 0.20/0.46 = ( append @ A @ Zs3 @ Xs3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Sublist.suffix_def
% 0.20/0.46 thf(fact_252_suffix__append,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ Zs ) )
% 0.20/0.46 = ( ( suffix @ A @ Xs @ Zs )
% 0.20/0.46 | ? [Xs6: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 = ( append @ A @ Xs6 @ Zs ) )
% 0.20/0.46 & ( suffix @ A @ Xs6 @ Ys ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_append
% 0.20/0.46 thf(fact_253_suffix__appendD,axiom,
% 0.20/0.46 ! [A: $tType,Zs: list @ A,Xs: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ ( append @ A @ Zs @ Xs ) @ Ys )
% 0.20/0.46 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_appendD
% 0.20/0.46 thf(fact_254_suffix__appendI,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.20/0.46 ( ( suffix @ A @ Xs @ Ys )
% 0.20/0.46 => ( suffix @ A @ Xs @ ( append @ A @ Zs @ Ys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % suffix_appendI
% 0.20/0.46
% 0.20/0.46 % Subclasses (2)
% 0.20/0.46 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A )
% 0.20/0.46 => ( type @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A )
% 0.20/0.46 => ( ord @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % Type constructors (4)
% 0.20/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.20/0.46 ! [A6: $tType,A7: $tType] :
% 0.20/0.46 ( ( ord @ A7 )
% 0.20/0.46 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(tcon_Set_Oset___Orderings_Oord_1,axiom,
% 0.20/0.46 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.20/0.46 linorder @ $o ).
% 0.20/0.46
% 0.20/0.46 thf(tcon_HOL_Obool___Orderings_Oord_2,axiom,
% 0.20/0.46 ord @ $o ).
% 0.20/0.46
% 0.20/0.46 % Free types (2)
% 0.20/0.46 thf(tfree_0,hypothesis,
% 0.20/0.46 linorder @ node ).
% 0.20/0.46
% 0.20/0.46 thf(tfree_1,hypothesis,
% 0.20/0.46 linorder @ val ).
% 0.20/0.46
% 0.20/0.46 % Conjectures (1)
% 0.20/0.46 thf(conj_0,conjecture,
% 0.20/0.46 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons @ node @ i @ rs_rest ) @ pred_phi_r ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 2.52/1.48 ---- Embedded in THF ---
% 2.52/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.52/1.48 %%% Generated on Tue Feb 24 08:26:02 EST 2026
% 2.52/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.52/1.48 %%% Logic specification used:
% 2.52/1.48 %%% thf(spec, logic, $$dhol).
% 2.52/1.48
% 2.52/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WhTG5ILRVb/DTF2DTF22669.p
% 2.52/1.48 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.52/1.48 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.52/1.48 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.52/1.48 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.52/1.48 thf(ty_tf_edgeD, type, edgeD: $tType).
% 2.52/1.48 thf(ty_tf_node, type, node: $tType).
% 2.52/1.48 thf(ty_tf_val, type, val: $tType).
% 2.52/1.48 thf(ty_tf_g, type, g: $tType).
% 2.52/1.48 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.52/1.48 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.52/1.48 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.52/1.48 thf(sy_c_Graph__path_Ograph__path__base_Opath, type, graph_1146196722h_path: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > ((list @ Node) > $o)))))))).
% 2.52/1.48 thf(sy_c_Graph__path_Ograph__path__base_Opath2, type, graph_1661282752_path2: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > ((list @ Node) > (Node > $o)))))))))).
% 2.52/1.48 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors, type, graph_1201503639essors: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > (list @ Node))))))).
% 2.52/1.48 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.52/1.48 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.52/1.48 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.52/1.48 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.52/1.48 thf(sy_c_List_Olist_Ohd, type, hd: (!> [A:$tType]: (((list @ A) > A)))).
% 2.52/1.48 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.52/1.48 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.52/1.48 thf(sy_c_Minimality_Ograph__path_OpathsConverge, type, graph_pathsConverge: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > ((list @ Node) > (Node > ((list @ Node) > (Node > $o)))))))))))).
% 2.52/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.52/1.48 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses, type, sSA_CFG_SSA_phiUses: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (set @ Val))))))))).
% 2.52/1.48 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode, type, sSA_CF1081484811efNode: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > Node)))))))).
% 2.52/1.48 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 > $o))))))))).
% 2.52/1.48 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.52/1.48 thf(sy_c_Sublist_Oprefix, type, prefix: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.52/1.48 thf(sy_c_Sublist_Osuffix, type, suffix: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.52/1.48 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.52/1.48 thf(sy_v__092_060alpha_062n, type, alpha_n: (g > (list @ node))).
% 2.52/1.48 thf(sy_v__092_060phi_062_092_060_094sub_062r, type, phi_r: val).
% 2.52/1.48 thf(sy_v_defs, type, defs: (g > (node > (set @ val)))).
% 2.52/1.48 thf(sy_v_g, type, g2: g).
% 2.52/1.48 thf(sy_v_i____, type, i: node).
% 2.52/1.48 thf(sy_v_inEdges_H, type, inEdges: (g > (node > (list @ ((product_prod @ node) @ edgeD))))).
% 2.52/1.48 thf(sy_v_invar, type, invar: (g > $o)).
% 2.52/1.48 thf(sy_v_m, type, m: node).
% 2.52/1.48 thf(sy_v_ms, type, ms: (list @ node)).
% 2.52/1.48 thf(sy_v_ms_H____, type, ms2: (list @ node)).
% 2.52/1.48 thf(sy_v_n, type, n: node).
% 2.52/1.48 thf(sy_v_ns, type, ns: (list @ node)).
% 2.52/1.48 thf(sy_v_phis, type, phis: (g > (((product_prod @ node) @ val) > (option @ (list @ val))))).
% 2.52/1.48 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____, type, pred_phi_r: node).
% 2.52/1.48 thf(sy_v_r, type, r: val).
% 2.52/1.48 thf(sy_v_ri____, type, ri: (list @ node)).
% 2.52/1.48 thf(sy_v_rs_H____, type, rs: (list @ node)).
% 2.52/1.48 thf(sy_v_rs_H__rest____, type, rs_rest: (list @ node)).
% 2.52/1.48 thf(sy_v_rs____, type, rs2: (list @ node)).
% 2.52/1.48 thf(sy_v_s, type, s: val).
% 2.52/1.48 thf(sy_v_tmp____, type, tmp: (list @ node)).
% 2.52/1.48 thf(fact_0_m__i__differ_I2_J, axiom, (m != i)).
% 2.52/1.48 thf(fact_1_rs_H__rest__def, axiom, (rs = (((append @ node) @ tmp) @ (((cons @ node) @ i) @ rs_rest)))).
% 2.52/1.48 thf(fact_2_old_Oinvar, axiom, (! [G2:g]: ((invar @ G2)))).
% 2.52/1.48 thf(fact_3_old_Opath2__split_I2_J, axiom, (! [G2:g,N:node,Ns:(list @ node),N2:node,Ns2:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ N2) @ Ns2))) @ M) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N2) @ (((cons @ node) @ N2) @ Ns2)) @ M))))).
% 2.52/1.49 thf(fact_4_False, axiom, (r != phi_r)).
% 2.52/1.49 thf(fact_5_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)).
% 2.52/1.49 thf(fact_6_ms_H__props_I1_J, axiom, ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ m) @ ms2) @ i)).
% 2.52/1.49 thf(fact_7_rs_H__rest__prop, axiom, (rs = (((append @ node) @ ri) @ rs_rest))).
% 2.52/1.49 thf(fact_8_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))).
% 2.52/1.49 thf(fact_9_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)))))).
% 2.52/1.49 thf(fact_10_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)))))).
% 2.52/1.49 thf(fact_11_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))))))).
% 2.52/1.49 thf(fact_12_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)))))).
% 2.52/1.49 thf(fact_13_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)))))))).
% 2.52/1.49 thf(fact_14_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)))))).
% 2.52/1.49 thf(fact_15_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))))))).
% 2.52/1.49 thf(fact_16_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))))).
% 2.52/1.49 thf(fact_17_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)))))).
% 2.52/1.49 thf(fact_18__092_060open_062ri_A_061_Atmp_A_064_A_091i_093_092_060close_062, axiom, (ri = (((append @ node) @ tmp) @ (((cons @ node) @ i) @ (nil @ node))))).
% 2.52/1.49 thf(fact_19__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H__rest_O_Ars_H_A_061_Ari_A_064_Ars_H__rest_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Rs_rest:(list @ node)]: ((rs != (((append @ node) @ ri) @ Rs_rest))))))).
% 2.52/1.49 thf(fact_20_ri__props_I2_J, axiom, (((member @ node) @ i) @ ((set2 @ node) @ ms))).
% 2.52/1.49 thf(fact_21_m__i__differ_I1_J, axiom, (i != ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r))).
% 2.52/1.49 thf(fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tmp_O_Ari_A_061_Atmp_A_064_A_091i_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Tmp:(list @ node)]: ((ri != (((append @ node) @ Tmp) @ (((cons @ node) @ i) @ (nil @ node))))))))).
% 2.52/1.49 thf(fact_23_ri__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)) @ ri) @ i)).
% 2.52/1.49 thf(fact_24_old_Opath2__split_I1_J, axiom, (! [G2:g,N:node,Ns:(list @ node),N2:node,Ns2:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ N2) @ Ns2))) @ M) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ N2) @ (nil @ node)))) @ N2))))).
% 2.52/1.49 thf(fact_25__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062, axiom, (((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r) != ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r))).
% 2.52/1.49 thf(fact_26__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, ((i != ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r)) => (((i != ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r)) => (m != i)) => (~ (((i != ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r)) => (m = i))))))).
% 2.52/1.49 thf(fact_27_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)))))).
% 2.52/1.49 thf(fact_28_ms_H__props_I3_J, axiom, (~ ((((member @ node) @ i) @ ((set2 @ node) @ ((butlast @ node) @ ms2)))))).
% 2.52/1.49 thf(fact_29_assms_I10_J, axiom, (((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r) @ r)).
% 2.52/1.49 thf(fact_30_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))))).
% 2.52/1.49 thf(fact_31_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))).
% 2.52/1.49 thf(fact_32_rs__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)) @ rs2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r))).
% 2.52/1.49 thf(fact_33_rs__def, axiom, (rs2 = (((append @ node) @ rs) @ (((cons @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r)) @ (nil @ node))))).
% 2.52/1.49 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))).
% 2.52/1.49 thf(fact_35_rs_H__loopfree, axiom, (~ ((((member @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r)) @ ((set2 @ node) @ ((tl @ node) @ rs)))))).
% 2.52/1.49 thf(fact_36_hd__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Xs)))))).
% 2.52/1.49 thf(fact_37_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys) & (X = Y)))))).
% 2.52/1.49 thf(fact_38_list__ee__eq__leel_I1_J, axiom, (! [A:$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))))))))).
% 2.52/1.49 thf(fact_39_list__ee__eq__leel_I2_J, axiom, (! [A:$tType,L1:(list @ A),E12:A,E22:A,L2:(list @ A),E1:A,E2:A]: ((((((append @ A) @ L1) @ (((cons @ A) @ E12) @ (((cons @ A) @ E22) @ L2))) = (((cons @ A) @ E1) @ (((cons @ A) @ E2) @ (nil @ A)))) = ((L1 = (nil @ A)) & ((E1 = E12) & ((E2 = E22) & (L2 = (nil @ A))))))))).
% 2.52/1.49 thf(fact_40_list__se__match_I1_J, axiom, (! [A:$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)))))))).
% 2.52/1.49 thf(fact_41_ri__props_I3_J, axiom, (! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((butlast @ node) @ ri))) => (~ ((((member @ node) @ X2) @ ((set2 @ node) @ ms)))))))).
% 2.52/1.49 thf(fact_42_old_Oelem__set__implies__elem__tl__app__cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Y:A]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ Xs))))))))).
% 2.52/1.49 thf(fact_43_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.52/1.49 thf(fact_44_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs)) = (Ys = Zs))))).
% 2.52/1.49 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.52/1.49 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) = A3)))).
% 2.52/1.49 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.52/1.49 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G2:(A > B)]: (((! [X4:A]: (((F @ X4) = (G2 @ X4)))) => (F = G2))))).
% 2.52/1.49 thf(fact_49_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs) @ Xs)) = (Ys = Zs))))).
% 2.52/1.49 thf(fact_50_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)))))).
% 2.52/1.49 thf(fact_51_append_Oassoc, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((((append @ A) @ (((append @ A) @ A2) @ B2)) @ C) = (((append @ A) @ A2) @ (((append @ A) @ B2) @ C)))))).
% 2.52/1.49 thf(fact_52_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)))))))).
% 2.52/1.49 thf(fact_53_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))))))))).
% 2.52/1.49 thf(fact_54_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)))))))).
% 2.52/1.49 thf(fact_55_old_Opath2__app_H, 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) @ ((butlast @ node) @ Ns)) @ Ms)) @ L)))))).
% 2.52/1.49 thf(fact_56_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)))))).
% 2.52/1.49 thf(fact_57_append_Oright__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ A2) @ (nil @ A)) = A2)))).
% 2.52/1.49 thf(fact_58_empty__append__eq__id, axiom, (! [A:$tType]: ((((append @ A) @ (nil @ A)) = (^ [X3:(list @ A)]: (X3)))))).
% 2.52/1.49 thf(fact_59_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.52/1.49 thf(fact_60_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.52/1.49 thf(fact_61_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.52/1.49 thf(fact_62_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.52/1.49 thf(fact_63_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.52/1.49 thf(fact_64_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.52/1.49 thf(fact_65_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.52/1.49 thf(fact_66_old_Opath2__split__ex_H, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,X:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ X) @ ((set2 @ node) @ Ns)) => (~ ((! [Ns_1:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns_1) @ X) => (! [Ns_2:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ X) @ Ns_2) @ M) => (Ns != (((append @ node) @ ((butlast @ node) @ Ns_1)) @ Ns_2))))))))))))))).
% 2.52/1.49 thf(fact_67_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)) => ((! [Ns3:(list @ node),N3:node,N4:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N4) @ Ns3) @ M) => ((((P @ N4) @ Ns3) @ M) => ((((member @ node) @ N3) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N4))) => (((P @ N3) @ (((cons @ node) @ N3) @ Ns3)) @ M)))))) => (((P @ N) @ Ns) @ M))))))).
% 2.52/1.49 thf(fact_68_old_Opath2__split__ex, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,X:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ X) @ ((set2 @ node) @ Ns)) => (~ ((! [Ns_1:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns_1) @ X) => (! [Ns_2:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ X) @ Ns_2) @ M) => ((Ns = (((append @ node) @ Ns_1) @ ((tl @ node) @ Ns_2))) => (Ns != (((append @ node) @ ((butlast @ node) @ Ns_1)) @ Ns_2)))))))))))))))).
% 2.52/1.49 thf(fact_69_old_Opath2__rev__induct, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,P:(node > ((list @ node) > (node > $o)))]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => (((P @ N) @ (((cons @ node) @ N) @ (nil @ node))) @ N)) => ((! [Ns3:(list @ node),M2:node,M3:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns3) @ M2) => ((((P @ N) @ Ns3) @ M2) => ((((member @ node) @ M2) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ M3))) => (((P @ N) @ (((append @ node) @ Ns3) @ (((cons @ node) @ M3) @ (nil @ node)))) @ M3)))))) => (((P @ N) @ Ns) @ M))))))).
% 2.52/1.49 thf(fact_70_old_Opath2__snoc, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,M4:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ M) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ M4))) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ M4) @ (nil @ node)))) @ M4)))))).
% 2.52/1.49 thf(fact_71_list__e__eq__lel_I2_J, axiom, (! [A:$tType,L1:(list @ A),E:A,L2:(list @ A),E3:A]: ((((((append @ A) @ L1) @ (((cons @ A) @ E) @ L2)) = (((cons @ A) @ E3) @ (nil @ A))) = ((L1 = (nil @ A)) & ((E = E3) & (L2 = (nil @ A)))))))).
% 2.52/1.49 thf(fact_72_list__e__eq__lel_I1_J, axiom, (! [A:$tType,E3:A,L1:(list @ A),E:A,L2:(list @ A)]: ((((((cons @ A) @ E3) @ (nil @ A)) = (((append @ A) @ L1) @ (((cons @ A) @ E) @ L2))) = ((L1 = (nil @ A)) & ((E = E3) & (L2 = (nil @ A)))))))).
% 2.52/1.49 thf(fact_73_list__se__match_I4_J, axiom, (! [A:$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))))))))).
% 2.52/1.49 thf(fact_74_list__se__match_I3_J, axiom, (! [A:$tType,L1:(list @ A),A2:A,L2:(list @ A)]: (((L1 != (nil @ A)) => (((((cons @ A) @ A2) @ (nil @ A)) = (((append @ A) @ L1) @ L2)) = ((L1 = (((cons @ A) @ A2) @ (nil @ A))) & (L2 = (nil @ A)))))))).
% 2.52/1.49 thf(fact_75_list__se__match_I2_J, axiom, (! [A:$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))))))))).
% 2.52/1.49 thf(fact_76_tl__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != (nil @ A)) => (((tl @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ ((tl @ A) @ Xs)) @ Ys)))))).
% 2.52/1.49 thf(fact_77_old_Opath2__cases, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((Ns = (((cons @ node) @ N) @ (nil @ node))) => (M != N)) => (~ ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ ((hd @ node) @ ((tl @ node) @ Ns))) @ ((tl @ node) @ Ns)) @ M) => (~ ((((member @ node) @ N) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((hd @ node) @ ((tl @ node) @ Ns))))))))))))))).
% 2.52/1.49 thf(fact_78_rs__props_I3_J, axiom, (~ ((((member @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r)) @ ((set2 @ node) @ ((tl @ node) @ rs2)))))).
% 2.52/1.49 thf(fact_79_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = Xs)))).
% 2.52/1.49 thf(fact_80_list_Ocollapse, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List)) = List))))).
% 2.52/1.49 thf(fact_81_hd__Cons__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ Xs)) @ ((tl @ A) @ Xs)) = Xs))))).
% 2.52/1.49 thf(fact_82_in__hd__or__tl__conv, axiom, (! [A:$tType,L:(list @ A),X:A]: (((L != (nil @ A)) => (((X = ((hd @ A) @ L)) | (((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ L)))) = (((member @ A) @ X) @ ((set2 @ A) @ L))))))).
% 2.52/1.49 thf(fact_83_ri__props_I4_J, axiom, (((prefix @ node) @ ri) @ rs2)).
% 2.52/1.49 thf(fact_84_ms_H__props_I2_J, axiom, (((prefix @ node) @ ms2) @ ms)).
% 2.52/1.49 thf(fact_85_old_OCons__path2, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,N2:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ N2) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N))) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N2) @ (((cons @ node) @ N2) @ Ns)) @ M)))))).
% 2.52/1.49 thf(fact_86_butlast__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((butlast @ A) @ ((tl @ A) @ Xs)) = ((tl @ A) @ ((butlast @ A) @ Xs)))))).
% 2.52/1.49 thf(fact_87_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 2.52/1.49 thf(fact_88_list_Osel_I3_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((tl @ A) @ (((cons @ A) @ X21) @ X22)) = X22)))).
% 2.52/1.49 thf(fact_89_in__set__butlastD, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) => (((member @ A) @ X) @ ((set2 @ A) @ Xs)))))).
% 2.52/1.49 thf(fact_90_list_Osel_I2_J, axiom, (! [A:$tType]: ((((tl @ A) @ (nil @ A)) = (nil @ A))))).
% 2.52/1.49 thf(fact_91_butlast_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (nil @ A))) & ((Xs != (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((butlast @ A) @ Xs)))))))).
% 2.52/1.49 thf(fact_92_tl__obtain__elem, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((tl @ A) @ Xs) = (nil @ A)) => (~ ((! [E4:A]: ((Xs != (((cons @ A) @ E4) @ (nil @ A)))))))))))).
% 2.52/1.49 thf(fact_93_tl__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((tl @ A) @ Xs) = (nil @ A)) = ((Xs = (nil @ A)) | (? [X3:A]: ((Xs = (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.52/1.49 thf(fact_94_Nil__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((tl @ A) @ Xs)) = ((Xs = (nil @ A)) | (? [X3:A]: ((Xs = (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.52/1.49 thf(fact_95_butlast__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = ((butlast @ A) @ Xs))) & ((Ys != (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ Xs) @ ((butlast @ A) @ Ys)))))))).
% 2.52/1.49 thf(fact_96_list_Oset__sel_I2_J, axiom, (! [A:$tType,A2:(list @ A),X:A]: (((A2 != (nil @ A)) => ((((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ A2))) => (((member @ A) @ X) @ ((set2 @ A) @ A2))))))).
% 2.52/1.49 thf(fact_97_in__set__butlast__appendI, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: ((((((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) | (((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Ys)))) => (((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ (((append @ A) @ Xs) @ Ys)))))))).
% 2.52/1.49 thf(fact_98_list_Oexpand, axiom, (! [A:$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)))))).
% 2.52/1.49 thf(fact_99_not__hd__in__tl, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((X != ((hd @ A) @ Xs)) => ((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ Xs)))))))).
% 2.52/1.49 thf(fact_100_butlast__eq__cons__conv, axiom, (! [A:$tType,L:(list @ A),X:A,Xs:(list @ A)]: (((((butlast @ A) @ L) = (((cons @ A) @ X) @ Xs)) = (? [Xl:A]: ((L = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ (((cons @ A) @ Xl) @ (nil @ A))))))))))).
% 2.52/1.49 thf(fact_101_butlast__eq__consE, axiom, (! [A:$tType,L:(list @ A),X:A,Xs:(list @ A)]: (((((butlast @ A) @ L) = (((cons @ A) @ X) @ Xs)) => (~ ((! [Xl2:A]: ((L != (((cons @ A) @ X) @ (((append @ A) @ Xs) @ (((cons @ A) @ Xl2) @ (nil @ A))))))))))))).
% 2.52/1.49 thf(fact_102_list_Oexhaust__sel, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => (List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))).
% 2.52/1.49 thf(fact_103_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.52/1.49 thf(fact_104_list__tail__coinc, axiom, (! [A:$tType,N1:A,R1:(list @ A),N22:A,R2:(list @ A)]: ((((((cons @ A) @ N1) @ R1) = (((cons @ A) @ N22) @ R2)) => ((N1 = N22) & (R1 = R2)))))).
% 2.52/1.49 thf(fact_105_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs) @ Us)) & ((((append @ A) @ Us) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs) & (Ys = (((append @ A) @ Us) @ Ts)))))))))).
% 2.52/1.49 thf(fact_106_append__eq__appendI, axiom, (! [A:$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))))))).
% 2.52/1.49 thf(fact_107_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.52/1.49 thf(fact_108_neq__NilE, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) => (~ ((! [X4:A,Xs2:(list @ A)]: ((L != (((cons @ A) @ X4) @ Xs2)))))))))).
% 2.52/1.49 thf(fact_109_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.52/1.49 thf(fact_110_revg_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [A4:A,As:(list @ A),B3:(list @ A)]: ((((P @ As) @ (((cons @ A) @ A4) @ B3)) => ((P @ (((cons @ A) @ A4) @ As)) @ B3)))) => ((P @ A0) @ A1)))))).
% 2.52/1.49 thf(fact_111_zipf_Oinduct, axiom, (! [A:$tType,C2:$tType,B:$tType,P:((A > (B > C2)) > ((list @ A) > ((list @ B) > $o))),A0:(A > (B > C2)),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > (B > C2))]: ((((P @ F2) @ (nil @ A)) @ (nil @ B)))) => ((! [F2:(A > (B > C2)),A4:A,As:(list @ A),B3:B,Bs:(list @ B)]: (((((P @ F2) @ As) @ Bs) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ (((cons @ B) @ B3) @ Bs))))) => ((! [A4:(A > (B > C2)),V:A,Va:(list @ A)]: ((((P @ A4) @ (((cons @ A) @ V) @ Va)) @ (nil @ B)))) => ((! [A4:(A > (B > C2)),V:B,Va:(list @ B)]: ((((P @ A4) @ (nil @ A)) @ (((cons @ B) @ V) @ Va)))) => (((P @ A0) @ A1) @ A22)))))))).
% 2.52/1.49 thf(fact_112_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.52/1.49 thf(fact_113_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X1) @ X23))))) => (P @ List)))))).
% 2.52/1.49 thf(fact_114_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y2:A,Ys2:(list @ A)]: ((Xs = (((cons @ A) @ Y2) @ Ys2)))))))).
% 2.52/1.49 thf(fact_115_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X4) @ Xs2)) @ (nil @ B)))) => ((! [Y3:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y3) @ Ys3)))) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3))))) => ((P @ Xs) @ Ys)))))))).
% 2.52/1.49 thf(fact_116_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X4:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((P @ Ys3) @ Xs2) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ Ys3)))) => ((P @ A0) @ A1)))))).
% 2.52/1.49 thf(fact_117_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y3:A,Zs2:(list @ A)]: (((P @ Zs2) => ((P @ (((cons @ A) @ Y3) @ Zs2)) => (P @ (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Zs2))))))) => (P @ Xs))))))).
% 2.52/1.49 thf(fact_118_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X:(list @ A)]: (((! [X4:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X4) @ Xs2)))) => (X = (nil @ A))))))))).
% 2.52/1.49 thf(fact_119_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X4:A,Xs2:(list @ A)]: (((! [X213:A,X223:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X223)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X4) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 2.52/1.49 thf(fact_120_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X4:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y3) @ Ys3)) => (((P @ (((cons @ A) @ X4) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))) => ((P @ A0) @ A1))))))).
% 2.52/1.49 thf(fact_121_list__2pre__induct, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),W1:(list @ A),W2:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [E4:A,W12:(list @ A),W22:(list @ B)]: ((((P @ W12) @ W22) => ((P @ (((cons @ A) @ E4) @ W12)) @ W22)))) => ((! [E4:B,W13:(list @ A),W23:(list @ B)]: ((((P @ W13) @ W23) => ((P @ W13) @ (((cons @ B) @ E4) @ W23))))) => ((P @ W1) @ W2))))))).
% 2.52/1.49 thf(fact_122_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X4:A]: ((X != (((cons @ A) @ X4) @ (nil @ A))))) => (~ ((! [X4:A,Y3:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Xs2)))))))))))).
% 2.52/1.49 thf(fact_123_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 > $o)),X4:A,Ys3:(list @ A)]: ((((P @ P2) @ Ys3) => ((P @ P2) @ (((cons @ A) @ X4) @ Ys3))))) => ((P @ A0) @ A1)))))).
% 2.52/1.49 thf(fact_124_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y3:A,Xs2:(list @ A)]: ((((X4 = Y3) => (P @ (((cons @ A) @ X4) @ Xs2))) => (((X4 != Y3) => (P @ (((cons @ A) @ Y3) @ Xs2))) => (P @ (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Xs2))))))) => (P @ A0))))))).
% 2.52/1.49 thf(fact_125_list__induct__first2, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X1:A,X23:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((cons @ A) @ X1) @ (((cons @ A) @ X23) @ Xs2)))))) => (P @ Xs))))))).
% 2.52/1.49 thf(fact_126_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F2:(A > B),X4:A]: (((P @ F2) @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [F2:(A > B),X4:A,Y3:A,Zs2:(list @ A)]: ((((P @ F2) @ (((cons @ A) @ Y3) @ Zs2)) => ((P @ F2) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Zs2)))))) => ((! [A4:(A > B)]: (((P @ A4) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 2.52/1.49 thf(fact_127_successively_Oinduct, axiom, (! [A:$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)),X4:A]: (((P @ P2) @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [P2:(A > (A > $o)),X4:A,Y3:A,Xs2:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ Y3) @ Xs2)) => ((P @ P2) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 2.52/1.49 thf(fact_128_list__all__zip_Oinduct, axiom, (! [A:$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)),V:A,Va:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ V) @ Va)) @ (nil @ B)))) => ((! [P2:(A > (B > $o)),V:B,Va:(list @ B)]: ((((P @ P2) @ (nil @ A)) @ (((cons @ B) @ V) @ Va)))) => (((P @ A0) @ A1) @ A22)))))))).
% 2.52/1.49 thf(fact_129_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X4) @ Xs2)))))) => (P @ Xs))))))).
% 2.52/1.49 thf(fact_130_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X_1:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X_1))) => ((! [F2:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A4)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.52/1.49 thf(fact_131_mergesort__by__rel__merge_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > ((list @ A) > $o))),A0:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: (((! [R:(A > (A > $o)),X4:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: (((((R @ X4) @ Y3) => (((P @ R) @ Xs2) @ (((cons @ A) @ Y3) @ Ys3))) => (((~ (((R @ X4) @ Y3))) => (((P @ R) @ (((cons @ A) @ X4) @ Xs2)) @ Ys3)) => (((P @ R) @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))) => ((! [R:(A > (A > $o)),Xs2:(list @ A)]: ((((P @ R) @ Xs2) @ (nil @ A)))) => ((! [R:(A > (A > $o)),V:A,Va:(list @ A)]: ((((P @ R) @ (nil @ A)) @ (((cons @ A) @ V) @ Va)))) => (((P @ A0) @ A1) @ A22))))))).
% 2.52/1.49 thf(fact_132_mergesort__by__rel__merge__induct, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),R3:(A > (B > $o)),Xs:(list @ A),Ys:(list @ B)]: (((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ B)))) => ((! [X_1:(list @ B)]: (((P @ (nil @ A)) @ X_1))) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: ((((R3 @ X4) @ Y3) => (((P @ Xs2) @ (((cons @ B) @ Y3) @ Ys3)) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3)))))) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: (((~ (((R3 @ X4) @ Y3))) => (((P @ (((cons @ A) @ X4) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3)))))) => ((P @ Xs) @ Ys)))))))).
% 2.52/1.49 thf(fact_133_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A,Ys3:(list @ A)]: (((P @ Ys3) => (P @ (((cons @ A) @ X4) @ Ys3))))) => (P @ A0))))))))).
% 2.52/1.49 thf(fact_134_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X4:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X4) @ Xs2)) @ Xss))))))))))).
% 2.52/1.49 thf(fact_135_list_Oset__intros_I2_J, axiom, (! [A:$tType,Y:A,X22:(list @ A),X21:A]: (((((member @ A) @ Y) @ ((set2 @ A) @ X22)) => (((member @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22))))))).
% 2.52/1.49 thf(fact_136_list_Oset__intros_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((member @ A) @ X21) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22)))))).
% 2.52/1.49 thf(fact_137_set__ConsD, axiom, (! [A:$tType,Y:A,X:A,Xs:(list @ A)]: (((((member @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X) @ Xs))) => ((Y = X) | (((member @ A) @ Y) @ ((set2 @ A) @ Xs))))))).
% 2.52/1.49 thf(fact_138_list_Oset__cases, axiom, (! [A:$tType,E3:A,A2:(list @ A)]: (((((member @ A) @ E3) @ ((set2 @ A) @ A2)) => ((! [Z2:(list @ A)]: ((A2 != (((cons @ A) @ E3) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ A)]: (((A2 = (((cons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E3) @ ((set2 @ A) @ Z2)))))))))))))).
% 2.52/1.49 thf(fact_139_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys) => ((Xs = (((append @ A) @ Xs1) @ Zs)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs))))))).
% 2.52/1.49 thf(fact_140_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.52/1.49 thf(fact_141_list__match__lel__lel, axiom, (! [A:$tType,C1:(list @ A),Qs:A,C22:(list @ A),C12:(list @ A),Qs2:A,C23:(list @ A)]: ((((((append @ A) @ C1) @ (((cons @ A) @ Qs) @ C22)) = (((append @ A) @ C12) @ (((cons @ A) @ Qs2) @ C23))) => ((! [C21:(list @ A)]: (((C1 = (((append @ A) @ C12) @ (((cons @ A) @ Qs2) @ C21))) => (C23 != (((append @ A) @ C21) @ (((cons @ A) @ Qs) @ C22)))))) => (((C12 = C1) => ((Qs2 = Qs) => (C23 != C22))) => (~ ((! [C212:(list @ A)]: (((C12 = (((append @ A) @ C1) @ (((cons @ A) @ Qs) @ C212))) => (C22 != (((append @ A) @ C212) @ (((cons @ A) @ Qs2) @ C23)))))))))))))).
% 2.52/1.49 thf(fact_142_append_Oleft__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A2) = A2)))).
% 2.52/1.49 thf(fact_143_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.52/1.49 thf(fact_144_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 2.52/1.49 thf(fact_145_list_Osel_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((hd @ A) @ (((cons @ A) @ X21) @ X22)) = X21)))).
% 2.52/1.49 thf(fact_146_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.52/1.49 thf(fact_147_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys3:(list @ A),Y3:A]: ((Xs != (((append @ A) @ Ys3) @ (((cons @ A) @ Y3) @ (nil @ A)))))))))))).
% 2.52/1.49 thf(fact_148_neq__Nil__revE, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) => (~ ((! [Ll:(list @ A),E4:A]: ((L != (((append @ A) @ Ll) @ (((cons @ A) @ E4) @ (nil @ A)))))))))))).
% 2.52/1.49 thf(fact_149_rev__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Xs2:(list @ A)]: (((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (nil @ B)))) => ((! [Y3:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((append @ B) @ Ys3) @ (((cons @ B) @ Y3) @ (nil @ B)))))) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((append @ B) @ Ys3) @ (((cons @ B) @ Y3) @ (nil @ B))))))) => ((P @ Xs) @ Ys)))))))).
% 2.52/1.49 thf(fact_150_neq__Nil__rev__conv, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) = (? [Xs3:(list @ A),X3:A]: ((L = (((append @ A) @ Xs3) @ (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.52/1.49 thf(fact_151_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs)) | (? [Ys4:(list @ A)]: ((((((cons @ A) @ X) @ Ys4) = Ys) & (Xs = (((append @ A) @ Ys4) @ Zs)))))))))).
% 2.52/1.49 thf(fact_152_append__eq__Cons__conv, axiom, (! [A:$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))) | (? [Ys4:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys4)) & ((((append @ A) @ Ys4) @ Zs) = Xs))))))))).
% 2.52/1.49 thf(fact_153_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.52/1.49 thf(fact_154_rev__nonempty__induct2_H, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Ys:(list @ B),P:((list @ A) > ((list @ B) > $o))]: (((Xs != (nil @ A)) => ((Ys != (nil @ B)) => ((! [X4:A,Y3:B]: (((P @ (((cons @ A) @ X4) @ (nil @ A))) @ (((cons @ B) @ Y3) @ (nil @ B))))) => ((! [X4:A,Xs2:(list @ A),Y3:B]: (((Xs2 != (nil @ A)) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((cons @ B) @ Y3) @ (nil @ B)))))) => ((! [X4:A,Y3:B,Ys3:(list @ B)]: (((Ys3 != (nil @ B)) => ((P @ (((cons @ A) @ X4) @ (nil @ A))) @ (((append @ B) @ Ys3) @ (((cons @ B) @ Y3) @ (nil @ B))))))) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((Xs2 != (nil @ A)) => ((Ys3 != (nil @ B)) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((append @ B) @ Ys3) @ (((cons @ B) @ Y3) @ (nil @ B))))))))) => ((P @ Xs) @ Ys)))))))))).
% 2.52/1.49 thf(fact_155_list__Cons__eq__append__cases, axiom, (! [A:$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))) => (~ ((! [Ys5:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys5)) => ((((append @ A) @ Ys5) @ Zs) != Xs))))))))))).
% 2.52/1.49 thf(fact_156_list__append__eq__Cons__cases, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs) = (((cons @ A) @ X) @ Xs)) => (((Ys = (nil @ A)) => (Zs != (((cons @ A) @ X) @ Xs))) => (~ ((! [Ys5:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys5)) => ((((append @ A) @ Ys5) @ Zs) != Xs))))))))))).
% 2.52/1.49 thf(fact_157_split__list, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys3:(list @ A),Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))))))))).
% 2.52/1.49 thf(fact_158_split__list__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys3:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs2))))))))))).
% 2.52/1.49 thf(fact_159_split__list__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (? [Ys3:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X4) @ Zs2))))) & (P @ X4)))))))).
% 2.52/1.49 thf(fact_160_xy__in__set__cases, axiom, (! [A:$tType,X:A,L:(list @ A),Y:A]: (((((member @ A) @ X) @ ((set2 @ A) @ L)) => ((((member @ A) @ Y) @ ((set2 @ A) @ L)) => (((X = Y) => (! [L12:(list @ A),L22:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ Y) @ L22)))))) => (((X != Y) => (! [L12:(list @ A),L22:(list @ A),L3:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ X) @ (((append @ A) @ L22) @ (((cons @ A) @ Y) @ L3)))))))) => (~ (((X != Y) => (! [L12:(list @ A),L22:(list @ A),L3:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ Y) @ (((append @ A) @ L22) @ (((cons @ A) @ X) @ L3))))))))))))))))).
% 2.52/1.49 thf(fact_161_split__list__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys3:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys3))))))))))).
% 2.52/1.49 thf(fact_162_split__list__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (~ ((! [Ys3:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X4) @ Zs2))))) => (~ ((P @ X4)))))))))))).
% 2.52/1.49 thf(fact_163_append__Cons__eq__iff, axiom, (! [A:$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)))))))).
% 2.52/1.49 thf(fact_164_in__set__conv__decomp, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys2:(list @ A),Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))))))))).
% 2.52/1.49 thf(fact_165_in__set__list__format, axiom, (! [A:$tType,E3:A,L:(list @ A)]: (((((member @ A) @ E3) @ ((set2 @ A) @ L)) => (~ ((! [L12:(list @ A),L22:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ E3) @ L22))))))))))).
% 2.52/1.49 thf(fact_166_split__list__last__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (? [Ys3:(list @ A),X4:A,Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X4) @ Zs2))) & ((P @ X4) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs2)) => (~ ((P @ Xa)))))))))))))).
% 2.52/1.49 thf(fact_167_split__list__first__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (? [Ys3:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X4) @ Zs2))))) & ((P @ X4) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Xa)))))))))))))).
% 2.52/1.49 thf(fact_168_split__list__last__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (~ ((! [Ys3:(list @ A),X4:A,Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X4) @ Zs2))) => ((P @ X4) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs2)) => (~ ((P @ Xa)))))))))))))))))).
% 2.52/1.49 thf(fact_169_split__list__first__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (~ ((! [Ys3:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X4) @ Zs2))))) => ((P @ X4) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Xa)))))))))))))))))).
% 2.52/1.49 thf(fact_170_in__set__conv__decomp__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys2:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs3))))))))))).
% 2.52/1.49 thf(fact_171_in__set__conv__decomp__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys2:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys2))))))))))).
% 2.52/1.49 thf(fact_172_split__list__last__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys2:(list @ A),X3:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))) & ((P @ X3) & (! [Y2:A]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Y2)))))))))))))).
% 2.52/1.49 thf(fact_173_split__list__first__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) & ((P @ X3) & (! [Y2:A]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Y2)))))))))))))).
% 2.52/1.49 thf(fact_174_hd__in__set, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((member @ A) @ ((hd @ A) @ Xs)) @ ((set2 @ A) @ Xs)))))).
% 2.52/1.49 thf(fact_175_list_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(list @ A)]: (((A2 != (nil @ A)) => (((member @ A) @ ((hd @ A) @ A2)) @ ((set2 @ A) @ A2)))))).
% 2.52/1.49 thf(fact_176_longest__common__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((? [Ps:(list @ A),Xs5:(list @ A),Ys5:(list @ A)]: (((Xs = (((append @ A) @ Ps) @ Xs5)) & ((Ys = (((append @ A) @ Ps) @ Ys5)) & ((Xs5 = (nil @ A)) | ((Ys5 = (nil @ A)) | (((hd @ A) @ Xs5) != ((hd @ A) @ Ys5))))))))))).
% 2.52/1.49 thf(fact_177_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))))))).
% 2.52/1.49 thf(fact_178__092_060open_062old_OpathsConverge_Ag_Am_Ams_H_An_A_Ins_A_064_Atl_Ari_J_Ai_092_060close_062, axiom, ((((((((((((graph_pathsConverge @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ m) @ ms2) @ n) @ (((append @ node) @ ns) @ ((tl @ node) @ ri))) @ i)).
% 2.52/1.49 thf(fact_179__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [I:node,Ri:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r)) @ Ri) @ I) => ((((member @ node) @ I) @ ((set2 @ node) @ ms)) => ((! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((butlast @ node) @ Ri))) => (~ ((((member @ node) @ X2) @ ((set2 @ node) @ ms))))))) => (~ ((((prefix @ node) @ Ri) @ rs2))))))))))).
% 2.52/1.49 thf(fact_180__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Ms2:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ m) @ Ms2) @ i) => ((((prefix @ node) @ Ms2) @ ms) => (((member @ node) @ i) @ ((set2 @ node) @ ((butlast @ node) @ Ms2)))))))))).
% 2.52/1.49 thf(fact_181_old_Opath2__simple__loop, axiom, (! [G2:g,N:node,Ns:(list @ node),N2:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ N) => ((((member @ node) @ N2) @ ((set2 @ node) @ Ns)) => (~ ((! [Ns4:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns4) @ N) => ((((member @ node) @ N2) @ ((set2 @ node) @ Ns4)) => ((~ ((((member @ node) @ N) @ ((set2 @ node) @ ((tl @ node) @ ((butlast @ node) @ Ns4)))))) => (~ ((((ord_less_eq @ (set @ node)) @ ((set2 @ node) @ Ns4)) @ ((set2 @ node) @ Ns)))))))))))))))).
% 2.52/1.49 thf(fact_182_old_Opath_Ocases, axiom, (! [G2:g,A2:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ A2) => ((! [N4:node]: (((A2 = (((cons @ node) @ N4) @ (nil @ node))) => ((((member @ node) @ N4) @ ((set2 @ node) @ (alpha_n @ G2))) => (~ ((invar @ G2))))))) => (~ ((! [Ns3:(list @ node),N3:node]: (((A2 = (((cons @ node) @ N3) @ Ns3)) => (((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns3) => (~ ((((member @ node) @ N3) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((hd @ node) @ Ns3))))))))))))))))).
% 2.52/1.49 thf(fact_183_old_Opath_Oinducts, axiom, (! [G2:g,X:(list @ node),P:((list @ node) > $o)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ X) => ((! [N4:node]: (((((member @ node) @ N4) @ ((set2 @ node) @ (alpha_n @ G2))) => ((invar @ G2) => (P @ (((cons @ node) @ N4) @ (nil @ node))))))) => ((! [Ns3:(list @ node),N3:node]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns3) => ((P @ Ns3) => ((((member @ node) @ N3) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((hd @ node) @ Ns3)))) => (P @ (((cons @ node) @ N3) @ Ns3))))))) => (P @ X))))))).
% 2.52/1.49 thf(fact_184_old_Opath_Osimps, axiom, (! [G2:g,A2:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ A2) = ((? [N5:node]: (((A2 = (((cons @ node) @ N5) @ (nil @ node))) & ((((member @ node) @ N5) @ ((set2 @ node) @ (alpha_n @ G2))) & (invar @ G2))))) | (? [Ns5:(list @ node),N6:node]: (((A2 = (((cons @ node) @ N6) @ Ns5)) & (((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns5) & (((member @ node) @ N6) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((hd @ node) @ Ns5))))))))))))).
% 2.52/1.49 thf(fact_185_old_Opath__snoc, axiom, (! [G2:g,Ns:(list @ node),N:node,M:node]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((append @ node) @ Ns) @ (((cons @ node) @ N) @ (nil @ node)))) => ((((member @ node) @ N) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ M))) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((append @ node) @ Ns) @ (((cons @ node) @ N) @ (((cons @ node) @ M) @ (nil @ node)))))))))).
% 2.52/1.49 thf(fact_186_ri__rs_H__prefix, axiom, (((prefix @ node) @ ri) @ rs)).
% 2.52/1.49 thf(fact_187_old_Opath__not__Nil, axiom, (! [G2:g,Ns:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns) => (Ns != (nil @ node)))))).
% 2.52/1.49 thf(fact_188_old_Opath__hd, axiom, (! [G2:g,N:node,Ns:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N) @ Ns)) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N) @ (nil @ node))))))).
% 2.52/1.49 thf(fact_189_old_Opath__split_I2_J, axiom, (! [G2:g,Ns:(list @ node),M:node,Ns2:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((append @ node) @ Ns) @ (((cons @ node) @ M) @ Ns2))) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ M) @ Ns2)))))).
% 2.52/1.49 thf(fact_190_old_Oempty__path, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((invar @ G2) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N) @ (nil @ node)))))))).
% 2.52/1.49 thf(fact_191_old_Opath__split_I1_J, axiom, (! [G2:g,Ns:(list @ node),M:node,Ns2:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((append @ node) @ Ns) @ (((cons @ node) @ M) @ Ns2))) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((append @ node) @ Ns) @ (((cons @ node) @ M) @ (nil @ node)))))))).
% 2.52/1.49 thf(fact_192_old_Opath2__split__first__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) => ((? [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ Ns)) & (P @ X2)))) => (~ ((! [M2:node,Ns4:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns4) @ M2) => ((P @ M2) => ((! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((butlast @ node) @ Ns4))) => (~ ((P @ X2)))))) => (~ ((((prefix @ node) @ Ns4) @ Ns))))))))))))))).
% 2.52/1.49 thf(fact_193_old_Opath2__prefix__ex, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,M4:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ M4) @ ((set2 @ node) @ Ns)) => (~ ((! [Ns4:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns4) @ M4) => ((((prefix @ node) @ Ns4) @ Ns) => (((member @ node) @ M4) @ ((set2 @ node) @ ((butlast @ node) @ Ns4)))))))))))))).
% 2.52/1.49 thf(fact_194_old_OCons__path, axiom, (! [G2:g,Ns:(list @ node),N2:node]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns) => ((((member @ node) @ N2) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((hd @ node) @ Ns)))) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N2) @ Ns))))))).
% 2.52/1.49 thf(fact_195_old_Opath2__prefix, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,Ns2:(list @ node),M4:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((prefix @ node) @ (((append @ node) @ Ns2) @ (((cons @ node) @ M4) @ (nil @ node)))) @ Ns) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns2) @ (((cons @ node) @ M4) @ (nil @ node)))) @ M4)))))).
% 2.52/1.49 thf(fact_196_old_Opath__invar, axiom, (! [G2:g,Ns:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns) => (invar @ G2))))).
% 2.52/1.49 thf(fact_197_old_Opath__in___092_060alpha_062n, axiom, (! [G2:g,Ns:(list @ node),N:node]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns) => ((((member @ node) @ N) @ ((set2 @ node) @ Ns)) => (((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2)))))))).
% 2.52/1.49 thf(fact_198_old_Opath__by__tail, axiom, (! [G2:g,N:node,N2:node,Ns:(list @ node),Ms:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N) @ (((cons @ node) @ N2) @ Ns))) => ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N2) @ Ns)) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N2) @ Ms))) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N) @ (((cons @ node) @ N2) @ Ms)))))))).
% 2.52/1.49 thf(fact_199_subset__Collect__conv, axiom, (! [A:$tType,S:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ S) @ ((collect @ A) @ P)) = (! [X3:A]: (((((member @ A) @ X3) @ S) => (P @ X3)))))))).
% 2.52/1.49 thf(fact_200_ord__eq__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A,D:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => ((C = D) => (((ord_less_eq @ A) @ A2) @ D)))))))))).
% 2.52/1.49 thf(fact_201_subset__code_I1_J, axiom, (! [A:$tType,Xs:(list @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ B4) = (! [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) => (((member @ A) @ X3) @ B4)))))))).
% 2.52/1.49 thf(fact_202_set__subset__Cons, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((set2 @ A) @ (((cons @ A) @ X) @ Xs)))))).
% 2.52/1.49 thf(fact_203_tl__subset, axiom, (! [A:$tType,Xs:(list @ A),A3:(set @ A)]: (((Xs != (nil @ A)) => ((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ A3) => (((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ ((tl @ A) @ Xs))) @ A3)))))).
% 2.52/1.49 thf(fact_204_butlast__subset, axiom, (! [A:$tType,Xs:(list @ A),A3:(set @ A)]: (((Xs != (nil @ A)) => ((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ A3) => (((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) @ A3)))))).
% 2.52/1.49 thf(fact_205_prefix__snoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Y:A]: (((((prefix @ A) @ Xs) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) | (((prefix @ A) @ Xs) @ Ys)))))).
% 2.52/1.49 thf(fact_206_old_Opath2__split__first__last, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,X:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ X) @ ((set2 @ node) @ Ns)) => (~ ((! [Ns_1:(list @ node),Ns_3:(list @ node),Ns_2:(list @ node)]: (((Ns = (((append @ node) @ Ns_1) @ (((append @ node) @ Ns_3) @ Ns_2))) => ((((prefix @ node) @ (((append @ node) @ Ns_1) @ (((cons @ node) @ X) @ (nil @ node)))) @ Ns) => ((((suffix @ node) @ (((cons @ node) @ X) @ Ns_2)) @ Ns) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns_1) @ (((cons @ node) @ X) @ (nil @ node)))) @ X) => ((~ ((((member @ node) @ X) @ ((set2 @ node) @ Ns_1)))) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ X) @ Ns_3) @ X) => (((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ X) @ (((cons @ node) @ X) @ Ns_2)) @ M) => (((member @ node) @ X) @ ((set2 @ node) @ Ns_2)))))))))))))))))).
% 2.52/1.49 thf(fact_207_same__prefix__nil, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((prefix @ A) @ (((append @ A) @ Xs) @ Ys)) @ Xs) = (Ys = (nil @ A)))))).
% 2.52/1.49 thf(fact_208_prefix__order_Odual__order_Orefl, axiom, (! [A:$tType,A2:(list @ A)]: ((((prefix @ A) @ A2) @ A2)))).
% 2.52/1.49 thf(fact_209_prefix__order_Oorder__refl, axiom, (! [A:$tType,X:(list @ A)]: ((((prefix @ A) @ X) @ X)))).
% 2.52/1.49 thf(fact_210_suffix__order_Odual__order_Orefl, axiom, (! [A:$tType,A2:(list @ A)]: ((((suffix @ A) @ A2) @ A2)))).
% 2.52/1.49 thf(fact_211_suffix__order_Oorder__refl, axiom, (! [A:$tType,X:(list @ A)]: ((((suffix @ A) @ X) @ X)))).
% 2.52/1.49 thf(fact_212_Cons__prefix__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((prefix @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = ((X = Y) & (((prefix @ A) @ Xs) @ Ys)))))).
% 2.52/1.49 thf(fact_213_prefix__code_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: ((((prefix @ A) @ (nil @ A)) @ Xs)))).
% 2.52/1.49 thf(fact_214_prefix__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((prefix @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.52/1.49 thf(fact_215_prefix__bot_Obot_Oextremum__unique, axiom, (! [A:$tType,A2:(list @ A)]: (((((prefix @ A) @ A2) @ (nil @ A)) = (A2 = (nil @ A)))))).
% 2.52/1.49 thf(fact_216_suffix__bot_Obot_Oextremum__unique, axiom, (! [A:$tType,A2:(list @ A)]: (((((suffix @ A) @ A2) @ (nil @ A)) = (A2 = (nil @ A)))))).
% 2.52/1.49 thf(fact_217_suffix__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((suffix @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.52/1.49 thf(fact_218_same__prefix__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((prefix @ A) @ (((append @ A) @ Xs) @ Ys)) @ (((append @ A) @ Xs) @ Zs)) = (((prefix @ A) @ Ys) @ Zs))))).
% 2.52/1.49 thf(fact_219_same__suffix__suffix, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Ys) @ Xs)) @ (((append @ A) @ Zs) @ Xs)) = (((suffix @ A) @ Ys) @ Zs))))).
% 2.52/1.49 thf(fact_220_old_Opath2__split__last__prop, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,P:(node > $o)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((? [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ Ns)) & (P @ X2)))) => (~ ((! [N3:node,Ns4:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N3) @ Ns4) @ M) => ((P @ N3) => ((! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((tl @ node) @ Ns4))) => (~ ((P @ X2)))))) => (~ ((((suffix @ node) @ Ns4) @ Ns))))))))))))))).
% 2.52/1.49 thf(fact_221_same__suffix__nil, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Ys) @ Xs)) @ Xs) = (Ys = (nil @ A)))))).
% 2.52/1.49 thf(fact_222_snoc__suffix__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: (((((suffix @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((X = Y) & (((suffix @ A) @ Xs) @ Ys)))))).
% 2.52/1.49 thf(fact_223_suffix__snoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Y:A]: (((((suffix @ A) @ Xs) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = (nil @ A)) | (? [Zs3:(list @ A)]: (((Xs = (((append @ A) @ Zs3) @ (((cons @ A) @ Y) @ (nil @ A)))) & (((suffix @ A) @ Zs3) @ Ys))))))))).
% 2.52/1.49 thf(fact_224_suffix__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((suffix @ A) @ ((tl @ A) @ Xs)) @ Xs)))).
% 2.52/1.49 thf(fact_225_suffix__Cons, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((suffix @ A) @ Xs) @ (((cons @ A) @ Y) @ Ys)) = ((Xs = (((cons @ A) @ Y) @ Ys)) | (((suffix @ A) @ Xs) @ Ys)))))).
% 2.52/1.49 thf(fact_226_suffix__ConsD, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.52/1.49 thf(fact_227_suffix__ConsI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Y:A]: (((((suffix @ A) @ Xs) @ Ys) => (((suffix @ A) @ Xs) @ (((cons @ A) @ Y) @ Ys)))))).
% 2.52/1.49 thf(fact_228_suffix__ConsD2, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((suffix @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.52/1.49 thf(fact_229_suffix__bot_Obot_Oextremum__uniqueI, axiom, (! [A:$tType,A2:(list @ A)]: (((((suffix @ A) @ A2) @ (nil @ A)) => (A2 = (nil @ A)))))).
% 2.52/1.49 thf(fact_230_suffix__bot_Obot_Oextremum, axiom, (! [A:$tType,A2:(list @ A)]: ((((suffix @ A) @ (nil @ A)) @ A2)))).
% 2.52/1.49 thf(fact_231_Nil__suffix, axiom, (! [A:$tType,Xs:(list @ A)]: ((((suffix @ A) @ (nil @ A)) @ Xs)))).
% 2.52/1.49 thf(fact_232_set__mono__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ Xs) @ Ys) => (((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((set2 @ A) @ Ys)))))).
% 2.52/1.49 thf(fact_233_not__suffix__cases, axiom, (! [A:$tType,Ps2:(list @ A),Ls:(list @ A)]: (((~ ((((suffix @ A) @ Ps2) @ Ls))) => (((Ps2 != (nil @ A)) => (Ls != (nil @ A))) => ((! [A4:A,As:(list @ A)]: (((Ps2 = (((append @ A) @ As) @ (((cons @ A) @ A4) @ (nil @ A)))) => (! [X4:A,Xs2:(list @ A)]: (((Ls = (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) => ((X4 = A4) => (((suffix @ A) @ As) @ Xs2)))))))) => (~ ((! [A4:A]: (((? [As:(list @ A)]: ((Ps2 = (((append @ A) @ As) @ (((cons @ A) @ A4) @ (nil @ A)))))) => (! [X4:A]: (((? [Xs2:(list @ A)]: ((Ls = (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))))) => (X4 = A4))))))))))))))).
% 2.52/1.49 thf(fact_234_not__suffix__induct, axiom, (! [A:$tType,Ps2:(list @ A),Ls:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((~ ((((suffix @ A) @ Ps2) @ Ls))) => ((! [X4:A,Xs2:(list @ A)]: (((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (nil @ A)))) => ((! [X4:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: (((X4 != Y3) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((append @ A) @ Ys3) @ (((cons @ A) @ Y3) @ (nil @ A))))))) => ((! [X4:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: (((X4 = Y3) => ((~ ((((suffix @ A) @ Xs2) @ Ys3))) => (((P @ Xs2) @ Ys3) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((append @ A) @ Ys3) @ (((cons @ A) @ Y3) @ (nil @ A))))))))) => ((P @ Ps2) @ Ls)))))))).
% 2.52/1.49 thf(fact_235_suffix__order_Odual__order_Oantisym, axiom, (! [A:$tType,B2:(list @ A),A2:(list @ A)]: (((((suffix @ A) @ B2) @ A2) => ((((suffix @ A) @ A2) @ B2) => (A2 = B2)))))).
% 2.52/1.49 thf(fact_236_suffix__order_Odual__order_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z:(list @ A)]: ((Y4 = Z))) = (^ [A5:(list @ A),B5:(list @ A)]: (((((suffix @ A) @ B5) @ A5) & (((suffix @ A) @ A5) @ B5)))))))).
% 2.52/1.49 thf(fact_237_suffix__order_Odual__order_Otrans, axiom, (! [A:$tType,B2:(list @ A),A2:(list @ A),C:(list @ A)]: (((((suffix @ A) @ B2) @ A2) => ((((suffix @ A) @ C) @ B2) => (((suffix @ A) @ C) @ A2)))))).
% 2.52/1.49 thf(fact_238_suffix__order_Oord__le__eq__trans, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((((suffix @ A) @ A2) @ B2) => ((B2 = C) => (((suffix @ A) @ A2) @ C)))))).
% 2.52/1.49 thf(fact_239_suffix__order_Oord__eq__le__trans, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((A2 = B2) => ((((suffix @ A) @ B2) @ C) => (((suffix @ A) @ A2) @ C)))))).
% 2.52/1.49 thf(fact_240_suffix__order_Oorder_Oantisym, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A)]: (((((suffix @ A) @ A2) @ B2) => ((((suffix @ A) @ B2) @ A2) => (A2 = B2)))))).
% 2.52/1.49 thf(fact_241_suffix__order_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z:(list @ A)]: ((Y4 = Z))) = (^ [A5:(list @ A),B5:(list @ A)]: (((((suffix @ A) @ A5) @ B5) & (((suffix @ A) @ B5) @ A5)))))))).
% 2.52/1.49 thf(fact_242_suffix__order_Oantisym__conv, axiom, (! [A:$tType,Y:(list @ A),X:(list @ A)]: (((((suffix @ A) @ Y) @ X) => ((((suffix @ A) @ X) @ Y) = (X = Y)))))).
% 2.52/1.49 thf(fact_243_suffix__order_Oorder__trans, axiom, (! [A:$tType,X:(list @ A),Y:(list @ A),Z3:(list @ A)]: (((((suffix @ A) @ X) @ Y) => ((((suffix @ A) @ Y) @ Z3) => (((suffix @ A) @ X) @ Z3)))))).
% 2.52/1.49 thf(fact_244_suffix__order_Oorder_Otrans, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C:(list @ A)]: (((((suffix @ A) @ A2) @ B2) => ((((suffix @ A) @ B2) @ C) => (((suffix @ A) @ A2) @ C)))))).
% 2.52/1.49 thf(fact_245_suffix__order_Oeq__refl, axiom, (! [A:$tType,X:(list @ A),Y:(list @ A)]: (((X = Y) => (((suffix @ A) @ X) @ Y))))).
% 2.52/1.49 thf(fact_246_suffix__order_Oantisym, axiom, (! [A:$tType,X:(list @ A),Y:(list @ A)]: (((((suffix @ A) @ X) @ Y) => ((((suffix @ A) @ Y) @ X) => (X = Y)))))).
% 2.52/1.49 thf(fact_247_suffix__order_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z:(list @ A)]: ((Y4 = Z))) = (^ [X3:(list @ A),Y2:(list @ A)]: (((((suffix @ A) @ X3) @ Y2) & (((suffix @ A) @ Y2) @ X3)))))))).
% 2.52/1.49 thf(fact_248_suffix__same__cases, axiom, (! [A:$tType,Xs_1:(list @ A),Ys:(list @ A),Xs_2:(list @ A)]: (((((suffix @ A) @ Xs_1) @ Ys) => ((((suffix @ A) @ Xs_2) @ Ys) => ((((suffix @ A) @ Xs_1) @ Xs_2) | (((suffix @ A) @ Xs_2) @ Xs_1))))))).
% 2.52/1.49 thf(fact_249_suffixE, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ Xs) @ Ys) => (~ ((! [Zs2:(list @ A)]: ((Ys != (((append @ A) @ Zs2) @ Xs)))))))))).
% 2.52/1.49 thf(fact_250_suffixI, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Zs) @ Xs)) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.52/1.49 thf(fact_251_Sublist_Osuffix__def, axiom, (! [A:$tType]: (((suffix @ A) = (^ [Xs3:(list @ A),Ys2:(list @ A)]: ((? [Zs3:(list @ A)]: ((Ys2 = (((append @ A) @ Zs3) @ Xs3)))))))))).
% 2.52/1.49 thf(fact_252_suffix__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)) = ((((suffix @ A) @ Xs) @ Zs) | (? [Xs6:(list @ A)]: (((Xs = (((append @ A) @ Xs6) @ Zs)) & (((suffix @ A) @ Xs6) @ Ys))))))))).
% 2.52/1.49 thf(fact_253_suffix__appendD, axiom, (! [A:$tType,Zs:(list @ A),Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Zs) @ Xs)) @ Ys) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.52/1.49 thf(fact_254_suffix__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ Xs) @ Ys) => (((suffix @ A) @ Xs) @ (((append @ A) @ Zs) @ Ys)))))).
% 2.52/1.49 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 2.52/1.49 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: (((linorder @ A) => (ord @ A))))).
% 2.52/1.49 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.52/1.49 thf(tcon_Set_Oset___Orderings_Oord_1, axiom, (! [A6:$tType]: ((ord @ (set @ A6))))).
% 2.52/1.49 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.52/1.49 thf(tcon_HOL_Obool___Orderings_Oord_2, axiom, (ord @ $o)).
% 2.52/1.49 thf(tfree_0, hypothesis, (linorder @ node)).
% 2.52/1.49 thf(tfree_1, hypothesis, (linorder @ val)).
% 2.52/1.49 thf(conj_0, conjecture, ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ i) @ (((cons @ node) @ i) @ rs_rest)) @ pred_phi_r)).
% 2.52/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.WhTG5ILRVb/DTF2DTF22669.p
% 2.52/1.49 ------------------------
% 2.80/1.52 ---- Cleaned THF ---
% 2.80/1.52 thf(ty_t_Product__Type_Oprod,type,
% 2.80/1.52 product_prod: $tType > $tType > $tType ).
% 2.80/1.52
% 2.80/1.52 thf(ty_t_Option_Ooption,type,
% 2.80/1.52 option: $tType > $tType ).
% 2.80/1.52
% 2.80/1.52 thf(ty_t_List_Olist,type,
% 2.80/1.52 list: $tType > $tType ).
% 2.80/1.52
% 2.80/1.52 thf(ty_t_Set_Oset,type,
% 2.80/1.52 set: $tType > $tType ).
% 2.80/1.52
% 2.80/1.52 thf(ty_tf_edgeD,type,
% 2.80/1.52 edgeD: $tType ).
% 2.80/1.52
% 2.80/1.52 thf(ty_tf_node,type,
% 2.80/1.52 node: $tType ).
% 2.80/1.52
% 2.80/1.52 thf(ty_tf_val,type,
% 2.80/1.52 val: $tType ).
% 2.80/1.52
% 2.80/1.52 thf(ty_tf_g,type,
% 2.80/1.52 g: $tType ).
% 2.80/1.52
% 2.80/1.52 thf(sy_cl_HOL_Otype,type,
% 2.80/1.52 type:
% 2.80/1.52 !>[A: $tType] : $o ).
% 2.80/1.52
% 2.80/1.52 thf(sy_cl_Orderings_Oord,type,
% 2.80/1.52 ord:
% 2.80/1.52 !>[A: $tType] : $o ).
% 2.80/1.52
% 2.80/1.52 thf(sy_cl_Orderings_Olinorder,type,
% 2.80/1.52 linorder:
% 2.80/1.52 !>[A: $tType] : $o ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_Graph__path_Ograph__path__base_Opath,type,
% 2.80/1.52 graph_1146196722h_path:
% 2.80/1.52 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > ( list @ Node ) > $o ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_Graph__path_Ograph__path__base_Opath2,type,
% 2.80/1.52 graph_1661282752_path2:
% 2.80/1.52 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) > Node > $o ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors,type,
% 2.80/1.52 graph_1201503639essors:
% 2.80/1.52 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_List_Oappend,type,
% 2.80/1.52 append:
% 2.80/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_List_Obutlast,type,
% 2.80/1.52 butlast:
% 2.80/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_List_Olist_OCons,type,
% 2.80/1.52 cons:
% 2.80/1.52 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_List_Olist_ONil,type,
% 2.80/1.52 nil:
% 2.80/1.52 !>[A: $tType] : ( list @ A ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_List_Olist_Ohd,type,
% 2.80/1.52 hd:
% 2.80/1.52 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_List_Olist_Oset,type,
% 2.80/1.52 set2:
% 2.80/1.52 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_List_Olist_Otl,type,
% 2.80/1.52 tl:
% 2.80/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_Minimality_Ograph__path_OpathsConverge,type,
% 2.80/1.52 graph_pathsConverge:
% 2.80/1.52 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) > Node > ( list @ Node ) > Node > $o ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.80/1.52 ord_less_eq:
% 2.80/1.52 !>[A: $tType] : ( A > A > $o ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses,type,
% 2.80/1.52 sSA_CFG_SSA_phiUses:
% 2.80/1.52 !>[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 ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode,type,
% 2.80/1.52 sSA_CF1081484811efNode:
% 2.80/1.52 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Node ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg,type,
% 2.80/1.52 sSA_CF1165125185phiArg:
% 2.80/1.52 !>[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 ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_Set_OCollect,type,
% 2.80/1.52 collect:
% 2.80/1.52 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_Sublist_Oprefix,type,
% 2.80/1.52 prefix:
% 2.80/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_Sublist_Osuffix,type,
% 2.80/1.52 suffix:
% 2.80/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_c_member,type,
% 2.80/1.52 member:
% 2.80/1.52 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v__092_060alpha_062n,type,
% 2.80/1.52 alpha_n: g > ( list @ node ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 2.80/1.52 phi_r: val ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_defs,type,
% 2.80/1.52 defs: g > node > ( set @ val ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_g,type,
% 2.80/1.52 g2: g ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_i____,type,
% 2.80/1.52 i: node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_inEdges_H,type,
% 2.80/1.52 inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_invar,type,
% 2.80/1.52 invar: g > $o ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_m,type,
% 2.80/1.52 m: node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_ms,type,
% 2.80/1.52 ms: list @ node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_ms_H____,type,
% 2.80/1.52 ms2: list @ node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_n,type,
% 2.80/1.52 n: node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_ns,type,
% 2.80/1.52 ns: list @ node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_phis,type,
% 2.80/1.52 phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 2.80/1.52 pred_phi_r: node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_r,type,
% 2.80/1.52 r: val ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_ri____,type,
% 2.80/1.52 ri: list @ node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_rs_H____,type,
% 2.80/1.52 rs: list @ node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_rs_H__rest____,type,
% 2.80/1.52 rs_rest: list @ node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_rs____,type,
% 2.80/1.52 rs2: list @ node ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_s,type,
% 2.80/1.52 s: val ).
% 2.80/1.52
% 2.80/1.52 thf(sy_v_tmp____,type,
% 2.80/1.52 tmp: list @ node ).
% 2.80/1.52
% 2.80/1.52 thf(fact_0_m__i__differ_I2_J,axiom,
% 2.80/1.52 m != i ).
% 2.80/1.52
% 2.80/1.52 thf(fact_1_rs_H__rest__def,axiom,
% 2.80/1.52 ( rs
% 2.80/1.52 = ( append @ node @ tmp @ ( cons @ node @ i @ rs_rest ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_2_old_Oinvar,axiom,
% 2.80/1.52 ! [G2: g] : ( invar @ G2 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_3_old_Opath2__split_I2_J,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns2: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns2 ) ) @ M )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns2 ) @ M ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_4_False,axiom,
% 2.80/1.52 r != phi_r ).
% 2.80/1.52
% 2.80/1.52 thf(fact_5_rs_H__props_I1_J,axiom,
% 2.80/1.52 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 ).
% 2.80/1.52
% 2.80/1.52 thf(fact_6_ms_H__props_I1_J,axiom,
% 2.80/1.52 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 2.80/1.52
% 2.80/1.52 thf(fact_7_rs_H__rest__prop,axiom,
% 2.80/1.52 ( rs
% 2.80/1.52 = ( append @ node @ ri @ rs_rest ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_8_rs_H__props_I3_J,axiom,
% 2.80/1.52 member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_9_old_Opath2__not__Nil,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( Ns
% 2.80/1.52 != ( nil @ node ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_10_old_Opath2__not__Nil2,axiom,
% 2.80/1.52 ! [G2: g,N: node,M: node] :
% 2.80/1.52 ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( nil @ node ) @ M ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_11_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_12_old_Opath2__hd__in__ns,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( member @ node @ N @ ( set2 @ node @ Ns ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_13_old_Opath2__in___092_060alpha_062n,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,L: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( member @ node @ L @ ( set2 @ node @ Ns ) )
% 2.80/1.52 => ( member @ node @ L @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_14_old_Opath2__last__in__ns,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( member @ node @ M @ ( set2 @ node @ Ns ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_15_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_16_old_Opath2__forget__hd,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ Ns ) @ Ns @ M ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_17_old_Opath2__hd,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( N
% 2.80/1.52 = ( hd @ node @ Ns ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_18__092_060open_062ri_A_061_Atmp_A_064_A_091i_093_092_060close_062,axiom,
% 2.80/1.52 ( ri
% 2.80/1.52 = ( append @ node @ tmp @ ( cons @ node @ i @ ( nil @ node ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_19__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H__rest_O_Ars_H_A_061_Ari_A_064_Ars_H__rest_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.80/1.52 ~ ! [Rs_rest: list @ node] :
% 2.80/1.52 ( rs
% 2.80/1.52 != ( append @ node @ ri @ Rs_rest ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_20_ri__props_I2_J,axiom,
% 2.80/1.52 member @ node @ i @ ( set2 @ node @ ms ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_21_m__i__differ_I1_J,axiom,
% 2.80/1.52 ( i
% 2.80/1.52 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tmp_O_Ari_A_061_Atmp_A_064_A_091i_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.80/1.52 ~ ! [Tmp: list @ node] :
% 2.80/1.52 ( ri
% 2.80/1.52 != ( append @ node @ Tmp @ ( cons @ node @ i @ ( nil @ node ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_23_ri__props_I1_J,axiom,
% 2.80/1.52 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 2.80/1.52
% 2.80/1.52 thf(fact_24_old_Opath2__split_I1_J,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns2: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns2 ) ) @ M )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ ( nil @ node ) ) ) @ N2 ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_25__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 2.80/1.52 ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 2.80/1.52 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_26__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.80/1.52 ( ( i
% 2.80/1.52 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.80/1.52 => ( ( ( i
% 2.80/1.52 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.80/1.52 => ( m != i ) )
% 2.80/1.52 => ~ ( ( i
% 2.80/1.52 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.80/1.52 => ( m = i ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_27_old_Oempty__path2,axiom,
% 2.80/1.52 ! [N: node,G2: g] :
% 2.80/1.52 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.80/1.52 => ( ( invar @ G2 )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_28_ms_H__props_I3_J,axiom,
% 2.80/1.52 ~ ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ ms2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_29_assms_I10_J,axiom,
% 2.80/1.52 sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 2.80/1.52
% 2.80/1.52 thf(fact_30_rs_H__props_I4_J,axiom,
% 2.80/1.52 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 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_31_assms_I7_J,axiom,
% 2.80/1.52 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_32_rs__props_I1_J,axiom,
% 2.80/1.52 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_33_rs__def,axiom,
% 2.80/1.52 ( rs2
% 2.80/1.52 = ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_34_assms_I8_J,axiom,
% 2.80/1.52 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_35_rs_H__loopfree,axiom,
% 2.80/1.52 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_36_hd__append2,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( hd @ A @ Xs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_37_append1__eq__conv,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.80/1.52 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.80/1.52 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.80/1.52 = ( ( Xs = Ys )
% 2.80/1.52 & ( X = Y ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_38_list__ee__eq__leel_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,E1: A,E2: A,L1: list @ A,E12: A,E22: A,L2: list @ A] :
% 2.80/1.52 ( ( ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) )
% 2.80/1.52 = ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) ) )
% 2.80/1.52 = ( ( L1
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( E1 = E12 )
% 2.80/1.52 & ( E2 = E22 )
% 2.80/1.52 & ( L2
% 2.80/1.52 = ( nil @ A ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_39_list__ee__eq__leel_I2_J,axiom,
% 2.80/1.52 ! [A: $tType,L1: list @ A,E12: A,E22: A,L2: list @ A,E1: A,E2: A] :
% 2.80/1.52 ( ( ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) )
% 2.80/1.52 = ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) ) )
% 2.80/1.52 = ( ( L1
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( E1 = E12 )
% 2.80/1.52 & ( E2 = E22 )
% 2.80/1.52 & ( L2
% 2.80/1.52 = ( nil @ A ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_40_list__se__match_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,L1: list @ A,L2: list @ A,A2: A] :
% 2.80/1.52 ( ( L1
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ( append @ A @ L1 @ L2 )
% 2.80/1.52 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.80/1.52 = ( ( L1
% 2.80/1.52 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.80/1.52 & ( L2
% 2.80/1.52 = ( nil @ A ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_41_ri__props_I3_J,axiom,
% 2.80/1.52 ! [X2: node] :
% 2.80/1.52 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ ri ) ) )
% 2.80/1.52 => ~ ( member @ node @ X2 @ ( set2 @ node @ ms ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_42_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Y: A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ ( append @ A @ Ys @ ( cons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_43_list_Oinject,axiom,
% 2.80/1.52 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.80/1.52 ( ( ( cons @ A @ X21 @ X22 )
% 2.80/1.52 = ( cons @ A @ Y21 @ Y22 ) )
% 2.80/1.52 = ( ( X21 = Y21 )
% 2.80/1.52 & ( X22 = Y22 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_44_same__append__eq,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.80/1.52 = ( append @ A @ Xs @ Zs ) )
% 2.80/1.52 = ( Ys = Zs ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_45_mem__Collect__eq,axiom,
% 2.80/1.52 ! [A: $tType,A2: A,P: A > $o] :
% 2.80/1.52 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.80/1.52 = ( P @ A2 ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_46_Collect__mem__eq,axiom,
% 2.80/1.52 ! [A: $tType,A3: set @ A] :
% 2.80/1.52 ( ( collect @ A
% 2.80/1.52 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 2.80/1.52 = A3 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_47_Collect__cong,axiom,
% 2.80/1.52 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.80/1.52 ( ! [X4: A] :
% 2.80/1.52 ( ( P @ X4 )
% 2.80/1.52 = ( Q @ X4 ) )
% 2.80/1.52 => ( ( collect @ A @ P )
% 2.80/1.52 = ( collect @ A @ Q ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_48_ext,axiom,
% 2.80/1.52 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 2.80/1.52 ( ! [X4: A] :
% 2.80/1.52 ( ( F @ X4 )
% 2.80/1.52 = ( G2 @ X4 ) )
% 2.80/1.52 => ( F = G2 ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_49_append__same__eq,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Ys @ Xs )
% 2.80/1.52 = ( append @ A @ Zs @ Xs ) )
% 2.80/1.52 = ( Ys = Zs ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_50_append__assoc,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 2.80/1.52 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_51_append_Oassoc,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.80/1.52 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C )
% 2.80/1.52 = ( append @ A @ A2 @ ( append @ A @ B2 @ C ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_52_old_Opredecessor__is__node,axiom,
% 2.80/1.52 ! [N: node,G2: g,N2: node] :
% 2.80/1.52 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 2.80/1.52 => ( ( invar @ G2 )
% 2.80/1.52 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_53_old_Osuccessor__is__node,axiom,
% 2.80/1.52 ! [N: node,G2: g,N2: node] :
% 2.80/1.52 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 2.80/1.52 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.80/1.52 => ( ( invar @ G2 )
% 2.80/1.52 => ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_54_old_Osuccessor__in___092_060alpha_062n,axiom,
% 2.80/1.52 ! [G2: g,N: node] :
% 2.80/1.52 ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N )
% 2.80/1.52 != ( nil @ node ) )
% 2.80/1.52 => ( ( invar @ G2 )
% 2.80/1.52 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_55_old_Opath2__app_H,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ ( butlast @ node @ Ns ) @ Ms ) @ L ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_56_old_Opath2__app,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( tl @ node @ Ms ) ) @ L ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_57_append_Oright__neutral,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] :
% 2.80/1.52 ( ( append @ A @ A2 @ ( nil @ A ) )
% 2.80/1.52 = A2 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_58_empty__append__eq__id,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( append @ A @ ( nil @ A ) )
% 2.80/1.52 = ( ^ [X3: list @ A] : X3 ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_59_append__is__Nil__conv,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 = ( ( Xs
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( Ys
% 2.80/1.52 = ( nil @ A ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_60_Nil__is__append__conv,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( ( nil @ A )
% 2.80/1.52 = ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( ( Xs
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( Ys
% 2.80/1.52 = ( nil @ A ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_61_self__append__conv2,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.80/1.52 ( ( Ys
% 2.80/1.52 = ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( Xs
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_62_append__self__conv2,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.80/1.52 = Ys )
% 2.80/1.52 = ( Xs
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_63_self__append__conv,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( Ys
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_64_append__self__conv,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.80/1.52 = Xs )
% 2.80/1.52 = ( Ys
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_65_append__Nil2,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.80/1.52 = Xs ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_66_old_Opath2__split__ex_H,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 2.80/1.52 => ~ ! [Ns_1: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns_1 @ X )
% 2.80/1.52 => ! [Ns_2: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_2 @ M )
% 2.80/1.52 => ( Ns
% 2.80/1.52 != ( append @ node @ ( butlast @ node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_67_old_Opath2__induct,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( ( invar @ G2 )
% 2.80/1.52 => ( P @ M @ ( cons @ node @ M @ ( nil @ node ) ) @ M ) )
% 2.80/1.52 => ( ! [Ns3: list @ node,N3: node,N4: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N4 @ Ns3 @ M )
% 2.80/1.52 => ( ( P @ N4 @ Ns3 @ M )
% 2.80/1.52 => ( ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N4 ) ) )
% 2.80/1.52 => ( P @ N3 @ ( cons @ node @ N3 @ Ns3 ) @ M ) ) ) )
% 2.80/1.52 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_68_old_Opath2__split__ex,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 2.80/1.52 => ~ ! [Ns_1: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns_1 @ X )
% 2.80/1.52 => ! [Ns_2: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_2 @ M )
% 2.80/1.52 => ( ( Ns
% 2.80/1.52 = ( append @ node @ Ns_1 @ ( tl @ node @ Ns_2 ) ) )
% 2.80/1.52 => ( Ns
% 2.80/1.52 != ( append @ node @ ( butlast @ node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_69_old_Opath2__rev__induct,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.80/1.52 => ( P @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) )
% 2.80/1.52 => ( ! [Ns3: list @ node,M2: node,M3: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns3 @ M2 )
% 2.80/1.52 => ( ( P @ N @ Ns3 @ M2 )
% 2.80/1.52 => ( ( member @ node @ M2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M3 ) ) )
% 2.80/1.52 => ( P @ N @ ( append @ node @ Ns3 @ ( cons @ node @ M3 @ ( nil @ node ) ) ) @ M3 ) ) ) )
% 2.80/1.52 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_70_old_Opath2__snoc,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,M4: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M4 ) ) )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ M4 @ ( nil @ node ) ) ) @ M4 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_71_list__e__eq__lel_I2_J,axiom,
% 2.80/1.52 ! [A: $tType,L1: list @ A,E: A,L2: list @ A,E3: A] :
% 2.80/1.52 ( ( ( append @ A @ L1 @ ( cons @ A @ E @ L2 ) )
% 2.80/1.52 = ( cons @ A @ E3 @ ( nil @ A ) ) )
% 2.80/1.52 = ( ( L1
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( E = E3 )
% 2.80/1.52 & ( L2
% 2.80/1.52 = ( nil @ A ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_72_list__e__eq__lel_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,E3: A,L1: list @ A,E: A,L2: list @ A] :
% 2.80/1.52 ( ( ( cons @ A @ E3 @ ( nil @ A ) )
% 2.80/1.52 = ( append @ A @ L1 @ ( cons @ A @ E @ L2 ) ) )
% 2.80/1.52 = ( ( L1
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( E = E3 )
% 2.80/1.52 & ( L2
% 2.80/1.52 = ( nil @ A ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_73_list__se__match_I4_J,axiom,
% 2.80/1.52 ! [A: $tType,L2: list @ A,A2: A,L1: list @ A] :
% 2.80/1.52 ( ( L2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 2.80/1.52 = ( append @ A @ L1 @ L2 ) )
% 2.80/1.52 = ( ( L1
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( L2
% 2.80/1.52 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_74_list__se__match_I3_J,axiom,
% 2.80/1.52 ! [A: $tType,L1: list @ A,A2: A,L2: list @ A] :
% 2.80/1.52 ( ( L1
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 2.80/1.52 = ( append @ A @ L1 @ L2 ) )
% 2.80/1.52 = ( ( L1
% 2.80/1.52 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.80/1.52 & ( L2
% 2.80/1.52 = ( nil @ A ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_75_list__se__match_I2_J,axiom,
% 2.80/1.52 ! [A: $tType,L2: list @ A,L1: list @ A,A2: A] :
% 2.80/1.52 ( ( L2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ( append @ A @ L1 @ L2 )
% 2.80/1.52 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.80/1.52 = ( ( L1
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( L2
% 2.80/1.52 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_76_tl__append2,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( tl @ A @ ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( append @ A @ ( tl @ A @ Xs ) @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_77_old_Opath2__cases,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( ( Ns
% 2.80/1.52 = ( cons @ node @ N @ ( nil @ node ) ) )
% 2.80/1.52 => ( M != N ) )
% 2.80/1.52 => ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) @ ( tl @ node @ Ns ) @ M )
% 2.80/1.52 => ~ ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_78_rs__props_I3_J,axiom,
% 2.80/1.52 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_79_butlast__snoc,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,X: A] :
% 2.80/1.52 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.80/1.52 = Xs ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_80_list_Ocollapse,axiom,
% 2.80/1.52 ! [A: $tType,List: list @ A] :
% 2.80/1.52 ( ( List
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 2.80/1.52 = List ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_81_hd__Cons__tl,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 2.80/1.52 = Xs ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_82_in__hd__or__tl__conv,axiom,
% 2.80/1.52 ! [A: $tType,L: list @ A,X: A] :
% 2.80/1.52 ( ( L
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ( X
% 2.80/1.52 = ( hd @ A @ L ) )
% 2.80/1.52 | ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ L ) ) ) )
% 2.80/1.52 = ( member @ A @ X @ ( set2 @ A @ L ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_83_ri__props_I4_J,axiom,
% 2.80/1.52 prefix @ node @ ri @ rs2 ).
% 2.80/1.52
% 2.80/1.52 thf(fact_84_ms_H__props_I2_J,axiom,
% 2.80/1.52 prefix @ node @ ms2 @ ms ).
% 2.80/1.52
% 2.80/1.52 thf(fact_85_old_OCons__path2,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,N2: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns ) @ M ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_86_butlast__tl,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 2.80/1.52 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_87_butlast_Osimps_I1_J,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( butlast @ A @ ( nil @ A ) )
% 2.80/1.52 = ( nil @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_88_list_Osel_I3_J,axiom,
% 2.80/1.52 ! [A: $tType,X21: A,X22: list @ A] :
% 2.80/1.52 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 2.80/1.52 = X22 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_89_in__set__butlastD,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 2.80/1.52 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_90_list_Osel_I2_J,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( tl @ A @ ( nil @ A ) )
% 2.80/1.52 = ( nil @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_91_butlast_Osimps_I2_J,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,X: A] :
% 2.80/1.52 ( ( ( Xs
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.80/1.52 = ( nil @ A ) ) )
% 2.80/1.52 & ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.80/1.52 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_92_tl__obtain__elem,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ( tl @ A @ Xs )
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 => ~ ! [E4: A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 != ( cons @ A @ E4 @ ( nil @ A ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_93_tl__Nil,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( ( tl @ A @ Xs )
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 = ( ( Xs
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 | ? [X3: A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_94_Nil__tl,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( ( nil @ A )
% 2.80/1.52 = ( tl @ A @ Xs ) )
% 2.80/1.52 = ( ( Xs
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 | ? [X3: A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_95_butlast__append,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.80/1.52 ( ( ( Ys
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( butlast @ A @ Xs ) ) )
% 2.80/1.52 & ( ( Ys
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_96_list_Oset__sel_I2_J,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A,X: A] :
% 2.80/1.52 ( ( A2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ A2 ) ) )
% 2.80/1.52 => ( member @ A @ X @ ( set2 @ A @ A2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_97_in__set__butlast__appendI,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 2.80/1.52 | ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 2.80/1.52 => ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_98_list_Oexpand,axiom,
% 2.80/1.52 ! [A: $tType,List: list @ A,List2: list @ A] :
% 2.80/1.52 ( ( ( List
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 = ( List2
% 2.80/1.52 = ( nil @ A ) ) )
% 2.80/1.52 => ( ( ( List
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( List2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ( hd @ A @ List )
% 2.80/1.52 = ( hd @ A @ List2 ) )
% 2.80/1.52 & ( ( tl @ A @ List )
% 2.80/1.52 = ( tl @ A @ List2 ) ) ) ) )
% 2.80/1.52 => ( List = List2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_99_not__hd__in__tl,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( X
% 2.80/1.52 != ( hd @ A @ Xs ) )
% 2.80/1.52 => ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_100_butlast__eq__cons__conv,axiom,
% 2.80/1.52 ! [A: $tType,L: list @ A,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( ( butlast @ A @ L )
% 2.80/1.52 = ( cons @ A @ X @ Xs ) )
% 2.80/1.52 = ( ? [Xl: A] :
% 2.80/1.52 ( L
% 2.80/1.52 = ( cons @ A @ X @ ( append @ A @ Xs @ ( cons @ A @ Xl @ ( nil @ A ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_101_butlast__eq__consE,axiom,
% 2.80/1.52 ! [A: $tType,L: list @ A,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( ( butlast @ A @ L )
% 2.80/1.52 = ( cons @ A @ X @ Xs ) )
% 2.80/1.52 => ~ ! [Xl2: A] :
% 2.80/1.52 ( L
% 2.80/1.52 != ( cons @ A @ X @ ( append @ A @ Xs @ ( cons @ A @ Xl2 @ ( nil @ A ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_102_list_Oexhaust__sel,axiom,
% 2.80/1.52 ! [A: $tType,List: list @ A] :
% 2.80/1.52 ( ( List
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( List
% 2.80/1.52 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_103_not__Cons__self2,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( cons @ A @ X @ Xs )
% 2.80/1.52 != Xs ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_104_list__tail__coinc,axiom,
% 2.80/1.52 ! [A: $tType,N1: A,R1: list @ A,N22: A,R2: list @ A] :
% 2.80/1.52 ( ( ( cons @ A @ N1 @ R1 )
% 2.80/1.52 = ( cons @ A @ N22 @ R2 ) )
% 2.80/1.52 => ( ( N1 = N22 )
% 2.80/1.52 & ( R1 = R2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_105_append__eq__append__conv2,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.80/1.52 = ( append @ A @ Zs @ Ts ) )
% 2.80/1.52 = ( ? [Us: list @ A] :
% 2.80/1.52 ( ( ( Xs
% 2.80/1.52 = ( append @ A @ Zs @ Us ) )
% 2.80/1.52 & ( ( append @ A @ Us @ Ys )
% 2.80/1.52 = Ts ) )
% 2.80/1.52 | ( ( ( append @ A @ Xs @ Us )
% 2.80/1.52 = Zs )
% 2.80/1.52 & ( Ys
% 2.80/1.52 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_106_append__eq__appendI,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us2: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Xs @ Xs1 )
% 2.80/1.52 = Zs )
% 2.80/1.52 => ( ( Ys
% 2.80/1.52 = ( append @ A @ Xs1 @ Us2 ) )
% 2.80/1.52 => ( ( append @ A @ Xs @ Ys )
% 2.80/1.52 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_107_list_Odistinct_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,X21: A,X22: list @ A] :
% 2.80/1.52 ( ( nil @ A )
% 2.80/1.52 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_108_neq__NilE,axiom,
% 2.80/1.52 ! [A: $tType,L: list @ A] :
% 2.80/1.52 ( ( L
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ~ ! [X4: A,Xs2: list @ A] :
% 2.80/1.52 ( L
% 2.80/1.52 != ( cons @ A @ X4 @ Xs2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_109_list_OdiscI,axiom,
% 2.80/1.52 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.80/1.52 ( ( List
% 2.80/1.52 = ( cons @ A @ X21 @ X22 ) )
% 2.80/1.52 => ( List
% 2.80/1.52 != ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_110_revg_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.80/1.52 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.80/1.52 => ( ! [A4: A,As: list @ A,B3: list @ A] :
% 2.80/1.52 ( ( P @ As @ ( cons @ A @ A4 @ B3 ) )
% 2.80/1.52 => ( P @ ( cons @ A @ A4 @ As ) @ B3 ) )
% 2.80/1.52 => ( P @ A0 @ A1 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_111_zipf_Oinduct,axiom,
% 2.80/1.52 ! [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] :
% 2.80/1.52 ( ! [F2: A > B > C2] : ( P @ F2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [F2: A > B > C2,A4: A,As: list @ A,B3: B,Bs: list @ B] :
% 2.80/1.52 ( ( P @ F2 @ As @ Bs )
% 2.80/1.52 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B @ B3 @ Bs ) ) )
% 2.80/1.52 => ( ! [A4: A > B > C2,V: A,Va: list @ A] : ( P @ A4 @ ( cons @ A @ V @ Va ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [A4: A > B > C2,V: B,Va: list @ B] : ( P @ A4 @ ( nil @ A ) @ ( cons @ B @ V @ Va ) )
% 2.80/1.52 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_112_list_Oexhaust,axiom,
% 2.80/1.52 ! [A: $tType,Y: list @ A] :
% 2.80/1.52 ( ( Y
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ~ ! [X212: A,X222: list @ A] :
% 2.80/1.52 ( Y
% 2.80/1.52 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_113_list_Oinducts,axiom,
% 2.80/1.52 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.80/1.52 ( ( P @ ( nil @ A ) )
% 2.80/1.52 => ( ! [X1: A,X23: list @ A] :
% 2.80/1.52 ( ( P @ X23 )
% 2.80/1.52 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 2.80/1.52 => ( P @ List ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_114_neq__Nil__conv,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 = ( ? [Y2: A,Ys2: list @ A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( cons @ A @ Y2 @ Ys2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_115_list__induct2_H,axiom,
% 2.80/1.52 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.80/1.52 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 2.80/1.52 ( ( P @ Xs2 @ Ys3 )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
% 2.80/1.52 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_116_splice_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.80/1.52 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.80/1.52 ( ( P @ Ys3 @ Xs2 )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 ) )
% 2.80/1.52 => ( P @ A0 @ A1 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_117_induct__list012,axiom,
% 2.80/1.52 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.80/1.52 ( ( P @ ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.80/1.52 => ( ! [X4: A,Y3: A,Zs2: list @ A] :
% 2.80/1.52 ( ( P @ Zs2 )
% 2.80/1.52 => ( ( P @ ( cons @ A @ Y3 @ Zs2 ) )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs2 ) ) ) ) )
% 2.80/1.52 => ( P @ Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_118_min__list_Ocases,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( ord @ A )
% 2.80/1.52 => ! [X: list @ A] :
% 2.80/1.52 ( ! [X4: A,Xs2: list @ A] :
% 2.80/1.52 ( X
% 2.80/1.52 != ( cons @ A @ X4 @ Xs2 ) )
% 2.80/1.52 => ( X
% 2.80/1.52 = ( nil @ A ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_119_min__list_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( ord @ A )
% 2.80/1.52 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.80/1.52 ( ! [X4: A,Xs2: list @ A] :
% 2.80/1.52 ( ! [X213: A,X223: list @ A] :
% 2.80/1.52 ( ( Xs2
% 2.80/1.52 = ( cons @ A @ X213 @ X223 ) )
% 2.80/1.52 => ( P @ Xs2 ) )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 2.80/1.52 => ( ( P @ ( nil @ A ) )
% 2.80/1.52 => ( P @ A0 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_120_shuffles_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.80/1.52 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.80/1.52 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 2.80/1.52 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
% 2.80/1.52 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 2.80/1.52 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_121_list__2pre__induct,axiom,
% 2.80/1.52 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,W1: list @ A,W2: list @ B] :
% 2.80/1.52 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [E4: A,W12: list @ A,W22: list @ B] :
% 2.80/1.52 ( ( P @ W12 @ W22 )
% 2.80/1.52 => ( P @ ( cons @ A @ E4 @ W12 ) @ W22 ) )
% 2.80/1.52 => ( ! [E4: B,W13: list @ A,W23: list @ B] :
% 2.80/1.52 ( ( P @ W13 @ W23 )
% 2.80/1.52 => ( P @ W13 @ ( cons @ B @ E4 @ W23 ) ) )
% 2.80/1.52 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_122_remdups__adj_Ocases,axiom,
% 2.80/1.52 ! [A: $tType,X: list @ A] :
% 2.80/1.52 ( ( X
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A] :
% 2.80/1.52 ( X
% 2.80/1.52 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.80/1.52 => ~ ! [X4: A,Y3: A,Xs2: list @ A] :
% 2.80/1.52 ( X
% 2.80/1.52 != ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_123_sorted__wrt_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.80/1.52 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 2.80/1.52 => ( ! [P2: A > A > $o,X4: A,Ys3: list @ A] :
% 2.80/1.52 ( ( P @ P2 @ Ys3 )
% 2.80/1.52 => ( P @ P2 @ ( cons @ A @ X4 @ Ys3 ) ) )
% 2.80/1.52 => ( P @ A0 @ A1 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_124_remdups__adj_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.80/1.52 ( ( P @ ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.80/1.52 => ( ! [X4: A,Y3: A,Xs2: list @ A] :
% 2.80/1.52 ( ( ( X4 = Y3 )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 2.80/1.52 => ( ( ( X4 != Y3 )
% 2.80/1.52 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 2.80/1.52 => ( P @ A0 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_125_list__induct__first2,axiom,
% 2.80/1.52 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.80/1.52 ( ( P @ ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.80/1.52 => ( ! [X1: A,X23: A,Xs2: list @ A] :
% 2.80/1.52 ( ( P @ Xs2 )
% 2.80/1.52 => ( P @ ( cons @ A @ X1 @ ( cons @ A @ X23 @ Xs2 ) ) ) )
% 2.80/1.52 => ( P @ Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_126_arg__min__list_Oinduct,axiom,
% 2.80/1.52 ! [B: $tType,A: $tType] :
% 2.80/1.52 ( ( linorder @ B )
% 2.80/1.52 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 2.80/1.52 ( ! [F2: A > B,X4: A] : ( P @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.80/1.52 => ( ! [F2: A > B,X4: A,Y3: A,Zs2: list @ A] :
% 2.80/1.52 ( ( P @ F2 @ ( cons @ A @ Y3 @ Zs2 ) )
% 2.80/1.52 => ( P @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs2 ) ) ) )
% 2.80/1.52 => ( ! [A4: A > B] : ( P @ A4 @ ( nil @ A ) )
% 2.80/1.52 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_127_successively_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.80/1.52 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 2.80/1.52 => ( ! [P2: A > A > $o,X4: A] : ( P @ P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.80/1.52 => ( ! [P2: A > A > $o,X4: A,Y3: A,Xs2: list @ A] :
% 2.80/1.52 ( ( P @ P2 @ ( cons @ A @ Y3 @ Xs2 ) )
% 2.80/1.52 => ( P @ P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 2.80/1.52 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_128_list__all__zip_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,B: $tType,P: ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > $o,A1: list @ A,A22: list @ B] :
% 2.80/1.52 ( ! [P2: A > B > $o] : ( P @ P2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [P2: A > B > $o,A4: A,As: list @ A,B3: B,Bs: list @ B] :
% 2.80/1.52 ( ( P @ P2 @ As @ Bs )
% 2.80/1.52 => ( P @ P2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B @ B3 @ Bs ) ) )
% 2.80/1.52 => ( ! [P2: A > B > $o,V: A,Va: list @ A] : ( P @ P2 @ ( cons @ A @ V @ Va ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [P2: A > B > $o,V: B,Va: list @ B] : ( P @ P2 @ ( nil @ A ) @ ( cons @ B @ V @ Va ) )
% 2.80/1.52 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_129_list__nonempty__induct,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A] :
% 2.80/1.52 ( ( Xs2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( P @ Xs2 )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 2.80/1.52 => ( P @ Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_130_map__tailrec__rev_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.80/1.52 ( ! [F2: A > B,X_1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 2.80/1.52 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.80/1.52 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 2.80/1.52 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.80/1.52 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_131_mergesort__by__rel__merge_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.80/1.52 ( ! [R: A > A > $o,X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 2.80/1.52 ( ( ( R @ X4 @ Y3 )
% 2.80/1.52 => ( P @ R @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 2.80/1.52 => ( ( ~ ( R @ X4 @ Y3 )
% 2.80/1.52 => ( P @ R @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 ) )
% 2.80/1.52 => ( P @ R @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 2.80/1.52 => ( ! [R: A > A > $o,Xs2: list @ A] : ( P @ R @ Xs2 @ ( nil @ A ) )
% 2.80/1.52 => ( ! [R: A > A > $o,V: A,Va: list @ A] : ( P @ R @ ( nil @ A ) @ ( cons @ A @ V @ Va ) )
% 2.80/1.52 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_132_mergesort__by__rel__merge__induct,axiom,
% 2.80/1.52 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,R3: A > B > $o,Xs: list @ A,Ys: list @ B] :
% 2.80/1.52 ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ B ) )
% 2.80/1.52 => ( ! [X_1: list @ B] : ( P @ ( nil @ A ) @ X_1 )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 2.80/1.52 ( ( R3 @ X4 @ Y3 )
% 2.80/1.52 => ( ( P @ Xs2 @ ( cons @ B @ Y3 @ Ys3 ) )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 2.80/1.52 ( ~ ( R3 @ X4 @ Y3 )
% 2.80/1.52 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) )
% 2.80/1.52 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_133_strict__sorted_Oinduct,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( linorder @ A )
% 2.80/1.52 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.80/1.52 ( ( P @ ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A,Ys3: list @ A] :
% 2.80/1.52 ( ( P @ Ys3 )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ Ys3 ) ) )
% 2.80/1.52 => ( P @ A0 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_134_transpose_Ocases,axiom,
% 2.80/1.52 ! [A: $tType,X: list @ ( list @ A )] :
% 2.80/1.52 ( ( X
% 2.80/1.52 != ( nil @ ( list @ A ) ) )
% 2.80/1.52 => ( ! [Xss: list @ ( list @ A )] :
% 2.80/1.52 ( X
% 2.80/1.52 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.80/1.52 => ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.80/1.52 ( X
% 2.80/1.52 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_135_list_Oset__intros_I2_J,axiom,
% 2.80/1.52 ! [A: $tType,Y: A,X22: list @ A,X21: A] :
% 2.80/1.52 ( ( member @ A @ Y @ ( set2 @ A @ X22 ) )
% 2.80/1.52 => ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_136_list_Oset__intros_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,X21: A,X22: list @ A] : ( member @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_137_set__ConsD,axiom,
% 2.80/1.52 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 2.80/1.52 => ( ( Y = X )
% 2.80/1.52 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_138_list_Oset__cases,axiom,
% 2.80/1.52 ! [A: $tType,E3: A,A2: list @ A] :
% 2.80/1.52 ( ( member @ A @ E3 @ ( set2 @ A @ A2 ) )
% 2.80/1.52 => ( ! [Z2: list @ A] :
% 2.80/1.52 ( A2
% 2.80/1.52 != ( cons @ A @ E3 @ Z2 ) )
% 2.80/1.52 => ~ ! [Z1: A,Z2: list @ A] :
% 2.80/1.52 ( ( A2
% 2.80/1.52 = ( cons @ A @ Z1 @ Z2 ) )
% 2.80/1.52 => ~ ( member @ A @ E3 @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_139_Cons__eq__appendI,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( ( cons @ A @ X @ Xs1 )
% 2.80/1.52 = Ys )
% 2.80/1.52 => ( ( Xs
% 2.80/1.52 = ( append @ A @ Xs1 @ Zs ) )
% 2.80/1.52 => ( ( cons @ A @ X @ Xs )
% 2.80/1.52 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_140_append__Cons,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.80/1.52 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_141_list__match__lel__lel,axiom,
% 2.80/1.52 ! [A: $tType,C1: list @ A,Qs: A,C22: list @ A,C12: list @ A,Qs2: A,C23: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ C1 @ ( cons @ A @ Qs @ C22 ) )
% 2.80/1.52 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C23 ) ) )
% 2.80/1.52 => ( ! [C21: list @ A] :
% 2.80/1.52 ( ( C1
% 2.80/1.52 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C21 ) ) )
% 2.80/1.52 => ( C23
% 2.80/1.52 != ( append @ A @ C21 @ ( cons @ A @ Qs @ C22 ) ) ) )
% 2.80/1.52 => ( ( ( C12 = C1 )
% 2.80/1.52 => ( ( Qs2 = Qs )
% 2.80/1.52 => ( C23 != C22 ) ) )
% 2.80/1.52 => ~ ! [C212: list @ A] :
% 2.80/1.52 ( ( C12
% 2.80/1.52 = ( append @ A @ C1 @ ( cons @ A @ Qs @ C212 ) ) )
% 2.80/1.52 => ( C22
% 2.80/1.52 != ( append @ A @ C212 @ ( cons @ A @ Qs2 @ C23 ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_142_append_Oleft__neutral,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] :
% 2.80/1.52 ( ( append @ A @ ( nil @ A ) @ A2 )
% 2.80/1.52 = A2 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_143_append__Nil,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A] :
% 2.80/1.52 ( ( append @ A @ ( nil @ A ) @ Ys )
% 2.80/1.52 = Ys ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_144_eq__Nil__appendI,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( Xs = Ys )
% 2.80/1.52 => ( Xs
% 2.80/1.52 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_145_list_Osel_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,X21: A,X22: list @ A] :
% 2.80/1.52 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 2.80/1.52 = X21 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_146_rev__induct,axiom,
% 2.80/1.52 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.80/1.52 ( ( P @ ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A] :
% 2.80/1.52 ( ( P @ Xs2 )
% 2.80/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 2.80/1.52 => ( P @ Xs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_147_rev__exhaust,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ~ ! [Ys3: list @ A,Y3: A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 != ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_148_neq__Nil__revE,axiom,
% 2.80/1.52 ! [A: $tType,L: list @ A] :
% 2.80/1.52 ( ( L
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ~ ! [Ll: list @ A,E4: A] :
% 2.80/1.52 ( L
% 2.80/1.52 != ( append @ A @ Ll @ ( cons @ A @ E4 @ ( nil @ A ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_149_rev__induct2_H,axiom,
% 2.80/1.52 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.80/1.52 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( nil @ B ) )
% 2.80/1.52 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 2.80/1.52 ( ( P @ Xs2 @ Ys3 )
% 2.80/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) ) )
% 2.80/1.52 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_150_neq__Nil__rev__conv,axiom,
% 2.80/1.52 ! [A: $tType,L: list @ A] :
% 2.80/1.52 ( ( L
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 = ( ? [Xs3: list @ A,X3: A] :
% 2.80/1.52 ( L
% 2.80/1.52 = ( append @ A @ Xs3 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_151_Cons__eq__append__conv,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( ( cons @ A @ X @ Xs )
% 2.80/1.52 = ( append @ A @ Ys @ Zs ) )
% 2.80/1.52 = ( ( ( Ys
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( ( cons @ A @ X @ Xs )
% 2.80/1.52 = Zs ) )
% 2.80/1.52 | ? [Ys4: list @ A] :
% 2.80/1.52 ( ( ( cons @ A @ X @ Ys4 )
% 2.80/1.52 = Ys )
% 2.80/1.52 & ( Xs
% 2.80/1.52 = ( append @ A @ Ys4 @ Zs ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_152_append__eq__Cons__conv,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Ys @ Zs )
% 2.80/1.52 = ( cons @ A @ X @ Xs ) )
% 2.80/1.52 = ( ( ( Ys
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 & ( Zs
% 2.80/1.52 = ( cons @ A @ X @ Xs ) ) )
% 2.80/1.52 | ? [Ys4: list @ A] :
% 2.80/1.52 ( ( Ys
% 2.80/1.52 = ( cons @ A @ X @ Ys4 ) )
% 2.80/1.52 & ( ( append @ A @ Ys4 @ Zs )
% 2.80/1.52 = Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_153_rev__nonempty__induct,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A] :
% 2.80/1.52 ( ( Xs2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( P @ Xs2 )
% 2.80/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 2.80/1.52 => ( P @ Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_154_rev__nonempty__induct2_H,axiom,
% 2.80/1.52 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( Ys
% 2.80/1.52 != ( nil @ B ) )
% 2.80/1.52 => ( ! [X4: A,Y3: B] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) @ ( cons @ B @ Y3 @ ( nil @ B ) ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: B] :
% 2.80/1.52 ( ( Xs2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) )
% 2.80/1.52 => ( ! [X4: A,Y3: B,Ys3: list @ B] :
% 2.80/1.52 ( ( Ys3
% 2.80/1.52 != ( nil @ B ) )
% 2.80/1.52 => ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 2.80/1.52 ( ( P @ Xs2 @ Ys3 )
% 2.80/1.52 => ( ( Xs2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( Ys3
% 2.80/1.52 != ( nil @ B ) )
% 2.80/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ B @ Ys3 @ ( cons @ B @ Y3 @ ( nil @ B ) ) ) ) ) ) )
% 2.80/1.52 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_155_list__Cons__eq__append__cases,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( ( cons @ A @ X @ Xs )
% 2.80/1.52 = ( append @ A @ Ys @ Zs ) )
% 2.80/1.52 => ( ( ( Ys
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 => ( Zs
% 2.80/1.52 != ( cons @ A @ X @ Xs ) ) )
% 2.80/1.52 => ~ ! [Ys5: list @ A] :
% 2.80/1.52 ( ( Ys
% 2.80/1.52 = ( cons @ A @ X @ Ys5 ) )
% 2.80/1.52 => ( ( append @ A @ Ys5 @ Zs )
% 2.80/1.52 != Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_156_list__append__eq__Cons__cases,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( ( append @ A @ Ys @ Zs )
% 2.80/1.52 = ( cons @ A @ X @ Xs ) )
% 2.80/1.52 => ( ( ( Ys
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 => ( Zs
% 2.80/1.52 != ( cons @ A @ X @ Xs ) ) )
% 2.80/1.52 => ~ ! [Ys5: list @ A] :
% 2.80/1.52 ( ( Ys
% 2.80/1.52 = ( cons @ A @ X @ Ys5 ) )
% 2.80/1.52 => ( ( append @ A @ Ys5 @ Zs )
% 2.80/1.52 != Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_157_split__list,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 => ? [Ys3: list @ A,Zs2: list @ A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_158_split__list__last,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 => ? [Ys3: list @ A,Zs2: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.80/1.52 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_159_split__list__prop,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.80/1.52 ( ? [X2: A] :
% 2.80/1.52 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 & ( P @ X2 ) )
% 2.80/1.52 => ? [Ys3: list @ A,X4: A] :
% 2.80/1.52 ( ? [Zs2: list @ A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.80/1.52 & ( P @ X4 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_160_xy__in__set__cases,axiom,
% 2.80/1.52 ! [A: $tType,X: A,L: list @ A,Y: A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ L ) )
% 2.80/1.52 => ( ( member @ A @ Y @ ( set2 @ A @ L ) )
% 2.80/1.52 => ( ( ( X = Y )
% 2.80/1.52 => ! [L12: list @ A,L22: list @ A] :
% 2.80/1.52 ( L
% 2.80/1.52 != ( append @ A @ L12 @ ( cons @ A @ Y @ L22 ) ) ) )
% 2.80/1.52 => ( ( ( X != Y )
% 2.80/1.52 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 2.80/1.52 ( L
% 2.80/1.52 != ( append @ A @ L12 @ ( cons @ A @ X @ ( append @ A @ L22 @ ( cons @ A @ Y @ L3 ) ) ) ) ) )
% 2.80/1.52 => ~ ( ( X != Y )
% 2.80/1.52 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 2.80/1.52 ( L
% 2.80/1.52 != ( append @ A @ L12 @ ( cons @ A @ Y @ ( append @ A @ L22 @ ( cons @ A @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_161_split__list__first,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 => ? [Ys3: list @ A,Zs2: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.80/1.52 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_162_split__list__propE,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.80/1.52 ( ? [X2: A] :
% 2.80/1.52 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 & ( P @ X2 ) )
% 2.80/1.52 => ~ ! [Ys3: list @ A,X4: A] :
% 2.80/1.52 ( ? [Zs2: list @ A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.80/1.52 => ~ ( P @ X4 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_163_append__Cons__eq__iff,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Xs4: list @ A,Ys6: list @ A] :
% 2.80/1.52 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 => ( ~ ( member @ A @ X @ ( set2 @ A @ Ys ) )
% 2.80/1.52 => ( ( ( append @ A @ Xs @ ( cons @ A @ X @ Ys ) )
% 2.80/1.52 = ( append @ A @ Xs4 @ ( cons @ A @ X @ Ys6 ) ) )
% 2.80/1.52 = ( ( Xs = Xs4 )
% 2.80/1.52 & ( Ys = Ys6 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_164_in__set__conv__decomp,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 = ( ? [Ys2: list @ A,Zs3: list @ A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_165_in__set__list__format,axiom,
% 2.80/1.52 ! [A: $tType,E3: A,L: list @ A] :
% 2.80/1.52 ( ( member @ A @ E3 @ ( set2 @ A @ L ) )
% 2.80/1.52 => ~ ! [L12: list @ A,L22: list @ A] :
% 2.80/1.52 ( L
% 2.80/1.52 != ( append @ A @ L12 @ ( cons @ A @ E3 @ L22 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_166_split__list__last__prop,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.80/1.52 ( ? [X2: A] :
% 2.80/1.52 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 & ( P @ X2 ) )
% 2.80/1.52 => ? [Ys3: list @ A,X4: A,Zs2: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.80/1.52 & ( P @ X4 )
% 2.80/1.52 & ! [Xa: A] :
% 2.80/1.52 ( ( member @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 2.80/1.52 => ~ ( P @ Xa ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_167_split__list__first__prop,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.80/1.52 ( ? [X2: A] :
% 2.80/1.52 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 & ( P @ X2 ) )
% 2.80/1.52 => ? [Ys3: list @ A,X4: A] :
% 2.80/1.52 ( ? [Zs2: list @ A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.80/1.52 & ( P @ X4 )
% 2.80/1.52 & ! [Xa: A] :
% 2.80/1.52 ( ( member @ A @ Xa @ ( set2 @ A @ Ys3 ) )
% 2.80/1.52 => ~ ( P @ Xa ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_168_split__list__last__propE,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.80/1.52 ( ? [X2: A] :
% 2.80/1.52 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 & ( P @ X2 ) )
% 2.80/1.52 => ~ ! [Ys3: list @ A,X4: A,Zs2: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.80/1.52 => ( ( P @ X4 )
% 2.80/1.52 => ~ ! [Xa: A] :
% 2.80/1.52 ( ( member @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 2.80/1.52 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_169_split__list__first__propE,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.80/1.52 ( ? [X2: A] :
% 2.80/1.52 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 & ( P @ X2 ) )
% 2.80/1.52 => ~ ! [Ys3: list @ A,X4: A] :
% 2.80/1.52 ( ? [Zs2: list @ A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( append @ A @ Ys3 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.80/1.52 => ( ( P @ X4 )
% 2.80/1.52 => ~ ! [Xa: A] :
% 2.80/1.52 ( ( member @ A @ Xa @ ( set2 @ A @ Ys3 ) )
% 2.80/1.52 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_170_in__set__conv__decomp__last,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 = ( ? [Ys2: list @ A,Zs3: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.80/1.52 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_171_in__set__conv__decomp__first,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.52 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.80/1.52 = ( ? [Ys2: list @ A,Zs3: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.80/1.52 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_172_split__list__last__prop__iff,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.80/1.52 ( ( ? [X3: A] :
% 2.80/1.52 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 & ( P @ X3 ) ) )
% 2.80/1.52 = ( ? [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.80/1.52 & ( P @ X3 )
% 2.80/1.52 & ! [Y2: A] :
% 2.80/1.52 ( ( member @ A @ Y2 @ ( set2 @ A @ Zs3 ) )
% 2.80/1.52 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_173_split__list__first__prop__iff,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.80/1.52 ( ( ? [X3: A] :
% 2.80/1.52 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 & ( P @ X3 ) ) )
% 2.80/1.52 = ( ? [Ys2: list @ A,X3: A] :
% 2.80/1.52 ( ? [Zs3: list @ A] :
% 2.80/1.52 ( Xs
% 2.80/1.52 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.80/1.52 & ( P @ X3 )
% 2.80/1.52 & ! [Y2: A] :
% 2.80/1.52 ( ( member @ A @ Y2 @ ( set2 @ A @ Ys2 ) )
% 2.80/1.52 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_174_hd__in__set,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( member @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ Xs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_175_list_Oset__sel_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] :
% 2.80/1.52 ( ( A2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( member @ A @ ( hd @ A @ A2 ) @ ( set2 @ A @ A2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_176_longest__common__prefix,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ? [Ps: list @ A,Xs5: list @ A,Ys5: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Ps @ Xs5 ) )
% 2.80/1.52 & ( Ys
% 2.80/1.52 = ( append @ A @ Ps @ Ys5 ) )
% 2.80/1.52 & ( ( Xs5
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 | ( Ys5
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 | ( ( hd @ A @ Xs5 )
% 2.80/1.52 != ( hd @ A @ Ys5 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_177_hd__append,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( ( Xs
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( hd @ A @ Ys ) ) )
% 2.80/1.52 & ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.80/1.52 = ( hd @ A @ Xs ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_178__092_060open_062old_OpathsConverge_Ag_Am_Ams_H_An_A_Ins_A_064_Atl_Ari_J_Ai_092_060close_062,axiom,
% 2.80/1.52 graph_pathsConverge @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ n @ ( append @ node @ ns @ ( tl @ node @ ri ) ) @ i ).
% 2.80/1.52
% 2.80/1.52 thf(fact_179__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.80/1.52 ~ ! [I: node,Ri: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 2.80/1.52 => ( ( member @ node @ I @ ( set2 @ node @ ms ) )
% 2.80/1.52 => ( ! [X2: node] :
% 2.80/1.52 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ Ri ) ) )
% 2.80/1.52 => ~ ( member @ node @ X2 @ ( set2 @ node @ ms ) ) )
% 2.80/1.52 => ~ ( prefix @ node @ Ri @ rs2 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_180__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.80/1.52 ~ ! [Ms2: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 2.80/1.52 => ( ( prefix @ node @ Ms2 @ ms )
% 2.80/1.52 => ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ Ms2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_181_old_Opath2__simple__loop,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,N2: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ N )
% 2.80/1.52 => ( ( member @ node @ N2 @ ( set2 @ node @ Ns ) )
% 2.80/1.52 => ~ ! [Ns4: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns4 @ N )
% 2.80/1.52 => ( ( member @ node @ N2 @ ( set2 @ node @ Ns4 ) )
% 2.80/1.52 => ( ~ ( member @ node @ N @ ( set2 @ node @ ( tl @ node @ ( butlast @ node @ Ns4 ) ) ) )
% 2.80/1.52 => ~ ( ord_less_eq @ ( set @ node ) @ ( set2 @ node @ Ns4 ) @ ( set2 @ node @ Ns ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_182_old_Opath_Ocases,axiom,
% 2.80/1.52 ! [G2: g,A2: list @ node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ A2 )
% 2.80/1.52 => ( ! [N4: node] :
% 2.80/1.52 ( ( A2
% 2.80/1.52 = ( cons @ node @ N4 @ ( nil @ node ) ) )
% 2.80/1.52 => ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.80/1.52 => ~ ( invar @ G2 ) ) )
% 2.80/1.52 => ~ ! [Ns3: list @ node,N3: node] :
% 2.80/1.52 ( ( A2
% 2.80/1.52 = ( cons @ node @ N3 @ Ns3 ) )
% 2.80/1.52 => ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns3 )
% 2.80/1.52 => ~ ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns3 ) ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_183_old_Opath_Oinducts,axiom,
% 2.80/1.52 ! [G2: g,X: list @ node,P: ( list @ node ) > $o] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X )
% 2.80/1.52 => ( ! [N4: node] :
% 2.80/1.52 ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.80/1.52 => ( ( invar @ G2 )
% 2.80/1.52 => ( P @ ( cons @ node @ N4 @ ( nil @ node ) ) ) ) )
% 2.80/1.52 => ( ! [Ns3: list @ node,N3: node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns3 )
% 2.80/1.52 => ( ( P @ Ns3 )
% 2.80/1.52 => ( ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns3 ) ) ) )
% 2.80/1.52 => ( P @ ( cons @ node @ N3 @ Ns3 ) ) ) ) )
% 2.80/1.52 => ( P @ X ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_184_old_Opath_Osimps,axiom,
% 2.80/1.52 ! [G2: g,A2: list @ node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ A2 )
% 2.80/1.52 = ( ? [N5: node] :
% 2.80/1.52 ( ( A2
% 2.80/1.52 = ( cons @ node @ N5 @ ( nil @ node ) ) )
% 2.80/1.52 & ( member @ node @ N5 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.80/1.52 & ( invar @ G2 ) )
% 2.80/1.52 | ? [Ns5: list @ node,N6: node] :
% 2.80/1.52 ( ( A2
% 2.80/1.52 = ( cons @ node @ N6 @ Ns5 ) )
% 2.80/1.52 & ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns5 )
% 2.80/1.52 & ( member @ node @ N6 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns5 ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_185_old_Opath__snoc,axiom,
% 2.80/1.52 ! [G2: g,Ns: list @ node,N: node,M: node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ N @ ( nil @ node ) ) ) )
% 2.80/1.52 => ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M ) ) )
% 2.80/1.52 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ N @ ( cons @ node @ M @ ( nil @ node ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_186_ri__rs_H__prefix,axiom,
% 2.80/1.52 prefix @ node @ ri @ rs ).
% 2.80/1.52
% 2.80/1.52 thf(fact_187_old_Opath__not__Nil,axiom,
% 2.80/1.52 ! [G2: g,Ns: list @ node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 2.80/1.52 => ( Ns
% 2.80/1.52 != ( nil @ node ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_188_old_Opath__hd,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ Ns ) )
% 2.80/1.52 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_189_old_Opath__split_I2_J,axiom,
% 2.80/1.52 ! [G2: g,Ns: list @ node,M: node,Ns2: list @ node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ Ns2 ) ) )
% 2.80/1.52 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ M @ Ns2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_190_old_Oempty__path,axiom,
% 2.80/1.52 ! [N: node,G2: g] :
% 2.80/1.52 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.80/1.52 => ( ( invar @ G2 )
% 2.80/1.52 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_191_old_Opath__split_I1_J,axiom,
% 2.80/1.52 ! [G2: g,Ns: list @ node,M: node,Ns2: list @ node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ Ns2 ) ) )
% 2.80/1.52 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ ( nil @ node ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_192_old_Opath2__split__first__prop,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ? [X2: node] :
% 2.80/1.52 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 2.80/1.52 & ( P @ X2 ) )
% 2.80/1.52 => ~ ! [M2: node,Ns4: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns4 @ M2 )
% 2.80/1.52 => ( ( P @ M2 )
% 2.80/1.52 => ( ! [X2: node] :
% 2.80/1.52 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ Ns4 ) ) )
% 2.80/1.52 => ~ ( P @ X2 ) )
% 2.80/1.52 => ~ ( prefix @ node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_193_old_Opath2__prefix__ex,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,M4: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( member @ node @ M4 @ ( set2 @ node @ Ns ) )
% 2.80/1.52 => ~ ! [Ns4: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns4 @ M4 )
% 2.80/1.52 => ( ( prefix @ node @ Ns4 @ Ns )
% 2.80/1.52 => ( member @ node @ M4 @ ( set2 @ node @ ( butlast @ node @ Ns4 ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_194_old_OCons__path,axiom,
% 2.80/1.52 ! [G2: g,Ns: list @ node,N2: node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 2.80/1.52 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns ) ) ) )
% 2.80/1.52 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ns ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_195_old_Opath2__prefix,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,Ns2: list @ node,M4: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( prefix @ node @ ( append @ node @ Ns2 @ ( cons @ node @ M4 @ ( nil @ node ) ) ) @ Ns )
% 2.80/1.52 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns2 @ ( cons @ node @ M4 @ ( nil @ node ) ) ) @ M4 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_196_old_Opath__invar,axiom,
% 2.80/1.52 ! [G2: g,Ns: list @ node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 2.80/1.52 => ( invar @ G2 ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_197_old_Opath__in___092_060alpha_062n,axiom,
% 2.80/1.52 ! [G2: g,Ns: list @ node,N: node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 2.80/1.52 => ( ( member @ node @ N @ ( set2 @ node @ Ns ) )
% 2.80/1.52 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_198_old_Opath__by__tail,axiom,
% 2.80/1.52 ! [G2: g,N: node,N2: node,Ns: list @ node,Ms: list @ node] :
% 2.80/1.52 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( cons @ node @ N2 @ Ns ) ) )
% 2.80/1.52 => ( ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ns ) )
% 2.80/1.52 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ms ) ) )
% 2.80/1.52 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( cons @ node @ N2 @ Ms ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_199_subset__Collect__conv,axiom,
% 2.80/1.52 ! [A: $tType,S: set @ A,P: A > $o] :
% 2.80/1.52 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 2.80/1.52 = ( ! [X3: A] :
% 2.80/1.52 ( ( member @ A @ X3 @ S )
% 2.80/1.52 => ( P @ X3 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_200_ord__eq__le__eq__trans,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( ord @ A )
% 2.80/1.52 => ! [A2: A,B2: A,C: A,D: A] :
% 2.80/1.52 ( ( A2 = B2 )
% 2.80/1.52 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.80/1.52 => ( ( C = D )
% 2.80/1.52 => ( ord_less_eq @ A @ A2 @ D ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_201_subset__code_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,B4: set @ A] :
% 2.80/1.52 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ B4 )
% 2.80/1.52 = ( ! [X3: A] :
% 2.80/1.52 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.80/1.52 => ( member @ A @ X3 @ B4 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_202_set__subset__Cons,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,X: A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_203_tl__subset,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,A3: set @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A3 )
% 2.80/1.52 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( tl @ A @ Xs ) ) @ A3 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_204_butlast__subset,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,A3: set @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A3 )
% 2.80/1.52 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( butlast @ A @ Xs ) ) @ A3 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_205_prefix__snoc,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 2.80/1.52 ( ( prefix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.80/1.52 = ( ( Xs
% 2.80/1.52 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.80/1.52 | ( prefix @ A @ Xs @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_206_old_Opath2__split__first__last,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 2.80/1.52 => ~ ! [Ns_1: list @ node,Ns_3: list @ node,Ns_2: list @ node] :
% 2.80/1.52 ( ( Ns
% 2.80/1.52 = ( append @ node @ Ns_1 @ ( append @ node @ Ns_3 @ Ns_2 ) ) )
% 2.80/1.52 => ( ( prefix @ node @ ( append @ node @ Ns_1 @ ( cons @ node @ X @ ( nil @ node ) ) ) @ Ns )
% 2.80/1.52 => ( ( suffix @ node @ ( cons @ node @ X @ Ns_2 ) @ Ns )
% 2.80/1.52 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns_1 @ ( cons @ node @ X @ ( nil @ node ) ) ) @ X )
% 2.80/1.52 => ( ~ ( member @ node @ X @ ( set2 @ node @ Ns_1 ) )
% 2.80/1.52 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_3 @ X )
% 2.80/1.52 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ ( cons @ node @ X @ Ns_2 ) @ M )
% 2.80/1.52 => ( member @ node @ X @ ( set2 @ node @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_207_same__prefix__nil,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( prefix @ A @ ( append @ A @ Xs @ Ys ) @ Xs )
% 2.80/1.52 = ( Ys
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_208_prefix__order_Odual__order_Orefl,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] : ( prefix @ A @ A2 @ A2 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_209_prefix__order_Oorder__refl,axiom,
% 2.80/1.52 ! [A: $tType,X: list @ A] : ( prefix @ A @ X @ X ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_210_suffix__order_Odual__order_Orefl,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] : ( suffix @ A @ A2 @ A2 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_211_suffix__order_Oorder__refl,axiom,
% 2.80/1.52 ! [A: $tType,X: list @ A] : ( suffix @ A @ X @ X ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_212_Cons__prefix__Cons,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.80/1.52 ( ( prefix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.80/1.52 = ( ( X = Y )
% 2.80/1.52 & ( prefix @ A @ Xs @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_213_prefix__code_I1_J,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] : ( prefix @ A @ ( nil @ A ) @ Xs ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_214_prefix__Nil,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( prefix @ A @ Xs @ ( nil @ A ) )
% 2.80/1.52 = ( Xs
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_215_prefix__bot_Obot_Oextremum__unique,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] :
% 2.80/1.52 ( ( prefix @ A @ A2 @ ( nil @ A ) )
% 2.80/1.52 = ( A2
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_216_suffix__bot_Obot_Oextremum__unique,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 2.80/1.52 = ( A2
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_217_suffix__Nil,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ Xs @ ( nil @ A ) )
% 2.80/1.52 = ( Xs
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_218_same__prefix__prefix,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( prefix @ A @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs ) )
% 2.80/1.52 = ( prefix @ A @ Ys @ Zs ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_219_same__suffix__suffix,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ ( append @ A @ Zs @ Xs ) )
% 2.80/1.52 = ( suffix @ A @ Ys @ Zs ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_220_old_Opath2__split__last__prop,axiom,
% 2.80/1.52 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.80/1.52 => ( ? [X2: node] :
% 2.80/1.52 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 2.80/1.52 & ( P @ X2 ) )
% 2.80/1.52 => ~ ! [N3: node,Ns4: list @ node] :
% 2.80/1.52 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N3 @ Ns4 @ M )
% 2.80/1.52 => ( ( P @ N3 )
% 2.80/1.52 => ( ! [X2: node] :
% 2.80/1.52 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ns4 ) ) )
% 2.80/1.52 => ~ ( P @ X2 ) )
% 2.80/1.52 => ~ ( suffix @ node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_221_same__suffix__nil,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ Xs )
% 2.80/1.52 = ( Ys
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_222_snoc__suffix__snoc,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.80/1.52 ( ( suffix @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.80/1.52 = ( ( X = Y )
% 2.80/1.52 & ( suffix @ A @ Xs @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_223_suffix__snoc,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 2.80/1.52 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.80/1.52 = ( ( Xs
% 2.80/1.52 = ( nil @ A ) )
% 2.80/1.52 | ? [Zs3: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Zs3 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.80/1.52 & ( suffix @ A @ Zs3 @ Ys ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_224_suffix__tl,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( tl @ A @ Xs ) @ Xs ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_225_suffix__Cons,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ Xs @ ( cons @ A @ Y @ Ys ) )
% 2.80/1.52 = ( ( Xs
% 2.80/1.52 = ( cons @ A @ Y @ Ys ) )
% 2.80/1.52 | ( suffix @ A @ Xs @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_226_suffix__ConsD,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.80/1.52 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_227_suffix__ConsI,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 2.80/1.52 ( ( suffix @ A @ Xs @ Ys )
% 2.80/1.52 => ( suffix @ A @ Xs @ ( cons @ A @ Y @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_228_suffix__ConsD2,axiom,
% 2.80/1.52 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.80/1.52 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_229_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 2.80/1.52 => ( A2
% 2.80/1.52 = ( nil @ A ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_230_suffix__bot_Obot_Oextremum,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A] : ( suffix @ A @ ( nil @ A ) @ A2 ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_231_Nil__suffix,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( nil @ A ) @ Xs ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_232_set__mono__suffix,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ Xs @ Ys )
% 2.80/1.52 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_233_not__suffix__cases,axiom,
% 2.80/1.52 ! [A: $tType,Ps2: list @ A,Ls: list @ A] :
% 2.80/1.52 ( ~ ( suffix @ A @ Ps2 @ Ls )
% 2.80/1.52 => ( ( ( Ps2
% 2.80/1.52 != ( nil @ A ) )
% 2.80/1.52 => ( Ls
% 2.80/1.52 != ( nil @ A ) ) )
% 2.80/1.52 => ( ! [A4: A,As: list @ A] :
% 2.80/1.52 ( ( Ps2
% 2.80/1.52 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 2.80/1.52 => ! [X4: A,Xs2: list @ A] :
% 2.80/1.52 ( ( Ls
% 2.80/1.52 = ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 2.80/1.52 => ( ( X4 = A4 )
% 2.80/1.52 => ( suffix @ A @ As @ Xs2 ) ) ) )
% 2.80/1.52 => ~ ! [A4: A] :
% 2.80/1.52 ( ? [As: list @ A] :
% 2.80/1.52 ( Ps2
% 2.80/1.52 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 2.80/1.52 => ! [X4: A] :
% 2.80/1.52 ( ? [Xs2: list @ A] :
% 2.80/1.52 ( Ls
% 2.80/1.52 = ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 2.80/1.52 => ( X4 = A4 ) ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_234_not__suffix__induct,axiom,
% 2.80/1.52 ! [A: $tType,Ps2: list @ A,Ls: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.80/1.52 ( ~ ( suffix @ A @ Ps2 @ Ls )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( nil @ A ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 2.80/1.52 ( ( X4 != Y3 )
% 2.80/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) )
% 2.80/1.52 => ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 2.80/1.52 ( ( X4 = Y3 )
% 2.80/1.52 => ( ~ ( suffix @ A @ Xs2 @ Ys3 )
% 2.80/1.52 => ( ( P @ Xs2 @ Ys3 )
% 2.80/1.52 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ) )
% 2.80/1.52 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_235_suffix__order_Odual__order_Oantisym,axiom,
% 2.80/1.52 ! [A: $tType,B2: list @ A,A2: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ B2 @ A2 )
% 2.80/1.52 => ( ( suffix @ A @ A2 @ B2 )
% 2.80/1.52 => ( A2 = B2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_236_suffix__order_Odual__order_Oeq__iff,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 2.80/1.52 = ( ^ [A5: list @ A,B5: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ B5 @ A5 )
% 2.80/1.52 & ( suffix @ A @ A5 @ B5 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_237_suffix__order_Odual__order_Otrans,axiom,
% 2.80/1.52 ! [A: $tType,B2: list @ A,A2: list @ A,C: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ B2 @ A2 )
% 2.80/1.52 => ( ( suffix @ A @ C @ B2 )
% 2.80/1.52 => ( suffix @ A @ C @ A2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_238_suffix__order_Oord__le__eq__trans,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ A2 @ B2 )
% 2.80/1.52 => ( ( B2 = C )
% 2.80/1.52 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_239_suffix__order_Oord__eq__le__trans,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.80/1.52 ( ( A2 = B2 )
% 2.80/1.52 => ( ( suffix @ A @ B2 @ C )
% 2.80/1.52 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_240_suffix__order_Oorder_Oantisym,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A,B2: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ A2 @ B2 )
% 2.80/1.52 => ( ( suffix @ A @ B2 @ A2 )
% 2.80/1.52 => ( A2 = B2 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_241_suffix__order_Oorder_Oeq__iff,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 2.80/1.52 = ( ^ [A5: list @ A,B5: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ A5 @ B5 )
% 2.80/1.52 & ( suffix @ A @ B5 @ A5 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_242_suffix__order_Oantisym__conv,axiom,
% 2.80/1.52 ! [A: $tType,Y: list @ A,X: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ Y @ X )
% 2.80/1.52 => ( ( suffix @ A @ X @ Y )
% 2.80/1.52 = ( X = Y ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_243_suffix__order_Oorder__trans,axiom,
% 2.80/1.52 ! [A: $tType,X: list @ A,Y: list @ A,Z3: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ X @ Y )
% 2.80/1.52 => ( ( suffix @ A @ Y @ Z3 )
% 2.80/1.52 => ( suffix @ A @ X @ Z3 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_244_suffix__order_Oorder_Otrans,axiom,
% 2.80/1.52 ! [A: $tType,A2: list @ A,B2: list @ A,C: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ A2 @ B2 )
% 2.80/1.52 => ( ( suffix @ A @ B2 @ C )
% 2.80/1.52 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_245_suffix__order_Oeq__refl,axiom,
% 2.80/1.52 ! [A: $tType,X: list @ A,Y: list @ A] :
% 2.80/1.52 ( ( X = Y )
% 2.80/1.52 => ( suffix @ A @ X @ Y ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_246_suffix__order_Oantisym,axiom,
% 2.80/1.52 ! [A: $tType,X: list @ A,Y: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ X @ Y )
% 2.80/1.52 => ( ( suffix @ A @ Y @ X )
% 2.80/1.52 => ( X = Y ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_247_suffix__order_Oeq__iff,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 2.80/1.52 = ( ^ [X3: list @ A,Y2: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ X3 @ Y2 )
% 2.80/1.52 & ( suffix @ A @ Y2 @ X3 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_248_suffix__same__cases,axiom,
% 2.80/1.52 ! [A: $tType,Xs_1: list @ A,Ys: list @ A,Xs_2: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ Xs_1 @ Ys )
% 2.80/1.52 => ( ( suffix @ A @ Xs_2 @ Ys )
% 2.80/1.52 => ( ( suffix @ A @ Xs_1 @ Xs_2 )
% 2.80/1.52 | ( suffix @ A @ Xs_2 @ Xs_1 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_249_suffixE,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ Xs @ Ys )
% 2.80/1.52 => ~ ! [Zs2: list @ A] :
% 2.80/1.52 ( Ys
% 2.80/1.52 != ( append @ A @ Zs2 @ Xs ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_250_suffixI,axiom,
% 2.80/1.52 ! [A: $tType,Ys: list @ A,Zs: list @ A,Xs: list @ A] :
% 2.80/1.52 ( ( Ys
% 2.80/1.52 = ( append @ A @ Zs @ Xs ) )
% 2.80/1.52 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_251_Sublist_Osuffix__def,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( suffix @ A )
% 2.80/1.52 = ( ^ [Xs3: list @ A,Ys2: list @ A] :
% 2.80/1.52 ? [Zs3: list @ A] :
% 2.80/1.52 ( Ys2
% 2.80/1.52 = ( append @ A @ Zs3 @ Xs3 ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_252_suffix__append,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ Zs ) )
% 2.80/1.52 = ( ( suffix @ A @ Xs @ Zs )
% 2.80/1.52 | ? [Xs6: list @ A] :
% 2.80/1.52 ( ( Xs
% 2.80/1.52 = ( append @ A @ Xs6 @ Zs ) )
% 2.80/1.52 & ( suffix @ A @ Xs6 @ Ys ) ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_253_suffix__appendD,axiom,
% 2.80/1.52 ! [A: $tType,Zs: list @ A,Xs: list @ A,Ys: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ ( append @ A @ Zs @ Xs ) @ Ys )
% 2.80/1.52 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(fact_254_suffix__appendI,axiom,
% 2.80/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.80/1.52 ( ( suffix @ A @ Xs @ Ys )
% 2.80/1.52 => ( suffix @ A @ Xs @ ( append @ A @ Zs @ Ys ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( linorder @ A )
% 2.80/1.52 => ( type @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 2.80/1.52 ! [A: $tType] :
% 2.80/1.52 ( ( linorder @ A )
% 2.80/1.52 => ( ord @ A ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(tcon_fun___Orderings_Oord,axiom,
% 2.80/1.52 ! [A6: $tType,A7: $tType] :
% 2.80/1.52 ( ( ord @ A7 )
% 2.80/1.52 => ( ord @ ( A6 > A7 ) ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(tcon_Set_Oset___Orderings_Oord_1,axiom,
% 2.80/1.52 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 2.80/1.52
% 2.80/1.52 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.80/1.52 linorder @ $o ).
% 2.80/1.52
% 2.80/1.52 thf(tcon_HOL_Obool___Orderings_Oord_2,axiom,
% 2.80/1.52 ord @ $o ).
% 2.80/1.52
% 2.80/1.52 thf(tfree_0,hypothesis,
% 2.80/1.52 linorder @ node ).
% 2.80/1.52
% 2.80/1.52 thf(tfree_1,hypothesis,
% 2.80/1.52 linorder @ val ).
% 2.80/1.52
% 2.80/1.52 thf(conj_0,conjecture,
% 2.80/1.52 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons @ node @ i @ rs_rest ) @ pred_phi_r ).
% 2.80/1.52 ------------------------
% 2.80/1.55 % (22862)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_22669 for (2999ds/4Mi)
% 2.80/1.55 % (22867)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/18Mi)
% 2.80/1.55 % (22866)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_22669 for (2999ds/275Mi)
% 2.80/1.55 % (22862)Instruction limit reached!
% 2.80/1.55 % (22862)------------------------------
% 2.80/1.55 % (22862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.55 % (22862)Termination reason: Unknown
% 2.80/1.55 % (22862)Termination phase: shuffling
% 2.80/1.55
% 2.80/1.55 % (22862)Memory used [KB]: 1535
% 2.80/1.55 % (22862)Time elapsed: 0.004 s
% 2.80/1.55 % (22862)Instructions burned: 6 (million)
% 2.80/1.55 % (22862)------------------------------
% 2.80/1.55 % (22862)------------------------------
% 2.80/1.55 % (22865)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_22669 for (2999ds/2Mi)
% 2.80/1.55 % (22863)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_22669 for (2999ds/27Mi)
% 2.80/1.55 % (22861)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/183Mi)
% 2.80/1.55 % (22867)Instruction limit reached!
% 2.80/1.55 % (22867)------------------------------
% 2.80/1.55 % (22867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.55 % (22867)Termination reason: Unknown
% 2.80/1.55 % (22867)Termination phase: shuffling
% 2.80/1.55
% 2.80/1.55 % (22867)Memory used [KB]: 1663
% 2.80/1.55 % (22867)Time elapsed: 0.008 s
% 2.80/1.55 % (22867)Instructions burned: 20 (million)
% 2.80/1.55 % (22867)------------------------------
% 2.80/1.55 % (22867)------------------------------
% 2.80/1.55 % (22865)Instruction limit reached!
% 2.80/1.55 % (22865)------------------------------
% 2.80/1.55 % (22865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.55 % (22865)Termination reason: Unknown
% 2.80/1.55 % (22865)Termination phase: shuffling
% 2.80/1.55
% 2.80/1.55 % (22865)Memory used [KB]: 1407
% 2.80/1.55 % (22865)Time elapsed: 0.003 s
% 2.80/1.55 % (22865)Instructions burned: 3 (million)
% 2.80/1.55 % (22865)------------------------------
% 2.80/1.55 % (22865)------------------------------
% 2.80/1.56 % (22868)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/3Mi)
% 2.80/1.56 % (22868)Instruction limit reached!
% 2.80/1.56 % (22868)------------------------------
% 2.80/1.56 % (22868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.56 % (22868)Termination reason: Unknown
% 2.80/1.56 % (22868)Termination phase: shuffling
% 2.80/1.56
% 2.80/1.56 % (22868)Memory used [KB]: 1407
% 2.80/1.56 % (22868)Time elapsed: 0.002 s
% 2.80/1.56 % (22868)Instructions burned: 3 (million)
% 2.80/1.56 % (22868)------------------------------
% 2.80/1.56 % (22868)------------------------------
% 2.80/1.56 % (22863)Instruction limit reached!
% 2.80/1.56 % (22863)------------------------------
% 2.80/1.56 % (22863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.56 % (22863)Termination reason: Unknown
% 2.80/1.56 % (22863)Termination phase: shuffling
% 2.80/1.56
% 2.80/1.56 % (22863)Memory used [KB]: 1791
% 2.80/1.56 % (22863)Time elapsed: 0.012 s
% 2.80/1.56 % (22863)Instructions burned: 29 (million)
% 2.80/1.56 % (22863)------------------------------
% 2.80/1.56 % (22863)------------------------------
% 2.80/1.56 % (22869)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_22669 for (2999ds/37Mi)
% 2.80/1.57 % (22864)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/2Mi)
% 2.80/1.57 % (22864)Instruction limit reached!
% 2.80/1.57 % (22864)------------------------------
% 2.80/1.57 % (22864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.57 % (22864)Termination reason: Unknown
% 2.80/1.57 % (22864)Termination phase: shuffling
% 2.80/1.57
% 2.80/1.57 % (22864)Memory used [KB]: 1407
% 2.80/1.57 % (22864)Time elapsed: 0.003 s
% 2.80/1.57 % (22864)Instructions burned: 3 (million)
% 2.80/1.57 % (22864)------------------------------
% 2.80/1.57 % (22864)------------------------------
% 2.80/1.57 % (22870)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_22669 for (2999ds/15Mi)
% 2.80/1.57 % (22871)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_22669 for (2999ds/3Mi)
% 2.80/1.57 % (22871)Instruction limit reached!
% 2.80/1.57 % (22871)------------------------------
% 2.80/1.57 % (22871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.57 % (22871)Termination reason: Unknown
% 2.80/1.57 % (22871)Termination phase: shuffling
% 2.80/1.57
% 2.80/1.57 % (22871)Memory used [KB]: 1407
% 2.80/1.57 % (22871)Time elapsed: 0.002 s
% 2.80/1.57 % (22871)Instructions burned: 3 (million)
% 2.80/1.57 % (22871)------------------------------
% 2.80/1.57 % (22871)------------------------------
% 2.80/1.58 % (22869)Instruction limit reached!
% 2.80/1.58 % (22869)------------------------------
% 2.80/1.58 % (22869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (22869)Termination reason: Unknown
% 2.80/1.58 % (22869)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.58 % (22869)Memory used [KB]: 2174
% 2.80/1.58 % (22869)Time elapsed: 0.012 s
% 2.80/1.58 % (22869)Instructions burned: 40 (million)
% 2.80/1.58 % (22869)------------------------------
% 2.80/1.58 % (22869)------------------------------
% 2.80/1.58 % (22870)Instruction limit reached!
% 2.80/1.58 % (22870)------------------------------
% 2.80/1.58 % (22870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (22870)Termination reason: Unknown
% 2.80/1.58 % (22870)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.58 % (22870)Memory used [KB]: 1535
% 2.80/1.58 % (22870)Time elapsed: 0.008 s
% 2.80/1.58 % (22870)Instructions burned: 16 (million)
% 2.80/1.58 % (22870)------------------------------
% 2.80/1.58 % (22870)------------------------------
% 2.80/1.58 % (22872)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_22669 for (2999ds/1041Mi)
% 2.80/1.58 % (22873)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/7Mi)
% 2.80/1.58 % (22874)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/16Mi)
% 2.80/1.58 % (22873)Instruction limit reached!
% 2.80/1.58 % (22873)------------------------------
% 2.80/1.58 % (22873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (22873)Termination reason: Unknown
% 2.80/1.58 % (22873)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.58 % (22873)Memory used [KB]: 1535
% 2.80/1.58 % (22873)Time elapsed: 0.004 s
% 2.80/1.58 % (22873)Instructions burned: 9 (million)
% 2.80/1.58 % (22873)------------------------------
% 2.80/1.58 % (22873)------------------------------
% 2.80/1.58 % (22875)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_22669 for (2999ds/3Mi)
% 2.80/1.58 % (22874)Instruction limit reached!
% 2.80/1.58 % (22874)------------------------------
% 2.80/1.58 % (22874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (22874)Termination reason: Unknown
% 2.80/1.58 % (22874)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.58 % (22874)Memory used [KB]: 1535
% 2.80/1.59 % (22874)Time elapsed: 0.006 s
% 2.80/1.59 % (22874)Instructions burned: 16 (million)
% 2.80/1.59 % (22874)------------------------------
% 2.80/1.59 % (22874)------------------------------
% 2.80/1.59 % (22875)Instruction limit reached!
% 2.80/1.59 % (22875)------------------------------
% 2.80/1.59 % (22875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.59 % (22875)Termination reason: Unknown
% 2.80/1.59 % (22875)Termination phase: shuffling
% 2.80/1.59
% 2.80/1.59 % (22875)Memory used [KB]: 1407
% 2.80/1.59 % (22875)Time elapsed: 0.002 s
% 2.80/1.59 % (22875)Instructions burned: 3 (million)
% 2.80/1.59 % (22875)------------------------------
% 2.80/1.59 % (22875)------------------------------
% 2.80/1.59 % (22876)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_22669 for (2999ds/3Mi)
% 2.80/1.59 % (22876)Instruction limit reached!
% 2.80/1.59 % (22876)------------------------------
% 2.80/1.59 % (22876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.59 % (22876)Termination reason: Unknown
% 2.80/1.59 % (22876)Termination phase: shuffling
% 2.80/1.59
% 2.80/1.59 % (22876)Memory used [KB]: 1407
% 2.80/1.59 % (22876)Time elapsed: 0.003 s
% 2.80/1.59 % (22876)Instructions burned: 4 (million)
% 2.80/1.59 % (22876)------------------------------
% 2.80/1.59 % (22876)------------------------------
% 2.80/1.59 % (22877)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/7Mi)
% 2.80/1.59 % (22878)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/3Mi)
% 2.80/1.59 % (22877)Instruction limit reached!
% 2.80/1.59 % (22877)------------------------------
% 2.80/1.59 % (22877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.59 % (22877)Termination reason: Unknown
% 2.80/1.59 % (22877)Termination phase: shuffling
% 2.80/1.59
% 2.80/1.59 % (22877)Memory used [KB]: 1535
% 2.80/1.59 % (22877)Time elapsed: 0.005 s
% 2.80/1.59 % (22877)Instructions burned: 9 (million)
% 2.80/1.59 % (22877)------------------------------
% 2.80/1.59 % (22877)------------------------------
% 2.80/1.59 % (22879)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/4Mi)
% 2.80/1.60 % (22878)Instruction limit reached!
% 2.80/1.60 % (22878)------------------------------
% 2.80/1.60 % (22878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.60 % (22878)Termination reason: Unknown
% 2.80/1.60 % (22878)Termination phase: shuffling
% 2.80/1.60
% 2.80/1.60 % (22878)Memory used [KB]: 1407
% 2.80/1.60 % (22878)Time elapsed: 0.002 s
% 2.80/1.60 % (22878)Instructions burned: 4 (million)
% 2.80/1.60 % (22878)------------------------------
% 2.80/1.60 % (22878)------------------------------
% 2.82/1.60 % (22879)Instruction limit reached!
% 2.82/1.60 % (22879)------------------------------
% 2.82/1.60 % (22879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.60 % (22879)Termination reason: Unknown
% 2.82/1.60 % (22879)Termination phase: shuffling
% 2.82/1.60
% 2.82/1.60 % (22879)Memory used [KB]: 1407
% 2.82/1.60 % (22879)Time elapsed: 0.003 s
% 2.82/1.60 % (22879)Instructions burned: 6 (million)
% 2.82/1.60 % (22879)------------------------------
% 2.82/1.60 % (22879)------------------------------
% 2.82/1.60 % (22880)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/18Mi)
% 2.82/1.60 % (22882)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/6Mi)
% 2.82/1.60 % (22881)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/710Mi)
% 2.82/1.61 % (22883)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_22669 for (2999ds/902Mi)
% 2.82/1.61 % (22866)Refutation not found, incomplete strategy
% 2.82/1.61 % (22866)------------------------------
% 2.82/1.61 % (22866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (22866)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.61
% 2.82/1.61
% 2.82/1.61 % (22866)Memory used [KB]: 7547
% 2.82/1.61 % (22866)Time elapsed: 0.058 s
% 2.82/1.61 % (22866)Instructions burned: 186 (million)
% 2.82/1.61 % (22866)------------------------------
% 2.82/1.61 % (22866)------------------------------
% 2.82/1.61 % (22882)Instruction limit reached!
% 2.82/1.61 % (22882)------------------------------
% 2.82/1.61 % (22882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (22882)Termination reason: Unknown
% 2.82/1.61 % (22882)Termination phase: shuffling
% 2.82/1.61
% 2.82/1.61 % (22882)Memory used [KB]: 1407
% 2.82/1.61 % (22882)Time elapsed: 0.003 s
% 2.82/1.61 % (22882)Instructions burned: 6 (million)
% 2.82/1.61 % (22882)------------------------------
% 2.82/1.61 % (22882)------------------------------
% 2.82/1.61 % (22880)Instruction limit reached!
% 2.82/1.61 % (22880)------------------------------
% 2.82/1.61 % (22880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (22880)Termination reason: Unknown
% 2.82/1.61 % (22880)Termination phase: shuffling
% 2.82/1.61
% 2.82/1.61 % (22880)Memory used [KB]: 1663
% 2.82/1.61 % (22880)Time elapsed: 0.009 s
% 2.82/1.61 % (22880)Instructions burned: 18 (million)
% 2.82/1.61 % (22880)------------------------------
% 2.82/1.61 % (22880)------------------------------
% 2.82/1.62 % (22884)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_22669 for (2999ds/21Mi)
% 2.82/1.62 % (22885)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/5Mi)
% 2.82/1.62 % (22861)Instruction limit reached!
% 2.82/1.62 % (22861)------------------------------
% 2.82/1.62 % (22861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (22861)Termination reason: Unknown
% 2.82/1.62 % (22861)Termination phase: Saturation
% 2.82/1.62
% 2.82/1.62 % (22861)Memory used [KB]: 7291
% 2.82/1.62 % (22861)Time elapsed: 0.066 s
% 2.82/1.62 % (22861)Instructions burned: 184 (million)
% 2.82/1.62 % (22861)------------------------------
% 2.82/1.62 % (22861)------------------------------
% 2.82/1.62 % (22885)Instruction limit reached!
% 2.82/1.62 % (22885)------------------------------
% 2.82/1.62 % (22885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (22885)Termination reason: Unknown
% 2.82/1.62 % (22885)Termination phase: shuffling
% 2.82/1.62
% 2.82/1.62 % (22885)Memory used [KB]: 1535
% 2.82/1.62 % (22885)Time elapsed: 0.003 s
% 2.82/1.62 % (22885)Instructions burned: 7 (million)
% 2.82/1.62 % (22885)------------------------------
% 2.82/1.62 % (22885)------------------------------
% 2.82/1.62 % (22886)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_22669 for (2999ds/6Mi)
% 2.82/1.62 % (22884)Instruction limit reached!
% 2.82/1.62 % (22884)------------------------------
% 2.82/1.62 % (22884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (22884)Termination reason: Unknown
% 2.82/1.62 % (22884)Termination phase: shuffling
% 2.82/1.62
% 2.82/1.62 % (22884)Memory used [KB]: 1663
% 2.82/1.62 % (22884)Time elapsed: 0.008 s
% 2.82/1.62 % (22884)Instructions burned: 22 (million)
% 2.82/1.62 % (22884)------------------------------
% 2.82/1.62 % (22884)------------------------------
% 2.82/1.62 % (22886)Instruction limit reached!
% 2.82/1.62 % (22886)------------------------------
% 2.82/1.62 % (22886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (22886)Termination reason: Unknown
% 2.82/1.62 % (22886)Termination phase: shuffling
% 2.82/1.62
% 2.82/1.62 % (22886)Memory used [KB]: 1535
% 2.82/1.62 % (22886)Time elapsed: 0.005 s
% 2.82/1.62 % (22886)Instructions burned: 7 (million)
% 2.82/1.62 % (22886)------------------------------
% 2.82/1.62 % (22886)------------------------------
% 2.82/1.63 % (22893)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_22669 for (2999ds/779Mi)
% 2.82/1.63 % (22892)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/377Mi)
% 2.82/1.63 % (22894)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_22669 for (2999ds/19Mi)
% 2.82/1.64 % (22894)Instruction limit reached!
% 2.82/1.64 % (22894)------------------------------
% 2.82/1.64 % (22894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.64 % (22894)Termination reason: Unknown
% 2.82/1.64 % (22894)Termination phase: shuffling
% 2.82/1.64
% 2.82/1.64 % (22894)Memory used [KB]: 1663
% 2.82/1.64 % (22894)Time elapsed: 0.006 s
% 2.82/1.64 % (22894)Instructions burned: 19 (million)
% 2.82/1.64 % (22894)------------------------------
% 2.82/1.64 % (22894)------------------------------
% 2.82/1.64 % (22895)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/879Mi)
% 2.82/1.65 % (22896)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22669 for (2999ds/17Mi)
% 2.82/1.65 % (22896)Instruction limit reached!
% 2.82/1.65 % (22896)------------------------------
% 2.82/1.65 % (22896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.65 % (22896)Termination reason: Unknown
% 2.82/1.65 % (22896)Termination phase: shuffling
% 2.82/1.65
% 2.82/1.65 % (22896)Memory used [KB]: 1663
% 2.82/1.65 % (22896)Time elapsed: 0.007 s
% 2.82/1.65 % (22896)Instructions burned: 18 (million)
% 2.82/1.65 % (22896)------------------------------
% 2.82/1.65 % (22896)------------------------------
% 2.82/1.66 % (22899)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22669 for (2998ds/3Mi)
% 2.82/1.66 % (22899)Instruction limit reached!
% 2.82/1.66 % (22899)------------------------------
% 2.82/1.66 % (22899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.66 % (22899)Termination reason: Unknown
% 2.82/1.66 % (22899)Termination phase: shuffling
% 2.82/1.66
% 2.82/1.66 % (22899)Memory used [KB]: 1407
% 2.82/1.66 % (22899)Time elapsed: 0.003 s
% 2.82/1.66 % (22899)Instructions burned: 5 (million)
% 2.82/1.66 % (22899)------------------------------
% 2.82/1.66 % (22899)------------------------------
% 2.82/1.68 % (22883)Refutation not found, incomplete strategy
% 2.82/1.68 % (22883)------------------------------
% 2.82/1.68 % (22883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.68 % (22883)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.68
% 2.82/1.68
% 2.82/1.68 % (22883)Memory used [KB]: 7931
% 2.82/1.68 % (22883)Time elapsed: 0.071 s
% 2.82/1.68 % (22883)Instructions burned: 244 (million)
% 2.82/1.68 % (22883)------------------------------
% 2.82/1.68 % (22883)------------------------------
% 2.82/1.68 % (22907)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22669 for (2998ds/30Mi)
% 2.82/1.69 % (22909)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22669 for (2998ds/127Mi)
% 2.82/1.69 % (22907)Instruction limit reached!
% 2.82/1.69 % (22907)------------------------------
% 2.82/1.69 % (22907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.69 % (22907)Termination reason: Unknown
% 2.82/1.69 % (22907)Termination phase: shuffling
% 2.82/1.69
% 2.82/1.69 % (22907)Memory used [KB]: 1791
% 2.82/1.69 % (22907)Time elapsed: 0.012 s
% 2.82/1.69 % (22907)Instructions burned: 32 (million)
% 2.82/1.69 % (22907)------------------------------
% 2.82/1.69 % (22907)------------------------------
% 2.82/1.71 % (22913)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22669 for (2998ds/100Mi)
% 2.82/1.75 % (22909)Instruction limit reached!
% 2.82/1.75 % (22909)------------------------------
% 2.82/1.75 % (22909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.75 % (22909)Termination reason: Unknown
% 2.82/1.75 % (22909)Termination phase: Function definition elimination
% 2.82/1.75
% 2.82/1.75 % (22909)Memory used [KB]: 2558
% 2.82/1.75 % (22909)Time elapsed: 0.060 s
% 2.82/1.75 % (22909)Instructions burned: 127 (million)
% 2.82/1.75 % (22909)------------------------------
% 2.82/1.75 % (22909)------------------------------
% 2.82/1.75 % (22913)Instruction limit reached!
% 2.82/1.75 % (22913)------------------------------
% 2.82/1.75 % (22913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.75 % (22913)Termination reason: Unknown
% 2.82/1.75 % (22913)Termination phase: Preprocessing 3
% 2.82/1.75
% 2.82/1.75 % (22913)Memory used [KB]: 2430
% 2.82/1.75 % (22913)Time elapsed: 0.047 s
% 2.82/1.75 % (22913)Instructions burned: 101 (million)
% 2.82/1.75 % (22913)------------------------------
% 2.82/1.75 % (22913)------------------------------
% 2.82/1.76 % (22892)Instruction limit reached!
% 2.82/1.76 % (22892)------------------------------
% 2.82/1.76 % (22892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.76 % (22892)Termination reason: Unknown
% 2.82/1.76 % (22892)Termination phase: Saturation
% 2.82/1.76
% 2.82/1.76 % (22892)Memory used [KB]: 8443
% 2.82/1.76 % (22892)Time elapsed: 0.135 s
% 2.82/1.76 % (22892)Instructions burned: 379 (million)
% 2.82/1.76 % (22892)------------------------------
% 2.82/1.76 % (22892)------------------------------
% 2.82/1.77 % (22929)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_22669 for (2997ds/20Mi)
% 2.82/1.77 % (22927)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_22669 for (2997ds/3Mi)
% 2.82/1.77 % (22927)Instruction limit reached!
% 2.82/1.77 % (22927)------------------------------
% 2.82/1.77 % (22927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.77 % (22927)Termination reason: Unknown
% 2.82/1.77 % (22927)Termination phase: shuffling
% 2.82/1.77
% 2.82/1.77 % (22927)Memory used [KB]: 1407
% 2.82/1.77 % (22927)Time elapsed: 0.004 s
% 2.82/1.77 % (22927)Instructions burned: 4 (million)
% 2.82/1.77 % (22927)------------------------------
% 2.82/1.77 % (22927)------------------------------
% 2.82/1.77 % (22932)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_22669 for (2997ds/86Mi)
% 2.82/1.78 % (22895)First to succeed.
% 2.82/1.78 % (22929)Instruction limit reached!
% 2.82/1.78 % (22929)------------------------------
% 2.82/1.78 % (22929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.78 % (22929)Termination reason: Unknown
% 2.82/1.78 % (22929)Termination phase: shuffling
% 2.82/1.78
% 2.82/1.78 % (22929)Memory used [KB]: 1663
% 2.82/1.78 % (22929)Time elapsed: 0.011 s
% 2.82/1.78 % (22929)Instructions burned: 20 (million)
% 2.82/1.78 % (22929)------------------------------
% 2.82/1.78 % (22929)------------------------------
% 2.82/1.78 % (22895)Refutation found. Thanks to Tanya!
% 2.82/1.78 % SZS status Theorem for DTF2THF_22669
% 2.82/1.78 % SZS output start Proof for DTF2THF_22669
% 2.82/1.78 thf(type_def_5, type, list: ($tType) > $tType).
% 2.82/1.78 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 2.82/1.78 thf(type_def_8, type, set: ($tType) > $tType).
% 2.82/1.78 thf(type_def_9, type, option: ($tType) > $tType).
% 2.82/1.78 thf(type_def_10, type, g: $tType).
% 2.82/1.78 thf(type_def_11, type, node: $tType).
% 2.82/1.78 thf(type_def_12, type, val: $tType).
% 2.82/1.78 thf(type_def_13, type, edgeD: $tType).
% 2.82/1.78 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 2.82/1.78 thf(func_def_1, type, option: ($tType) > $tType).
% 2.82/1.78 thf(func_def_2, type, list: ($tType) > $tType).
% 2.82/1.78 thf(func_def_3, type, set: ($tType) > $tType).
% 2.82/1.78 thf(func_def_4, type, edgeD: $tType).
% 2.82/1.78 thf(func_def_5, type, node: $tType).
% 2.82/1.78 thf(func_def_6, type, val: $tType).
% 2.82/1.78 thf(func_def_7, type, g: $tType).
% 2.82/1.78 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 2.82/1.78 thf(func_def_9, type, ord: !>[X0: $tType]:($o)).
% 2.82/1.78 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 2.82/1.78 thf(func_def_11, type, graph_1146196722h_path: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > list @ X1 > $o)).
% 2.82/1.78 thf(func_def_12, 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)).
% 2.82/1.78 thf(func_def_13, type, graph_1201503639essors: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1)).
% 2.82/1.78 thf(func_def_14, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.82/1.78 thf(func_def_15, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.82/1.78 thf(func_def_16, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.82/1.78 thf(func_def_17, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.82/1.78 thf(func_def_18, type, hd: !>[X0: $tType]:(list @ X0 > X0)).
% 2.82/1.78 thf(func_def_19, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 2.82/1.78 thf(func_def_20, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.82/1.78 thf(func_def_21, type, graph_pathsConverge: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > $o) > (X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1 > X1 > list @ X1 > X1 > $o)).
% 2.82/1.78 thf(func_def_22, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.82/1.78 thf(func_def_23, type, sSA_CFG_SSA_phiUses: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > X1 > set @ X3)).
% 2.82/1.78 thf(func_def_24, type, sSA_CF1081484811efNode: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > X1)).
% 2.82/1.78 thf(func_def_25, type, sSA_CF1165125185phiArg: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > X2 > $o)).
% 2.82/1.78 thf(func_def_26, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.82/1.78 thf(func_def_27, type, prefix: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.82/1.78 thf(func_def_28, type, suffix: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.82/1.78 thf(func_def_29, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.82/1.78 thf(func_def_30, type, alpha_n: g > list @ node).
% 2.82/1.78 thf(func_def_31, type, phi_r: val).
% 2.82/1.78 thf(func_def_32, type, defs: g > node > set @ val).
% 2.82/1.78 thf(func_def_33, type, g2: g).
% 2.82/1.78 thf(func_def_34, type, i: node).
% 2.82/1.78 thf(func_def_35, type, inEdges: g > node > list @ product_prod @ node @ edgeD).
% 2.82/1.78 thf(func_def_36, type, invar: g > $o).
% 2.82/1.78 thf(func_def_37, type, m: node).
% 2.82/1.78 thf(func_def_38, type, ms: list @ node).
% 2.82/1.78 thf(func_def_39, type, ms2: list @ node).
% 2.82/1.78 thf(func_def_40, type, n: node).
% 2.82/1.78 thf(func_def_41, type, ns: list @ node).
% 2.82/1.78 thf(func_def_42, type, phis: g > product_prod @ node @ val > option @ list @ val).
% 2.82/1.78 thf(func_def_43, type, pred_phi_r: node).
% 2.82/1.78 thf(func_def_44, type, r: val).
% 2.82/1.78 thf(func_def_45, type, ri: list @ node).
% 2.82/1.78 thf(func_def_46, type, rs: list @ node).
% 2.82/1.78 thf(func_def_47, type, rs_rest: list @ node).
% 2.82/1.78 thf(func_def_48, type, rs2: list @ node).
% 2.82/1.78 thf(func_def_49, type, s: val).
% 2.82/1.78 thf(func_def_50, type, tmp: list @ node).
% 2.82/1.78 thf(func_def_66, type, sK0: node).
% 2.82/1.78 thf(func_def_67, type, sK1: list @ node).
% 2.82/1.78 thf(func_def_68, type, sK2: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.82/1.78 thf(func_def_69, type, sK3: (node > $o) > node > list @ node > g > node).
% 2.82/1.78 thf(func_def_70, type, sK4: (node > $o) > node > list @ node > g > list @ node).
% 2.82/1.78 thf(func_def_71, type, sK5: node > node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_72, type, sK6: node > node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_73, type, sK7: (node > $o) > list @ node > node > g > node).
% 2.82/1.78 thf(func_def_74, type, sK8: (node > $o) > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_75, type, sK9: list @ node).
% 2.82/1.78 thf(func_def_76, type, sK10: (node > list @ node > node > $o) > node > g > list @ node).
% 2.82/1.78 thf(func_def_77, type, sK11: (node > list @ node > node > $o) > node > g > node).
% 2.82/1.78 thf(func_def_78, type, sK12: (node > list @ node > node > $o) > node > g > node).
% 2.82/1.78 thf(func_def_79, type, sK13: list @ node).
% 2.82/1.78 thf(func_def_80, type, sK14: (node > list @ node > node > $o) > node > g > list @ node).
% 2.82/1.78 thf(func_def_81, type, sK15: (node > list @ node > node > $o) > node > g > node).
% 2.82/1.78 thf(func_def_82, type, sK16: (node > list @ node > node > $o) > node > g > node).
% 2.82/1.78 thf(func_def_83, type, sK17: node > node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_84, type, sK18: node > node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_85, type, sK19: node > node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_86, type, sK20: node > node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_87, type, sK21: node > node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_88, type, sK22: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.82/1.78 thf(func_def_89, type, sK23: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.82/1.78 thf(func_def_90, type, sK24: node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_91, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 2.82/1.78 thf(func_def_92, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 2.82/1.78 thf(func_def_93, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 2.82/1.78 thf(func_def_94, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 2.82/1.78 thf(func_def_95, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 2.82/1.78 thf(func_def_96, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > list @ X1)).
% 2.82/1.78 thf(func_def_97, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 2.82/1.78 thf(func_def_98, type, sK32: node > list @ node > node > g > list @ node).
% 2.82/1.78 thf(func_def_100, type, ph34: !>[X0: $tType]:(X0)).
% 2.82/1.78 thf(f1137,plain,(
% 2.82/1.78 $false),
% 2.82/1.78 inference(subsumption_resolution,[status(thm)],[f1136,f862])).
% 2.82/1.78 thf(f862,plain,(
% 2.82/1.78 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons @ node @ i @ rs_rest) @ pred_phi_r) != $true)),
% 2.82/1.78 inference(cnf_transformation,[status(thm)],[f683])).
% 2.82/1.78 thf(f683,plain,(
% 2.82/1.78 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons @ node @ i @ rs_rest) @ pred_phi_r) != $true)),
% 2.82/1.78 inference(flattening,[status(thm)],[f338])).
% 2.82/1.78 thf(f338,plain,(
% 2.82/1.78 ~((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons @ node @ i @ rs_rest) @ pred_phi_r) = $true)),
% 2.82/1.78 inference(fool_elimination,[status(thm)],[f337])).
% 2.82/1.78 thf(f337,plain,(
% 2.82/1.78 ~(graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons @ node @ i @ rs_rest) @ pred_phi_r)),
% 2.82/1.78 inference(rectify,[status(thm)],[f265])).
% 2.82/1.78 thf(f265,negated_conjecture,(
% 2.82/1.78 ~(graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons @ node @ i @ rs_rest) @ pred_phi_r)),
% 2.82/1.78 inference(negated_conjecture,[status(cth)],[f264])).
% 2.82/1.78 thf(f264,conjecture,(
% 2.82/1.78 (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons @ node @ i @ rs_rest) @ pred_phi_r)),
% 2.82/1.78 file('/export/starexec/sandbox/tmp/tmp.WhTG5ILRVb/DTF2THF_22669.p',conj_0)).
% 2.82/1.78 thf(f1136,plain,(
% 2.82/1.78 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons @ node @ i @ rs_rest) @ pred_phi_r) = $true)),
% 2.82/1.78 inference(trivial_inequality_removal,[status(thm)],[f1135])).
% 2.82/1.78 thf(f1135,plain,(
% 2.82/1.78 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons @ node @ i @ rs_rest) @ pred_phi_r) = $true) | ($true != $true)),
% 2.82/1.78 inference(superposition,[status(thm)],[f861,f921])).
% 2.82/1.78 thf(f921,plain,(
% 2.82/1.78 ($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ (append @ node @ tmp @ (cons @ node @ i @ rs_rest)) @ pred_phi_r))),
% 2.82/1.78 inference(backward_demodulation,[status(thm)],[f915,f916])).
% 2.82/1.78 thf(f916,plain,(
% 2.82/1.78 ((append @ node @ tmp @ (cons @ node @ i @ rs_rest)) = (append @ node @ (append @ node @ tmp @ (cons @ node @ i @ nil @ node)) @ rs_rest))),
% 2.82/1.78 inference(definition_unfolding,[status(thm)],[f904,f906])).
% 2.82/1.78 thf(f906,plain,(
% 2.82/1.78 (rs = (append @ node @ (append @ node @ tmp @ (cons @ node @ i @ nil @ node)) @ rs_rest))),
% 2.82/1.78 inference(definition_unfolding,[status(thm)],[f826,f812])).
% 2.82/1.78 thf(f812,plain,(
% 2.82/1.78 (ri = (append @ node @ tmp @ (cons @ node @ i @ nil @ node)))),
% 2.82/1.78 inference(cnf_transformation,[status(thm)],[f19])).
% 2.82/1.78 thf(f19,axiom,(
% 2.82/1.78 (ri = (append @ node @ tmp @ (cons @ node @ i @ nil @ node)))),
% 2.82/1.78 file('/export/starexec/sandbox/tmp/tmp.WhTG5ILRVb/DTF2THF_22669.p',fact_18__092_060open_062ri_A_061_Atmp_A_064_A_091i_093_092_060close_062)).
% 2.82/1.78 thf(f826,plain,(
% 2.82/1.78 (rs = (append @ node @ ri @ rs_rest))),
% 2.82/1.78 inference(cnf_transformation,[status(thm)],[f8])).
% 2.82/1.78 thf(f8,axiom,(
% 2.82/1.78 (rs = (append @ node @ ri @ rs_rest))),
% 2.82/1.78 file('/export/starexec/sandbox/tmp/tmp.WhTG5ILRVb/DTF2THF_22669.p',fact_7_rs_H__rest__prop)).
% 2.82/1.78 thf(f904,plain,(
% 2.82/1.78 (rs = (append @ node @ tmp @ (cons @ node @ i @ rs_rest)))),
% 2.82/1.78 inference(cnf_transformation,[status(thm)],[f2])).
% 2.82/1.78 thf(f2,axiom,(
% 2.82/1.78 (rs = (append @ node @ tmp @ (cons @ node @ i @ rs_rest)))),
% 2.82/1.78 file('/export/starexec/sandbox/tmp/tmp.WhTG5ILRVb/DTF2THF_22669.p',fact_1_rs_H__rest__def)).
% 2.82/1.78 thf(f915,plain,(
% 2.82/1.78 ($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ (append @ node @ (append @ node @ tmp @ (cons @ node @ i @ nil @ node)) @ rs_rest) @ pred_phi_r))),
% 2.82/1.78 inference(definition_unfolding,[status(thm)],[f903,f906])).
% 2.82/1.78 thf(f903,plain,(
% 2.82/1.78 ((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)),
% 2.82/1.78 inference(cnf_transformation,[status(thm)],[f476])).
% 2.82/1.78 thf(f476,plain,(
% 2.82/1.78 ((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)),
% 2.82/1.78 inference(fool_elimination,[status(thm)],[f475])).
% 2.82/1.78 thf(f475,plain,(
% 2.82/1.78 (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)),
% 2.82/1.78 inference(rectify,[status(thm)],[f6])).
% 2.82/1.78 thf(f6,axiom,(
% 2.82/1.78 (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)),
% 2.82/1.78 file('/export/starexec/sandbox/tmp/tmp.WhTG5ILRVb/DTF2THF_22669.p',fact_5_rs_H__props_I1_J)).
% 2.82/1.78 thf(f861,plain,(
% 2.82/1.78 ( ! [X2 : list @ node,X3 : node,X0 : g,X1 : node,X4 : list @ node,X5 : node] : (((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (cons @ node @ X3 @ X4)) @ X5) != $true) | ($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ (cons @ node @ X3 @ X4) @ X5))) )),
% 2.82/1.78 inference(cnf_transformation,[status(thm)],[f725])).
% 2.82/1.78 thf(f725,plain,(
% 2.82/1.78 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node,X4 : list @ node,X5 : node] : (((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (cons @ node @ X3 @ X4)) @ X5) != $true) | ($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ (cons @ node @ X3 @ X4) @ X5)))),
% 2.82/1.78 inference(ennf_transformation,[status(thm)],[f682])).
% 2.82/1.78 thf(f682,plain,(
% 2.82/1.78 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node,X4 : list @ node,X5 : node] : (((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (cons @ node @ X3 @ X4)) @ X5) = $true) => ($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ (cons @ node @ X3 @ X4) @ X5)))),
% 2.82/1.78 inference(fool_elimination,[status(thm)],[f681])).
% 2.82/1.78 thf(f681,plain,(
% 2.82/1.78 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node,X4 : list @ node,X5 : node] : ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (cons @ node @ X3 @ X4)) @ X5) => (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ (cons @ node @ X3 @ X4) @ X5))),
% 2.82/1.78 inference(rectify,[status(thm)],[f4])).
% 2.82/1.78 thf(f4,axiom,(
% 2.82/1.78 ! [X5 : g,X6 : node,X7 : list @ node,X8 : node,X9 : list @ node,X10 : node] : ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X5 @ X6 @ (append @ node @ X7 @ (cons @ node @ X8 @ X9)) @ X10) => (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X5 @ X8 @ (cons @ node @ X8 @ X9) @ X10))),
% 2.82/1.78 file('/export/starexec/sandbox/tmp/tmp.WhTG5ILRVb/DTF2THF_22669.p',fact_3_old_Opath2__split_I2_J)).
% 2.82/1.78 % SZS output end Proof for DTF2THF_22669
% 2.82/1.78 % (22895)------------------------------
% 2.82/1.78 % (22895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.78 % (22895)Termination reason: Refutation
% 2.82/1.78
% 2.82/1.78 % (22895)Memory used [KB]: 7164
% 2.82/1.78 % (22895)Time elapsed: 0.161 s
% 2.82/1.78 % (22895)Instructions burned: 219 (million)
% 2.82/1.78 % (22895)------------------------------
% 2.82/1.78 % (22895)------------------------------
% 2.82/1.78 % (22860)Success in time 0.251 s
%------------------------------------------------------------------------------