%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP081^2 : 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 : n024.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 2.45s 1.50s
% Output : Refutation 2.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP081^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n024.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 03:25:25 EST 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.33 ---- Original DTF file ---
% 0.09/0.33 thf(spec,logic,$$dhol).
% 0.09/0.33 %------------------------------------------------------------------------------
% 0.09/0.33 % File : ITP081^2 : TPTP v9.2.1. Released v7.5.0.
% 0.09/0.33 % Domain : Interactive Theorem Proving
% 0.09/0.33 % Problem : Sledgehammer Irreducible problem prob_472__6626992_1
% 0.09/0.33 % Version : Especial.
% 0.09/0.33 % English :
% 0.09/0.33
% 0.09/0.33 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.09/0.33 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.09/0.33 % Source : [Des21]
% 0.09/0.33 % Names : Irreducible/prob_472__6626992_1 [Des21]
% 0.09/0.33
% 0.09/0.33 % Status : Theorem
% 0.09/0.33 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0
% 0.09/0.33 % Syntax : Number of formulae : 313 ( 100 unt; 49 typ; 0 def)
% 0.09/0.33 % Number of atoms : 789 ( 363 equ; 0 cnn)
% 0.09/0.33 % Maximal formula atoms : 14 ( 2 avg)
% 0.09/0.33 % Number of connectives : 5276 ( 155 ~; 17 |; 67 &;4624 @)
% 0.09/0.33 % ( 0 <=>; 413 =>; 0 <=; 0 <~>)
% 0.09/0.33 % Maximal formula depth : 29 ( 10 avg)
% 0.09/0.33 % Number of types : 5 ( 4 usr)
% 0.09/0.33 % Number of type conns : 220 ( 220 >; 0 *; 0 +; 0 <<)
% 0.09/0.33 % Number of symbols : 46 ( 45 usr; 14 con; 0-10 aty)
% 0.09/0.33 % Number of variables : 1167 ( 20 ^;1051 !; 61 ?;1167 :)
% 0.09/0.33 % ( 35 !>; 0 ?*; 0 @-; 0 @+)
% 0.09/0.33 % SPC : TH1_THM_EQU_NAR
% 0.09/0.33
% 0.09/0.33 % Comments : This file was generated by Sledgehammer 2021-02-23 16:25:57.144
% 0.09/0.33 %------------------------------------------------------------------------------
% 0.09/0.33 % Could-be-implicit typings (8)
% 0.09/0.33 thf(ty_t_Product__Type_Oprod,type,
% 0.09/0.33 product_prod: $tType > $tType > $tType ).
% 0.09/0.33
% 0.09/0.33 thf(ty_t_Option_Ooption,type,
% 0.09/0.33 option: $tType > $tType ).
% 0.09/0.33
% 0.09/0.33 thf(ty_t_List_Olist,type,
% 0.09/0.33 list: $tType > $tType ).
% 0.09/0.33
% 0.09/0.33 thf(ty_t_Set_Oset,type,
% 0.09/0.33 set: $tType > $tType ).
% 0.09/0.33
% 0.09/0.33 thf(ty_tf_edgeD,type,
% 0.09/0.33 edgeD: $tType ).
% 0.09/0.33
% 0.09/0.33 thf(ty_tf_node,type,
% 0.09/0.33 node: $tType ).
% 0.09/0.33
% 0.09/0.33 thf(ty_tf_val,type,
% 0.09/0.33 val: $tType ).
% 0.09/0.33
% 0.09/0.33 thf(ty_tf_g,type,
% 0.09/0.33 g: $tType ).
% 0.09/0.33
% 0.09/0.33 % Explicit typings (41)
% 0.09/0.33 thf(sy_cl_HOL_Otype,type,
% 0.09/0.33 type:
% 0.09/0.33 !>[A: $tType] : $o ).
% 0.09/0.33
% 0.09/0.33 thf(sy_cl_Orderings_Oord,type,
% 0.09/0.33 ord:
% 0.09/0.33 !>[A: $tType] : $o ).
% 0.09/0.33
% 0.09/0.33 thf(sy_cl_Orderings_Olinorder,type,
% 0.09/0.33 linorder:
% 0.09/0.33 !>[A: $tType] : $o ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_Finite__Set_Ofinite,type,
% 0.09/0.33 finite_finite:
% 0.09/0.33 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_Graph__path_Ograph__path__base_Opath,type,
% 0.09/0.33 graph_1146196722h_path:
% 0.09/0.33 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > ( list @ Node ) > $o ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_Graph__path_Ograph__path__base_Opath2,type,
% 0.09/0.33 graph_1661282752_path2:
% 0.09/0.33 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) > Node > $o ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors,type,
% 0.09/0.33 graph_1201503639essors:
% 0.09/0.33 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_List_Oappend,type,
% 0.09/0.33 append:
% 0.09/0.33 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_List_Obutlast,type,
% 0.09/0.33 butlast:
% 0.09/0.33 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_List_Olist_OCons,type,
% 0.09/0.33 cons:
% 0.09/0.33 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_List_Olist_ONil,type,
% 0.09/0.33 nil:
% 0.09/0.33 !>[A: $tType] : ( list @ A ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_List_Olist_Ohd,type,
% 0.09/0.33 hd:
% 0.09/0.33 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_List_Olist_Oset,type,
% 0.09/0.33 set2:
% 0.09/0.33 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_List_Olist_Otl,type,
% 0.09/0.33 tl:
% 0.09/0.33 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.09/0.33 ord_less_eq:
% 0.09/0.33 !>[A: $tType] : ( A > A > $o ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses,type,
% 0.09/0.33 sSA_CFG_SSA_phiUses:
% 0.09/0.33 !>[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 ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode,type,
% 0.09/0.33 sSA_CF1081484811efNode:
% 0.09/0.33 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Node ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg,type,
% 0.09/0.33 sSA_CF1165125185phiArg:
% 0.09/0.33 !>[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 ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_Set_OCollect,type,
% 0.09/0.33 collect:
% 0.09/0.33 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_Sublist_Oprefix,type,
% 0.09/0.33 prefix:
% 0.09/0.33 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_Sublist_Osuffix,type,
% 0.09/0.33 suffix:
% 0.09/0.33 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_c_member,type,
% 0.09/0.33 member:
% 0.09/0.33 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v__092_060alpha_062n,type,
% 0.09/0.33 alpha_n: g > ( list @ node ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 0.09/0.33 phi_r: val ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_defs,type,
% 0.09/0.33 defs: g > node > ( set @ val ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_g,type,
% 0.09/0.33 g2: g ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_i____,type,
% 0.09/0.33 i: node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_inEdges_H,type,
% 0.09/0.33 inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_invar,type,
% 0.09/0.33 invar: g > $o ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_m,type,
% 0.09/0.33 m: node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_ms,type,
% 0.09/0.33 ms: list @ node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_ms_H____,type,
% 0.09/0.33 ms2: list @ node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_n,type,
% 0.09/0.33 n: node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_ns,type,
% 0.09/0.33 ns: list @ node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_phis,type,
% 0.09/0.33 phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 0.09/0.33 pred_phi_r: node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_r,type,
% 0.09/0.33 r: val ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_ri____,type,
% 0.09/0.33 ri: list @ node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_rs_H____,type,
% 0.09/0.33 rs: list @ node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_rs____,type,
% 0.09/0.33 rs2: list @ node ).
% 0.09/0.33
% 0.09/0.33 thf(sy_v_s,type,
% 0.09/0.33 s: val ).
% 0.09/0.33
% 0.09/0.33 % Relevant facts (255)
% 0.09/0.33 thf(fact_0_False,axiom,
% 0.09/0.33 r != phi_r ).
% 0.09/0.33
% 0.09/0.33 % False
% 0.09/0.33 thf(fact_1_ri__is__valid,axiom,
% 0.09/0.33 ( i
% 0.09/0.33 = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 0.09/0.33
% 0.09/0.33 % ri_is_valid
% 0.09/0.33 thf(fact_2_old_Oinvar,axiom,
% 0.09/0.33 ! [G2: g] : ( invar @ G2 ) ).
% 0.09/0.33
% 0.09/0.33 % old.invar
% 0.09/0.33 thf(fact_3_assms_I7_J,axiom,
% 0.09/0.33 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 0.09/0.33
% 0.09/0.33 % assms(7)
% 0.09/0.33 thf(fact_4_ri__props_I1_J,axiom,
% 0.09/0.33 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 0.09/0.33
% 0.09/0.33 % ri_props(1)
% 0.09/0.33 thf(fact_5_old_Opath2__app,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 0.09/0.33 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( tl @ node @ Ms ) ) @ L ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_app
% 0.09/0.33 thf(fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 0.09/0.33 ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 0.09/0.33 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 0.09/0.33
% 0.09/0.33 % \<open>defNode g \<phi>\<^sub>r \<noteq> defNode g r\<close>
% 0.09/0.33 thf(fact_7_rs_H__props_I1_J,axiom,
% 0.09/0.33 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 ).
% 0.09/0.33
% 0.09/0.33 % rs'_props(1)
% 0.09/0.33 thf(fact_8_assms_I10_J,axiom,
% 0.09/0.33 sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 0.09/0.33
% 0.09/0.33 % assms(10)
% 0.09/0.33 thf(fact_9_rs__props_I1_J,axiom,
% 0.09/0.33 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 ) ).
% 0.09/0.33
% 0.09/0.33 % rs_props(1)
% 0.09/0.33 thf(fact_10_ms_H__props_I1_J,axiom,
% 0.09/0.33 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 0.09/0.33
% 0.09/0.33 % ms'_props(1)
% 0.09/0.33 thf(fact_11__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,
% 0.09/0.33 ( ( i
% 0.09/0.33 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.09/0.33 => ( ( ( i
% 0.09/0.33 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.09/0.33 => ( m != i ) )
% 0.09/0.33 => ~ ( ( i
% 0.09/0.33 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.09/0.33 => ( m = i ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % \<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>
% 0.09/0.33 thf(fact_12_old_Opath2__split_I2_J,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns2: list @ node,M: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns2 ) ) @ M )
% 0.09/0.33 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns2 ) @ M ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_split(2)
% 0.09/0.33 thf(fact_13_old_Opath2__not__Nil,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( Ns
% 0.09/0.33 != ( nil @ node ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_not_Nil
% 0.09/0.33 thf(fact_14_old_Opath2__not__Nil2,axiom,
% 0.09/0.33 ! [G2: g,N: node,M: node] :
% 0.09/0.33 ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( nil @ node ) @ M ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_not_Nil2
% 0.09/0.33 thf(fact_15_rs_H__props_I3_J,axiom,
% 0.09/0.33 member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 0.09/0.33
% 0.09/0.33 % rs'_props(3)
% 0.09/0.33 thf(fact_16_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_hd_in_\<alpha>n
% 0.09/0.33 thf(fact_17_old_Opath2__hd__in__ns,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( member @ node @ N @ ( set2 @ node @ Ns ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_hd_in_ns
% 0.09/0.33 thf(fact_18_old_Opath2__in___092_060alpha_062n,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,L: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( member @ node @ L @ ( set2 @ node @ Ns ) )
% 0.09/0.33 => ( member @ node @ L @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_in_\<alpha>n
% 0.09/0.33 thf(fact_19_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Y: A] :
% 0.09/0.33 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.33 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ ( append @ A @ Ys @ ( cons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.elem_set_implies_elem_tl_app_cons
% 0.09/0.33 thf(fact_20_ri__props_I2_J,axiom,
% 0.09/0.33 member @ node @ i @ ( set2 @ node @ ms ) ).
% 0.09/0.33
% 0.09/0.33 % ri_props(2)
% 0.09/0.33 thf(fact_21_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_tl_in_\<alpha>n
% 0.09/0.33 thf(fact_22_old_Opath2__last__in__ns,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( member @ node @ M @ ( set2 @ node @ Ns ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_last_in_ns
% 0.09/0.33 thf(fact_23_old_Opath2__split_I1_J,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns2: list @ node,M: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns2 ) ) @ M )
% 0.09/0.33 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ ( nil @ node ) ) ) @ N2 ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_split(1)
% 0.09/0.33 thf(fact_24_rs__props_I3_J,axiom,
% 0.09/0.33 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs2 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rs_props(3)
% 0.09/0.33 thf(fact_25_rs_H__loopfree,axiom,
% 0.09/0.33 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rs'_loopfree
% 0.09/0.33 thf(fact_26_rs__def,axiom,
% 0.09/0.33 ( rs2
% 0.09/0.33 = ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rs_def
% 0.09/0.33 thf(fact_27_ri__props_I4_J,axiom,
% 0.09/0.33 prefix @ node @ ri @ rs2 ).
% 0.09/0.33
% 0.09/0.33 % ri_props(4)
% 0.09/0.33 thf(fact_28_old_Oempty__path2,axiom,
% 0.09/0.33 ! [N: node,G2: g] :
% 0.09/0.33 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.09/0.33 => ( ( invar @ G2 )
% 0.09/0.33 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.empty_path2
% 0.09/0.33 thf(fact_29_ms_H__props_I3_J,axiom,
% 0.09/0.33 ~ ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ ms2 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % ms'_props(3)
% 0.09/0.33 thf(fact_30_rs_H__props_I4_J,axiom,
% 0.09/0.33 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 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rs'_props(4)
% 0.09/0.33 thf(fact_31_assms_I8_J,axiom,
% 0.09/0.33 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 0.09/0.33
% 0.09/0.33 % assms(8)
% 0.09/0.33 thf(fact_32_tl__append2,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( tl @ A @ ( append @ A @ Xs @ Ys ) )
% 0.09/0.33 = ( append @ A @ ( tl @ A @ Xs ) @ Ys ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % tl_append2
% 0.09/0.33 thf(fact_33_list__e__eq__lel_I2_J,axiom,
% 0.09/0.33 ! [A: $tType,L1: list @ A,E: A,L2: list @ A,E2: A] :
% 0.09/0.33 ( ( ( append @ A @ L1 @ ( cons @ A @ E @ L2 ) )
% 0.09/0.33 = ( cons @ A @ E2 @ ( nil @ A ) ) )
% 0.09/0.33 = ( ( L1
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( E = E2 )
% 0.09/0.33 & ( L2
% 0.09/0.33 = ( nil @ A ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_e_eq_lel(2)
% 0.09/0.33 thf(fact_34_list__e__eq__lel_I1_J,axiom,
% 0.09/0.33 ! [A: $tType,E2: A,L1: list @ A,E: A,L2: list @ A] :
% 0.09/0.33 ( ( ( cons @ A @ E2 @ ( nil @ A ) )
% 0.09/0.33 = ( append @ A @ L1 @ ( cons @ A @ E @ L2 ) ) )
% 0.09/0.33 = ( ( L1
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( E = E2 )
% 0.09/0.33 & ( L2
% 0.09/0.33 = ( nil @ A ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_e_eq_lel(1)
% 0.09/0.33 thf(fact_35_list__se__match_I4_J,axiom,
% 0.09/0.33 ! [A: $tType,L2: list @ A,A2: A,L1: list @ A] :
% 0.09/0.33 ( ( L2
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 0.09/0.33 = ( append @ A @ L1 @ L2 ) )
% 0.09/0.33 = ( ( L1
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( L2
% 0.09/0.33 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_se_match(4)
% 0.09/0.33 thf(fact_36_list__se__match_I3_J,axiom,
% 0.09/0.33 ! [A: $tType,L1: list @ A,A2: A,L2: list @ A] :
% 0.09/0.33 ( ( L1
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 0.09/0.33 = ( append @ A @ L1 @ L2 ) )
% 0.09/0.33 = ( ( L1
% 0.09/0.33 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.09/0.33 & ( L2
% 0.09/0.33 = ( nil @ A ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_se_match(3)
% 0.09/0.33 thf(fact_37_list__se__match_I2_J,axiom,
% 0.09/0.33 ! [A: $tType,L2: list @ A,L1: list @ A,A2: A] :
% 0.09/0.33 ( ( L2
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( ( append @ A @ L1 @ L2 )
% 0.09/0.33 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.09/0.33 = ( ( L1
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( L2
% 0.09/0.33 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_se_match(2)
% 0.09/0.33 thf(fact_38_list__se__match_I1_J,axiom,
% 0.09/0.33 ! [A: $tType,L1: list @ A,L2: list @ A,A2: A] :
% 0.09/0.33 ( ( L1
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( ( append @ A @ L1 @ L2 )
% 0.09/0.33 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.09/0.33 = ( ( L1
% 0.09/0.33 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 0.09/0.33 & ( L2
% 0.09/0.33 = ( nil @ A ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_se_match(1)
% 0.09/0.33 thf(fact_39_list__ee__eq__leel_I2_J,axiom,
% 0.09/0.33 ! [A: $tType,L1: list @ A,E1: A,E22: A,L2: list @ A,E12: A,E23: A] :
% 0.09/0.33 ( ( ( append @ A @ L1 @ ( cons @ A @ E1 @ ( cons @ A @ E22 @ L2 ) ) )
% 0.09/0.33 = ( cons @ A @ E12 @ ( cons @ A @ E23 @ ( nil @ A ) ) ) )
% 0.09/0.33 = ( ( L1
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( E12 = E1 )
% 0.09/0.33 & ( E23 = E22 )
% 0.09/0.33 & ( L2
% 0.09/0.33 = ( nil @ A ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_ee_eq_leel(2)
% 0.09/0.33 thf(fact_40_list__ee__eq__leel_I1_J,axiom,
% 0.09/0.33 ! [A: $tType,E12: A,E23: A,L1: list @ A,E1: A,E22: A,L2: list @ A] :
% 0.09/0.33 ( ( ( cons @ A @ E12 @ ( cons @ A @ E23 @ ( nil @ A ) ) )
% 0.09/0.33 = ( append @ A @ L1 @ ( cons @ A @ E1 @ ( cons @ A @ E22 @ L2 ) ) ) )
% 0.09/0.33 = ( ( L1
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( E12 = E1 )
% 0.09/0.33 & ( E23 = E22 )
% 0.09/0.33 & ( L2
% 0.09/0.33 = ( nil @ A ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_ee_eq_leel(1)
% 0.09/0.33 thf(fact_41_ms_H__props_I2_J,axiom,
% 0.09/0.33 prefix @ node @ ms2 @ ms ).
% 0.09/0.33
% 0.09/0.33 % ms'_props(2)
% 0.09/0.33 thf(fact_42_ri__props_I3_J,axiom,
% 0.09/0.33 ! [X2: node] :
% 0.09/0.33 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ ri ) ) )
% 0.09/0.33 => ~ ( member @ node @ X2 @ ( set2 @ node @ ms ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % ri_props(3)
% 0.09/0.33 thf(fact_43_list_Oinject,axiom,
% 0.09/0.33 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.09/0.33 ( ( ( cons @ A @ X21 @ X22 )
% 0.09/0.33 = ( cons @ A @ Y21 @ Y22 ) )
% 0.09/0.33 = ( ( X21 = Y21 )
% 0.09/0.33 & ( X22 = Y22 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.inject
% 0.09/0.33 thf(fact_44_append_Oassoc,axiom,
% 0.09/0.33 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 0.09/0.33 ( ( append @ A @ ( append @ A @ A2 @ B ) @ C )
% 0.09/0.33 = ( append @ A @ A2 @ ( append @ A @ B @ C ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append.assoc
% 0.09/0.33 thf(fact_45_mem__Collect__eq,axiom,
% 0.09/0.33 ! [A: $tType,A2: A,P: A > $o] :
% 0.09/0.33 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.09/0.33 = ( P @ A2 ) ) ).
% 0.09/0.33
% 0.09/0.33 % mem_Collect_eq
% 0.09/0.33 thf(fact_46_Collect__mem__eq,axiom,
% 0.09/0.33 ! [A: $tType,A3: set @ A] :
% 0.09/0.33 ( ( collect @ A
% 0.09/0.33 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.09/0.33 = A3 ) ).
% 0.09/0.33
% 0.09/0.33 % Collect_mem_eq
% 0.09/0.33 thf(fact_47_Collect__cong,axiom,
% 0.09/0.33 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.09/0.33 ( ! [X4: A] :
% 0.09/0.33 ( ( P @ X4 )
% 0.09/0.33 = ( Q @ X4 ) )
% 0.09/0.33 => ( ( collect @ A @ P )
% 0.09/0.33 = ( collect @ A @ Q ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % Collect_cong
% 0.09/0.33 thf(fact_48_ext,axiom,
% 0.09/0.33 ! [B2: $tType,A: $tType,F: A > B2,G2: A > B2] :
% 0.09/0.33 ( ! [X4: A] :
% 0.09/0.33 ( ( F @ X4 )
% 0.09/0.33 = ( G2 @ X4 ) )
% 0.09/0.33 => ( F = G2 ) ) ).
% 0.09/0.33
% 0.09/0.33 % ext
% 0.09/0.33 thf(fact_49_append__assoc,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.09/0.33 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 0.09/0.33 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_assoc
% 0.09/0.33 thf(fact_50_append__same__eq,axiom,
% 0.09/0.33 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Ys @ Xs )
% 0.09/0.33 = ( append @ A @ Zs @ Xs ) )
% 0.09/0.33 = ( Ys = Zs ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_same_eq
% 0.09/0.33 thf(fact_51_same__append__eq,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Xs @ Ys )
% 0.09/0.33 = ( append @ A @ Xs @ Zs ) )
% 0.09/0.33 = ( Ys = Zs ) ) ).
% 0.09/0.33
% 0.09/0.33 % same_append_eq
% 0.09/0.33 thf(fact_52_old_Opredecessor__is__node,axiom,
% 0.09/0.33 ! [N: node,G2: g,N2: node] :
% 0.09/0.33 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 0.09/0.33 => ( ( invar @ G2 )
% 0.09/0.33 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.predecessor_is_node
% 0.09/0.33 thf(fact_53_old_Osuccessor__is__node,axiom,
% 0.09/0.33 ! [N: node,G2: g,N2: node] :
% 0.09/0.33 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 0.09/0.33 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.09/0.33 => ( ( invar @ G2 )
% 0.09/0.33 => ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.successor_is_node
% 0.09/0.33 thf(fact_54_old_Osuccessor__in___092_060alpha_062n,axiom,
% 0.09/0.33 ! [G2: g,N: node] :
% 0.09/0.33 ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N )
% 0.09/0.33 != ( nil @ node ) )
% 0.09/0.33 => ( ( invar @ G2 )
% 0.09/0.33 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.successor_in_\<alpha>n
% 0.09/0.33 thf(fact_55_old_Opath2__app_H,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 0.09/0.33 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ ( butlast @ node @ Ns ) @ Ms ) @ L ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_app'
% 0.09/0.33 thf(fact_56_append__Nil2,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A] :
% 0.09/0.33 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.09/0.33 = Xs ) ).
% 0.09/0.33
% 0.09/0.33 % append_Nil2
% 0.09/0.33 thf(fact_57_append__self__conv,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Xs @ Ys )
% 0.09/0.33 = Xs )
% 0.09/0.33 = ( Ys
% 0.09/0.33 = ( nil @ A ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_self_conv
% 0.09/0.33 thf(fact_58_self__append__conv,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 = ( append @ A @ Xs @ Ys ) )
% 0.09/0.33 = ( Ys
% 0.09/0.33 = ( nil @ A ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % self_append_conv
% 0.09/0.33 thf(fact_59_append__self__conv2,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Xs @ Ys )
% 0.09/0.33 = Ys )
% 0.09/0.33 = ( Xs
% 0.09/0.33 = ( nil @ A ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_self_conv2
% 0.09/0.33 thf(fact_60_self__append__conv2,axiom,
% 0.09/0.33 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.09/0.33 ( ( Ys
% 0.09/0.33 = ( append @ A @ Xs @ Ys ) )
% 0.09/0.33 = ( Xs
% 0.09/0.33 = ( nil @ A ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % self_append_conv2
% 0.09/0.33 thf(fact_61_Nil__is__append__conv,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( ( nil @ A )
% 0.09/0.33 = ( append @ A @ Xs @ Ys ) )
% 0.09/0.33 = ( ( Xs
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( Ys
% 0.09/0.33 = ( nil @ A ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % Nil_is_append_conv
% 0.09/0.33 thf(fact_62_append__is__Nil__conv,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Xs @ Ys )
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 = ( ( Xs
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( Ys
% 0.09/0.33 = ( nil @ A ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_is_Nil_conv
% 0.09/0.33 thf(fact_63_empty__append__eq__id,axiom,
% 0.09/0.33 ! [A: $tType] :
% 0.09/0.33 ( ( append @ A @ ( nil @ A ) )
% 0.09/0.33 = ( ^ [X3: list @ A] : X3 ) ) ).
% 0.09/0.33
% 0.09/0.33 % empty_append_eq_id
% 0.09/0.33 thf(fact_64_append_Oright__neutral,axiom,
% 0.09/0.33 ! [A: $tType,A2: list @ A] :
% 0.09/0.33 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.09/0.33 = A2 ) ).
% 0.09/0.33
% 0.09/0.33 % append.right_neutral
% 0.09/0.33 thf(fact_65_old_Opath2__split__ex_H,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 0.09/0.33 => ~ ! [Ns_1: list @ node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns_1 @ X )
% 0.09/0.33 => ! [Ns_2: list @ node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_2 @ M )
% 0.09/0.33 => ( Ns
% 0.09/0.33 != ( append @ node @ ( butlast @ node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_split_ex'
% 0.09/0.33 thf(fact_66_old_Opath2__prefix__ex,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,M2: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( member @ node @ M2 @ ( set2 @ node @ Ns ) )
% 0.09/0.33 => ~ ! [Ns3: list @ node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns3 @ M2 )
% 0.09/0.33 => ( ( prefix @ node @ Ns3 @ Ns )
% 0.09/0.33 => ( member @ node @ M2 @ ( set2 @ node @ ( butlast @ node @ Ns3 ) ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_prefix_ex
% 0.09/0.33 thf(fact_67_old_Opath2__split__first__prop,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ? [X2: node] :
% 0.09/0.33 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 0.09/0.33 & ( P @ X2 ) )
% 0.09/0.33 => ~ ! [M3: node,Ns3: list @ node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns3 @ M3 )
% 0.09/0.33 => ( ( P @ M3 )
% 0.09/0.33 => ( ! [X2: node] :
% 0.09/0.33 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ Ns3 ) ) )
% 0.09/0.33 => ~ ( P @ X2 ) )
% 0.09/0.33 => ~ ( prefix @ node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_split_first_prop
% 0.09/0.33 thf(fact_68_old_Opath2__induct,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( ( invar @ G2 )
% 0.09/0.33 => ( P @ M @ ( cons @ node @ M @ ( nil @ node ) ) @ M ) )
% 0.09/0.33 => ( ! [Ns4: list @ node,N3: node,N4: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N4 @ Ns4 @ M )
% 0.09/0.33 => ( ( P @ N4 @ Ns4 @ M )
% 0.09/0.33 => ( ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N4 ) ) )
% 0.09/0.33 => ( P @ N3 @ ( cons @ node @ N3 @ Ns4 ) @ M ) ) ) )
% 0.09/0.33 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_induct
% 0.09/0.33 thf(fact_69_old_Opath2__split__ex,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 0.09/0.33 => ~ ! [Ns_1: list @ node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns_1 @ X )
% 0.09/0.33 => ! [Ns_2: list @ node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_2 @ M )
% 0.09/0.33 => ( ( Ns
% 0.09/0.33 = ( append @ node @ Ns_1 @ ( tl @ node @ Ns_2 ) ) )
% 0.09/0.33 => ( Ns
% 0.09/0.33 != ( append @ node @ ( butlast @ node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_split_ex
% 0.09/0.33 thf(fact_70_old_Opath2__prefix,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,Ns2: list @ node,M2: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( prefix @ node @ ( append @ node @ Ns2 @ ( cons @ node @ M2 @ ( nil @ node ) ) ) @ Ns )
% 0.09/0.33 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns2 @ ( cons @ node @ M2 @ ( nil @ node ) ) ) @ M2 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_prefix
% 0.09/0.33 thf(fact_71_old_Opath2__rev__induct,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.09/0.33 => ( P @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) )
% 0.09/0.33 => ( ! [Ns4: list @ node,M3: node,M4: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns4 @ M3 )
% 0.09/0.33 => ( ( P @ N @ Ns4 @ M3 )
% 0.09/0.33 => ( ( member @ node @ M3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M4 ) ) )
% 0.09/0.33 => ( P @ N @ ( append @ node @ Ns4 @ ( cons @ node @ M4 @ ( nil @ node ) ) ) @ M4 ) ) ) )
% 0.09/0.33 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_rev_induct
% 0.09/0.33 thf(fact_72_old_Opath2__snoc,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,M2: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M2 ) ) )
% 0.09/0.33 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ M2 @ ( nil @ node ) ) ) @ M2 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.path2_snoc
% 0.09/0.33 thf(fact_73_append1__eq__conv,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.09/0.33 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.09/0.33 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.09/0.33 = ( ( Xs = Ys )
% 0.09/0.33 & ( X = Y ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append1_eq_conv
% 0.09/0.33 thf(fact_74_butlast__snoc,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,X: A] :
% 0.09/0.33 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.09/0.33 = Xs ) ).
% 0.09/0.33
% 0.09/0.33 % butlast_snoc
% 0.09/0.33 thf(fact_75__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,
% 0.09/0.33 ~ ! [Ms2: list @ node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 0.09/0.33 => ( ( prefix @ node @ Ms2 @ ms )
% 0.09/0.33 => ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ Ms2 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % \<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>
% 0.09/0.33 thf(fact_76__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,
% 0.09/0.33 ~ ! [I: node,Ri: list @ node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 0.09/0.33 => ( ( member @ node @ I @ ( set2 @ node @ ms ) )
% 0.09/0.33 => ( ! [X2: node] :
% 0.09/0.33 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ Ri ) ) )
% 0.09/0.33 => ~ ( member @ node @ X2 @ ( set2 @ node @ ms ) ) )
% 0.09/0.33 => ~ ( prefix @ node @ Ri @ rs2 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % \<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>
% 0.09/0.33 thf(fact_77_old_OCons__path2,axiom,
% 0.09/0.33 ! [G2: g,N: node,Ns: list @ node,M: node,N2: node] :
% 0.09/0.33 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.33 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 0.09/0.33 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns ) @ M ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % old.Cons_path2
% 0.09/0.33 thf(fact_78_butlast_Osimps_I1_J,axiom,
% 0.09/0.33 ! [A: $tType] :
% 0.09/0.33 ( ( butlast @ A @ ( nil @ A ) )
% 0.09/0.33 = ( nil @ A ) ) ).
% 0.09/0.33
% 0.09/0.33 % butlast.simps(1)
% 0.09/0.33 thf(fact_79_in__set__butlastD,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.09/0.33 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % in_set_butlastD
% 0.09/0.33 thf(fact_80_butlast__tl,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A] :
% 0.09/0.33 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 0.09/0.33 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % butlast_tl
% 0.09/0.33 thf(fact_81_butlast_Osimps_I2_J,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,X: A] :
% 0.09/0.33 ( ( ( Xs
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.09/0.33 = ( nil @ A ) ) )
% 0.09/0.33 & ( ( Xs
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.09/0.33 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % butlast.simps(2)
% 0.09/0.33 thf(fact_82_butlast__append,axiom,
% 0.09/0.33 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.09/0.33 ( ( ( Ys
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.09/0.33 = ( butlast @ A @ Xs ) ) )
% 0.09/0.33 & ( ( Ys
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.09/0.33 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % butlast_append
% 0.09/0.33 thf(fact_83_in__set__butlast__appendI,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.09/0.33 | ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 0.09/0.33 => ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % in_set_butlast_appendI
% 0.09/0.33 thf(fact_84_butlast__eq__cons__conv,axiom,
% 0.09/0.33 ! [A: $tType,L: list @ A,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( ( butlast @ A @ L )
% 0.09/0.33 = ( cons @ A @ X @ Xs ) )
% 0.09/0.33 = ( ? [Xl: A] :
% 0.09/0.33 ( L
% 0.09/0.33 = ( cons @ A @ X @ ( append @ A @ Xs @ ( cons @ A @ Xl @ ( nil @ A ) ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % butlast_eq_cons_conv
% 0.09/0.33 thf(fact_85_butlast__eq__consE,axiom,
% 0.09/0.33 ! [A: $tType,L: list @ A,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( ( butlast @ A @ L )
% 0.09/0.33 = ( cons @ A @ X @ Xs ) )
% 0.09/0.33 => ~ ! [Xl2: A] :
% 0.09/0.33 ( L
% 0.09/0.33 != ( cons @ A @ X @ ( append @ A @ Xs @ ( cons @ A @ Xl2 @ ( nil @ A ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % butlast_eq_consE
% 0.09/0.33 thf(fact_86_list__tail__coinc,axiom,
% 0.09/0.33 ! [A: $tType,N1: A,R1: list @ A,N22: A,R2: list @ A] :
% 0.09/0.33 ( ( ( cons @ A @ N1 @ R1 )
% 0.09/0.33 = ( cons @ A @ N22 @ R2 ) )
% 0.09/0.33 => ( ( N1 = N22 )
% 0.09/0.33 & ( R1 = R2 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_tail_coinc
% 0.09/0.33 thf(fact_87_not__Cons__self2,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( cons @ A @ X @ Xs )
% 0.09/0.33 != Xs ) ).
% 0.09/0.33
% 0.09/0.33 % not_Cons_self2
% 0.09/0.33 thf(fact_88_append__eq__appendI,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Xs @ Xs1 )
% 0.09/0.33 = Zs )
% 0.09/0.33 => ( ( Ys
% 0.09/0.33 = ( append @ A @ Xs1 @ Us ) )
% 0.09/0.33 => ( ( append @ A @ Xs @ Ys )
% 0.09/0.33 = ( append @ A @ Zs @ Us ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_eq_appendI
% 0.09/0.33 thf(fact_89_append__eq__append__conv2,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Xs @ Ys )
% 0.09/0.33 = ( append @ A @ Zs @ Ts ) )
% 0.09/0.33 = ( ? [Us2: list @ A] :
% 0.09/0.33 ( ( ( Xs
% 0.09/0.33 = ( append @ A @ Zs @ Us2 ) )
% 0.09/0.33 & ( ( append @ A @ Us2 @ Ys )
% 0.09/0.33 = Ts ) )
% 0.09/0.33 | ( ( ( append @ A @ Xs @ Us2 )
% 0.09/0.33 = Zs )
% 0.09/0.33 & ( Ys
% 0.09/0.33 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_eq_append_conv2
% 0.09/0.33 thf(fact_90_strict__sorted_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType] :
% 0.09/0.33 ( ( linorder @ A )
% 0.09/0.33 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.09/0.33 ( ( P @ ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A,Ys2: list @ A] :
% 0.09/0.33 ( ( P @ Ys2 )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Ys2 ) ) )
% 0.09/0.33 => ( P @ A0 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % strict_sorted.induct
% 0.09/0.33 thf(fact_91_mergesort__by__rel__merge__induct,axiom,
% 0.09/0.33 ! [A: $tType,B2: $tType,P: ( list @ A ) > ( list @ B2 ) > $o,R: A > B2 > $o,Xs: list @ A,Ys: list @ B2] :
% 0.09/0.33 ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [X_1: list @ B2] : ( P @ ( nil @ A ) @ X_1 )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 0.09/0.33 ( ( R @ X4 @ Y2 )
% 0.09/0.33 => ( ( P @ Xs2 @ ( cons @ B2 @ Y2 @ Ys2 ) )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B2 @ Y2 @ Ys2 ) ) ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 0.09/0.33 ( ~ ( R @ X4 @ Y2 )
% 0.09/0.33 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys2 )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B2 @ Y2 @ Ys2 ) ) ) )
% 0.09/0.33 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % mergesort_by_rel_merge_induct
% 0.09/0.33 thf(fact_92_mergesort__by__rel__merge_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.09/0.33 ( ! [R3: A > A > $o,X4: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.09/0.33 ( ( ( R3 @ X4 @ Y2 )
% 0.09/0.33 => ( P @ R3 @ Xs2 @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.09/0.33 => ( ( ~ ( R3 @ X4 @ Y2 )
% 0.09/0.33 => ( P @ R3 @ ( cons @ A @ X4 @ Xs2 ) @ Ys2 ) )
% 0.09/0.33 => ( P @ R3 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) )
% 0.09/0.33 => ( ! [R3: A > A > $o,Xs2: list @ A] : ( P @ R3 @ Xs2 @ ( nil @ A ) )
% 0.09/0.33 => ( ! [R3: A > A > $o,V: A,Va: list @ A] : ( P @ R3 @ ( nil @ A ) @ ( cons @ A @ V @ Va ) )
% 0.09/0.33 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % mergesort_by_rel_merge.induct
% 0.09/0.33 thf(fact_93_map__tailrec__rev_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,B2: $tType,P: ( A > B2 ) > ( list @ A ) > ( list @ B2 ) > $o,A0: A > B2,A1: list @ A,A22: list @ B2] :
% 0.09/0.33 ( ! [F2: A > B2,X_1: list @ B2] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 0.09/0.33 => ( ! [F2: A > B2,A4: A,As: list @ A,Bs: list @ B2] :
% 0.09/0.33 ( ( P @ F2 @ As @ ( cons @ B2 @ ( F2 @ A4 ) @ Bs ) )
% 0.09/0.33 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.09/0.33 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % map_tailrec_rev.induct
% 0.09/0.33 thf(fact_94_list__nonempty__induct,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A] :
% 0.09/0.33 ( ( Xs2
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( P @ Xs2 )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 0.09/0.33 => ( P @ Xs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_nonempty_induct
% 0.09/0.33 thf(fact_95_list__all__zip_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,B2: $tType,P: ( A > B2 > $o ) > ( list @ A ) > ( list @ B2 ) > $o,A0: A > B2 > $o,A1: list @ A,A22: list @ B2] :
% 0.09/0.33 ( ! [P2: A > B2 > $o] : ( P @ P2 @ ( nil @ A ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [P2: A > B2 > $o,A4: A,As: list @ A,B3: B2,Bs: list @ B2] :
% 0.09/0.33 ( ( P @ P2 @ As @ Bs )
% 0.09/0.33 => ( P @ P2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B2 @ B3 @ Bs ) ) )
% 0.09/0.33 => ( ! [P2: A > B2 > $o,V: A,Va: list @ A] : ( P @ P2 @ ( cons @ A @ V @ Va ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [P2: A > B2 > $o,V: B2,Va: list @ B2] : ( P @ P2 @ ( nil @ A ) @ ( cons @ B2 @ V @ Va ) )
% 0.09/0.33 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_all_zip.induct
% 0.09/0.33 thf(fact_96_successively_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.09/0.33 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.09/0.33 => ( ! [P2: A > A > $o,X4: A] : ( P @ P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.09/0.33 => ( ! [P2: A > A > $o,X4: A,Y2: A,Xs2: list @ A] :
% 0.09/0.33 ( ( P @ P2 @ ( cons @ A @ Y2 @ Xs2 ) )
% 0.09/0.33 => ( P @ P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Xs2 ) ) ) )
% 0.09/0.33 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % successively.induct
% 0.09/0.33 thf(fact_97_arg__min__list_Oinduct,axiom,
% 0.09/0.33 ! [B2: $tType,A: $tType] :
% 0.09/0.33 ( ( linorder @ B2 )
% 0.09/0.33 => ! [P: ( A > B2 ) > ( list @ A ) > $o,A0: A > B2,A1: list @ A] :
% 0.09/0.33 ( ! [F2: A > B2,X4: A] : ( P @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.09/0.33 => ( ! [F2: A > B2,X4: A,Y2: A,Zs2: list @ A] :
% 0.09/0.33 ( ( P @ F2 @ ( cons @ A @ Y2 @ Zs2 ) )
% 0.09/0.33 => ( P @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Zs2 ) ) ) )
% 0.09/0.33 => ( ! [A4: A > B2] : ( P @ A4 @ ( nil @ A ) )
% 0.09/0.33 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % arg_min_list.induct
% 0.09/0.33 thf(fact_98_list__induct__first2,axiom,
% 0.09/0.33 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.09/0.33 ( ( P @ ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.09/0.33 => ( ! [X1: A,X23: A,Xs2: list @ A] :
% 0.09/0.33 ( ( P @ Xs2 )
% 0.09/0.33 => ( P @ ( cons @ A @ X1 @ ( cons @ A @ X23 @ Xs2 ) ) ) )
% 0.09/0.33 => ( P @ Xs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_induct_first2
% 0.09/0.33 thf(fact_99_remdups__adj_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.09/0.33 ( ( P @ ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.09/0.33 => ( ! [X4: A,Y2: A,Xs2: list @ A] :
% 0.09/0.33 ( ( ( X4 = Y2 )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 0.09/0.33 => ( ( ( X4 != Y2 )
% 0.09/0.33 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.09/0.33 => ( P @ A0 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % remdups_adj.induct
% 0.09/0.33 thf(fact_100_sorted__wrt_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.09/0.33 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.09/0.33 => ( ! [P2: A > A > $o,X4: A,Ys2: list @ A] :
% 0.09/0.33 ( ( P @ P2 @ Ys2 )
% 0.09/0.33 => ( P @ P2 @ ( cons @ A @ X4 @ Ys2 ) ) )
% 0.09/0.33 => ( P @ A0 @ A1 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % sorted_wrt.induct
% 0.09/0.33 thf(fact_101_remdups__adj_Ocases,axiom,
% 0.09/0.33 ! [A: $tType,X: list @ A] :
% 0.09/0.33 ( ( X
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A] :
% 0.09/0.33 ( X
% 0.09/0.33 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.09/0.33 => ~ ! [X4: A,Y2: A,Xs2: list @ A] :
% 0.09/0.33 ( X
% 0.09/0.33 != ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % remdups_adj.cases
% 0.09/0.33 thf(fact_102_list__2pre__induct,axiom,
% 0.09/0.33 ! [A: $tType,B2: $tType,P: ( list @ A ) > ( list @ B2 ) > $o,W1: list @ A,W2: list @ B2] :
% 0.09/0.33 ( ( P @ ( nil @ A ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [E3: A,W12: list @ A,W22: list @ B2] :
% 0.09/0.33 ( ( P @ W12 @ W22 )
% 0.09/0.33 => ( P @ ( cons @ A @ E3 @ W12 ) @ W22 ) )
% 0.09/0.33 => ( ! [E3: B2,W13: list @ A,W23: list @ B2] :
% 0.09/0.33 ( ( P @ W13 @ W23 )
% 0.09/0.33 => ( P @ W13 @ ( cons @ B2 @ E3 @ W23 ) ) )
% 0.09/0.33 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_2pre_induct
% 0.09/0.33 thf(fact_103_transpose_Ocases,axiom,
% 0.09/0.33 ! [A: $tType,X: list @ ( list @ A )] :
% 0.09/0.33 ( ( X
% 0.09/0.33 != ( nil @ ( list @ A ) ) )
% 0.09/0.33 => ( ! [Xss: list @ ( list @ A )] :
% 0.09/0.33 ( X
% 0.09/0.33 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.09/0.33 => ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.09/0.33 ( X
% 0.09/0.33 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % transpose.cases
% 0.09/0.33 thf(fact_104_shuffles_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.09/0.33 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.09/0.33 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.09/0.33 ( ( P @ Xs2 @ ( cons @ A @ Y2 @ Ys2 ) )
% 0.09/0.33 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys2 )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) )
% 0.09/0.33 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % shuffles.induct
% 0.09/0.33 thf(fact_105_min__list_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType] :
% 0.09/0.33 ( ( ord @ A )
% 0.09/0.33 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.09/0.33 ( ! [X4: A,Xs2: list @ A] :
% 0.09/0.33 ( ! [X212: A,X222: list @ A] :
% 0.09/0.33 ( ( Xs2
% 0.09/0.33 = ( cons @ A @ X212 @ X222 ) )
% 0.09/0.33 => ( P @ Xs2 ) )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 0.09/0.33 => ( ( P @ ( nil @ A ) )
% 0.09/0.33 => ( P @ A0 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % min_list.induct
% 0.09/0.33 thf(fact_106_min__list_Ocases,axiom,
% 0.09/0.33 ! [A: $tType] :
% 0.09/0.33 ( ( ord @ A )
% 0.09/0.33 => ! [X: list @ A] :
% 0.09/0.33 ( ! [X4: A,Xs2: list @ A] :
% 0.09/0.33 ( X
% 0.09/0.33 != ( cons @ A @ X4 @ Xs2 ) )
% 0.09/0.33 => ( X
% 0.09/0.33 = ( nil @ A ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % min_list.cases
% 0.09/0.33 thf(fact_107_induct__list012,axiom,
% 0.09/0.33 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.09/0.33 ( ( P @ ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.09/0.33 => ( ! [X4: A,Y2: A,Zs2: list @ A] :
% 0.09/0.33 ( ( P @ Zs2 )
% 0.09/0.33 => ( ( P @ ( cons @ A @ Y2 @ Zs2 ) )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Zs2 ) ) ) ) )
% 0.09/0.33 => ( P @ Xs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % induct_list012
% 0.09/0.33 thf(fact_108_splice_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.09/0.33 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A,Ys2: list @ A] :
% 0.09/0.33 ( ( P @ Ys2 @ Xs2 )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys2 ) )
% 0.09/0.33 => ( P @ A0 @ A1 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % splice.induct
% 0.09/0.33 thf(fact_109_list__induct2_H,axiom,
% 0.09/0.33 ! [A: $tType,B2: $tType,P: ( list @ A ) > ( list @ B2 ) > $o,Xs: list @ A,Ys: list @ B2] :
% 0.09/0.33 ( ( P @ ( nil @ A ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [Y2: B2,Ys2: list @ B2] : ( P @ ( nil @ A ) @ ( cons @ B2 @ Y2 @ Ys2 ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 0.09/0.33 ( ( P @ Xs2 @ Ys2 )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B2 @ Y2 @ Ys2 ) ) )
% 0.09/0.33 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_induct2'
% 0.09/0.33 thf(fact_110_neq__Nil__conv,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 = ( ? [Y3: A,Ys3: list @ A] :
% 0.09/0.33 ( Xs
% 0.09/0.33 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % neq_Nil_conv
% 0.09/0.33 thf(fact_111_list_Oinducts,axiom,
% 0.09/0.33 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.09/0.33 ( ( P @ ( nil @ A ) )
% 0.09/0.33 => ( ! [X1: A,X23: list @ A] :
% 0.09/0.33 ( ( P @ X23 )
% 0.09/0.33 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 0.09/0.33 => ( P @ List ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.inducts
% 0.09/0.33 thf(fact_112_list_Oexhaust,axiom,
% 0.09/0.33 ! [A: $tType,Y: list @ A] :
% 0.09/0.33 ( ( Y
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ~ ! [X213: A,X223: list @ A] :
% 0.09/0.33 ( Y
% 0.09/0.33 != ( cons @ A @ X213 @ X223 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.exhaust
% 0.09/0.33 thf(fact_113_zipf_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,C2: $tType,B2: $tType,P: ( A > B2 > C2 ) > ( list @ A ) > ( list @ B2 ) > $o,A0: A > B2 > C2,A1: list @ A,A22: list @ B2] :
% 0.09/0.33 ( ! [F2: A > B2 > C2] : ( P @ F2 @ ( nil @ A ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [F2: A > B2 > C2,A4: A,As: list @ A,B3: B2,Bs: list @ B2] :
% 0.09/0.33 ( ( P @ F2 @ As @ Bs )
% 0.09/0.33 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B2 @ B3 @ Bs ) ) )
% 0.09/0.33 => ( ! [A4: A > B2 > C2,V: A,Va: list @ A] : ( P @ A4 @ ( cons @ A @ V @ Va ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [A4: A > B2 > C2,V: B2,Va: list @ B2] : ( P @ A4 @ ( nil @ A ) @ ( cons @ B2 @ V @ Va ) )
% 0.09/0.33 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % zipf.induct
% 0.09/0.33 thf(fact_114_revg_Oinduct,axiom,
% 0.09/0.33 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.09/0.33 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.09/0.33 => ( ! [A4: A,As: list @ A,B3: list @ A] :
% 0.09/0.33 ( ( P @ As @ ( cons @ A @ A4 @ B3 ) )
% 0.09/0.33 => ( P @ ( cons @ A @ A4 @ As ) @ B3 ) )
% 0.09/0.33 => ( P @ A0 @ A1 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % revg.induct
% 0.09/0.33 thf(fact_115_list_OdiscI,axiom,
% 0.09/0.33 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.09/0.33 ( ( List
% 0.09/0.33 = ( cons @ A @ X21 @ X22 ) )
% 0.09/0.33 => ( List
% 0.09/0.33 != ( nil @ A ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.discI
% 0.09/0.33 thf(fact_116_neq__NilE,axiom,
% 0.09/0.33 ! [A: $tType,L: list @ A] :
% 0.09/0.33 ( ( L
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ~ ! [X4: A,Xs2: list @ A] :
% 0.09/0.33 ( L
% 0.09/0.33 != ( cons @ A @ X4 @ Xs2 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % neq_NilE
% 0.09/0.33 thf(fact_117_list_Odistinct_I1_J,axiom,
% 0.09/0.33 ! [A: $tType,X21: A,X22: list @ A] :
% 0.09/0.33 ( ( nil @ A )
% 0.09/0.33 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.distinct(1)
% 0.09/0.33 thf(fact_118_list_Oset__cases,axiom,
% 0.09/0.33 ! [A: $tType,E2: A,A2: list @ A] :
% 0.09/0.33 ( ( member @ A @ E2 @ ( set2 @ A @ A2 ) )
% 0.09/0.33 => ( ! [Z2: list @ A] :
% 0.09/0.33 ( A2
% 0.09/0.33 != ( cons @ A @ E2 @ Z2 ) )
% 0.09/0.33 => ~ ! [Z1: A,Z2: list @ A] :
% 0.09/0.33 ( ( A2
% 0.09/0.33 = ( cons @ A @ Z1 @ Z2 ) )
% 0.09/0.33 => ~ ( member @ A @ E2 @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.set_cases
% 0.09/0.33 thf(fact_119_set__ConsD,axiom,
% 0.09/0.33 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 0.09/0.33 => ( ( Y = X )
% 0.09/0.33 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % set_ConsD
% 0.09/0.33 thf(fact_120_list_Oset__intros_I1_J,axiom,
% 0.09/0.33 ! [A: $tType,X21: A,X22: list @ A] : ( member @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.set_intros(1)
% 0.09/0.33 thf(fact_121_list_Oset__intros_I2_J,axiom,
% 0.09/0.33 ! [A: $tType,Y: A,X22: list @ A,X21: A] :
% 0.09/0.33 ( ( member @ A @ Y @ ( set2 @ A @ X22 ) )
% 0.09/0.33 => ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.set_intros(2)
% 0.09/0.33 thf(fact_122_Cons__eq__appendI,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.09/0.33 ( ( ( cons @ A @ X @ Xs1 )
% 0.09/0.33 = Ys )
% 0.09/0.33 => ( ( Xs
% 0.09/0.33 = ( append @ A @ Xs1 @ Zs ) )
% 0.09/0.33 => ( ( cons @ A @ X @ Xs )
% 0.09/0.33 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % Cons_eq_appendI
% 0.09/0.33 thf(fact_123_append__Cons,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.09/0.33 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_Cons
% 0.09/0.33 thf(fact_124_list__match__lel__lel,axiom,
% 0.09/0.33 ! [A: $tType,C1: list @ A,Qs: A,C22: list @ A,C12: list @ A,Qs2: A,C23: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ C1 @ ( cons @ A @ Qs @ C22 ) )
% 0.09/0.33 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C23 ) ) )
% 0.09/0.33 => ( ! [C21: list @ A] :
% 0.09/0.33 ( ( C1
% 0.09/0.33 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C21 ) ) )
% 0.09/0.33 => ( C23
% 0.09/0.33 != ( append @ A @ C21 @ ( cons @ A @ Qs @ C22 ) ) ) )
% 0.09/0.33 => ( ( ( C12 = C1 )
% 0.09/0.33 => ( ( Qs2 = Qs )
% 0.09/0.33 => ( C23 != C22 ) ) )
% 0.09/0.33 => ~ ! [C212: list @ A] :
% 0.09/0.33 ( ( C12
% 0.09/0.33 = ( append @ A @ C1 @ ( cons @ A @ Qs @ C212 ) ) )
% 0.09/0.33 => ( C22
% 0.09/0.33 != ( append @ A @ C212 @ ( cons @ A @ Qs2 @ C23 ) ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_match_lel_lel
% 0.09/0.33 thf(fact_125_eq__Nil__appendI,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.33 ( ( Xs = Ys )
% 0.09/0.33 => ( Xs
% 0.09/0.33 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % eq_Nil_appendI
% 0.09/0.33 thf(fact_126_append__Nil,axiom,
% 0.09/0.33 ! [A: $tType,Ys: list @ A] :
% 0.09/0.33 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.09/0.33 = Ys ) ).
% 0.09/0.33
% 0.09/0.33 % append_Nil
% 0.09/0.33 thf(fact_127_append_Oleft__neutral,axiom,
% 0.09/0.33 ! [A: $tType,A2: list @ A] :
% 0.09/0.33 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.09/0.33 = A2 ) ).
% 0.09/0.33
% 0.09/0.33 % append.left_neutral
% 0.09/0.33 thf(fact_128_list_Osel_I3_J,axiom,
% 0.09/0.33 ! [A: $tType,X21: A,X22: list @ A] :
% 0.09/0.33 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.09/0.33 = X22 ) ).
% 0.09/0.33
% 0.09/0.33 % list.sel(3)
% 0.09/0.33 thf(fact_129_list_Osel_I2_J,axiom,
% 0.09/0.33 ! [A: $tType] :
% 0.09/0.33 ( ( tl @ A @ ( nil @ A ) )
% 0.09/0.33 = ( nil @ A ) ) ).
% 0.09/0.33
% 0.09/0.33 % list.sel(2)
% 0.09/0.33 thf(fact_130_list__append__eq__Cons__cases,axiom,
% 0.09/0.33 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Ys @ Zs )
% 0.09/0.33 = ( cons @ A @ X @ Xs ) )
% 0.09/0.33 => ( ( ( Ys
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 => ( Zs
% 0.09/0.33 != ( cons @ A @ X @ Xs ) ) )
% 0.09/0.33 => ~ ! [Ys4: list @ A] :
% 0.09/0.33 ( ( Ys
% 0.09/0.33 = ( cons @ A @ X @ Ys4 ) )
% 0.09/0.33 => ( ( append @ A @ Ys4 @ Zs )
% 0.09/0.33 != Xs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_append_eq_Cons_cases
% 0.09/0.33 thf(fact_131_list__Cons__eq__append__cases,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.09/0.33 ( ( ( cons @ A @ X @ Xs )
% 0.09/0.33 = ( append @ A @ Ys @ Zs ) )
% 0.09/0.33 => ( ( ( Ys
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 => ( Zs
% 0.09/0.33 != ( cons @ A @ X @ Xs ) ) )
% 0.09/0.33 => ~ ! [Ys4: list @ A] :
% 0.09/0.33 ( ( Ys
% 0.09/0.33 = ( cons @ A @ X @ Ys4 ) )
% 0.09/0.33 => ( ( append @ A @ Ys4 @ Zs )
% 0.09/0.33 != Xs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % list_Cons_eq_append_cases
% 0.09/0.33 thf(fact_132_rev__nonempty__induct2_H,axiom,
% 0.09/0.33 ! [A: $tType,B2: $tType,Xs: list @ A,Ys: list @ B2,P: ( list @ A ) > ( list @ B2 ) > $o] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( Ys
% 0.09/0.33 != ( nil @ B2 ) )
% 0.09/0.33 => ( ! [X4: A,Y2: B2] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A,Y2: B2] :
% 0.09/0.33 ( ( Xs2
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) )
% 0.09/0.33 => ( ! [X4: A,Y2: B2,Ys2: list @ B2] :
% 0.09/0.33 ( ( Ys2
% 0.09/0.33 != ( nil @ B2 ) )
% 0.09/0.33 => ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) @ ( append @ B2 @ Ys2 @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 0.09/0.33 ( ( P @ Xs2 @ Ys2 )
% 0.09/0.33 => ( ( Xs2
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( Ys2
% 0.09/0.33 != ( nil @ B2 ) )
% 0.09/0.33 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ B2 @ Ys2 @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) ) ) ) )
% 0.09/0.33 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rev_nonempty_induct2'
% 0.09/0.33 thf(fact_133_rev__nonempty__induct,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A] :
% 0.09/0.33 ( ( Xs2
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ( ( P @ Xs2 )
% 0.09/0.33 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 0.09/0.33 => ( P @ Xs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rev_nonempty_induct
% 0.09/0.33 thf(fact_134_append__eq__Cons__conv,axiom,
% 0.09/0.33 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( ( append @ A @ Ys @ Zs )
% 0.09/0.33 = ( cons @ A @ X @ Xs ) )
% 0.09/0.33 = ( ( ( Ys
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( Zs
% 0.09/0.33 = ( cons @ A @ X @ Xs ) ) )
% 0.09/0.33 | ? [Ys5: list @ A] :
% 0.09/0.33 ( ( Ys
% 0.09/0.33 = ( cons @ A @ X @ Ys5 ) )
% 0.09/0.33 & ( ( append @ A @ Ys5 @ Zs )
% 0.09/0.33 = Xs ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % append_eq_Cons_conv
% 0.09/0.33 thf(fact_135_Cons__eq__append__conv,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.09/0.33 ( ( ( cons @ A @ X @ Xs )
% 0.09/0.33 = ( append @ A @ Ys @ Zs ) )
% 0.09/0.33 = ( ( ( Ys
% 0.09/0.33 = ( nil @ A ) )
% 0.09/0.33 & ( ( cons @ A @ X @ Xs )
% 0.09/0.33 = Zs ) )
% 0.09/0.33 | ? [Ys5: list @ A] :
% 0.09/0.33 ( ( ( cons @ A @ X @ Ys5 )
% 0.09/0.33 = Ys )
% 0.09/0.33 & ( Xs
% 0.09/0.33 = ( append @ A @ Ys5 @ Zs ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % Cons_eq_append_conv
% 0.09/0.33 thf(fact_136_neq__Nil__rev__conv,axiom,
% 0.09/0.33 ! [A: $tType,L: list @ A] :
% 0.09/0.33 ( ( L
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 = ( ? [Xs3: list @ A,X3: A] :
% 0.09/0.33 ( L
% 0.09/0.33 = ( append @ A @ Xs3 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % neq_Nil_rev_conv
% 0.09/0.33 thf(fact_137_rev__induct2_H,axiom,
% 0.09/0.33 ! [A: $tType,B2: $tType,P: ( list @ A ) > ( list @ B2 ) > $o,Xs: list @ A,Ys: list @ B2] :
% 0.09/0.33 ( ( P @ ( nil @ A ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( nil @ B2 ) )
% 0.09/0.33 => ( ! [Y2: B2,Ys2: list @ B2] : ( P @ ( nil @ A ) @ ( append @ B2 @ Ys2 @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 0.09/0.33 ( ( P @ Xs2 @ Ys2 )
% 0.09/0.33 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ B2 @ Ys2 @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) ) )
% 0.09/0.33 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rev_induct2'
% 0.09/0.33 thf(fact_138_neq__Nil__revE,axiom,
% 0.09/0.33 ! [A: $tType,L: list @ A] :
% 0.09/0.33 ( ( L
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ~ ! [Ll: list @ A,E3: A] :
% 0.09/0.33 ( L
% 0.09/0.33 != ( append @ A @ Ll @ ( cons @ A @ E3 @ ( nil @ A ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % neq_Nil_revE
% 0.09/0.33 thf(fact_139_rev__exhaust,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 != ( nil @ A ) )
% 0.09/0.33 => ~ ! [Ys2: list @ A,Y2: A] :
% 0.09/0.33 ( Xs
% 0.09/0.33 != ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rev_exhaust
% 0.09/0.33 thf(fact_140_rev__induct,axiom,
% 0.09/0.33 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.09/0.33 ( ( P @ ( nil @ A ) )
% 0.09/0.33 => ( ! [X4: A,Xs2: list @ A] :
% 0.09/0.33 ( ( P @ Xs2 )
% 0.09/0.33 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 0.09/0.33 => ( P @ Xs ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % rev_induct
% 0.09/0.33 thf(fact_141_split__list__first__prop__iff,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.09/0.33 ( ( ? [X3: A] :
% 0.09/0.33 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.09/0.33 & ( P @ X3 ) ) )
% 0.09/0.33 = ( ? [Ys3: list @ A,X3: A] :
% 0.09/0.33 ( ? [Zs3: list @ A] :
% 0.09/0.33 ( Xs
% 0.09/0.33 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.09/0.33 & ( P @ X3 )
% 0.09/0.33 & ! [Y3: A] :
% 0.09/0.33 ( ( member @ A @ Y3 @ ( set2 @ A @ Ys3 ) )
% 0.09/0.33 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % split_list_first_prop_iff
% 0.09/0.33 thf(fact_142_split__list__last__prop__iff,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.09/0.33 ( ( ? [X3: A] :
% 0.09/0.33 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.09/0.33 & ( P @ X3 ) ) )
% 0.09/0.33 = ( ? [Ys3: list @ A,X3: A,Zs3: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.09/0.33 & ( P @ X3 )
% 0.09/0.33 & ! [Y3: A] :
% 0.09/0.33 ( ( member @ A @ Y3 @ ( set2 @ A @ Zs3 ) )
% 0.09/0.33 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % split_list_last_prop_iff
% 0.09/0.33 thf(fact_143_in__set__conv__decomp__first,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.33 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.09/0.33 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % in_set_conv_decomp_first
% 0.09/0.33 thf(fact_144_in__set__conv__decomp__last,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.33 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.09/0.33 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % in_set_conv_decomp_last
% 0.09/0.33 thf(fact_145_split__list__first__propE,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.09/0.33 ( ? [X2: A] :
% 0.09/0.33 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.09/0.33 & ( P @ X2 ) )
% 0.09/0.33 => ~ ! [Ys2: list @ A,X4: A] :
% 0.09/0.33 ( ? [Zs2: list @ A] :
% 0.09/0.33 ( Xs
% 0.09/0.33 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.09/0.33 => ( ( P @ X4 )
% 0.09/0.33 => ~ ! [Xa: A] :
% 0.09/0.33 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.09/0.33 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % split_list_first_propE
% 0.09/0.33 thf(fact_146_split__list__last__propE,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.09/0.33 ( ? [X2: A] :
% 0.09/0.33 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.09/0.33 & ( P @ X2 ) )
% 0.09/0.33 => ~ ! [Ys2: list @ A,X4: A,Zs2: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.09/0.33 => ( ( P @ X4 )
% 0.09/0.33 => ~ ! [Xa: A] :
% 0.09/0.33 ( ( member @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 0.09/0.33 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % split_list_last_propE
% 0.09/0.33 thf(fact_147_split__list__first__prop,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.09/0.33 ( ? [X2: A] :
% 0.09/0.33 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.09/0.33 & ( P @ X2 ) )
% 0.09/0.33 => ? [Ys2: list @ A,X4: A] :
% 0.09/0.33 ( ? [Zs2: list @ A] :
% 0.09/0.33 ( Xs
% 0.09/0.33 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.09/0.33 & ( P @ X4 )
% 0.09/0.33 & ! [Xa: A] :
% 0.09/0.33 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.09/0.33 => ~ ( P @ Xa ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % split_list_first_prop
% 0.09/0.33 thf(fact_148_split__list__last__prop,axiom,
% 0.09/0.33 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.09/0.33 ( ? [X2: A] :
% 0.09/0.33 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.09/0.33 & ( P @ X2 ) )
% 0.09/0.33 => ? [Ys2: list @ A,X4: A,Zs2: list @ A] :
% 0.09/0.33 ( ( Xs
% 0.09/0.33 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.09/0.33 & ( P @ X4 )
% 0.09/0.33 & ! [Xa: A] :
% 0.09/0.33 ( ( member @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 0.09/0.33 => ~ ( P @ Xa ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % split_list_last_prop
% 0.09/0.33 thf(fact_149_in__set__list__format,axiom,
% 0.09/0.33 ! [A: $tType,E2: A,L: list @ A] :
% 0.09/0.33 ( ( member @ A @ E2 @ ( set2 @ A @ L ) )
% 0.09/0.33 => ~ ! [L12: list @ A,L22: list @ A] :
% 0.09/0.33 ( L
% 0.09/0.33 != ( append @ A @ L12 @ ( cons @ A @ E2 @ L22 ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % in_set_list_format
% 0.09/0.33 thf(fact_150_in__set__conv__decomp,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.33 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.33 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.09/0.33 ( Xs
% 0.09/0.33 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) ) ) ) ).
% 0.09/0.33
% 0.09/0.33 % in_set_conv_decomp
% 0.09/0.33 thf(fact_151_append__Cons__eq__iff,axiom,
% 0.09/0.33 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Xs4: list @ A,Ys6: list @ A] :
% 0.09/0.33 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.33 => ( ~ ( member @ A @ X @ ( set2 @ A @ Ys ) )
% 0.09/0.33 => ( ( ( append @ A @ Xs @ ( cons @ A @ X @ Ys ) )
% 0.09/0.34 = ( append @ A @ Xs4 @ ( cons @ A @ X @ Ys6 ) ) )
% 0.09/0.34 = ( ( Xs = Xs4 )
% 0.09/0.34 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % append_Cons_eq_iff
% 0.09/0.34 thf(fact_152_split__list__propE,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.09/0.34 ( ? [X2: A] :
% 0.09/0.34 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.09/0.34 & ( P @ X2 ) )
% 0.09/0.34 => ~ ! [Ys2: list @ A,X4: A] :
% 0.09/0.34 ( ? [Zs2: list @ A] :
% 0.09/0.34 ( Xs
% 0.09/0.34 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.09/0.34 => ~ ( P @ X4 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % split_list_propE
% 0.09/0.34 thf(fact_153_split__list__first,axiom,
% 0.09/0.34 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.34 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.34 => ? [Ys2: list @ A,Zs2: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.09/0.34 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % split_list_first
% 0.09/0.34 thf(fact_154_xy__in__set__cases,axiom,
% 0.09/0.34 ! [A: $tType,X: A,L: list @ A,Y: A] :
% 0.09/0.34 ( ( member @ A @ X @ ( set2 @ A @ L ) )
% 0.09/0.34 => ( ( member @ A @ Y @ ( set2 @ A @ L ) )
% 0.09/0.34 => ( ( ( X = Y )
% 0.09/0.34 => ! [L12: list @ A,L22: list @ A] :
% 0.09/0.34 ( L
% 0.09/0.34 != ( append @ A @ L12 @ ( cons @ A @ Y @ L22 ) ) ) )
% 0.09/0.34 => ( ( ( X != Y )
% 0.09/0.34 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 0.09/0.34 ( L
% 0.09/0.34 != ( append @ A @ L12 @ ( cons @ A @ X @ ( append @ A @ L22 @ ( cons @ A @ Y @ L3 ) ) ) ) ) )
% 0.09/0.34 => ~ ( ( X != Y )
% 0.09/0.34 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 0.09/0.34 ( L
% 0.09/0.34 != ( append @ A @ L12 @ ( cons @ A @ Y @ ( append @ A @ L22 @ ( cons @ A @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % xy_in_set_cases
% 0.09/0.34 thf(fact_155_split__list__prop,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.09/0.34 ( ? [X2: A] :
% 0.09/0.34 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.09/0.34 & ( P @ X2 ) )
% 0.09/0.34 => ? [Ys2: list @ A,X4: A] :
% 0.09/0.34 ( ? [Zs2: list @ A] :
% 0.09/0.34 ( Xs
% 0.09/0.34 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 0.09/0.34 & ( P @ X4 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % split_list_prop
% 0.09/0.34 thf(fact_156_split__list__last,axiom,
% 0.09/0.34 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.34 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.34 => ? [Ys2: list @ A,Zs2: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.09/0.34 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % split_list_last
% 0.09/0.34 thf(fact_157_split__list,axiom,
% 0.09/0.34 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.34 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.34 => ? [Ys2: list @ A,Zs2: list @ A] :
% 0.09/0.34 ( Xs
% 0.09/0.34 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % split_list
% 0.09/0.34 thf(fact_158_tl__obtain__elem,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( ( tl @ A @ Xs )
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 => ~ ! [E3: A] :
% 0.09/0.34 ( Xs
% 0.09/0.34 != ( cons @ A @ E3 @ ( nil @ A ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % tl_obtain_elem
% 0.09/0.34 thf(fact_159_tl__Nil,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] :
% 0.09/0.34 ( ( ( tl @ A @ Xs )
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 = ( ( Xs
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 | ? [X3: A] :
% 0.09/0.34 ( Xs
% 0.09/0.34 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % tl_Nil
% 0.09/0.34 thf(fact_160_Nil__tl,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] :
% 0.09/0.34 ( ( ( nil @ A )
% 0.09/0.34 = ( tl @ A @ Xs ) )
% 0.09/0.34 = ( ( Xs
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 | ? [X3: A] :
% 0.09/0.34 ( Xs
% 0.09/0.34 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % Nil_tl
% 0.09/0.34 thf(fact_161_list_Oset__sel_I2_J,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A,X: A] :
% 0.09/0.34 ( ( A2
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ A2 ) ) )
% 0.09/0.34 => ( member @ A @ X @ ( set2 @ A @ A2 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % list.set_sel(2)
% 0.09/0.34 thf(fact_162_prefix__snoc,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 0.09/0.34 ( ( prefix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.09/0.34 = ( ( Xs
% 0.09/0.34 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.09/0.34 | ( prefix @ A @ Xs @ Ys ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_snoc
% 0.09/0.34 thf(fact_163_old_Opath2__split__first__last,axiom,
% 0.09/0.34 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 0.09/0.34 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.34 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 0.09/0.34 => ~ ! [Ns_1: list @ node,Ns_3: list @ node,Ns_2: list @ node] :
% 0.09/0.34 ( ( Ns
% 0.09/0.34 = ( append @ node @ Ns_1 @ ( append @ node @ Ns_3 @ Ns_2 ) ) )
% 0.09/0.34 => ( ( prefix @ node @ ( append @ node @ Ns_1 @ ( cons @ node @ X @ ( nil @ node ) ) ) @ Ns )
% 0.09/0.34 => ( ( suffix @ node @ ( cons @ node @ X @ Ns_2 ) @ Ns )
% 0.09/0.34 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns_1 @ ( cons @ node @ X @ ( nil @ node ) ) ) @ X )
% 0.09/0.34 => ( ~ ( member @ node @ X @ ( set2 @ node @ Ns_1 ) )
% 0.09/0.34 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_3 @ X )
% 0.09/0.34 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ ( cons @ node @ X @ Ns_2 ) @ M )
% 0.09/0.34 => ( member @ node @ X @ ( set2 @ node @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path2_split_first_last
% 0.09/0.34 thf(fact_164_same__prefix__nil,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ ( append @ A @ Xs @ Ys ) @ Xs )
% 0.09/0.34 = ( Ys
% 0.09/0.34 = ( nil @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % same_prefix_nil
% 0.09/0.34 thf(fact_165_old_Opath2__simple__loop,axiom,
% 0.09/0.34 ! [G2: g,N: node,Ns: list @ node,N2: node] :
% 0.09/0.34 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ N )
% 0.09/0.34 => ( ( member @ node @ N2 @ ( set2 @ node @ Ns ) )
% 0.09/0.34 => ~ ! [Ns3: list @ node] :
% 0.09/0.34 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns3 @ N )
% 0.09/0.34 => ( ( member @ node @ N2 @ ( set2 @ node @ Ns3 ) )
% 0.09/0.34 => ( ~ ( member @ node @ N @ ( set2 @ node @ ( tl @ node @ ( butlast @ node @ Ns3 ) ) ) )
% 0.09/0.34 => ~ ( ord_less_eq @ ( set @ node ) @ ( set2 @ node @ Ns3 ) @ ( set2 @ node @ Ns ) ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path2_simple_loop
% 0.09/0.34 thf(fact_166_old_Opath2__cases,axiom,
% 0.09/0.34 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.09/0.34 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.34 => ( ( ( Ns
% 0.09/0.34 = ( cons @ node @ N @ ( nil @ node ) ) )
% 0.09/0.34 => ( M != N ) )
% 0.09/0.34 => ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) @ ( tl @ node @ Ns ) @ M )
% 0.09/0.34 => ~ ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path2_cases
% 0.09/0.34 thf(fact_167_old_Opath__snoc,axiom,
% 0.09/0.34 ! [G2: g,Ns: list @ node,N: node,M: node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ N @ ( nil @ node ) ) ) )
% 0.09/0.34 => ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M ) ) )
% 0.09/0.34 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ N @ ( cons @ node @ M @ ( nil @ node ) ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path_snoc
% 0.09/0.34 thf(fact_168_phiUses__finite,axiom,
% 0.09/0.34 ! [N: node,G2: g] :
% 0.09/0.34 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.09/0.34 => ( finite_finite @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % phiUses_finite
% 0.09/0.34 thf(fact_169_old_Opath2__split__last__prop,axiom,
% 0.09/0.34 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 0.09/0.34 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.34 => ( ? [X2: node] :
% 0.09/0.34 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 0.09/0.34 & ( P @ X2 ) )
% 0.09/0.34 => ~ ! [N3: node,Ns3: list @ node] :
% 0.09/0.34 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N3 @ Ns3 @ M )
% 0.09/0.34 => ( ( P @ N3 )
% 0.09/0.34 => ( ! [X2: node] :
% 0.09/0.34 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ns3 ) ) )
% 0.09/0.34 => ~ ( P @ X2 ) )
% 0.09/0.34 => ~ ( suffix @ node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path2_split_last_prop
% 0.09/0.34 thf(fact_170_defs__finite,axiom,
% 0.09/0.34 ! [G2: g,N: node] : ( finite_finite @ val @ ( defs @ G2 @ N ) ) ).
% 0.09/0.34
% 0.09/0.34 % defs_finite
% 0.09/0.34 thf(fact_171_prefix__order_Oorder__refl,axiom,
% 0.09/0.34 ! [A: $tType,X: list @ A] : ( prefix @ A @ X @ X ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_order.order_refl
% 0.09/0.34 thf(fact_172_prefix__order_Odual__order_Orefl,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A] : ( prefix @ A @ A2 @ A2 ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_order.dual_order.refl
% 0.09/0.34 thf(fact_173_suffix__order_Oorder__refl,axiom,
% 0.09/0.34 ! [A: $tType,X: list @ A] : ( suffix @ A @ X @ X ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.order_refl
% 0.09/0.34 thf(fact_174_suffix__order_Odual__order_Orefl,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A] : ( suffix @ A @ A2 @ A2 ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.dual_order.refl
% 0.09/0.34 thf(fact_175_old_Opath__not__Nil,axiom,
% 0.09/0.34 ! [G2: g,Ns: list @ node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 0.09/0.34 => ( Ns
% 0.09/0.34 != ( nil @ node ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path_not_Nil
% 0.09/0.34 thf(fact_176_old_Opath2__hd,axiom,
% 0.09/0.34 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.09/0.34 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.34 => ( N
% 0.09/0.34 = ( hd @ node @ Ns ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path2_hd
% 0.09/0.34 thf(fact_177_old_Opath2__forget__hd,axiom,
% 0.09/0.34 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 0.09/0.34 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 0.09/0.34 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ Ns ) @ Ns @ M ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path2_forget_hd
% 0.09/0.34 thf(fact_178_old_Opath__hd,axiom,
% 0.09/0.34 ! [G2: g,N: node,Ns: list @ node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ Ns ) )
% 0.09/0.34 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path_hd
% 0.09/0.34 thf(fact_179_old_Opath__split_I2_J,axiom,
% 0.09/0.34 ! [G2: g,Ns: list @ node,M: node,Ns2: list @ node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ Ns2 ) ) )
% 0.09/0.34 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ M @ Ns2 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path_split(2)
% 0.09/0.34 thf(fact_180_List_Ofinite__set,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] : ( finite_finite @ A @ ( set2 @ A @ Xs ) ) ).
% 0.09/0.34
% 0.09/0.34 % List.finite_set
% 0.09/0.34 thf(fact_181_Cons__prefix__Cons,axiom,
% 0.09/0.34 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.09/0.34 = ( ( X = Y )
% 0.09/0.34 & ( prefix @ A @ Xs @ Ys ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % Cons_prefix_Cons
% 0.09/0.34 thf(fact_182_prefix__code_I1_J,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] : ( prefix @ A @ ( nil @ A ) @ Xs ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_code(1)
% 0.09/0.34 thf(fact_183_prefix__Nil,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ Xs @ ( nil @ A ) )
% 0.09/0.34 = ( Xs
% 0.09/0.34 = ( nil @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_Nil
% 0.09/0.34 thf(fact_184_prefix__bot_Obot_Oextremum__unique,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ A2 @ ( nil @ A ) )
% 0.09/0.34 = ( A2
% 0.09/0.34 = ( nil @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_bot.bot.extremum_unique
% 0.09/0.34 thf(fact_185_suffix__bot_Obot_Oextremum__unique,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 0.09/0.34 = ( A2
% 0.09/0.34 = ( nil @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_bot.bot.extremum_unique
% 0.09/0.34 thf(fact_186_suffix__Nil,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ Xs @ ( nil @ A ) )
% 0.09/0.34 = ( Xs
% 0.09/0.34 = ( nil @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_Nil
% 0.09/0.34 thf(fact_187_same__prefix__prefix,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs ) )
% 0.09/0.34 = ( prefix @ A @ Ys @ Zs ) ) ).
% 0.09/0.34
% 0.09/0.34 % same_prefix_prefix
% 0.09/0.34 thf(fact_188_same__suffix__suffix,axiom,
% 0.09/0.34 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ ( append @ A @ Zs @ Xs ) )
% 0.09/0.34 = ( suffix @ A @ Ys @ Zs ) ) ).
% 0.09/0.34
% 0.09/0.34 % same_suffix_suffix
% 0.09/0.34 thf(fact_189_old_Oempty__path,axiom,
% 0.09/0.34 ! [N: node,G2: g] :
% 0.09/0.34 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.09/0.34 => ( ( invar @ G2 )
% 0.09/0.34 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.empty_path
% 0.09/0.34 thf(fact_190_old_Opath__split_I1_J,axiom,
% 0.09/0.34 ! [G2: g,Ns: list @ node,M: node,Ns2: list @ node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ Ns2 ) ) )
% 0.09/0.34 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ ( nil @ node ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path_split(1)
% 0.09/0.34 thf(fact_191_old_OCons__path,axiom,
% 0.09/0.34 ! [G2: g,Ns: list @ node,N2: node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 0.09/0.34 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns ) ) ) )
% 0.09/0.34 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ns ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.Cons_path
% 0.09/0.34 thf(fact_192_old_Opath_Osimps,axiom,
% 0.09/0.34 ! [G2: g,A2: list @ node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ A2 )
% 0.09/0.34 = ( ? [N5: node] :
% 0.09/0.34 ( ( A2
% 0.09/0.34 = ( cons @ node @ N5 @ ( nil @ node ) ) )
% 0.09/0.34 & ( member @ node @ N5 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.09/0.34 & ( invar @ G2 ) )
% 0.09/0.34 | ? [Ns5: list @ node,N6: node] :
% 0.09/0.34 ( ( A2
% 0.09/0.34 = ( cons @ node @ N6 @ Ns5 ) )
% 0.09/0.34 & ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns5 )
% 0.09/0.34 & ( member @ node @ N6 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns5 ) ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path.simps
% 0.09/0.34 thf(fact_193_old_Opath_Oinducts,axiom,
% 0.09/0.34 ! [G2: g,X: list @ node,P: ( list @ node ) > $o] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X )
% 0.09/0.34 => ( ! [N4: node] :
% 0.09/0.34 ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.09/0.34 => ( ( invar @ G2 )
% 0.09/0.34 => ( P @ ( cons @ node @ N4 @ ( nil @ node ) ) ) ) )
% 0.09/0.34 => ( ! [Ns4: list @ node,N3: node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns4 )
% 0.09/0.34 => ( ( P @ Ns4 )
% 0.09/0.34 => ( ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns4 ) ) ) )
% 0.09/0.34 => ( P @ ( cons @ node @ N3 @ Ns4 ) ) ) ) )
% 0.09/0.34 => ( P @ X ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path.inducts
% 0.09/0.34 thf(fact_194_old_Opath_Ocases,axiom,
% 0.09/0.34 ! [G2: g,A2: list @ node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ A2 )
% 0.09/0.34 => ( ! [N4: node] :
% 0.09/0.34 ( ( A2
% 0.09/0.34 = ( cons @ node @ N4 @ ( nil @ node ) ) )
% 0.09/0.34 => ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 0.09/0.34 => ~ ( invar @ G2 ) ) )
% 0.09/0.34 => ~ ! [Ns4: list @ node,N3: node] :
% 0.09/0.34 ( ( A2
% 0.09/0.34 = ( cons @ node @ N3 @ Ns4 ) )
% 0.09/0.34 => ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns4 )
% 0.09/0.34 => ~ ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns4 ) ) ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path.cases
% 0.09/0.34 thf(fact_195_same__suffix__nil,axiom,
% 0.09/0.34 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ Xs )
% 0.09/0.34 = ( Ys
% 0.09/0.34 = ( nil @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % same_suffix_nil
% 0.09/0.34 thf(fact_196_hd__append2,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.09/0.34 = ( hd @ A @ Xs ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % hd_append2
% 0.09/0.34 thf(fact_197_suffix__snoc,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 0.09/0.34 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.09/0.34 = ( ( Xs
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 | ? [Zs3: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 = ( append @ A @ Zs3 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.09/0.34 & ( suffix @ A @ Zs3 @ Ys ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_snoc
% 0.09/0.34 thf(fact_198_snoc__suffix__snoc,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.09/0.34 ( ( suffix @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.09/0.34 = ( ( X = Y )
% 0.09/0.34 & ( suffix @ A @ Xs @ Ys ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % snoc_suffix_snoc
% 0.09/0.34 thf(fact_199_hd__Cons__tl,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 0.09/0.34 = Xs ) ) ).
% 0.09/0.34
% 0.09/0.34 % hd_Cons_tl
% 0.09/0.34 thf(fact_200_list_Ocollapse,axiom,
% 0.09/0.34 ! [A: $tType,List: list @ A] :
% 0.09/0.34 ( ( List
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 0.09/0.34 = List ) ) ).
% 0.09/0.34
% 0.09/0.34 % list.collapse
% 0.09/0.34 thf(fact_201_in__hd__or__tl__conv,axiom,
% 0.09/0.34 ! [A: $tType,L: list @ A,X: A] :
% 0.09/0.34 ( ( L
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( ( X
% 0.09/0.34 = ( hd @ A @ L ) )
% 0.09/0.34 | ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ L ) ) ) )
% 0.09/0.34 = ( member @ A @ X @ ( set2 @ A @ L ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % in_hd_or_tl_conv
% 0.09/0.34 thf(fact_202_old_Opath__invar,axiom,
% 0.09/0.34 ! [G2: g,Ns: list @ node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 0.09/0.34 => ( invar @ G2 ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path_invar
% 0.09/0.34 thf(fact_203_old_Opath__in___092_060alpha_062n,axiom,
% 0.09/0.34 ! [G2: g,Ns: list @ node,N: node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 0.09/0.34 => ( ( member @ node @ N @ ( set2 @ node @ Ns ) )
% 0.09/0.34 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path_in_\<alpha>n
% 0.09/0.34 thf(fact_204_old_Opath__by__tail,axiom,
% 0.09/0.34 ! [G2: g,N: node,N2: node,Ns: list @ node,Ms: list @ node] :
% 0.09/0.34 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( cons @ node @ N2 @ Ns ) ) )
% 0.09/0.34 => ( ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ns ) )
% 0.09/0.34 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ms ) ) )
% 0.09/0.34 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( cons @ node @ N2 @ Ms ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % old.path_by_tail
% 0.09/0.34 thf(fact_205_set__mono__suffix,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ Xs @ Ys )
% 0.09/0.34 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % set_mono_suffix
% 0.09/0.34 thf(fact_206_subset__Collect__conv,axiom,
% 0.09/0.34 ! [A: $tType,S: set @ A,P: A > $o] :
% 0.09/0.34 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 0.09/0.34 = ( ! [X3: A] :
% 0.09/0.34 ( ( member @ A @ X3 @ S )
% 0.09/0.34 => ( P @ X3 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % subset_Collect_conv
% 0.09/0.34 thf(fact_207_ord__eq__le__eq__trans,axiom,
% 0.09/0.34 ! [A: $tType] :
% 0.09/0.34 ( ( ord @ A )
% 0.09/0.34 => ! [A2: A,B: A,C: A,D: A] :
% 0.09/0.34 ( ( A2 = B )
% 0.09/0.34 => ( ( ord_less_eq @ A @ B @ C )
% 0.09/0.34 => ( ( C = D )
% 0.09/0.34 => ( ord_less_eq @ A @ A2 @ D ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % ord_eq_le_eq_trans
% 0.09/0.34 thf(fact_208_suffix__ConsD2,axiom,
% 0.09/0.34 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.09/0.34 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_ConsD2
% 0.09/0.34 thf(fact_209_suffix__ConsI,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 0.09/0.34 ( ( suffix @ A @ Xs @ Ys )
% 0.09/0.34 => ( suffix @ A @ Xs @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_ConsI
% 0.09/0.34 thf(fact_210_suffix__ConsD,axiom,
% 0.09/0.34 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.09/0.34 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_ConsD
% 0.09/0.34 thf(fact_211_suffix__Cons,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ Xs @ ( cons @ A @ Y @ Ys ) )
% 0.09/0.34 = ( ( Xs
% 0.09/0.34 = ( cons @ A @ Y @ Ys ) )
% 0.09/0.34 | ( suffix @ A @ Xs @ Ys ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_Cons
% 0.09/0.34 thf(fact_212_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 0.09/0.34 => ( A2
% 0.09/0.34 = ( nil @ A ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_bot.bot.extremum_uniqueI
% 0.09/0.34 thf(fact_213_suffix__bot_Obot_Oextremum,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A] : ( suffix @ A @ ( nil @ A ) @ A2 ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_bot.bot.extremum
% 0.09/0.34 thf(fact_214_Nil__suffix,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( nil @ A ) @ Xs ) ).
% 0.09/0.34
% 0.09/0.34 % Nil_suffix
% 0.09/0.34 thf(fact_215_suffixE,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ Xs @ Ys )
% 0.09/0.34 => ~ ! [Zs2: list @ A] :
% 0.09/0.34 ( Ys
% 0.09/0.34 != ( append @ A @ Zs2 @ Xs ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffixE
% 0.09/0.34 thf(fact_216_suffixI,axiom,
% 0.09/0.34 ! [A: $tType,Ys: list @ A,Zs: list @ A,Xs: list @ A] :
% 0.09/0.34 ( ( Ys
% 0.09/0.34 = ( append @ A @ Zs @ Xs ) )
% 0.09/0.34 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffixI
% 0.09/0.34 thf(fact_217_Sublist_Osuffix__def,axiom,
% 0.09/0.34 ! [A: $tType] :
% 0.09/0.34 ( ( suffix @ A )
% 0.09/0.34 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 0.09/0.34 ? [Zs3: list @ A] :
% 0.09/0.34 ( Ys3
% 0.09/0.34 = ( append @ A @ Zs3 @ Xs3 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % Sublist.suffix_def
% 0.09/0.34 thf(fact_218_suffix__append,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ Zs ) )
% 0.09/0.34 = ( ( suffix @ A @ Xs @ Zs )
% 0.09/0.34 | ? [Xs5: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 = ( append @ A @ Xs5 @ Zs ) )
% 0.09/0.34 & ( suffix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_append
% 0.09/0.34 thf(fact_219_suffix__appendD,axiom,
% 0.09/0.34 ! [A: $tType,Zs: list @ A,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ ( append @ A @ Zs @ Xs ) @ Ys )
% 0.09/0.34 => ( suffix @ A @ Xs @ Ys ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_appendD
% 0.09/0.34 thf(fact_220_suffix__appendI,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ Xs @ Ys )
% 0.09/0.34 => ( suffix @ A @ Xs @ ( append @ A @ Zs @ Ys ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_appendI
% 0.09/0.34 thf(fact_221_suffix__tl,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( tl @ A @ Xs ) @ Xs ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_tl
% 0.09/0.34 thf(fact_222_suffix__same__cases,axiom,
% 0.09/0.34 ! [A: $tType,Xs_1: list @ A,Ys: list @ A,Xs_2: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ Xs_1 @ Ys )
% 0.09/0.34 => ( ( suffix @ A @ Xs_2 @ Ys )
% 0.09/0.34 => ( ( suffix @ A @ Xs_1 @ Xs_2 )
% 0.09/0.34 | ( suffix @ A @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_same_cases
% 0.09/0.34 thf(fact_223_suffix__order_Oeq__iff,axiom,
% 0.09/0.34 ! [A: $tType] :
% 0.09/0.34 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 0.09/0.34 = ( ^ [X3: list @ A,Y3: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ X3 @ Y3 )
% 0.09/0.34 & ( suffix @ A @ Y3 @ X3 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.eq_iff
% 0.09/0.34 thf(fact_224_suffix__order_Oantisym,axiom,
% 0.09/0.34 ! [A: $tType,X: list @ A,Y: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ X @ Y )
% 0.09/0.34 => ( ( suffix @ A @ Y @ X )
% 0.09/0.34 => ( X = Y ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.antisym
% 0.09/0.34 thf(fact_225_suffix__order_Oeq__refl,axiom,
% 0.09/0.34 ! [A: $tType,X: list @ A,Y: list @ A] :
% 0.09/0.34 ( ( X = Y )
% 0.09/0.34 => ( suffix @ A @ X @ Y ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.eq_refl
% 0.09/0.34 thf(fact_226_suffix__order_Oorder_Otrans,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ A2 @ B )
% 0.09/0.34 => ( ( suffix @ A @ B @ C )
% 0.09/0.34 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.order.trans
% 0.09/0.34 thf(fact_227_suffix__order_Oorder__trans,axiom,
% 0.09/0.34 ! [A: $tType,X: list @ A,Y: list @ A,Z3: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ X @ Y )
% 0.09/0.34 => ( ( suffix @ A @ Y @ Z3 )
% 0.09/0.34 => ( suffix @ A @ X @ Z3 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.order_trans
% 0.09/0.34 thf(fact_228_suffix__order_Oantisym__conv,axiom,
% 0.09/0.34 ! [A: $tType,Y: list @ A,X: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ Y @ X )
% 0.09/0.34 => ( ( suffix @ A @ X @ Y )
% 0.09/0.34 = ( X = Y ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.antisym_conv
% 0.09/0.34 thf(fact_229_suffix__order_Oorder_Oeq__iff,axiom,
% 0.09/0.34 ! [A: $tType] :
% 0.09/0.34 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 0.09/0.34 = ( ^ [A5: list @ A,B4: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ A5 @ B4 )
% 0.09/0.34 & ( suffix @ A @ B4 @ A5 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.order.eq_iff
% 0.09/0.34 thf(fact_230_suffix__order_Oorder_Oantisym,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A,B: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ A2 @ B )
% 0.09/0.34 => ( ( suffix @ A @ B @ A2 )
% 0.09/0.34 => ( A2 = B ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.order.antisym
% 0.09/0.34 thf(fact_231_suffix__order_Oord__eq__le__trans,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 0.09/0.34 ( ( A2 = B )
% 0.09/0.34 => ( ( suffix @ A @ B @ C )
% 0.09/0.34 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.ord_eq_le_trans
% 0.09/0.34 thf(fact_232_suffix__order_Oord__le__eq__trans,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ A2 @ B )
% 0.09/0.34 => ( ( B = C )
% 0.09/0.34 => ( suffix @ A @ A2 @ C ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.ord_le_eq_trans
% 0.09/0.34 thf(fact_233_suffix__order_Odual__order_Otrans,axiom,
% 0.09/0.34 ! [A: $tType,B: list @ A,A2: list @ A,C: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ B @ A2 )
% 0.09/0.34 => ( ( suffix @ A @ C @ B )
% 0.09/0.34 => ( suffix @ A @ C @ A2 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.dual_order.trans
% 0.09/0.34 thf(fact_234_suffix__order_Odual__order_Oeq__iff,axiom,
% 0.09/0.34 ! [A: $tType] :
% 0.09/0.34 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 0.09/0.34 = ( ^ [A5: list @ A,B4: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ B4 @ A5 )
% 0.09/0.34 & ( suffix @ A @ A5 @ B4 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.dual_order.eq_iff
% 0.09/0.34 thf(fact_235_suffix__order_Odual__order_Oantisym,axiom,
% 0.09/0.34 ! [A: $tType,B: list @ A,A2: list @ A] :
% 0.09/0.34 ( ( suffix @ A @ B @ A2 )
% 0.09/0.34 => ( ( suffix @ A @ A2 @ B )
% 0.09/0.34 => ( A2 = B ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % suffix_order.dual_order.antisym
% 0.09/0.34 thf(fact_236_list_Osel_I1_J,axiom,
% 0.09/0.34 ! [A: $tType,X21: A,X22: list @ A] :
% 0.09/0.34 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.09/0.34 = X21 ) ).
% 0.09/0.34
% 0.09/0.34 % list.sel(1)
% 0.09/0.34 thf(fact_237_finite__list,axiom,
% 0.09/0.34 ! [A: $tType,A3: set @ A] :
% 0.09/0.34 ( ( finite_finite @ A @ A3 )
% 0.09/0.34 => ? [Xs2: list @ A] :
% 0.09/0.34 ( ( set2 @ A @ Xs2 )
% 0.09/0.34 = A3 ) ) ).
% 0.09/0.34
% 0.09/0.34 % finite_list
% 0.09/0.34 thf(fact_238_subset__code_I1_J,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,B5: set @ A] :
% 0.09/0.34 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ B5 )
% 0.09/0.34 = ( ! [X3: A] :
% 0.09/0.34 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.09/0.34 => ( member @ A @ X3 @ B5 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % subset_code(1)
% 0.09/0.34 thf(fact_239_set__mono__prefix,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ Xs @ Ys )
% 0.09/0.34 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % set_mono_prefix
% 0.09/0.34 thf(fact_240_list_Oset__sel_I1_J,axiom,
% 0.09/0.34 ! [A: $tType,A2: list @ A] :
% 0.09/0.34 ( ( A2
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( member @ A @ ( hd @ A @ A2 ) @ ( set2 @ A @ A2 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % list.set_sel(1)
% 0.09/0.34 thf(fact_241_hd__in__set,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( member @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ Xs ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % hd_in_set
% 0.09/0.34 thf(fact_242_hd__append,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ( ( ( Xs
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.09/0.34 = ( hd @ A @ Ys ) ) )
% 0.09/0.34 & ( ( Xs
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.09/0.34 = ( hd @ A @ Xs ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % hd_append
% 0.09/0.34 thf(fact_243_longest__common__prefix,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.09/0.34 ? [Ps: list @ A,Xs6: list @ A,Ys4: list @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 = ( append @ A @ Ps @ Xs6 ) )
% 0.09/0.34 & ( Ys
% 0.09/0.34 = ( append @ A @ Ps @ Ys4 ) )
% 0.09/0.34 & ( ( Xs6
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 | ( Ys4
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 | ( ( hd @ A @ Xs6 )
% 0.09/0.34 != ( hd @ A @ Ys4 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % longest_common_prefix
% 0.09/0.34 thf(fact_244_not__suffix__cases,axiom,
% 0.09/0.34 ! [A: $tType,Ps2: list @ A,Ls: list @ A] :
% 0.09/0.34 ( ~ ( suffix @ A @ Ps2 @ Ls )
% 0.09/0.34 => ( ( ( Ps2
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( Ls
% 0.09/0.34 != ( nil @ A ) ) )
% 0.09/0.34 => ( ! [A4: A,As: list @ A] :
% 0.09/0.34 ( ( Ps2
% 0.09/0.34 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 0.09/0.34 => ! [X4: A,Xs2: list @ A] :
% 0.09/0.34 ( ( Ls
% 0.09/0.34 = ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 0.09/0.34 => ( ( X4 = A4 )
% 0.09/0.34 => ( suffix @ A @ As @ Xs2 ) ) ) )
% 0.09/0.34 => ~ ! [A4: A] :
% 0.09/0.34 ( ? [As: list @ A] :
% 0.09/0.34 ( Ps2
% 0.09/0.34 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 0.09/0.34 => ! [X4: A] :
% 0.09/0.34 ( ? [Xs2: list @ A] :
% 0.09/0.34 ( Ls
% 0.09/0.34 = ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 0.09/0.34 => ( X4 = A4 ) ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % not_suffix_cases
% 0.09/0.34 thf(fact_245_not__suffix__induct,axiom,
% 0.09/0.34 ! [A: $tType,Ps2: list @ A,Ls: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.09/0.34 ( ~ ( suffix @ A @ Ps2 @ Ls )
% 0.09/0.34 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( nil @ A ) )
% 0.09/0.34 => ( ! [X4: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.09/0.34 ( ( X4 != Y2 )
% 0.09/0.34 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) )
% 0.09/0.34 => ( ! [X4: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.09/0.34 ( ( X4 = Y2 )
% 0.09/0.34 => ( ~ ( suffix @ A @ Xs2 @ Ys2 )
% 0.09/0.34 => ( ( P @ Xs2 @ Ys2 )
% 0.09/0.34 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ) )
% 0.09/0.34 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % not_suffix_induct
% 0.09/0.34 thf(fact_246_list_Oexpand,axiom,
% 0.09/0.34 ! [A: $tType,List: list @ A,List2: list @ A] :
% 0.09/0.34 ( ( ( List
% 0.09/0.34 = ( nil @ A ) )
% 0.09/0.34 = ( List2
% 0.09/0.34 = ( nil @ A ) ) )
% 0.09/0.34 => ( ( ( List
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( List2
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( ( hd @ A @ List )
% 0.09/0.34 = ( hd @ A @ List2 ) )
% 0.09/0.34 & ( ( tl @ A @ List )
% 0.09/0.34 = ( tl @ A @ List2 ) ) ) ) )
% 0.09/0.34 => ( List = List2 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % list.expand
% 0.09/0.34 thf(fact_247_not__hd__in__tl,axiom,
% 0.09/0.34 ! [A: $tType,X: A,Xs: list @ A] :
% 0.09/0.34 ( ( X
% 0.09/0.34 != ( hd @ A @ Xs ) )
% 0.09/0.34 => ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.09/0.34 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % not_hd_in_tl
% 0.09/0.34 thf(fact_248_set__subset__Cons,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,X: A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % set_subset_Cons
% 0.09/0.34 thf(fact_249_list_Oexhaust__sel,axiom,
% 0.09/0.34 ! [A: $tType,List: list @ A] :
% 0.09/0.34 ( ( List
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( List
% 0.09/0.34 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % list.exhaust_sel
% 0.09/0.34 thf(fact_250_tl__subset,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,A3: set @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A3 )
% 0.09/0.34 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( tl @ A @ Xs ) ) @ A3 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % tl_subset
% 0.09/0.34 thf(fact_251_butlast__subset,axiom,
% 0.09/0.34 ! [A: $tType,Xs: list @ A,A3: set @ A] :
% 0.09/0.34 ( ( Xs
% 0.09/0.34 != ( nil @ A ) )
% 0.09/0.34 => ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A3 )
% 0.09/0.34 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( butlast @ A @ Xs ) ) @ A3 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % butlast_subset
% 0.09/0.34 thf(fact_252_prefix__same__cases,axiom,
% 0.09/0.34 ! [A: $tType,Xs_1: list @ A,Ys: list @ A,Xs_2: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ Xs_1 @ Ys )
% 0.09/0.34 => ( ( prefix @ A @ Xs_2 @ Ys )
% 0.09/0.34 => ( ( prefix @ A @ Xs_1 @ Xs_2 )
% 0.09/0.34 | ( prefix @ A @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_same_cases
% 0.09/0.34 thf(fact_253_prefix__order_Oeq__iff,axiom,
% 0.09/0.34 ! [A: $tType] :
% 0.09/0.34 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 0.09/0.34 = ( ^ [X3: list @ A,Y3: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ X3 @ Y3 )
% 0.09/0.34 & ( prefix @ A @ Y3 @ X3 ) ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_order.eq_iff
% 0.09/0.34 thf(fact_254_prefix__order_Oantisym,axiom,
% 0.09/0.34 ! [A: $tType,X: list @ A,Y: list @ A] :
% 0.09/0.34 ( ( prefix @ A @ X @ Y )
% 0.09/0.34 => ( ( prefix @ A @ Y @ X )
% 0.09/0.34 => ( X = Y ) ) ) ).
% 0.09/0.34
% 0.09/0.34 % prefix_order.antisym
% 0.09/0.34
% 0.09/0.34 % Subclasses (2)
% 0.09/0.34 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.09/0.34 ! [A: $tType] :
% 0.09/0.34 ( ( linorder @ A )
% 0.09/0.34 => ( type @ A ) ) ).
% 0.09/0.34
% 0.09/0.34 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.09/0.34 ! [A: $tType] :
% 0.09/0.34 ( ( linorder @ A )
% 0.09/0.34 => ( ord @ A ) ) ).
% 0.09/0.34
% 0.09/0.34 % Type constructors (4)
% 0.09/0.34 thf(tcon_fun___Orderings_Oord,axiom,
% 0.09/0.34 ! [A6: $tType,A7: $tType] :
% 0.09/0.34 ( ( ord @ A7 )
% 0.09/0.34 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.09/0.34
% 0.09/0.34 thf(tcon_Set_Oset___Orderings_Oord_1,axiom,
% 0.09/0.34 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 0.09/0.34
% 0.09/0.34 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.09/0.34 linorder @ $o ).
% 0.09/0.34
% 0.09/0.34 thf(tcon_HOL_Obool___Orderings_Oord_2,axiom,
% 0.09/0.34 ord @ $o ).
% 0.09/0.34
% 0.09/0.34 % Free types (2)
% 0.09/0.34 thf(tfree_0,hypothesis,
% 0.09/0.34 linorder @ val ).
% 0.09/0.34
% 0.09/0.34 thf(tfree_1,hypothesis,
% 0.09/0.34 linorder @ node ).
% 0.09/0.34
% 0.09/0.34 % Conjectures (1)
% 0.09/0.34 thf(conj_0,conjecture,
% 0.09/0.34 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append @ node @ ns @ ( tl @ node @ ri ) ) @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 0.09/0.34
% 0.09/0.34 %------------------------------------------------------------------------------
% 0.09/0.34 ------------------------
% 2.15/1.38 ---- Embedded in THF ---
% 2.15/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.15/1.38 %%% Generated on Tue Feb 24 03:25:26 EST 2026
% 2.15/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 2.15/1.38 %%% Logic specification used:
% 2.15/1.38 %%% thf(spec, logic, $$dhol).
% 2.15/1.38
% 2.15/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FAhNdHU93a/DTF2DTF28396.p
% 2.15/1.38 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.15/1.38 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.15/1.38 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.15/1.38 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.15/1.38 thf(ty_tf_edgeD, type, edgeD: $tType).
% 2.15/1.38 thf(ty_tf_node, type, node: $tType).
% 2.15/1.38 thf(ty_tf_val, type, val: $tType).
% 2.15/1.38 thf(ty_tf_g, type, g: $tType).
% 2.15/1.38 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.15/1.38 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.15/1.38 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.15/1.38 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.15/1.38 thf(sy_c_Graph__path_Ograph__path__base_Opath, type, graph_1146196722h_path: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > ((list @ Node) > $o)))))))).
% 2.15/1.38 thf(sy_c_Graph__path_Ograph__path__base_Opath2, type, graph_1661282752_path2: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (list @ Node)) > ((G > $o) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > ((list @ Node) > (Node > $o)))))))))).
% 2.15/1.38 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors, type, graph_1201503639essors: (!> [G:$tType,Node:$tType,EdgeD:$tType]: (((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > (G > (Node > (list @ Node))))))).
% 2.15/1.38 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.15/1.38 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.15/1.38 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.15/1.38 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.15/1.38 thf(sy_c_List_Olist_Ohd, type, hd: (!> [A:$tType]: (((list @ A) > A)))).
% 2.15/1.38 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.15/1.38 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.15/1.38 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.15/1.38 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses, type, sSA_CFG_SSA_phiUses: (!> [G:$tType,Node:$tType,EdgeD:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (list @ ((product_prod @ Node) @ EdgeD)))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Node > (set @ Val))))))))).
% 2.15/1.38 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode, type, sSA_CF1081484811efNode: (!> [G:$tType,Node:$tType,Val:$tType]: (((G > (list @ Node)) > ((G > (Node > (set @ Val))) > ((G > (((product_prod @ Node) @ Val) > (option @ (list @ Val)))) > (G > (Val > Node)))))))).
% 2.15/1.38 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 > $o))))))))).
% 2.15/1.38 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.15/1.38 thf(sy_c_Sublist_Oprefix, type, prefix: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.15/1.38 thf(sy_c_Sublist_Osuffix, type, suffix: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.15/1.38 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.15/1.38 thf(sy_v__092_060alpha_062n, type, alpha_n: (g > (list @ node))).
% 2.15/1.38 thf(sy_v__092_060phi_062_092_060_094sub_062r, type, phi_r: val).
% 2.15/1.38 thf(sy_v_defs, type, defs: (g > (node > (set @ val)))).
% 2.15/1.38 thf(sy_v_g, type, g2: g).
% 2.15/1.38 thf(sy_v_i____, type, i: node).
% 2.15/1.38 thf(sy_v_inEdges_H, type, inEdges: (g > (node > (list @ ((product_prod @ node) @ edgeD))))).
% 2.15/1.38 thf(sy_v_invar, type, invar: (g > $o)).
% 2.15/1.38 thf(sy_v_m, type, m: node).
% 2.15/1.38 thf(sy_v_ms, type, ms: (list @ node)).
% 2.15/1.38 thf(sy_v_ms_H____, type, ms2: (list @ node)).
% 2.15/1.38 thf(sy_v_n, type, n: node).
% 2.15/1.38 thf(sy_v_ns, type, ns: (list @ node)).
% 2.15/1.38 thf(sy_v_phis, type, phis: (g > (((product_prod @ node) @ val) > (option @ (list @ val))))).
% 2.15/1.38 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____, type, pred_phi_r: node).
% 2.15/1.38 thf(sy_v_r, type, r: val).
% 2.15/1.38 thf(sy_v_ri____, type, ri: (list @ node)).
% 2.15/1.38 thf(sy_v_rs_H____, type, rs: (list @ node)).
% 2.15/1.38 thf(sy_v_rs____, type, rs2: (list @ node)).
% 2.15/1.38 thf(sy_v_s, type, s: val).
% 2.15/1.38 thf(fact_0_False, axiom, (r != phi_r)).
% 2.15/1.38 thf(fact_1_ri__is__valid, axiom, (i = ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r))).
% 2.15/1.38 thf(fact_2_old_Oinvar, axiom, (! [G2:g]: ((invar @ G2)))).
% 2.15/1.38 thf(fact_3_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))).
% 2.15/1.38 thf(fact_4_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)).
% 2.15/1.38 thf(fact_5_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)))))).
% 2.15/1.38 thf(fact_6__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))).
% 2.15/1.38 thf(fact_7_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)).
% 2.15/1.38 thf(fact_8_assms_I10_J, axiom, (((((((((sSA_CF1165125185phiArg @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r) @ r)).
% 2.15/1.38 thf(fact_9_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))).
% 2.15/1.38 thf(fact_10_ms_H__props_I1_J, axiom, ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ m) @ ms2) @ i)).
% 2.15/1.38 thf(fact_11__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))))))).
% 2.15/1.38 thf(fact_12_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))))).
% 2.15/1.38 thf(fact_13_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)))))).
% 2.15/1.38 thf(fact_14_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)))))).
% 2.15/1.38 thf(fact_15_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))).
% 2.15/1.38 thf(fact_16_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))))))).
% 2.15/1.38 thf(fact_17_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)))))).
% 2.15/1.38 thf(fact_18_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)))))))).
% 2.15/1.38 thf(fact_19_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))))))))).
% 2.15/1.38 thf(fact_20_ri__props_I2_J, axiom, (((member @ node) @ i) @ ((set2 @ node) @ ms))).
% 2.15/1.38 thf(fact_21_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))))))).
% 2.15/1.38 thf(fact_22_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)))))).
% 2.15/1.38 thf(fact_23_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))))).
% 2.15/1.38 thf(fact_24_rs__props_I3_J, axiom, (~ ((((member @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r)) @ ((set2 @ node) @ ((tl @ node) @ rs2)))))).
% 2.15/1.38 thf(fact_25_rs_H__loopfree, axiom, (~ ((((member @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ r)) @ ((set2 @ node) @ ((tl @ node) @ rs)))))).
% 2.15/1.38 thf(fact_26_rs__def, axiom, (rs2 = (((append @ node) @ rs) @ (((cons @ node) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r)) @ (nil @ node))))).
% 2.15/1.38 thf(fact_27_ri__props_I4_J, axiom, (((prefix @ node) @ ri) @ rs2)).
% 2.15/1.38 thf(fact_28_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)))))).
% 2.15/1.38 thf(fact_29_ms_H__props_I3_J, axiom, (~ ((((member @ node) @ i) @ ((set2 @ node) @ ((butlast @ node) @ ms2)))))).
% 2.15/1.38 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))))).
% 2.15/1.38 thf(fact_31_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))).
% 2.15/1.38 thf(fact_32_tl__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != (nil @ A)) => (((tl @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ ((tl @ A) @ Xs)) @ Ys)))))).
% 2.15/1.38 thf(fact_33_list__e__eq__lel_I2_J, axiom, (! [A:$tType,L1:(list @ A),E:A,L2:(list @ A),E2:A]: ((((((append @ A) @ L1) @ (((cons @ A) @ E) @ L2)) = (((cons @ A) @ E2) @ (nil @ A))) = ((L1 = (nil @ A)) & ((E = E2) & (L2 = (nil @ A)))))))).
% 2.15/1.38 thf(fact_34_list__e__eq__lel_I1_J, axiom, (! [A:$tType,E2:A,L1:(list @ A),E:A,L2:(list @ A)]: ((((((cons @ A) @ E2) @ (nil @ A)) = (((append @ A) @ L1) @ (((cons @ A) @ E) @ L2))) = ((L1 = (nil @ A)) & ((E = E2) & (L2 = (nil @ A)))))))).
% 2.15/1.38 thf(fact_35_list__se__match_I4_J, axiom, (! [A:$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))))))))).
% 2.15/1.38 thf(fact_36_list__se__match_I3_J, axiom, (! [A:$tType,L1:(list @ A),A2:A,L2:(list @ A)]: (((L1 != (nil @ A)) => (((((cons @ A) @ A2) @ (nil @ A)) = (((append @ A) @ L1) @ L2)) = ((L1 = (((cons @ A) @ A2) @ (nil @ A))) & (L2 = (nil @ A)))))))).
% 2.15/1.38 thf(fact_37_list__se__match_I2_J, axiom, (! [A:$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))))))))).
% 2.15/1.38 thf(fact_38_list__se__match_I1_J, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A),A2:A]: (((L1 != (nil @ A)) => (((((append @ A) @ L1) @ L2) = (((cons @ A) @ A2) @ (nil @ A))) = ((L1 = (((cons @ A) @ A2) @ (nil @ A))) & (L2 = (nil @ A)))))))).
% 2.15/1.38 thf(fact_39_list__ee__eq__leel_I2_J, axiom, (! [A:$tType,L1:(list @ A),E1:A,E22:A,L2:(list @ A),E12:A,E23:A]: ((((((append @ A) @ L1) @ (((cons @ A) @ E1) @ (((cons @ A) @ E22) @ L2))) = (((cons @ A) @ E12) @ (((cons @ A) @ E23) @ (nil @ A)))) = ((L1 = (nil @ A)) & ((E12 = E1) & ((E23 = E22) & (L2 = (nil @ A))))))))).
% 2.15/1.38 thf(fact_40_list__ee__eq__leel_I1_J, axiom, (! [A:$tType,E12:A,E23:A,L1:(list @ A),E1:A,E22:A,L2:(list @ A)]: ((((((cons @ A) @ E12) @ (((cons @ A) @ E23) @ (nil @ A))) = (((append @ A) @ L1) @ (((cons @ A) @ E1) @ (((cons @ A) @ E22) @ L2)))) = ((L1 = (nil @ A)) & ((E12 = E1) & ((E23 = E22) & (L2 = (nil @ A))))))))).
% 2.15/1.38 thf(fact_41_ms_H__props_I2_J, axiom, (((prefix @ node) @ ms2) @ ms)).
% 2.15/1.38 thf(fact_42_ri__props_I3_J, axiom, (! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((butlast @ node) @ ri))) => (~ ((((member @ node) @ X2) @ ((set2 @ node) @ ms)))))))).
% 2.15/1.38 thf(fact_43_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.15/1.38 thf(fact_44_append_Oassoc, axiom, (! [A:$tType,A2:(list @ A),B:(list @ A),C:(list @ A)]: (((((append @ A) @ (((append @ A) @ A2) @ B)) @ C) = (((append @ A) @ A2) @ (((append @ A) @ B) @ C)))))).
% 2.15/1.38 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.15/1.38 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) = A3)))).
% 2.15/1.38 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.15/1.38 thf(fact_48_ext, axiom, (! [B2:$tType,A:$tType,F:(A > B2),G2:(A > B2)]: (((! [X4:A]: (((F @ X4) = (G2 @ X4)))) => (F = G2))))).
% 2.15/1.38 thf(fact_49_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)))))).
% 2.15/1.38 thf(fact_50_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs) @ Xs)) = (Ys = Zs))))).
% 2.15/1.38 thf(fact_51_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs)) = (Ys = Zs))))).
% 2.15/1.38 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)))))))).
% 2.15/1.38 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))))))))).
% 2.15/1.38 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)))))))).
% 2.15/1.38 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)))))).
% 2.15/1.38 thf(fact_56_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.15/1.38 thf(fact_57_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.15/1.38 thf(fact_58_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.15/1.38 thf(fact_59_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.15/1.38 thf(fact_60_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.15/1.38 thf(fact_61_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.15/1.38 thf(fact_62_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.15/1.38 thf(fact_63_empty__append__eq__id, axiom, (! [A:$tType]: ((((append @ A) @ (nil @ A)) = (^ [X3:(list @ A)]: (X3)))))).
% 2.15/1.38 thf(fact_64_append_Oright__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ A2) @ (nil @ A)) = A2)))).
% 2.15/1.38 thf(fact_65_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))))))))))))))).
% 2.15/1.38 thf(fact_66_old_Opath2__prefix__ex, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,M2:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ M2) @ ((set2 @ node) @ Ns)) => (~ ((! [Ns3:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns3) @ M2) => ((((prefix @ node) @ Ns3) @ Ns) => (((member @ node) @ M2) @ ((set2 @ node) @ ((butlast @ node) @ Ns3)))))))))))))).
% 2.15/1.38 thf(fact_67_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)))) => (~ ((! [M3:node,Ns3:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns3) @ M3) => ((P @ M3) => ((! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((butlast @ node) @ Ns3))) => (~ ((P @ X2)))))) => (~ ((((prefix @ node) @ Ns3) @ Ns))))))))))))))).
% 2.15/1.38 thf(fact_68_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)) => ((! [Ns4:(list @ node),N3:node,N4:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N4) @ Ns4) @ M) => ((((P @ N4) @ Ns4) @ M) => ((((member @ node) @ N3) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ N4))) => (((P @ N3) @ (((cons @ node) @ N3) @ Ns4)) @ M)))))) => (((P @ N) @ Ns) @ M))))))).
% 2.15/1.38 thf(fact_69_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)))))))))))))))).
% 2.15/1.38 thf(fact_70_old_Opath2__prefix, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,Ns2:(list @ node),M2:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((prefix @ node) @ (((append @ node) @ Ns2) @ (((cons @ node) @ M2) @ (nil @ node)))) @ Ns) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns2) @ (((cons @ node) @ M2) @ (nil @ node)))) @ M2)))))).
% 2.15/1.38 thf(fact_71_old_Opath2__rev__induct, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,P:(node > ((list @ node) > (node > $o)))]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => (((P @ N) @ (((cons @ node) @ N) @ (nil @ node))) @ N)) => ((! [Ns4:(list @ node),M3:node,M4:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns4) @ M3) => ((((P @ N) @ Ns4) @ M3) => ((((member @ node) @ M3) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ M4))) => (((P @ N) @ (((append @ node) @ Ns4) @ (((cons @ node) @ M4) @ (nil @ node)))) @ M4)))))) => (((P @ N) @ Ns) @ M))))))).
% 2.15/1.38 thf(fact_72_old_Opath2__snoc, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,M2:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((member @ node) @ M) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ M2))) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ (((append @ node) @ Ns) @ (((cons @ node) @ M2) @ (nil @ node)))) @ M2)))))).
% 2.15/1.38 thf(fact_73_append1__eq__conv, axiom, (! [A:$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)))))).
% 2.15/1.38 thf(fact_74_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = Xs)))).
% 2.15/1.38 thf(fact_75__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)))))))))).
% 2.15/1.38 thf(fact_76__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))))))))))).
% 2.15/1.38 thf(fact_77_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)))))).
% 2.15/1.38 thf(fact_78_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 2.15/1.38 thf(fact_79_in__set__butlastD, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) => (((member @ A) @ X) @ ((set2 @ A) @ Xs)))))).
% 2.15/1.38 thf(fact_80_butlast__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((butlast @ A) @ ((tl @ A) @ Xs)) = ((tl @ A) @ ((butlast @ A) @ Xs)))))).
% 2.15/1.38 thf(fact_81_butlast_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (nil @ A))) & ((Xs != (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((butlast @ A) @ Xs)))))))).
% 2.15/1.38 thf(fact_82_butlast__append, axiom, (! [A:$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)))))))).
% 2.15/1.38 thf(fact_83_in__set__butlast__appendI, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: ((((((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) | (((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Ys)))) => (((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ (((append @ A) @ Xs) @ Ys)))))))).
% 2.15/1.38 thf(fact_84_butlast__eq__cons__conv, axiom, (! [A:$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))))))))))).
% 2.15/1.38 thf(fact_85_butlast__eq__consE, axiom, (! [A:$tType,L:(list @ A),X:A,Xs:(list @ A)]: (((((butlast @ A) @ L) = (((cons @ A) @ X) @ Xs)) => (~ ((! [Xl2:A]: ((L != (((cons @ A) @ X) @ (((append @ A) @ Xs) @ (((cons @ A) @ Xl2) @ (nil @ A))))))))))))).
% 2.15/1.38 thf(fact_86_list__tail__coinc, axiom, (! [A:$tType,N1:A,R1:(list @ A),N22:A,R2:(list @ A)]: ((((((cons @ A) @ N1) @ R1) = (((cons @ A) @ N22) @ R2)) => ((N1 = N22) & (R1 = R2)))))).
% 2.15/1.38 thf(fact_87_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.15/1.38 thf(fact_88_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs:(list @ A),Ys:(list @ A),Us:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs) => ((Ys = (((append @ A) @ Xs1) @ Us)) => ((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Us))))))).
% 2.15/1.38 thf(fact_89_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Ts)) = (? [Us2:(list @ A)]: ((((Xs = (((append @ A) @ Zs) @ Us2)) & ((((append @ A) @ Us2) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us2) = Zs) & (Ys = (((append @ A) @ Us2) @ Ts)))))))))).
% 2.15/1.38 thf(fact_90_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A,Ys2:(list @ A)]: (((P @ Ys2) => (P @ (((cons @ A) @ X4) @ Ys2))))) => (P @ A0))))))))).
% 2.15/1.38 thf(fact_91_mergesort__by__rel__merge__induct, axiom, (! [A:$tType,B2:$tType,P:((list @ A) > ((list @ B2) > $o)),R:(A > (B2 > $o)),Xs:(list @ A),Ys:(list @ B2)]: (((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ B2)))) => ((! [X_1:(list @ B2)]: (((P @ (nil @ A)) @ X_1))) => ((! [X4:A,Xs2:(list @ A),Y2:B2,Ys2:(list @ B2)]: ((((R @ X4) @ Y2) => (((P @ Xs2) @ (((cons @ B2) @ Y2) @ Ys2)) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B2) @ Y2) @ Ys2)))))) => ((! [X4:A,Xs2:(list @ A),Y2:B2,Ys2:(list @ B2)]: (((~ (((R @ X4) @ Y2))) => (((P @ (((cons @ A) @ X4) @ Xs2)) @ Ys2) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B2) @ Y2) @ Ys2)))))) => ((P @ Xs) @ Ys)))))))).
% 2.15/1.38 thf(fact_92_mergesort__by__rel__merge_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > ((list @ A) > $o))),A0:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: (((! [R3:(A > (A > $o)),X4:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: (((((R3 @ X4) @ Y2) => (((P @ R3) @ Xs2) @ (((cons @ A) @ Y2) @ Ys2))) => (((~ (((R3 @ X4) @ Y2))) => (((P @ R3) @ (((cons @ A) @ X4) @ Xs2)) @ Ys2)) => (((P @ R3) @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2)))))) => ((! [R3:(A > (A > $o)),Xs2:(list @ A)]: ((((P @ R3) @ Xs2) @ (nil @ A)))) => ((! [R3:(A > (A > $o)),V:A,Va:(list @ A)]: ((((P @ R3) @ (nil @ A)) @ (((cons @ A) @ V) @ Va)))) => (((P @ A0) @ A1) @ A22))))))).
% 2.15/1.38 thf(fact_93_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B2:$tType,P:((A > B2) > ((list @ A) > ((list @ B2) > $o))),A0:(A > B2),A1:(list @ A),A22:(list @ B2)]: (((! [F2:(A > B2),X_1:(list @ B2)]: ((((P @ F2) @ (nil @ A)) @ X_1))) => ((! [F2:(A > B2),A4:A,As:(list @ A),Bs:(list @ B2)]: (((((P @ F2) @ As) @ (((cons @ B2) @ (F2 @ A4)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.15/1.38 thf(fact_94_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X4) @ Xs2)))))) => (P @ Xs))))))).
% 2.15/1.38 thf(fact_95_list__all__zip_Oinduct, axiom, (! [A:$tType,B2:$tType,P:((A > (B2 > $o)) > ((list @ A) > ((list @ B2) > $o))),A0:(A > (B2 > $o)),A1:(list @ A),A22:(list @ B2)]: (((! [P2:(A > (B2 > $o))]: ((((P @ P2) @ (nil @ A)) @ (nil @ B2)))) => ((! [P2:(A > (B2 > $o)),A4:A,As:(list @ A),B3:B2,Bs:(list @ B2)]: (((((P @ P2) @ As) @ Bs) => (((P @ P2) @ (((cons @ A) @ A4) @ As)) @ (((cons @ B2) @ B3) @ Bs))))) => ((! [P2:(A > (B2 > $o)),V:A,Va:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ V) @ Va)) @ (nil @ B2)))) => ((! [P2:(A > (B2 > $o)),V:B2,Va:(list @ B2)]: ((((P @ P2) @ (nil @ A)) @ (((cons @ B2) @ V) @ Va)))) => (((P @ A0) @ A1) @ A22)))))))).
% 2.15/1.38 thf(fact_96_successively_Oinduct, axiom, (! [A:$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 > $o)),X4:A,Y2:A,Xs2:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ Y2) @ Xs2)) => ((P @ P2) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y2) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 2.15/1.38 thf(fact_97_arg__min__list_Oinduct, axiom, (! [B2:$tType,A:$tType]: (((linorder @ B2) => (! [P:((A > B2) > ((list @ A) > $o)),A0:(A > B2),A1:(list @ A)]: (((! [F2:(A > B2),X4:A]: (((P @ F2) @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [F2:(A > B2),X4:A,Y2:A,Zs2:(list @ A)]: ((((P @ F2) @ (((cons @ A) @ Y2) @ Zs2)) => ((P @ F2) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y2) @ Zs2)))))) => ((! [A4:(A > B2)]: (((P @ A4) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 2.15/1.38 thf(fact_98_list__induct__first2, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X1:A,X23:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((cons @ A) @ X1) @ (((cons @ A) @ X23) @ Xs2)))))) => (P @ Xs))))))).
% 2.15/1.38 thf(fact_99_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y2:A,Xs2:(list @ A)]: ((((X4 = Y2) => (P @ (((cons @ A) @ X4) @ Xs2))) => (((X4 != Y2) => (P @ (((cons @ A) @ Y2) @ Xs2))) => (P @ (((cons @ A) @ X4) @ (((cons @ A) @ Y2) @ Xs2))))))) => (P @ A0))))))).
% 2.15/1.38 thf(fact_100_sorted__wrt_Oinduct, axiom, (! [A:$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 > $o)),X4:A,Ys2:(list @ A)]: ((((P @ P2) @ Ys2) => ((P @ P2) @ (((cons @ A) @ X4) @ Ys2))))) => ((P @ A0) @ A1)))))).
% 2.15/1.38 thf(fact_101_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X4:A]: ((X != (((cons @ A) @ X4) @ (nil @ A))))) => (~ ((! [X4:A,Y2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X4) @ (((cons @ A) @ Y2) @ Xs2)))))))))))).
% 2.15/1.38 thf(fact_102_list__2pre__induct, axiom, (! [A:$tType,B2:$tType,P:((list @ A) > ((list @ B2) > $o)),W1:(list @ A),W2:(list @ B2)]: ((((P @ (nil @ A)) @ (nil @ B2)) => ((! [E3:A,W12:(list @ A),W22:(list @ B2)]: ((((P @ W12) @ W22) => ((P @ (((cons @ A) @ E3) @ W12)) @ W22)))) => ((! [E3:B2,W13:(list @ A),W23:(list @ B2)]: ((((P @ W13) @ W23) => ((P @ W13) @ (((cons @ B2) @ E3) @ W23))))) => ((P @ W1) @ W2))))))).
% 2.15/1.38 thf(fact_103_transpose_Ocases, axiom, (! [A:$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))))))))))).
% 2.15/1.38 thf(fact_104_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X4:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y2) @ Ys2)) => (((P @ (((cons @ A) @ X4) @ Xs2)) @ Ys2) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2)))))) => ((P @ A0) @ A1))))))).
% 2.15/1.38 thf(fact_105_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X4:A,Xs2:(list @ A)]: (((! [X212:A,X222:(list @ A)]: (((Xs2 = (((cons @ A) @ X212) @ X222)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X4) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 2.15/1.38 thf(fact_106_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X:(list @ A)]: (((! [X4:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X4) @ Xs2)))) => (X = (nil @ A))))))))).
% 2.15/1.38 thf(fact_107_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y2:A,Zs2:(list @ A)]: (((P @ Zs2) => ((P @ (((cons @ A) @ Y2) @ Zs2)) => (P @ (((cons @ A) @ X4) @ (((cons @ A) @ Y2) @ Zs2))))))) => (P @ Xs))))))).
% 2.15/1.38 thf(fact_108_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X4:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((P @ Ys2) @ Xs2) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ Ys2)))) => ((P @ A0) @ A1)))))).
% 2.15/1.38 thf(fact_109_list__induct2_H, axiom, (! [A:$tType,B2:$tType,P:((list @ A) > ((list @ B2) > $o)),Xs:(list @ A),Ys:(list @ B2)]: ((((P @ (nil @ A)) @ (nil @ B2)) => ((! [X4:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X4) @ Xs2)) @ (nil @ B2)))) => ((! [Y2:B2,Ys2:(list @ B2)]: (((P @ (nil @ A)) @ (((cons @ B2) @ Y2) @ Ys2)))) => ((! [X4:A,Xs2:(list @ A),Y2:B2,Ys2:(list @ B2)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B2) @ Y2) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 2.15/1.38 thf(fact_110_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys3)))))))).
% 2.15/1.38 thf(fact_111_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X1) @ X23))))) => (P @ List)))))).
% 2.15/1.38 thf(fact_112_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X213:A,X223:(list @ A)]: ((Y != (((cons @ A) @ X213) @ X223)))))))))).
% 2.15/1.38 thf(fact_113_zipf_Oinduct, axiom, (! [A:$tType,C2:$tType,B2:$tType,P:((A > (B2 > C2)) > ((list @ A) > ((list @ B2) > $o))),A0:(A > (B2 > C2)),A1:(list @ A),A22:(list @ B2)]: (((! [F2:(A > (B2 > C2))]: ((((P @ F2) @ (nil @ A)) @ (nil @ B2)))) => ((! [F2:(A > (B2 > C2)),A4:A,As:(list @ A),B3:B2,Bs:(list @ B2)]: (((((P @ F2) @ As) @ Bs) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ (((cons @ B2) @ B3) @ Bs))))) => ((! [A4:(A > (B2 > C2)),V:A,Va:(list @ A)]: ((((P @ A4) @ (((cons @ A) @ V) @ Va)) @ (nil @ B2)))) => ((! [A4:(A > (B2 > C2)),V:B2,Va:(list @ B2)]: ((((P @ A4) @ (nil @ A)) @ (((cons @ B2) @ V) @ Va)))) => (((P @ A0) @ A1) @ A22)))))))).
% 2.15/1.38 thf(fact_114_revg_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [A4:A,As:(list @ A),B3:(list @ A)]: ((((P @ As) @ (((cons @ A) @ A4) @ B3)) => ((P @ (((cons @ A) @ A4) @ As)) @ B3)))) => ((P @ A0) @ A1)))))).
% 2.15/1.38 thf(fact_115_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.15/1.38 thf(fact_116_neq__NilE, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) => (~ ((! [X4:A,Xs2:(list @ A)]: ((L != (((cons @ A) @ X4) @ Xs2)))))))))).
% 2.15/1.38 thf(fact_117_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.15/1.38 thf(fact_118_list_Oset__cases, axiom, (! [A:$tType,E2:A,A2:(list @ A)]: (((((member @ A) @ E2) @ ((set2 @ A) @ A2)) => ((! [Z2:(list @ A)]: ((A2 != (((cons @ A) @ E2) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ A)]: (((A2 = (((cons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E2) @ ((set2 @ A) @ Z2)))))))))))))).
% 2.15/1.38 thf(fact_119_set__ConsD, axiom, (! [A:$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))))))).
% 2.15/1.38 thf(fact_120_list_Oset__intros_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((member @ A) @ X21) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22)))))).
% 2.15/1.38 thf(fact_121_list_Oset__intros_I2_J, axiom, (! [A:$tType,Y:A,X22:(list @ A),X21:A]: (((((member @ A) @ Y) @ ((set2 @ A) @ X22)) => (((member @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X21) @ X22))))))).
% 2.15/1.38 thf(fact_122_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys) => ((Xs = (((append @ A) @ Xs1) @ Zs)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs))))))).
% 2.15/1.38 thf(fact_123_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.15/1.38 thf(fact_124_list__match__lel__lel, axiom, (! [A:$tType,C1:(list @ A),Qs:A,C22:(list @ A),C12:(list @ A),Qs2:A,C23:(list @ A)]: ((((((append @ A) @ C1) @ (((cons @ A) @ Qs) @ C22)) = (((append @ A) @ C12) @ (((cons @ A) @ Qs2) @ C23))) => ((! [C21:(list @ A)]: (((C1 = (((append @ A) @ C12) @ (((cons @ A) @ Qs2) @ C21))) => (C23 != (((append @ A) @ C21) @ (((cons @ A) @ Qs) @ C22)))))) => (((C12 = C1) => ((Qs2 = Qs) => (C23 != C22))) => (~ ((! [C212:(list @ A)]: (((C12 = (((append @ A) @ C1) @ (((cons @ A) @ Qs) @ C212))) => (C22 != (((append @ A) @ C212) @ (((cons @ A) @ Qs2) @ C23)))))))))))))).
% 2.15/1.38 thf(fact_125_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 2.15/1.38 thf(fact_126_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.15/1.38 thf(fact_127_append_Oleft__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A2) = A2)))).
% 2.15/1.38 thf(fact_128_list_Osel_I3_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((tl @ A) @ (((cons @ A) @ X21) @ X22)) = X22)))).
% 2.15/1.38 thf(fact_129_list_Osel_I2_J, axiom, (! [A:$tType]: ((((tl @ A) @ (nil @ A)) = (nil @ A))))).
% 2.15/1.38 thf(fact_130_list__append__eq__Cons__cases, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs) = (((cons @ A) @ X) @ Xs)) => (((Ys = (nil @ A)) => (Zs != (((cons @ A) @ X) @ Xs))) => (~ ((! [Ys4:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys4)) => ((((append @ A) @ Ys4) @ Zs) != Xs))))))))))).
% 2.15/1.38 thf(fact_131_list__Cons__eq__append__cases, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs)) => (((Ys = (nil @ A)) => (Zs != (((cons @ A) @ X) @ Xs))) => (~ ((! [Ys4:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys4)) => ((((append @ A) @ Ys4) @ Zs) != Xs))))))))))).
% 2.15/1.38 thf(fact_132_rev__nonempty__induct2_H, axiom, (! [A:$tType,B2:$tType,Xs:(list @ A),Ys:(list @ B2),P:((list @ A) > ((list @ B2) > $o))]: (((Xs != (nil @ A)) => ((Ys != (nil @ B2)) => ((! [X4:A,Y2:B2]: (((P @ (((cons @ A) @ X4) @ (nil @ A))) @ (((cons @ B2) @ Y2) @ (nil @ B2))))) => ((! [X4:A,Xs2:(list @ A),Y2:B2]: (((Xs2 != (nil @ A)) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((cons @ B2) @ Y2) @ (nil @ B2)))))) => ((! [X4:A,Y2:B2,Ys2:(list @ B2)]: (((Ys2 != (nil @ B2)) => ((P @ (((cons @ A) @ X4) @ (nil @ A))) @ (((append @ B2) @ Ys2) @ (((cons @ B2) @ Y2) @ (nil @ B2))))))) => ((! [X4:A,Xs2:(list @ A),Y2:B2,Ys2:(list @ B2)]: ((((P @ Xs2) @ Ys2) => ((Xs2 != (nil @ A)) => ((Ys2 != (nil @ B2)) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((append @ B2) @ Ys2) @ (((cons @ B2) @ Y2) @ (nil @ B2))))))))) => ((P @ Xs) @ Ys)))))))))).
% 2.15/1.38 thf(fact_133_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.15/1.38 thf(fact_134_append__eq__Cons__conv, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs) = (((cons @ A) @ X) @ Xs)) = (((Ys = (nil @ A)) & (Zs = (((cons @ A) @ X) @ Xs))) | (? [Ys5:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys5)) & ((((append @ A) @ Ys5) @ Zs) = Xs))))))))).
% 2.15/1.38 thf(fact_135_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs)) | (? [Ys5:(list @ A)]: ((((((cons @ A) @ X) @ Ys5) = Ys) & (Xs = (((append @ A) @ Ys5) @ Zs)))))))))).
% 2.15/1.38 thf(fact_136_neq__Nil__rev__conv, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) = (? [Xs3:(list @ A),X3:A]: ((L = (((append @ A) @ Xs3) @ (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.15/1.38 thf(fact_137_rev__induct2_H, axiom, (! [A:$tType,B2:$tType,P:((list @ A) > ((list @ B2) > $o)),Xs:(list @ A),Ys:(list @ B2)]: ((((P @ (nil @ A)) @ (nil @ B2)) => ((! [X4:A,Xs2:(list @ A)]: (((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (nil @ B2)))) => ((! [Y2:B2,Ys2:(list @ B2)]: (((P @ (nil @ A)) @ (((append @ B2) @ Ys2) @ (((cons @ B2) @ Y2) @ (nil @ B2)))))) => ((! [X4:A,Xs2:(list @ A),Y2:B2,Ys2:(list @ B2)]: ((((P @ Xs2) @ Ys2) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((append @ B2) @ Ys2) @ (((cons @ B2) @ Y2) @ (nil @ B2))))))) => ((P @ Xs) @ Ys)))))))).
% 2.15/1.38 thf(fact_138_neq__Nil__revE, axiom, (! [A:$tType,L:(list @ A)]: (((L != (nil @ A)) => (~ ((! [Ll:(list @ A),E3:A]: ((L != (((append @ A) @ Ll) @ (((cons @ A) @ E3) @ (nil @ A)))))))))))).
% 2.15/1.38 thf(fact_139_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys2:(list @ A),Y2:A]: ((Xs != (((append @ A) @ Ys2) @ (((cons @ A) @ Y2) @ (nil @ A)))))))))))).
% 2.15/1.38 thf(fact_140_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.15/1.38 thf(fact_141_split__list__first__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys3:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs3))))) & ((P @ X3) & (! [Y3:A]: (((((member @ A) @ Y3) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Y3)))))))))))))).
% 2.15/1.38 thf(fact_142_split__list__last__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys3:(list @ A),X3:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs3))) & ((P @ X3) & (! [Y3:A]: (((((member @ A) @ Y3) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Y3)))))))))))))).
% 2.15/1.38 thf(fact_143_in__set__conv__decomp__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys3))))))))))).
% 2.15/1.38 thf(fact_144_in__set__conv__decomp__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs3))))))))))).
% 2.15/1.38 thf(fact_145_split__list__first__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (~ ((! [Ys2:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X4) @ Zs2))))) => ((P @ X4) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))))))).
% 2.15/1.38 thf(fact_146_split__list__last__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (~ ((! [Ys2:(list @ A),X4:A,Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X4) @ Zs2))) => ((P @ X4) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs2)) => (~ ((P @ Xa)))))))))))))))))).
% 2.15/1.38 thf(fact_147_split__list__first__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (? [Ys2:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X4) @ Zs2))))) & ((P @ X4) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))).
% 2.15/1.38 thf(fact_148_split__list__last__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (? [Ys2:(list @ A),X4:A,Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X4) @ Zs2))) & ((P @ X4) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs2)) => (~ ((P @ Xa)))))))))))))).
% 2.15/1.38 thf(fact_149_in__set__list__format, axiom, (! [A:$tType,E2:A,L:(list @ A)]: (((((member @ A) @ E2) @ ((set2 @ A) @ L)) => (~ ((! [L12:(list @ A),L22:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ E2) @ L22))))))))))).
% 2.15/1.38 thf(fact_150_in__set__conv__decomp, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))))))))).
% 2.15/1.38 thf(fact_151_append__Cons__eq__iff, axiom, (! [A:$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)))))))).
% 2.15/1.38 thf(fact_152_split__list__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (~ ((! [Ys2:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X4) @ Zs2))))) => (~ ((P @ X4)))))))))))).
% 2.15/1.38 thf(fact_153_split__list__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys2))))))))))).
% 2.15/1.38 thf(fact_154_xy__in__set__cases, axiom, (! [A:$tType,X:A,L:(list @ A),Y:A]: (((((member @ A) @ X) @ ((set2 @ A) @ L)) => ((((member @ A) @ Y) @ ((set2 @ A) @ L)) => (((X = Y) => (! [L12:(list @ A),L22:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ Y) @ L22)))))) => (((X != Y) => (! [L12:(list @ A),L22:(list @ A),L3:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ X) @ (((append @ A) @ L22) @ (((cons @ A) @ Y) @ L3)))))))) => (~ (((X != Y) => (! [L12:(list @ A),L22:(list @ A),L3:(list @ A)]: ((L != (((append @ A) @ L12) @ (((cons @ A) @ Y) @ (((append @ A) @ L22) @ (((cons @ A) @ X) @ L3))))))))))))))))).
% 2.15/1.38 thf(fact_155_split__list__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) => (? [Ys2:(list @ A),X4:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X4) @ Zs2))))) & (P @ X4)))))))).
% 2.15/1.38 thf(fact_156_split__list__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs2))))))))))).
% 2.15/1.38 thf(fact_157_split__list, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs2))))))))).
% 2.15/1.38 thf(fact_158_tl__obtain__elem, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((tl @ A) @ Xs) = (nil @ A)) => (~ ((! [E3:A]: ((Xs != (((cons @ A) @ E3) @ (nil @ A)))))))))))).
% 2.15/1.38 thf(fact_159_tl__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((tl @ A) @ Xs) = (nil @ A)) = ((Xs = (nil @ A)) | (? [X3:A]: ((Xs = (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.15/1.38 thf(fact_160_Nil__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((tl @ A) @ Xs)) = ((Xs = (nil @ A)) | (? [X3:A]: ((Xs = (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.15/1.38 thf(fact_161_list_Oset__sel_I2_J, axiom, (! [A:$tType,A2:(list @ A),X:A]: (((A2 != (nil @ A)) => ((((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ A2))) => (((member @ A) @ X) @ ((set2 @ A) @ A2))))))).
% 2.15/1.38 thf(fact_162_prefix__snoc, axiom, (! [A:$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)))))).
% 2.15/1.38 thf(fact_163_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)))))))))))))))))).
% 2.15/1.38 thf(fact_164_same__prefix__nil, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((prefix @ A) @ (((append @ A) @ Xs) @ Ys)) @ Xs) = (Ys = (nil @ A)))))).
% 2.15/1.38 thf(fact_165_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)) => (~ ((! [Ns3:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns3) @ N) => ((((member @ node) @ N2) @ ((set2 @ node) @ Ns3)) => ((~ ((((member @ node) @ N) @ ((set2 @ node) @ ((tl @ node) @ ((butlast @ node) @ Ns3)))))) => (~ ((((ord_less_eq @ (set @ node)) @ ((set2 @ node) @ Ns3)) @ ((set2 @ node) @ Ns)))))))))))))))).
% 2.15/1.38 thf(fact_166_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))))))))))))))).
% 2.15/1.38 thf(fact_167_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)))))))))).
% 2.15/1.38 thf(fact_168_phiUses__finite, axiom, (! [N:node,G2:g]: (((((member @ node) @ N) @ ((set2 @ node) @ (alpha_n @ G2))) => ((finite_finite @ val) @ (((((((((sSA_CFG_SSA_phiUses @ g) @ node) @ edgeD) @ val) @ alpha_n) @ inEdges) @ phis) @ G2) @ N)))))).
% 2.15/1.38 thf(fact_169_old_Opath2__split__last__prop, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node,P:(node > $o)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((? [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ Ns)) & (P @ X2)))) => (~ ((! [N3:node,Ns3:(list @ node)]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N3) @ Ns3) @ M) => ((P @ N3) => ((! [X2:node]: (((((member @ node) @ X2) @ ((set2 @ node) @ ((tl @ node) @ Ns3))) => (~ ((P @ X2)))))) => (~ ((((suffix @ node) @ Ns3) @ Ns))))))))))))))).
% 2.15/1.38 thf(fact_170_defs__finite, axiom, (! [G2:g,N:node]: (((finite_finite @ val) @ ((defs @ G2) @ N))))).
% 2.15/1.38 thf(fact_171_prefix__order_Oorder__refl, axiom, (! [A:$tType,X:(list @ A)]: ((((prefix @ A) @ X) @ X)))).
% 2.15/1.38 thf(fact_172_prefix__order_Odual__order_Orefl, axiom, (! [A:$tType,A2:(list @ A)]: ((((prefix @ A) @ A2) @ A2)))).
% 2.15/1.38 thf(fact_173_suffix__order_Oorder__refl, axiom, (! [A:$tType,X:(list @ A)]: ((((suffix @ A) @ X) @ X)))).
% 2.15/1.38 thf(fact_174_suffix__order_Odual__order_Orefl, axiom, (! [A:$tType,A2:(list @ A)]: ((((suffix @ A) @ A2) @ A2)))).
% 2.15/1.38 thf(fact_175_old_Opath__not__Nil, axiom, (! [G2:g,Ns:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns) => (Ns != (nil @ node)))))).
% 2.15/1.38 thf(fact_176_old_Opath2__hd, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => (N = ((hd @ node) @ Ns)))))).
% 2.15/1.38 thf(fact_177_old_Opath2__forget__hd, axiom, (! [G2:g,N:node,Ns:(list @ node),M:node]: ((((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ N) @ Ns) @ M) => ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ ((hd @ node) @ Ns)) @ Ns) @ M))))).
% 2.15/1.38 thf(fact_178_old_Opath__hd, axiom, (! [G2:g,N:node,Ns:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N) @ Ns)) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ N) @ (nil @ node))))))).
% 2.15/1.38 thf(fact_179_old_Opath__split_I2_J, axiom, (! [G2:g,Ns:(list @ node),M:node,Ns2:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((append @ node) @ Ns) @ (((cons @ node) @ M) @ Ns2))) => ((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ (((cons @ node) @ M) @ Ns2)))))).
% 2.15/1.38 thf(fact_180_List_Ofinite__set, axiom, (! [A:$tType,Xs:(list @ A)]: (((finite_finite @ A) @ ((set2 @ A) @ Xs))))).
% 2.15/1.38 thf(fact_181_Cons__prefix__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((prefix @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = ((X = Y) & (((prefix @ A) @ Xs) @ Ys)))))).
% 2.15/1.38 thf(fact_182_prefix__code_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: ((((prefix @ A) @ (nil @ A)) @ Xs)))).
% 2.15/1.38 thf(fact_183_prefix__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((prefix @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.15/1.38 thf(fact_184_prefix__bot_Obot_Oextremum__unique, axiom, (! [A:$tType,A2:(list @ A)]: (((((prefix @ A) @ A2) @ (nil @ A)) = (A2 = (nil @ A)))))).
% 2.15/1.38 thf(fact_185_suffix__bot_Obot_Oextremum__unique, axiom, (! [A:$tType,A2:(list @ A)]: (((((suffix @ A) @ A2) @ (nil @ A)) = (A2 = (nil @ A)))))).
% 2.15/1.38 thf(fact_186_suffix__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((suffix @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.15/1.38 thf(fact_187_same__prefix__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((prefix @ A) @ (((append @ A) @ Xs) @ Ys)) @ (((append @ A) @ Xs) @ Zs)) = (((prefix @ A) @ Ys) @ Zs))))).
% 2.15/1.38 thf(fact_188_same__suffix__suffix, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Ys) @ Xs)) @ (((append @ A) @ Zs) @ Xs)) = (((suffix @ A) @ Ys) @ Zs))))).
% 2.15/1.38 thf(fact_189_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)))))))).
% 2.15/1.38 thf(fact_190_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)))))))).
% 2.15/1.38 thf(fact_191_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))))))).
% 2.15/1.38 thf(fact_192_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))))))))))))).
% 2.15/1.38 thf(fact_193_old_Opath_Oinducts, axiom, (! [G2:g,X:(list @ node),P:((list @ node) > $o)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ X) => ((! [N4:node]: (((((member @ node) @ N4) @ ((set2 @ node) @ (alpha_n @ G2))) => ((invar @ G2) => (P @ (((cons @ node) @ N4) @ (nil @ node))))))) => ((! [Ns4:(list @ node),N3:node]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns4) => ((P @ Ns4) => ((((member @ node) @ N3) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((hd @ node) @ Ns4)))) => (P @ (((cons @ node) @ N3) @ Ns4))))))) => (P @ X))))))).
% 2.15/1.38 thf(fact_194_old_Opath_Ocases, axiom, (! [G2:g,A2:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ A2) => ((! [N4:node]: (((A2 = (((cons @ node) @ N4) @ (nil @ node))) => ((((member @ node) @ N4) @ ((set2 @ node) @ (alpha_n @ G2))) => (~ ((invar @ G2))))))) => (~ ((! [Ns4:(list @ node),N3:node]: (((A2 = (((cons @ node) @ N3) @ Ns4)) => (((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns4) => (~ ((((member @ node) @ N3) @ ((set2 @ node) @ ((((((graph_1201503639essors @ g) @ node) @ edgeD) @ inEdges) @ G2) @ ((hd @ node) @ Ns4))))))))))))))))).
% 2.15/1.38 thf(fact_195_same__suffix__nil, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Ys) @ Xs)) @ Xs) = (Ys = (nil @ A)))))).
% 2.15/1.38 thf(fact_196_hd__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Xs)))))).
% 2.15/1.38 thf(fact_197_suffix__snoc, axiom, (! [A:$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))))))))).
% 2.15/1.38 thf(fact_198_snoc__suffix__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: (((((suffix @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((X = Y) & (((suffix @ A) @ Xs) @ Ys)))))).
% 2.15/1.38 thf(fact_199_hd__Cons__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ Xs)) @ ((tl @ A) @ Xs)) = Xs))))).
% 2.15/1.38 thf(fact_200_list_Ocollapse, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List)) = List))))).
% 2.15/1.38 thf(fact_201_in__hd__or__tl__conv, axiom, (! [A:$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))))))).
% 2.15/1.38 thf(fact_202_old_Opath__invar, axiom, (! [G2:g,Ns:(list @ node)]: ((((((((((graph_1146196722h_path @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ G2) @ Ns) => (invar @ G2))))).
% 2.15/1.38 thf(fact_203_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)))))))).
% 2.15/1.38 thf(fact_204_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)))))))).
% 2.15/1.38 thf(fact_205_set__mono__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ Xs) @ Ys) => (((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((set2 @ A) @ Ys)))))).
% 2.15/1.38 thf(fact_206_subset__Collect__conv, axiom, (! [A:$tType,S:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ S) @ ((collect @ A) @ P)) = (! [X3:A]: (((((member @ A) @ X3) @ S) => (P @ X3)))))))).
% 2.15/1.38 thf(fact_207_ord__eq__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B:A,C:A,D:A]: (((A2 = B) => ((((ord_less_eq @ A) @ B) @ C) => ((C = D) => (((ord_less_eq @ A) @ A2) @ D)))))))))).
% 2.15/1.38 thf(fact_208_suffix__ConsD2, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((suffix @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.15/1.38 thf(fact_209_suffix__ConsI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Y:A]: (((((suffix @ A) @ Xs) @ Ys) => (((suffix @ A) @ Xs) @ (((cons @ A) @ Y) @ Ys)))))).
% 2.15/1.38 thf(fact_210_suffix__ConsD, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.15/1.38 thf(fact_211_suffix__Cons, axiom, (! [A:$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)))))).
% 2.15/1.38 thf(fact_212_suffix__bot_Obot_Oextremum__uniqueI, axiom, (! [A:$tType,A2:(list @ A)]: (((((suffix @ A) @ A2) @ (nil @ A)) => (A2 = (nil @ A)))))).
% 2.15/1.38 thf(fact_213_suffix__bot_Obot_Oextremum, axiom, (! [A:$tType,A2:(list @ A)]: ((((suffix @ A) @ (nil @ A)) @ A2)))).
% 2.15/1.38 thf(fact_214_Nil__suffix, axiom, (! [A:$tType,Xs:(list @ A)]: ((((suffix @ A) @ (nil @ A)) @ Xs)))).
% 2.15/1.38 thf(fact_215_suffixE, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ Xs) @ Ys) => (~ ((! [Zs2:(list @ A)]: ((Ys != (((append @ A) @ Zs2) @ Xs)))))))))).
% 2.15/1.38 thf(fact_216_suffixI, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Zs) @ Xs)) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.15/1.38 thf(fact_217_Sublist_Osuffix__def, axiom, (! [A:$tType]: (((suffix @ A) = (^ [Xs3:(list @ A),Ys3:(list @ A)]: ((? [Zs3:(list @ A)]: ((Ys3 = (((append @ A) @ Zs3) @ Xs3)))))))))).
% 2.15/1.38 thf(fact_218_suffix__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)) = ((((suffix @ A) @ Xs) @ Zs) | (? [Xs5:(list @ A)]: (((Xs = (((append @ A) @ Xs5) @ Zs)) & (((suffix @ A) @ Xs5) @ Ys))))))))).
% 2.15/1.38 thf(fact_219_suffix__appendD, axiom, (! [A:$tType,Zs:(list @ A),Xs:(list @ A),Ys:(list @ A)]: (((((suffix @ A) @ (((append @ A) @ Zs) @ Xs)) @ Ys) => (((suffix @ A) @ Xs) @ Ys))))).
% 2.15/1.38 thf(fact_220_suffix__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((suffix @ A) @ Xs) @ Ys) => (((suffix @ A) @ Xs) @ (((append @ A) @ Zs) @ Ys)))))).
% 2.15/1.38 thf(fact_221_suffix__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((suffix @ A) @ ((tl @ A) @ Xs)) @ Xs)))).
% 2.15/1.38 thf(fact_222_suffix__same__cases, axiom, (! [A:$tType,Xs_1:(list @ A),Ys:(list @ A),Xs_2:(list @ A)]: (((((suffix @ A) @ Xs_1) @ Ys) => ((((suffix @ A) @ Xs_2) @ Ys) => ((((suffix @ A) @ Xs_1) @ Xs_2) | (((suffix @ A) @ Xs_2) @ Xs_1))))))).
% 2.15/1.38 thf(fact_223_suffix__order_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z:(list @ A)]: ((Y4 = Z))) = (^ [X3:(list @ A),Y3:(list @ A)]: (((((suffix @ A) @ X3) @ Y3) & (((suffix @ A) @ Y3) @ X3)))))))).
% 2.15/1.38 thf(fact_224_suffix__order_Oantisym, axiom, (! [A:$tType,X:(list @ A),Y:(list @ A)]: (((((suffix @ A) @ X) @ Y) => ((((suffix @ A) @ Y) @ X) => (X = Y)))))).
% 2.15/1.38 thf(fact_225_suffix__order_Oeq__refl, axiom, (! [A:$tType,X:(list @ A),Y:(list @ A)]: (((X = Y) => (((suffix @ A) @ X) @ Y))))).
% 2.15/1.38 thf(fact_226_suffix__order_Oorder_Otrans, axiom, (! [A:$tType,A2:(list @ A),B:(list @ A),C:(list @ A)]: (((((suffix @ A) @ A2) @ B) => ((((suffix @ A) @ B) @ C) => (((suffix @ A) @ A2) @ C)))))).
% 2.15/1.38 thf(fact_227_suffix__order_Oorder__trans, axiom, (! [A:$tType,X:(list @ A),Y:(list @ A),Z3:(list @ A)]: (((((suffix @ A) @ X) @ Y) => ((((suffix @ A) @ Y) @ Z3) => (((suffix @ A) @ X) @ Z3)))))).
% 2.15/1.38 thf(fact_228_suffix__order_Oantisym__conv, axiom, (! [A:$tType,Y:(list @ A),X:(list @ A)]: (((((suffix @ A) @ Y) @ X) => ((((suffix @ A) @ X) @ Y) = (X = Y)))))).
% 2.15/1.38 thf(fact_229_suffix__order_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z:(list @ A)]: ((Y4 = Z))) = (^ [A5:(list @ A),B4:(list @ A)]: (((((suffix @ A) @ A5) @ B4) & (((suffix @ A) @ B4) @ A5)))))))).
% 2.15/1.38 thf(fact_230_suffix__order_Oorder_Oantisym, axiom, (! [A:$tType,A2:(list @ A),B:(list @ A)]: (((((suffix @ A) @ A2) @ B) => ((((suffix @ A) @ B) @ A2) => (A2 = B)))))).
% 2.15/1.38 thf(fact_231_suffix__order_Oord__eq__le__trans, axiom, (! [A:$tType,A2:(list @ A),B:(list @ A),C:(list @ A)]: (((A2 = B) => ((((suffix @ A) @ B) @ C) => (((suffix @ A) @ A2) @ C)))))).
% 2.15/1.38 thf(fact_232_suffix__order_Oord__le__eq__trans, axiom, (! [A:$tType,A2:(list @ A),B:(list @ A),C:(list @ A)]: (((((suffix @ A) @ A2) @ B) => ((B = C) => (((suffix @ A) @ A2) @ C)))))).
% 2.15/1.38 thf(fact_233_suffix__order_Odual__order_Otrans, axiom, (! [A:$tType,B:(list @ A),A2:(list @ A),C:(list @ A)]: (((((suffix @ A) @ B) @ A2) => ((((suffix @ A) @ C) @ B) => (((suffix @ A) @ C) @ A2)))))).
% 2.15/1.38 thf(fact_234_suffix__order_Odual__order_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z:(list @ A)]: ((Y4 = Z))) = (^ [A5:(list @ A),B4:(list @ A)]: (((((suffix @ A) @ B4) @ A5) & (((suffix @ A) @ A5) @ B4)))))))).
% 2.15/1.38 thf(fact_235_suffix__order_Odual__order_Oantisym, axiom, (! [A:$tType,B:(list @ A),A2:(list @ A)]: (((((suffix @ A) @ B) @ A2) => ((((suffix @ A) @ A2) @ B) => (A2 = B)))))).
% 2.15/1.38 thf(fact_236_list_Osel_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((hd @ A) @ (((cons @ A) @ X21) @ X22)) = X21)))).
% 2.15/1.38 thf(fact_237_finite__list, axiom, (! [A:$tType,A3:(set @ A)]: ((((finite_finite @ A) @ A3) => (? [Xs2:(list @ A)]: ((((set2 @ A) @ Xs2) = A3))))))).
% 2.15/1.38 thf(fact_238_subset__code_I1_J, axiom, (! [A:$tType,Xs:(list @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ B5) = (! [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) => (((member @ A) @ X3) @ B5)))))))).
% 2.15/1.38 thf(fact_239_set__mono__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((prefix @ A) @ Xs) @ Ys) => (((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((set2 @ A) @ Ys)))))).
% 2.15/1.38 thf(fact_240_list_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(list @ A)]: (((A2 != (nil @ A)) => (((member @ A) @ ((hd @ A) @ A2)) @ ((set2 @ A) @ A2)))))).
% 2.15/1.38 thf(fact_241_hd__in__set, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((member @ A) @ ((hd @ A) @ Xs)) @ ((set2 @ A) @ Xs)))))).
% 2.15/1.38 thf(fact_242_hd__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((Xs = (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Ys))) & ((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Xs))))))).
% 2.15/1.38 thf(fact_243_longest__common__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((? [Ps:(list @ A),Xs6:(list @ A),Ys4:(list @ A)]: (((Xs = (((append @ A) @ Ps) @ Xs6)) & ((Ys = (((append @ A) @ Ps) @ Ys4)) & ((Xs6 = (nil @ A)) | ((Ys4 = (nil @ A)) | (((hd @ A) @ Xs6) != ((hd @ A) @ Ys4))))))))))).
% 2.15/1.38 thf(fact_244_not__suffix__cases, axiom, (! [A:$tType,Ps2:(list @ A),Ls:(list @ A)]: (((~ ((((suffix @ A) @ Ps2) @ Ls))) => (((Ps2 != (nil @ A)) => (Ls != (nil @ A))) => ((! [A4:A,As:(list @ A)]: (((Ps2 = (((append @ A) @ As) @ (((cons @ A) @ A4) @ (nil @ A)))) => (! [X4:A,Xs2:(list @ A)]: (((Ls = (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) => ((X4 = A4) => (((suffix @ A) @ As) @ Xs2)))))))) => (~ ((! [A4:A]: (((? [As:(list @ A)]: ((Ps2 = (((append @ A) @ As) @ (((cons @ A) @ A4) @ (nil @ A)))))) => (! [X4:A]: (((? [Xs2:(list @ A)]: ((Ls = (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))))) => (X4 = A4))))))))))))))).
% 2.15/1.38 thf(fact_245_not__suffix__induct, axiom, (! [A:$tType,Ps2:(list @ A),Ls:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((~ ((((suffix @ A) @ Ps2) @ Ls))) => ((! [X4:A,Xs2:(list @ A)]: (((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (nil @ A)))) => ((! [X4:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: (((X4 != Y2) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((append @ A) @ Ys2) @ (((cons @ A) @ Y2) @ (nil @ A))))))) => ((! [X4:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: (((X4 = Y2) => ((~ ((((suffix @ A) @ Xs2) @ Ys2))) => (((P @ Xs2) @ Ys2) => ((P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))) @ (((append @ A) @ Ys2) @ (((cons @ A) @ Y2) @ (nil @ A))))))))) => ((P @ Ps2) @ Ls)))))))).
% 2.15/1.38 thf(fact_246_list_Oexpand, axiom, (! [A:$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)))))).
% 2.15/1.38 thf(fact_247_not__hd__in__tl, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((X != ((hd @ A) @ Xs)) => ((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (((member @ A) @ X) @ ((set2 @ A) @ ((tl @ A) @ Xs)))))))).
% 2.15/1.38 thf(fact_248_set__subset__Cons, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((set2 @ A) @ (((cons @ A) @ X) @ Xs)))))).
% 2.15/1.38 thf(fact_249_list_Oexhaust__sel, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => (List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))).
% 2.15/1.38 thf(fact_250_tl__subset, axiom, (! [A:$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)))))).
% 2.15/1.38 thf(fact_251_butlast__subset, axiom, (! [A:$tType,Xs:(list @ A),A3:(set @ A)]: (((Xs != (nil @ A)) => ((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ A3) => (((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) @ A3)))))).
% 2.15/1.38 thf(fact_252_prefix__same__cases, axiom, (! [A:$tType,Xs_1:(list @ A),Ys:(list @ A),Xs_2:(list @ A)]: (((((prefix @ A) @ Xs_1) @ Ys) => ((((prefix @ A) @ Xs_2) @ Ys) => ((((prefix @ A) @ Xs_1) @ Xs_2) | (((prefix @ A) @ Xs_2) @ Xs_1))))))).
% 2.15/1.38 thf(fact_253_prefix__order_Oeq__iff, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z:(list @ A)]: ((Y4 = Z))) = (^ [X3:(list @ A),Y3:(list @ A)]: (((((prefix @ A) @ X3) @ Y3) & (((prefix @ A) @ Y3) @ X3)))))))).
% 2.15/1.38 thf(fact_254_prefix__order_Oantisym, axiom, (! [A:$tType,X:(list @ A),Y:(list @ A)]: (((((prefix @ A) @ X) @ Y) => ((((prefix @ A) @ Y) @ X) => (X = Y)))))).
% 2.15/1.38 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: (((linorder @ A) => (type @ A))))).
% 2.15/1.38 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: (((linorder @ A) => (ord @ A))))).
% 2.15/1.38 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.15/1.38 thf(tcon_Set_Oset___Orderings_Oord_1, axiom, (! [A6:$tType]: ((ord @ (set @ A6))))).
% 2.15/1.38 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.15/1.38 thf(tcon_HOL_Obool___Orderings_Oord_2, axiom, (ord @ $o)).
% 2.15/1.38 thf(tfree_0, hypothesis, (linorder @ val)).
% 2.15/1.38 thf(tfree_1, hypothesis, (linorder @ node)).
% 2.15/1.38 thf(conj_0, conjecture, ((((((((((graph_1661282752_path2 @ g) @ node) @ edgeD) @ alpha_n) @ invar) @ inEdges) @ g2) @ n) @ (((append @ node) @ ns) @ ((tl @ node) @ ri))) @ ((((((((sSA_CF1081484811efNode @ g) @ node) @ val) @ alpha_n) @ defs) @ phis) @ g2) @ phi_r))).
% 2.15/1.38 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.FAhNdHU93a/DTF2DTF28396.p
% 2.15/1.38 ------------------------
% 2.42/1.41 ---- Cleaned THF ---
% 2.42/1.41 thf(ty_t_Product__Type_Oprod,type,
% 2.42/1.41 product_prod: $tType > $tType > $tType ).
% 2.42/1.41
% 2.42/1.41 thf(ty_t_Option_Ooption,type,
% 2.42/1.41 option: $tType > $tType ).
% 2.42/1.41
% 2.42/1.41 thf(ty_t_List_Olist,type,
% 2.42/1.41 list: $tType > $tType ).
% 2.42/1.41
% 2.42/1.41 thf(ty_t_Set_Oset,type,
% 2.42/1.41 set: $tType > $tType ).
% 2.42/1.41
% 2.42/1.41 thf(ty_tf_edgeD,type,
% 2.42/1.41 edgeD: $tType ).
% 2.42/1.41
% 2.42/1.41 thf(ty_tf_node,type,
% 2.42/1.41 node: $tType ).
% 2.42/1.41
% 2.42/1.41 thf(ty_tf_val,type,
% 2.42/1.41 val: $tType ).
% 2.42/1.41
% 2.42/1.41 thf(ty_tf_g,type,
% 2.42/1.41 g: $tType ).
% 2.42/1.41
% 2.42/1.41 thf(sy_cl_HOL_Otype,type,
% 2.42/1.41 type:
% 2.42/1.41 !>[A: $tType] : $o ).
% 2.42/1.41
% 2.42/1.41 thf(sy_cl_Orderings_Oord,type,
% 2.42/1.41 ord:
% 2.42/1.41 !>[A: $tType] : $o ).
% 2.42/1.41
% 2.42/1.41 thf(sy_cl_Orderings_Olinorder,type,
% 2.42/1.41 linorder:
% 2.42/1.41 !>[A: $tType] : $o ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_Finite__Set_Ofinite,type,
% 2.42/1.41 finite_finite:
% 2.42/1.41 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_Graph__path_Ograph__path__base_Opath,type,
% 2.42/1.41 graph_1146196722h_path:
% 2.42/1.41 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > ( list @ Node ) > $o ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_Graph__path_Ograph__path__base_Opath2,type,
% 2.42/1.41 graph_1661282752_path2:
% 2.42/1.41 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > ( list @ Node ) ) > ( G > $o ) > ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) > Node > $o ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors,type,
% 2.42/1.41 graph_1201503639essors:
% 2.42/1.41 !>[G: $tType,Node: $tType,EdgeD: $tType] : ( ( G > Node > ( list @ ( product_prod @ Node @ EdgeD ) ) ) > G > Node > ( list @ Node ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_List_Oappend,type,
% 2.42/1.41 append:
% 2.42/1.41 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_List_Obutlast,type,
% 2.42/1.41 butlast:
% 2.42/1.41 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_List_Olist_OCons,type,
% 2.42/1.41 cons:
% 2.42/1.41 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_List_Olist_ONil,type,
% 2.42/1.41 nil:
% 2.42/1.41 !>[A: $tType] : ( list @ A ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_List_Olist_Ohd,type,
% 2.42/1.41 hd:
% 2.42/1.41 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_List_Olist_Oset,type,
% 2.42/1.41 set2:
% 2.42/1.41 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_List_Olist_Otl,type,
% 2.42/1.41 tl:
% 2.42/1.41 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.42/1.41 ord_less_eq:
% 2.42/1.41 !>[A: $tType] : ( A > A > $o ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses,type,
% 2.42/1.41 sSA_CFG_SSA_phiUses:
% 2.42/1.41 !>[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 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode,type,
% 2.42/1.41 sSA_CF1081484811efNode:
% 2.42/1.41 !>[G: $tType,Node: $tType,Val: $tType] : ( ( G > ( list @ Node ) ) > ( G > Node > ( set @ Val ) ) > ( G > ( product_prod @ Node @ Val ) > ( option @ ( list @ Val ) ) ) > G > Val > Node ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg,type,
% 2.42/1.41 sSA_CF1165125185phiArg:
% 2.42/1.41 !>[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 ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_Set_OCollect,type,
% 2.42/1.41 collect:
% 2.42/1.41 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_Sublist_Oprefix,type,
% 2.42/1.41 prefix:
% 2.42/1.41 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_Sublist_Osuffix,type,
% 2.42/1.41 suffix:
% 2.42/1.41 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_c_member,type,
% 2.42/1.41 member:
% 2.42/1.41 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v__092_060alpha_062n,type,
% 2.42/1.41 alpha_n: g > ( list @ node ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 2.42/1.41 phi_r: val ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_defs,type,
% 2.42/1.41 defs: g > node > ( set @ val ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_g,type,
% 2.42/1.41 g2: g ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_i____,type,
% 2.42/1.41 i: node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_inEdges_H,type,
% 2.42/1.41 inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_invar,type,
% 2.42/1.41 invar: g > $o ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_m,type,
% 2.42/1.41 m: node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_ms,type,
% 2.42/1.41 ms: list @ node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_ms_H____,type,
% 2.42/1.41 ms2: list @ node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_n,type,
% 2.42/1.41 n: node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_ns,type,
% 2.42/1.41 ns: list @ node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_phis,type,
% 2.42/1.41 phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 2.42/1.41 pred_phi_r: node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_r,type,
% 2.42/1.41 r: val ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_ri____,type,
% 2.42/1.41 ri: list @ node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_rs_H____,type,
% 2.42/1.41 rs: list @ node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_rs____,type,
% 2.42/1.41 rs2: list @ node ).
% 2.42/1.41
% 2.42/1.41 thf(sy_v_s,type,
% 2.42/1.41 s: val ).
% 2.42/1.41
% 2.42/1.41 thf(fact_0_False,axiom,
% 2.42/1.41 r != phi_r ).
% 2.42/1.41
% 2.42/1.41 thf(fact_1_ri__is__valid,axiom,
% 2.42/1.41 ( i
% 2.42/1.41 = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_2_old_Oinvar,axiom,
% 2.42/1.41 ! [G2: g] : ( invar @ G2 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_3_assms_I7_J,axiom,
% 2.42/1.41 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_4_ri__props_I1_J,axiom,
% 2.42/1.41 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 2.42/1.41
% 2.42/1.41 thf(fact_5_old_Opath2__app,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( tl @ node @ Ms ) ) @ L ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 2.42/1.41 ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 2.42/1.41 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_7_rs_H__props_I1_J,axiom,
% 2.42/1.41 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 ).
% 2.42/1.41
% 2.42/1.41 thf(fact_8_assms_I10_J,axiom,
% 2.42/1.41 sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 2.42/1.41
% 2.42/1.41 thf(fact_9_rs__props_I1_J,axiom,
% 2.42/1.41 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 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_10_ms_H__props_I1_J,axiom,
% 2.42/1.41 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 2.42/1.41
% 2.42/1.41 thf(fact_11__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,
% 2.42/1.41 ( ( i
% 2.42/1.41 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.42/1.41 => ( ( ( i
% 2.42/1.41 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.42/1.41 => ( m != i ) )
% 2.42/1.41 => ~ ( ( i
% 2.42/1.41 != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.42/1.41 => ( m = i ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_12_old_Opath2__split_I2_J,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns2: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns2 ) ) @ M )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns2 ) @ M ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_13_old_Opath2__not__Nil,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( Ns
% 2.42/1.41 != ( nil @ node ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_14_old_Opath2__not__Nil2,axiom,
% 2.42/1.41 ! [G2: g,N: node,M: node] :
% 2.42/1.41 ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( nil @ node ) @ M ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_15_rs_H__props_I3_J,axiom,
% 2.42/1.41 member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_16_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_17_old_Opath2__hd__in__ns,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( member @ node @ N @ ( set2 @ node @ Ns ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_18_old_Opath2__in___092_060alpha_062n,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,L: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( member @ node @ L @ ( set2 @ node @ Ns ) )
% 2.42/1.41 => ( member @ node @ L @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_19_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Y: A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ ( append @ A @ Ys @ ( cons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_20_ri__props_I2_J,axiom,
% 2.42/1.41 member @ node @ i @ ( set2 @ node @ ms ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_21_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( member @ node @ M @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_22_old_Opath2__last__in__ns,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( member @ node @ M @ ( set2 @ node @ Ns ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_23_old_Opath2__split_I1_J,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,N2: node,Ns2: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ Ns2 ) ) @ M )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ N2 @ ( nil @ node ) ) ) @ N2 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_24_rs__props_I3_J,axiom,
% 2.42/1.41 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_25_rs_H__loopfree,axiom,
% 2.42/1.41 ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_26_rs__def,axiom,
% 2.42/1.41 ( rs2
% 2.42/1.41 = ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_27_ri__props_I4_J,axiom,
% 2.42/1.41 prefix @ node @ ri @ rs2 ).
% 2.42/1.41
% 2.42/1.41 thf(fact_28_old_Oempty__path2,axiom,
% 2.42/1.41 ! [N: node,G2: g] :
% 2.42/1.41 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.42/1.41 => ( ( invar @ G2 )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_29_ms_H__props_I3_J,axiom,
% 2.42/1.41 ~ ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ ms2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_30_rs_H__props_I4_J,axiom,
% 2.42/1.41 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 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_31_assms_I8_J,axiom,
% 2.42/1.41 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_32_tl__append2,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( tl @ A @ ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( append @ A @ ( tl @ A @ Xs ) @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_33_list__e__eq__lel_I2_J,axiom,
% 2.42/1.41 ! [A: $tType,L1: list @ A,E: A,L2: list @ A,E2: A] :
% 2.42/1.41 ( ( ( append @ A @ L1 @ ( cons @ A @ E @ L2 ) )
% 2.42/1.41 = ( cons @ A @ E2 @ ( nil @ A ) ) )
% 2.42/1.41 = ( ( L1
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( E = E2 )
% 2.42/1.41 & ( L2
% 2.42/1.41 = ( nil @ A ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_34_list__e__eq__lel_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,E2: A,L1: list @ A,E: A,L2: list @ A] :
% 2.42/1.41 ( ( ( cons @ A @ E2 @ ( nil @ A ) )
% 2.42/1.41 = ( append @ A @ L1 @ ( cons @ A @ E @ L2 ) ) )
% 2.42/1.41 = ( ( L1
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( E = E2 )
% 2.42/1.41 & ( L2
% 2.42/1.41 = ( nil @ A ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_35_list__se__match_I4_J,axiom,
% 2.42/1.41 ! [A: $tType,L2: list @ A,A2: A,L1: list @ A] :
% 2.42/1.41 ( ( L2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 2.42/1.41 = ( append @ A @ L1 @ L2 ) )
% 2.42/1.41 = ( ( L1
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( L2
% 2.42/1.41 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_36_list__se__match_I3_J,axiom,
% 2.42/1.41 ! [A: $tType,L1: list @ A,A2: A,L2: list @ A] :
% 2.42/1.41 ( ( L1
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ( cons @ A @ A2 @ ( nil @ A ) )
% 2.42/1.41 = ( append @ A @ L1 @ L2 ) )
% 2.42/1.41 = ( ( L1
% 2.42/1.41 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.42/1.41 & ( L2
% 2.42/1.41 = ( nil @ A ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_37_list__se__match_I2_J,axiom,
% 2.42/1.41 ! [A: $tType,L2: list @ A,L1: list @ A,A2: A] :
% 2.42/1.41 ( ( L2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ( append @ A @ L1 @ L2 )
% 2.42/1.41 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.42/1.41 = ( ( L1
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( L2
% 2.42/1.41 = ( cons @ A @ A2 @ ( nil @ A ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_38_list__se__match_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,L1: list @ A,L2: list @ A,A2: A] :
% 2.42/1.41 ( ( L1
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ( append @ A @ L1 @ L2 )
% 2.42/1.41 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.42/1.41 = ( ( L1
% 2.42/1.41 = ( cons @ A @ A2 @ ( nil @ A ) ) )
% 2.42/1.41 & ( L2
% 2.42/1.41 = ( nil @ A ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_39_list__ee__eq__leel_I2_J,axiom,
% 2.42/1.41 ! [A: $tType,L1: list @ A,E1: A,E22: A,L2: list @ A,E12: A,E23: A] :
% 2.42/1.41 ( ( ( append @ A @ L1 @ ( cons @ A @ E1 @ ( cons @ A @ E22 @ L2 ) ) )
% 2.42/1.41 = ( cons @ A @ E12 @ ( cons @ A @ E23 @ ( nil @ A ) ) ) )
% 2.42/1.41 = ( ( L1
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( E12 = E1 )
% 2.42/1.41 & ( E23 = E22 )
% 2.42/1.41 & ( L2
% 2.42/1.41 = ( nil @ A ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_40_list__ee__eq__leel_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,E12: A,E23: A,L1: list @ A,E1: A,E22: A,L2: list @ A] :
% 2.42/1.41 ( ( ( cons @ A @ E12 @ ( cons @ A @ E23 @ ( nil @ A ) ) )
% 2.42/1.41 = ( append @ A @ L1 @ ( cons @ A @ E1 @ ( cons @ A @ E22 @ L2 ) ) ) )
% 2.42/1.41 = ( ( L1
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( E12 = E1 )
% 2.42/1.41 & ( E23 = E22 )
% 2.42/1.41 & ( L2
% 2.42/1.41 = ( nil @ A ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_41_ms_H__props_I2_J,axiom,
% 2.42/1.41 prefix @ node @ ms2 @ ms ).
% 2.42/1.41
% 2.42/1.41 thf(fact_42_ri__props_I3_J,axiom,
% 2.42/1.41 ! [X2: node] :
% 2.42/1.41 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ ri ) ) )
% 2.42/1.41 => ~ ( member @ node @ X2 @ ( set2 @ node @ ms ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_43_list_Oinject,axiom,
% 2.42/1.41 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.42/1.41 ( ( ( cons @ A @ X21 @ X22 )
% 2.42/1.41 = ( cons @ A @ Y21 @ Y22 ) )
% 2.42/1.41 = ( ( X21 = Y21 )
% 2.42/1.41 & ( X22 = Y22 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_44_append_Oassoc,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 2.42/1.41 ( ( append @ A @ ( append @ A @ A2 @ B ) @ C )
% 2.42/1.41 = ( append @ A @ A2 @ ( append @ A @ B @ C ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_45_mem__Collect__eq,axiom,
% 2.42/1.41 ! [A: $tType,A2: A,P: A > $o] :
% 2.42/1.41 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.42/1.41 = ( P @ A2 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_46_Collect__mem__eq,axiom,
% 2.42/1.41 ! [A: $tType,A3: set @ A] :
% 2.42/1.41 ( ( collect @ A
% 2.42/1.41 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 2.42/1.41 = A3 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_47_Collect__cong,axiom,
% 2.42/1.41 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.42/1.41 ( ! [X4: A] :
% 2.42/1.41 ( ( P @ X4 )
% 2.42/1.41 = ( Q @ X4 ) )
% 2.42/1.41 => ( ( collect @ A @ P )
% 2.42/1.41 = ( collect @ A @ Q ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_48_ext,axiom,
% 2.42/1.41 ! [B2: $tType,A: $tType,F: A > B2,G2: A > B2] :
% 2.42/1.41 ( ! [X4: A] :
% 2.42/1.41 ( ( F @ X4 )
% 2.42/1.41 = ( G2 @ X4 ) )
% 2.42/1.41 => ( F = G2 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_49_append__assoc,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 2.42/1.41 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_50_append__same__eq,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Ys @ Xs )
% 2.42/1.41 = ( append @ A @ Zs @ Xs ) )
% 2.42/1.41 = ( Ys = Zs ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_51_same__append__eq,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Xs @ Ys )
% 2.42/1.41 = ( append @ A @ Xs @ Zs ) )
% 2.42/1.41 = ( Ys = Zs ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_52_old_Opredecessor__is__node,axiom,
% 2.42/1.41 ! [N: node,G2: g,N2: node] :
% 2.42/1.41 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 2.42/1.41 => ( ( invar @ G2 )
% 2.42/1.41 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_53_old_Osuccessor__is__node,axiom,
% 2.42/1.41 ! [N: node,G2: g,N2: node] :
% 2.42/1.41 ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N2 ) ) )
% 2.42/1.41 => ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.42/1.41 => ( ( invar @ G2 )
% 2.42/1.41 => ( member @ node @ N2 @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_54_old_Osuccessor__in___092_060alpha_062n,axiom,
% 2.42/1.41 ! [G2: g,N: node] :
% 2.42/1.41 ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N )
% 2.42/1.41 != ( nil @ node ) )
% 2.42/1.41 => ( ( invar @ G2 )
% 2.42/1.41 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_55_old_Opath2__app_H,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,Ms: list @ node,L: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ M @ Ms @ L )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ ( butlast @ node @ Ns ) @ Ms ) @ L ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_56_append__Nil2,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.42/1.41 = Xs ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_57_append__self__conv,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Xs @ Ys )
% 2.42/1.41 = Xs )
% 2.42/1.41 = ( Ys
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_58_self__append__conv,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( Ys
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_59_append__self__conv2,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Xs @ Ys )
% 2.42/1.41 = Ys )
% 2.42/1.41 = ( Xs
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_60_self__append__conv2,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.42/1.41 ( ( Ys
% 2.42/1.41 = ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( Xs
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_61_Nil__is__append__conv,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( ( nil @ A )
% 2.42/1.41 = ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( ( Xs
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( Ys
% 2.42/1.41 = ( nil @ A ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_62_append__is__Nil__conv,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Xs @ Ys )
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 = ( ( Xs
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( Ys
% 2.42/1.41 = ( nil @ A ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_63_empty__append__eq__id,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( append @ A @ ( nil @ A ) )
% 2.42/1.41 = ( ^ [X3: list @ A] : X3 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_64_append_Oright__neutral,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] :
% 2.42/1.41 ( ( append @ A @ A2 @ ( nil @ A ) )
% 2.42/1.41 = A2 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_65_old_Opath2__split__ex_H,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 2.42/1.41 => ~ ! [Ns_1: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns_1 @ X )
% 2.42/1.41 => ! [Ns_2: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_2 @ M )
% 2.42/1.41 => ( Ns
% 2.42/1.41 != ( append @ node @ ( butlast @ node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_66_old_Opath2__prefix__ex,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,M2: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( member @ node @ M2 @ ( set2 @ node @ Ns ) )
% 2.42/1.41 => ~ ! [Ns3: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns3 @ M2 )
% 2.42/1.41 => ( ( prefix @ node @ Ns3 @ Ns )
% 2.42/1.41 => ( member @ node @ M2 @ ( set2 @ node @ ( butlast @ node @ Ns3 ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_67_old_Opath2__split__first__prop,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ? [X2: node] :
% 2.42/1.41 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 2.42/1.41 & ( P @ X2 ) )
% 2.42/1.41 => ~ ! [M3: node,Ns3: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns3 @ M3 )
% 2.42/1.41 => ( ( P @ M3 )
% 2.42/1.41 => ( ! [X2: node] :
% 2.42/1.41 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ Ns3 ) ) )
% 2.42/1.41 => ~ ( P @ X2 ) )
% 2.42/1.41 => ~ ( prefix @ node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_68_old_Opath2__induct,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( ( invar @ G2 )
% 2.42/1.41 => ( P @ M @ ( cons @ node @ M @ ( nil @ node ) ) @ M ) )
% 2.42/1.41 => ( ! [Ns4: list @ node,N3: node,N4: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N4 @ Ns4 @ M )
% 2.42/1.41 => ( ( P @ N4 @ Ns4 @ M )
% 2.42/1.41 => ( ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N4 ) ) )
% 2.42/1.41 => ( P @ N3 @ ( cons @ node @ N3 @ Ns4 ) @ M ) ) ) )
% 2.42/1.41 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_69_old_Opath2__split__ex,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 2.42/1.41 => ~ ! [Ns_1: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns_1 @ X )
% 2.42/1.41 => ! [Ns_2: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_2 @ M )
% 2.42/1.41 => ( ( Ns
% 2.42/1.41 = ( append @ node @ Ns_1 @ ( tl @ node @ Ns_2 ) ) )
% 2.42/1.41 => ( Ns
% 2.42/1.41 != ( append @ node @ ( butlast @ node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_70_old_Opath2__prefix,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,Ns2: list @ node,M2: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( prefix @ node @ ( append @ node @ Ns2 @ ( cons @ node @ M2 @ ( nil @ node ) ) ) @ Ns )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns2 @ ( cons @ node @ M2 @ ( nil @ node ) ) ) @ M2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_71_old_Opath2__rev__induct,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > ( list @ node ) > node > $o] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.42/1.41 => ( P @ N @ ( cons @ node @ N @ ( nil @ node ) ) @ N ) )
% 2.42/1.41 => ( ! [Ns4: list @ node,M3: node,M4: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns4 @ M3 )
% 2.42/1.41 => ( ( P @ N @ Ns4 @ M3 )
% 2.42/1.41 => ( ( member @ node @ M3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M4 ) ) )
% 2.42/1.41 => ( P @ N @ ( append @ node @ Ns4 @ ( cons @ node @ M4 @ ( nil @ node ) ) ) @ M4 ) ) ) )
% 2.42/1.41 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_72_old_Opath2__snoc,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,M2: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( member @ node @ M @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M2 ) ) )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns @ ( cons @ node @ M2 @ ( nil @ node ) ) ) @ M2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_73_append1__eq__conv,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.42/1.41 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.42/1.41 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.42/1.41 = ( ( Xs = Ys )
% 2.42/1.41 & ( X = Y ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_74_butlast__snoc,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,X: A] :
% 2.42/1.41 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.42/1.41 = Xs ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_75__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,
% 2.42/1.41 ~ ! [Ms2: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 2.42/1.41 => ( ( prefix @ node @ Ms2 @ ms )
% 2.42/1.41 => ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ Ms2 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_76__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,
% 2.42/1.41 ~ ! [I: node,Ri: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 2.42/1.41 => ( ( member @ node @ I @ ( set2 @ node @ ms ) )
% 2.42/1.41 => ( ! [X2: node] :
% 2.42/1.41 ( ( member @ node @ X2 @ ( set2 @ node @ ( butlast @ node @ Ri ) ) )
% 2.42/1.41 => ~ ( member @ node @ X2 @ ( set2 @ node @ ms ) ) )
% 2.42/1.41 => ~ ( prefix @ node @ Ri @ rs2 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_77_old_OCons__path2,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,N2: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ N ) ) )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N2 @ ( cons @ node @ N2 @ Ns ) @ M ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_78_butlast_Osimps_I1_J,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( butlast @ A @ ( nil @ A ) )
% 2.42/1.41 = ( nil @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_79_in__set__butlastD,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 2.42/1.41 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_80_butlast__tl,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 2.42/1.41 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_81_butlast_Osimps_I2_J,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,X: A] :
% 2.42/1.41 ( ( ( Xs
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.42/1.41 = ( nil @ A ) ) )
% 2.42/1.41 & ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.42/1.41 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_82_butlast__append,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.42/1.41 ( ( ( Ys
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( butlast @ A @ Xs ) ) )
% 2.42/1.41 & ( ( Ys
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_83_in__set__butlast__appendI,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 2.42/1.41 | ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 2.42/1.41 => ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_84_butlast__eq__cons__conv,axiom,
% 2.42/1.41 ! [A: $tType,L: list @ A,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( ( butlast @ A @ L )
% 2.42/1.41 = ( cons @ A @ X @ Xs ) )
% 2.42/1.41 = ( ? [Xl: A] :
% 2.42/1.41 ( L
% 2.42/1.41 = ( cons @ A @ X @ ( append @ A @ Xs @ ( cons @ A @ Xl @ ( nil @ A ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_85_butlast__eq__consE,axiom,
% 2.42/1.41 ! [A: $tType,L: list @ A,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( ( butlast @ A @ L )
% 2.42/1.41 = ( cons @ A @ X @ Xs ) )
% 2.42/1.41 => ~ ! [Xl2: A] :
% 2.42/1.41 ( L
% 2.42/1.41 != ( cons @ A @ X @ ( append @ A @ Xs @ ( cons @ A @ Xl2 @ ( nil @ A ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_86_list__tail__coinc,axiom,
% 2.42/1.41 ! [A: $tType,N1: A,R1: list @ A,N22: A,R2: list @ A] :
% 2.42/1.41 ( ( ( cons @ A @ N1 @ R1 )
% 2.42/1.41 = ( cons @ A @ N22 @ R2 ) )
% 2.42/1.41 => ( ( N1 = N22 )
% 2.42/1.41 & ( R1 = R2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_87_not__Cons__self2,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( cons @ A @ X @ Xs )
% 2.42/1.41 != Xs ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_88_append__eq__appendI,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Xs @ Xs1 )
% 2.42/1.41 = Zs )
% 2.42/1.41 => ( ( Ys
% 2.42/1.41 = ( append @ A @ Xs1 @ Us ) )
% 2.42/1.41 => ( ( append @ A @ Xs @ Ys )
% 2.42/1.41 = ( append @ A @ Zs @ Us ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_89_append__eq__append__conv2,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Xs @ Ys )
% 2.42/1.41 = ( append @ A @ Zs @ Ts ) )
% 2.42/1.41 = ( ? [Us2: list @ A] :
% 2.42/1.41 ( ( ( Xs
% 2.42/1.41 = ( append @ A @ Zs @ Us2 ) )
% 2.42/1.41 & ( ( append @ A @ Us2 @ Ys )
% 2.42/1.41 = Ts ) )
% 2.42/1.41 | ( ( ( append @ A @ Xs @ Us2 )
% 2.42/1.41 = Zs )
% 2.42/1.41 & ( Ys
% 2.42/1.41 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_90_strict__sorted_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( linorder @ A )
% 2.42/1.41 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.42/1.41 ( ( P @ ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A,Ys2: list @ A] :
% 2.42/1.41 ( ( P @ Ys2 )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Ys2 ) ) )
% 2.42/1.41 => ( P @ A0 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_91_mergesort__by__rel__merge__induct,axiom,
% 2.42/1.41 ! [A: $tType,B2: $tType,P: ( list @ A ) > ( list @ B2 ) > $o,R: A > B2 > $o,Xs: list @ A,Ys: list @ B2] :
% 2.42/1.41 ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [X_1: list @ B2] : ( P @ ( nil @ A ) @ X_1 )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 2.42/1.41 ( ( R @ X4 @ Y2 )
% 2.42/1.41 => ( ( P @ Xs2 @ ( cons @ B2 @ Y2 @ Ys2 ) )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B2 @ Y2 @ Ys2 ) ) ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 2.42/1.41 ( ~ ( R @ X4 @ Y2 )
% 2.42/1.41 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys2 )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B2 @ Y2 @ Ys2 ) ) ) )
% 2.42/1.41 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_92_mergesort__by__rel__merge_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.42/1.41 ( ! [R3: A > A > $o,X4: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.42/1.41 ( ( ( R3 @ X4 @ Y2 )
% 2.42/1.41 => ( P @ R3 @ Xs2 @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.42/1.41 => ( ( ~ ( R3 @ X4 @ Y2 )
% 2.42/1.41 => ( P @ R3 @ ( cons @ A @ X4 @ Xs2 ) @ Ys2 ) )
% 2.42/1.41 => ( P @ R3 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) )
% 2.42/1.41 => ( ! [R3: A > A > $o,Xs2: list @ A] : ( P @ R3 @ Xs2 @ ( nil @ A ) )
% 2.42/1.41 => ( ! [R3: A > A > $o,V: A,Va: list @ A] : ( P @ R3 @ ( nil @ A ) @ ( cons @ A @ V @ Va ) )
% 2.42/1.41 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_93_map__tailrec__rev_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,B2: $tType,P: ( A > B2 ) > ( list @ A ) > ( list @ B2 ) > $o,A0: A > B2,A1: list @ A,A22: list @ B2] :
% 2.42/1.41 ( ! [F2: A > B2,X_1: list @ B2] : ( P @ F2 @ ( nil @ A ) @ X_1 )
% 2.42/1.41 => ( ! [F2: A > B2,A4: A,As: list @ A,Bs: list @ B2] :
% 2.42/1.41 ( ( P @ F2 @ As @ ( cons @ B2 @ ( F2 @ A4 ) @ Bs ) )
% 2.42/1.41 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.42/1.41 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_94_list__nonempty__induct,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A] :
% 2.42/1.41 ( ( Xs2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( P @ Xs2 )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 2.42/1.41 => ( P @ Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_95_list__all__zip_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,B2: $tType,P: ( A > B2 > $o ) > ( list @ A ) > ( list @ B2 ) > $o,A0: A > B2 > $o,A1: list @ A,A22: list @ B2] :
% 2.42/1.41 ( ! [P2: A > B2 > $o] : ( P @ P2 @ ( nil @ A ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [P2: A > B2 > $o,A4: A,As: list @ A,B3: B2,Bs: list @ B2] :
% 2.42/1.41 ( ( P @ P2 @ As @ Bs )
% 2.42/1.41 => ( P @ P2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B2 @ B3 @ Bs ) ) )
% 2.42/1.41 => ( ! [P2: A > B2 > $o,V: A,Va: list @ A] : ( P @ P2 @ ( cons @ A @ V @ Va ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [P2: A > B2 > $o,V: B2,Va: list @ B2] : ( P @ P2 @ ( nil @ A ) @ ( cons @ B2 @ V @ Va ) )
% 2.42/1.41 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_96_successively_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.42/1.41 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 2.42/1.41 => ( ! [P2: A > A > $o,X4: A] : ( P @ P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.42/1.41 => ( ! [P2: A > A > $o,X4: A,Y2: A,Xs2: list @ A] :
% 2.42/1.41 ( ( P @ P2 @ ( cons @ A @ Y2 @ Xs2 ) )
% 2.42/1.41 => ( P @ P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Xs2 ) ) ) )
% 2.42/1.41 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_97_arg__min__list_Oinduct,axiom,
% 2.42/1.41 ! [B2: $tType,A: $tType] :
% 2.42/1.41 ( ( linorder @ B2 )
% 2.42/1.41 => ! [P: ( A > B2 ) > ( list @ A ) > $o,A0: A > B2,A1: list @ A] :
% 2.42/1.41 ( ! [F2: A > B2,X4: A] : ( P @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.42/1.41 => ( ! [F2: A > B2,X4: A,Y2: A,Zs2: list @ A] :
% 2.42/1.41 ( ( P @ F2 @ ( cons @ A @ Y2 @ Zs2 ) )
% 2.42/1.41 => ( P @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Zs2 ) ) ) )
% 2.42/1.41 => ( ! [A4: A > B2] : ( P @ A4 @ ( nil @ A ) )
% 2.42/1.41 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_98_list__induct__first2,axiom,
% 2.42/1.41 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.42/1.41 ( ( P @ ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.42/1.41 => ( ! [X1: A,X23: A,Xs2: list @ A] :
% 2.42/1.41 ( ( P @ Xs2 )
% 2.42/1.41 => ( P @ ( cons @ A @ X1 @ ( cons @ A @ X23 @ Xs2 ) ) ) )
% 2.42/1.41 => ( P @ Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_99_remdups__adj_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.42/1.41 ( ( P @ ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.42/1.41 => ( ! [X4: A,Y2: A,Xs2: list @ A] :
% 2.42/1.41 ( ( ( X4 = Y2 )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 2.42/1.41 => ( ( ( X4 != Y2 )
% 2.42/1.41 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 2.42/1.41 => ( P @ A0 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_100_sorted__wrt_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.42/1.41 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 2.42/1.41 => ( ! [P2: A > A > $o,X4: A,Ys2: list @ A] :
% 2.42/1.41 ( ( P @ P2 @ Ys2 )
% 2.42/1.41 => ( P @ P2 @ ( cons @ A @ X4 @ Ys2 ) ) )
% 2.42/1.41 => ( P @ A0 @ A1 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_101_remdups__adj_Ocases,axiom,
% 2.42/1.41 ! [A: $tType,X: list @ A] :
% 2.42/1.41 ( ( X
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A] :
% 2.42/1.41 ( X
% 2.42/1.41 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.42/1.41 => ~ ! [X4: A,Y2: A,Xs2: list @ A] :
% 2.42/1.41 ( X
% 2.42/1.41 != ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_102_list__2pre__induct,axiom,
% 2.42/1.41 ! [A: $tType,B2: $tType,P: ( list @ A ) > ( list @ B2 ) > $o,W1: list @ A,W2: list @ B2] :
% 2.42/1.41 ( ( P @ ( nil @ A ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [E3: A,W12: list @ A,W22: list @ B2] :
% 2.42/1.41 ( ( P @ W12 @ W22 )
% 2.42/1.41 => ( P @ ( cons @ A @ E3 @ W12 ) @ W22 ) )
% 2.42/1.41 => ( ! [E3: B2,W13: list @ A,W23: list @ B2] :
% 2.42/1.41 ( ( P @ W13 @ W23 )
% 2.42/1.41 => ( P @ W13 @ ( cons @ B2 @ E3 @ W23 ) ) )
% 2.42/1.41 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_103_transpose_Ocases,axiom,
% 2.42/1.41 ! [A: $tType,X: list @ ( list @ A )] :
% 2.42/1.41 ( ( X
% 2.42/1.41 != ( nil @ ( list @ A ) ) )
% 2.42/1.41 => ( ! [Xss: list @ ( list @ A )] :
% 2.42/1.41 ( X
% 2.42/1.41 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.42/1.41 => ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.42/1.41 ( X
% 2.42/1.41 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_104_shuffles_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.42/1.41 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.42/1.41 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.42/1.41 ( ( P @ Xs2 @ ( cons @ A @ Y2 @ Ys2 ) )
% 2.42/1.41 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys2 )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) )
% 2.42/1.41 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_105_min__list_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( ord @ A )
% 2.42/1.41 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.42/1.41 ( ! [X4: A,Xs2: list @ A] :
% 2.42/1.41 ( ! [X212: A,X222: list @ A] :
% 2.42/1.41 ( ( Xs2
% 2.42/1.41 = ( cons @ A @ X212 @ X222 ) )
% 2.42/1.41 => ( P @ Xs2 ) )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 2.42/1.41 => ( ( P @ ( nil @ A ) )
% 2.42/1.41 => ( P @ A0 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_106_min__list_Ocases,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( ord @ A )
% 2.42/1.41 => ! [X: list @ A] :
% 2.42/1.41 ( ! [X4: A,Xs2: list @ A] :
% 2.42/1.41 ( X
% 2.42/1.41 != ( cons @ A @ X4 @ Xs2 ) )
% 2.42/1.41 => ( X
% 2.42/1.41 = ( nil @ A ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_107_induct__list012,axiom,
% 2.42/1.41 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.42/1.41 ( ( P @ ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.42/1.41 => ( ! [X4: A,Y2: A,Zs2: list @ A] :
% 2.42/1.41 ( ( P @ Zs2 )
% 2.42/1.41 => ( ( P @ ( cons @ A @ Y2 @ Zs2 ) )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y2 @ Zs2 ) ) ) ) )
% 2.42/1.41 => ( P @ Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_108_splice_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.42/1.41 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Ys2: list @ A] :
% 2.42/1.41 ( ( P @ Ys2 @ Xs2 )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys2 ) )
% 2.42/1.41 => ( P @ A0 @ A1 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_109_list__induct2_H,axiom,
% 2.42/1.41 ! [A: $tType,B2: $tType,P: ( list @ A ) > ( list @ B2 ) > $o,Xs: list @ A,Ys: list @ B2] :
% 2.42/1.41 ( ( P @ ( nil @ A ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [Y2: B2,Ys2: list @ B2] : ( P @ ( nil @ A ) @ ( cons @ B2 @ Y2 @ Ys2 ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 2.42/1.41 ( ( P @ Xs2 @ Ys2 )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B2 @ Y2 @ Ys2 ) ) )
% 2.42/1.41 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_110_neq__Nil__conv,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 = ( ? [Y3: A,Ys3: list @ A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_111_list_Oinducts,axiom,
% 2.42/1.41 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.42/1.41 ( ( P @ ( nil @ A ) )
% 2.42/1.41 => ( ! [X1: A,X23: list @ A] :
% 2.42/1.41 ( ( P @ X23 )
% 2.42/1.41 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 2.42/1.41 => ( P @ List ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_112_list_Oexhaust,axiom,
% 2.42/1.41 ! [A: $tType,Y: list @ A] :
% 2.42/1.41 ( ( Y
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ~ ! [X213: A,X223: list @ A] :
% 2.42/1.41 ( Y
% 2.42/1.41 != ( cons @ A @ X213 @ X223 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_113_zipf_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,C2: $tType,B2: $tType,P: ( A > B2 > C2 ) > ( list @ A ) > ( list @ B2 ) > $o,A0: A > B2 > C2,A1: list @ A,A22: list @ B2] :
% 2.42/1.41 ( ! [F2: A > B2 > C2] : ( P @ F2 @ ( nil @ A ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [F2: A > B2 > C2,A4: A,As: list @ A,B3: B2,Bs: list @ B2] :
% 2.42/1.41 ( ( P @ F2 @ As @ Bs )
% 2.42/1.41 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ ( cons @ B2 @ B3 @ Bs ) ) )
% 2.42/1.41 => ( ! [A4: A > B2 > C2,V: A,Va: list @ A] : ( P @ A4 @ ( cons @ A @ V @ Va ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [A4: A > B2 > C2,V: B2,Va: list @ B2] : ( P @ A4 @ ( nil @ A ) @ ( cons @ B2 @ V @ Va ) )
% 2.42/1.41 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_114_revg_Oinduct,axiom,
% 2.42/1.41 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.42/1.41 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.42/1.41 => ( ! [A4: A,As: list @ A,B3: list @ A] :
% 2.42/1.41 ( ( P @ As @ ( cons @ A @ A4 @ B3 ) )
% 2.42/1.41 => ( P @ ( cons @ A @ A4 @ As ) @ B3 ) )
% 2.42/1.41 => ( P @ A0 @ A1 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_115_list_OdiscI,axiom,
% 2.42/1.41 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.42/1.41 ( ( List
% 2.42/1.41 = ( cons @ A @ X21 @ X22 ) )
% 2.42/1.41 => ( List
% 2.42/1.41 != ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_116_neq__NilE,axiom,
% 2.42/1.41 ! [A: $tType,L: list @ A] :
% 2.42/1.41 ( ( L
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ~ ! [X4: A,Xs2: list @ A] :
% 2.42/1.41 ( L
% 2.42/1.41 != ( cons @ A @ X4 @ Xs2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_117_list_Odistinct_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,X21: A,X22: list @ A] :
% 2.42/1.41 ( ( nil @ A )
% 2.42/1.41 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_118_list_Oset__cases,axiom,
% 2.42/1.41 ! [A: $tType,E2: A,A2: list @ A] :
% 2.42/1.41 ( ( member @ A @ E2 @ ( set2 @ A @ A2 ) )
% 2.42/1.41 => ( ! [Z2: list @ A] :
% 2.42/1.41 ( A2
% 2.42/1.41 != ( cons @ A @ E2 @ Z2 ) )
% 2.42/1.41 => ~ ! [Z1: A,Z2: list @ A] :
% 2.42/1.41 ( ( A2
% 2.42/1.41 = ( cons @ A @ Z1 @ Z2 ) )
% 2.42/1.41 => ~ ( member @ A @ E2 @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_119_set__ConsD,axiom,
% 2.42/1.41 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 2.42/1.41 => ( ( Y = X )
% 2.42/1.41 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_120_list_Oset__intros_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,X21: A,X22: list @ A] : ( member @ A @ X21 @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_121_list_Oset__intros_I2_J,axiom,
% 2.42/1.41 ! [A: $tType,Y: A,X22: list @ A,X21: A] :
% 2.42/1.41 ( ( member @ A @ Y @ ( set2 @ A @ X22 ) )
% 2.42/1.41 => ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X21 @ X22 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_122_Cons__eq__appendI,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( ( cons @ A @ X @ Xs1 )
% 2.42/1.41 = Ys )
% 2.42/1.41 => ( ( Xs
% 2.42/1.41 = ( append @ A @ Xs1 @ Zs ) )
% 2.42/1.41 => ( ( cons @ A @ X @ Xs )
% 2.42/1.41 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_123_append__Cons,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.42/1.41 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_124_list__match__lel__lel,axiom,
% 2.42/1.41 ! [A: $tType,C1: list @ A,Qs: A,C22: list @ A,C12: list @ A,Qs2: A,C23: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ C1 @ ( cons @ A @ Qs @ C22 ) )
% 2.42/1.41 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C23 ) ) )
% 2.42/1.41 => ( ! [C21: list @ A] :
% 2.42/1.41 ( ( C1
% 2.42/1.41 = ( append @ A @ C12 @ ( cons @ A @ Qs2 @ C21 ) ) )
% 2.42/1.41 => ( C23
% 2.42/1.41 != ( append @ A @ C21 @ ( cons @ A @ Qs @ C22 ) ) ) )
% 2.42/1.41 => ( ( ( C12 = C1 )
% 2.42/1.41 => ( ( Qs2 = Qs )
% 2.42/1.41 => ( C23 != C22 ) ) )
% 2.42/1.41 => ~ ! [C212: list @ A] :
% 2.42/1.41 ( ( C12
% 2.42/1.41 = ( append @ A @ C1 @ ( cons @ A @ Qs @ C212 ) ) )
% 2.42/1.41 => ( C22
% 2.42/1.41 != ( append @ A @ C212 @ ( cons @ A @ Qs2 @ C23 ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_125_eq__Nil__appendI,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( Xs = Ys )
% 2.42/1.41 => ( Xs
% 2.42/1.41 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_126_append__Nil,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A] :
% 2.42/1.41 ( ( append @ A @ ( nil @ A ) @ Ys )
% 2.42/1.41 = Ys ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_127_append_Oleft__neutral,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] :
% 2.42/1.41 ( ( append @ A @ ( nil @ A ) @ A2 )
% 2.42/1.41 = A2 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_128_list_Osel_I3_J,axiom,
% 2.42/1.41 ! [A: $tType,X21: A,X22: list @ A] :
% 2.42/1.41 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 2.42/1.41 = X22 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_129_list_Osel_I2_J,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( tl @ A @ ( nil @ A ) )
% 2.42/1.41 = ( nil @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_130_list__append__eq__Cons__cases,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Ys @ Zs )
% 2.42/1.41 = ( cons @ A @ X @ Xs ) )
% 2.42/1.41 => ( ( ( Ys
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 => ( Zs
% 2.42/1.41 != ( cons @ A @ X @ Xs ) ) )
% 2.42/1.41 => ~ ! [Ys4: list @ A] :
% 2.42/1.41 ( ( Ys
% 2.42/1.41 = ( cons @ A @ X @ Ys4 ) )
% 2.42/1.41 => ( ( append @ A @ Ys4 @ Zs )
% 2.42/1.41 != Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_131_list__Cons__eq__append__cases,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( ( cons @ A @ X @ Xs )
% 2.42/1.41 = ( append @ A @ Ys @ Zs ) )
% 2.42/1.41 => ( ( ( Ys
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 => ( Zs
% 2.42/1.41 != ( cons @ A @ X @ Xs ) ) )
% 2.42/1.41 => ~ ! [Ys4: list @ A] :
% 2.42/1.41 ( ( Ys
% 2.42/1.41 = ( cons @ A @ X @ Ys4 ) )
% 2.42/1.41 => ( ( append @ A @ Ys4 @ Zs )
% 2.42/1.41 != Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_132_rev__nonempty__induct2_H,axiom,
% 2.42/1.41 ! [A: $tType,B2: $tType,Xs: list @ A,Ys: list @ B2,P: ( list @ A ) > ( list @ B2 ) > $o] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( Ys
% 2.42/1.41 != ( nil @ B2 ) )
% 2.42/1.41 => ( ! [X4: A,Y2: B2] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: B2] :
% 2.42/1.41 ( ( Xs2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) )
% 2.42/1.41 => ( ! [X4: A,Y2: B2,Ys2: list @ B2] :
% 2.42/1.41 ( ( Ys2
% 2.42/1.41 != ( nil @ B2 ) )
% 2.42/1.41 => ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) @ ( append @ B2 @ Ys2 @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 2.42/1.41 ( ( P @ Xs2 @ Ys2 )
% 2.42/1.41 => ( ( Xs2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( Ys2
% 2.42/1.41 != ( nil @ B2 ) )
% 2.42/1.41 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ B2 @ Ys2 @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) ) ) ) )
% 2.42/1.41 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_133_rev__nonempty__induct,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A] :
% 2.42/1.41 ( ( Xs2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( P @ Xs2 )
% 2.42/1.41 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 2.42/1.41 => ( P @ Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_134_append__eq__Cons__conv,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( ( append @ A @ Ys @ Zs )
% 2.42/1.41 = ( cons @ A @ X @ Xs ) )
% 2.42/1.41 = ( ( ( Ys
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( Zs
% 2.42/1.41 = ( cons @ A @ X @ Xs ) ) )
% 2.42/1.41 | ? [Ys5: list @ A] :
% 2.42/1.41 ( ( Ys
% 2.42/1.41 = ( cons @ A @ X @ Ys5 ) )
% 2.42/1.41 & ( ( append @ A @ Ys5 @ Zs )
% 2.42/1.41 = Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_135_Cons__eq__append__conv,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( ( cons @ A @ X @ Xs )
% 2.42/1.41 = ( append @ A @ Ys @ Zs ) )
% 2.42/1.41 = ( ( ( Ys
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 & ( ( cons @ A @ X @ Xs )
% 2.42/1.41 = Zs ) )
% 2.42/1.41 | ? [Ys5: list @ A] :
% 2.42/1.41 ( ( ( cons @ A @ X @ Ys5 )
% 2.42/1.41 = Ys )
% 2.42/1.41 & ( Xs
% 2.42/1.41 = ( append @ A @ Ys5 @ Zs ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_136_neq__Nil__rev__conv,axiom,
% 2.42/1.41 ! [A: $tType,L: list @ A] :
% 2.42/1.41 ( ( L
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 = ( ? [Xs3: list @ A,X3: A] :
% 2.42/1.41 ( L
% 2.42/1.41 = ( append @ A @ Xs3 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_137_rev__induct2_H,axiom,
% 2.42/1.41 ! [A: $tType,B2: $tType,P: ( list @ A ) > ( list @ B2 ) > $o,Xs: list @ A,Ys: list @ B2] :
% 2.42/1.41 ( ( P @ ( nil @ A ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( nil @ B2 ) )
% 2.42/1.41 => ( ! [Y2: B2,Ys2: list @ B2] : ( P @ ( nil @ A ) @ ( append @ B2 @ Ys2 @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: B2,Ys2: list @ B2] :
% 2.42/1.41 ( ( P @ Xs2 @ Ys2 )
% 2.42/1.41 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ B2 @ Ys2 @ ( cons @ B2 @ Y2 @ ( nil @ B2 ) ) ) ) )
% 2.42/1.41 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_138_neq__Nil__revE,axiom,
% 2.42/1.41 ! [A: $tType,L: list @ A] :
% 2.42/1.41 ( ( L
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ~ ! [Ll: list @ A,E3: A] :
% 2.42/1.41 ( L
% 2.42/1.41 != ( append @ A @ Ll @ ( cons @ A @ E3 @ ( nil @ A ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_139_rev__exhaust,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ~ ! [Ys2: list @ A,Y2: A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 != ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_140_rev__induct,axiom,
% 2.42/1.41 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.42/1.41 ( ( P @ ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A] :
% 2.42/1.41 ( ( P @ Xs2 )
% 2.42/1.41 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 2.42/1.41 => ( P @ Xs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_141_split__list__first__prop__iff,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.42/1.41 ( ( ? [X3: A] :
% 2.42/1.41 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 & ( P @ X3 ) ) )
% 2.42/1.41 = ( ? [Ys3: list @ A,X3: A] :
% 2.42/1.41 ( ? [Zs3: list @ A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.42/1.41 & ( P @ X3 )
% 2.42/1.41 & ! [Y3: A] :
% 2.42/1.41 ( ( member @ A @ Y3 @ ( set2 @ A @ Ys3 ) )
% 2.42/1.41 => ~ ( P @ Y3 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_142_split__list__last__prop__iff,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.42/1.41 ( ( ? [X3: A] :
% 2.42/1.41 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 & ( P @ X3 ) ) )
% 2.42/1.41 = ( ? [Ys3: list @ A,X3: A,Zs3: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.42/1.41 & ( P @ X3 )
% 2.42/1.41 & ! [Y3: A] :
% 2.42/1.41 ( ( member @ A @ Y3 @ ( set2 @ A @ Zs3 ) )
% 2.42/1.41 => ~ ( P @ Y3 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_143_in__set__conv__decomp__first,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.42/1.41 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_144_in__set__conv__decomp__last,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.42/1.41 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_145_split__list__first__propE,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.42/1.41 ( ? [X2: A] :
% 2.42/1.41 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 & ( P @ X2 ) )
% 2.42/1.41 => ~ ! [Ys2: list @ A,X4: A] :
% 2.42/1.41 ( ? [Zs2: list @ A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.42/1.41 => ( ( P @ X4 )
% 2.42/1.41 => ~ ! [Xa: A] :
% 2.42/1.41 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 2.42/1.41 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_146_split__list__last__propE,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.42/1.41 ( ? [X2: A] :
% 2.42/1.41 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 & ( P @ X2 ) )
% 2.42/1.41 => ~ ! [Ys2: list @ A,X4: A,Zs2: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.42/1.41 => ( ( P @ X4 )
% 2.42/1.41 => ~ ! [Xa: A] :
% 2.42/1.41 ( ( member @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 2.42/1.41 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_147_split__list__first__prop,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.42/1.41 ( ? [X2: A] :
% 2.42/1.41 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 & ( P @ X2 ) )
% 2.42/1.41 => ? [Ys2: list @ A,X4: A] :
% 2.42/1.41 ( ? [Zs2: list @ A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.42/1.41 & ( P @ X4 )
% 2.42/1.41 & ! [Xa: A] :
% 2.42/1.41 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 2.42/1.41 => ~ ( P @ Xa ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_148_split__list__last__prop,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.42/1.41 ( ? [X2: A] :
% 2.42/1.41 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 & ( P @ X2 ) )
% 2.42/1.41 => ? [Ys2: list @ A,X4: A,Zs2: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.42/1.41 & ( P @ X4 )
% 2.42/1.41 & ! [Xa: A] :
% 2.42/1.41 ( ( member @ A @ Xa @ ( set2 @ A @ Zs2 ) )
% 2.42/1.41 => ~ ( P @ Xa ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_149_in__set__list__format,axiom,
% 2.42/1.41 ! [A: $tType,E2: A,L: list @ A] :
% 2.42/1.41 ( ( member @ A @ E2 @ ( set2 @ A @ L ) )
% 2.42/1.41 => ~ ! [L12: list @ A,L22: list @ A] :
% 2.42/1.41 ( L
% 2.42/1.41 != ( append @ A @ L12 @ ( cons @ A @ E2 @ L22 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_150_in__set__conv__decomp,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_151_append__Cons__eq__iff,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Xs4: list @ A,Ys6: list @ A] :
% 2.42/1.41 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 => ( ~ ( member @ A @ X @ ( set2 @ A @ Ys ) )
% 2.42/1.41 => ( ( ( append @ A @ Xs @ ( cons @ A @ X @ Ys ) )
% 2.42/1.41 = ( append @ A @ Xs4 @ ( cons @ A @ X @ Ys6 ) ) )
% 2.42/1.41 = ( ( Xs = Xs4 )
% 2.42/1.41 & ( Ys = Ys6 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_152_split__list__propE,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.42/1.41 ( ? [X2: A] :
% 2.42/1.41 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 & ( P @ X2 ) )
% 2.42/1.41 => ~ ! [Ys2: list @ A,X4: A] :
% 2.42/1.41 ( ? [Zs2: list @ A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.42/1.41 => ~ ( P @ X4 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_153_split__list__first,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 => ? [Ys2: list @ A,Zs2: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.42/1.41 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_154_xy__in__set__cases,axiom,
% 2.42/1.41 ! [A: $tType,X: A,L: list @ A,Y: A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ L ) )
% 2.42/1.41 => ( ( member @ A @ Y @ ( set2 @ A @ L ) )
% 2.42/1.41 => ( ( ( X = Y )
% 2.42/1.41 => ! [L12: list @ A,L22: list @ A] :
% 2.42/1.41 ( L
% 2.42/1.41 != ( append @ A @ L12 @ ( cons @ A @ Y @ L22 ) ) ) )
% 2.42/1.41 => ( ( ( X != Y )
% 2.42/1.41 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 2.42/1.41 ( L
% 2.42/1.41 != ( append @ A @ L12 @ ( cons @ A @ X @ ( append @ A @ L22 @ ( cons @ A @ Y @ L3 ) ) ) ) ) )
% 2.42/1.41 => ~ ( ( X != Y )
% 2.42/1.41 => ! [L12: list @ A,L22: list @ A,L3: list @ A] :
% 2.42/1.41 ( L
% 2.42/1.41 != ( append @ A @ L12 @ ( cons @ A @ Y @ ( append @ A @ L22 @ ( cons @ A @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_155_split__list__prop,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.42/1.41 ( ? [X2: A] :
% 2.42/1.41 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 & ( P @ X2 ) )
% 2.42/1.41 => ? [Ys2: list @ A,X4: A] :
% 2.42/1.41 ( ? [Zs2: list @ A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X4 @ Zs2 ) ) )
% 2.42/1.41 & ( P @ X4 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_156_split__list__last,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 => ? [Ys2: list @ A,Zs2: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.42/1.41 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_157_split__list,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 => ? [Ys2: list @ A,Zs2: list @ A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs2 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_158_tl__obtain__elem,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ( tl @ A @ Xs )
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 => ~ ! [E3: A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 != ( cons @ A @ E3 @ ( nil @ A ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_159_tl__Nil,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( ( tl @ A @ Xs )
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 = ( ( Xs
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 | ? [X3: A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_160_Nil__tl,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( ( nil @ A )
% 2.42/1.41 = ( tl @ A @ Xs ) )
% 2.42/1.41 = ( ( Xs
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 | ? [X3: A] :
% 2.42/1.41 ( Xs
% 2.42/1.41 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_161_list_Oset__sel_I2_J,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A,X: A] :
% 2.42/1.41 ( ( A2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ A2 ) ) )
% 2.42/1.41 => ( member @ A @ X @ ( set2 @ A @ A2 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_162_prefix__snoc,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 2.42/1.41 ( ( prefix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.42/1.41 = ( ( Xs
% 2.42/1.41 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.42/1.41 | ( prefix @ A @ Xs @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_163_old_Opath2__split__first__last,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,X: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( member @ node @ X @ ( set2 @ node @ Ns ) )
% 2.42/1.41 => ~ ! [Ns_1: list @ node,Ns_3: list @ node,Ns_2: list @ node] :
% 2.42/1.41 ( ( Ns
% 2.42/1.41 = ( append @ node @ Ns_1 @ ( append @ node @ Ns_3 @ Ns_2 ) ) )
% 2.42/1.41 => ( ( prefix @ node @ ( append @ node @ Ns_1 @ ( cons @ node @ X @ ( nil @ node ) ) ) @ Ns )
% 2.42/1.41 => ( ( suffix @ node @ ( cons @ node @ X @ Ns_2 ) @ Ns )
% 2.42/1.41 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ ( append @ node @ Ns_1 @ ( cons @ node @ X @ ( nil @ node ) ) ) @ X )
% 2.42/1.41 => ( ~ ( member @ node @ X @ ( set2 @ node @ Ns_1 ) )
% 2.42/1.41 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ Ns_3 @ X )
% 2.42/1.41 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X @ ( cons @ node @ X @ Ns_2 ) @ M )
% 2.42/1.41 => ( member @ node @ X @ ( set2 @ node @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_164_same__prefix__nil,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ ( append @ A @ Xs @ Ys ) @ Xs )
% 2.42/1.41 = ( Ys
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_165_old_Opath2__simple__loop,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,N2: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ N )
% 2.42/1.41 => ( ( member @ node @ N2 @ ( set2 @ node @ Ns ) )
% 2.42/1.41 => ~ ! [Ns3: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns3 @ N )
% 2.42/1.41 => ( ( member @ node @ N2 @ ( set2 @ node @ Ns3 ) )
% 2.42/1.41 => ( ~ ( member @ node @ N @ ( set2 @ node @ ( tl @ node @ ( butlast @ node @ Ns3 ) ) ) )
% 2.42/1.41 => ~ ( ord_less_eq @ ( set @ node ) @ ( set2 @ node @ Ns3 ) @ ( set2 @ node @ Ns ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_166_old_Opath2__cases,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ( ( Ns
% 2.42/1.41 = ( cons @ node @ N @ ( nil @ node ) ) )
% 2.42/1.41 => ( M != N ) )
% 2.42/1.41 => ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) @ ( tl @ node @ Ns ) @ M )
% 2.42/1.41 => ~ ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ ( tl @ node @ Ns ) ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_167_old_Opath__snoc,axiom,
% 2.42/1.41 ! [G2: g,Ns: list @ node,N: node,M: node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ N @ ( nil @ node ) ) ) )
% 2.42/1.41 => ( ( member @ node @ N @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ M ) ) )
% 2.42/1.41 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ N @ ( cons @ node @ M @ ( nil @ node ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_168_phiUses__finite,axiom,
% 2.42/1.41 ! [N: node,G2: g] :
% 2.42/1.41 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.42/1.41 => ( finite_finite @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ G2 @ N ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_169_old_Opath2__split__last__prop,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node,P: node > $o] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( ? [X2: node] :
% 2.42/1.41 ( ( member @ node @ X2 @ ( set2 @ node @ Ns ) )
% 2.42/1.41 & ( P @ X2 ) )
% 2.42/1.41 => ~ ! [N3: node,Ns3: list @ node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N3 @ Ns3 @ M )
% 2.42/1.41 => ( ( P @ N3 )
% 2.42/1.41 => ( ! [X2: node] :
% 2.42/1.41 ( ( member @ node @ X2 @ ( set2 @ node @ ( tl @ node @ Ns3 ) ) )
% 2.42/1.41 => ~ ( P @ X2 ) )
% 2.42/1.41 => ~ ( suffix @ node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_170_defs__finite,axiom,
% 2.42/1.41 ! [G2: g,N: node] : ( finite_finite @ val @ ( defs @ G2 @ N ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_171_prefix__order_Oorder__refl,axiom,
% 2.42/1.41 ! [A: $tType,X: list @ A] : ( prefix @ A @ X @ X ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_172_prefix__order_Odual__order_Orefl,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] : ( prefix @ A @ A2 @ A2 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_173_suffix__order_Oorder__refl,axiom,
% 2.42/1.41 ! [A: $tType,X: list @ A] : ( suffix @ A @ X @ X ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_174_suffix__order_Odual__order_Orefl,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] : ( suffix @ A @ A2 @ A2 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_175_old_Opath__not__Nil,axiom,
% 2.42/1.41 ! [G2: g,Ns: list @ node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 2.42/1.41 => ( Ns
% 2.42/1.41 != ( nil @ node ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_176_old_Opath2__hd,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( N
% 2.42/1.41 = ( hd @ node @ Ns ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_177_old_Opath2__forget__hd,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node,M: node] :
% 2.42/1.41 ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ N @ Ns @ M )
% 2.42/1.41 => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( hd @ node @ Ns ) @ Ns @ M ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_178_old_Opath__hd,axiom,
% 2.42/1.41 ! [G2: g,N: node,Ns: list @ node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ Ns ) )
% 2.42/1.41 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_179_old_Opath__split_I2_J,axiom,
% 2.42/1.41 ! [G2: g,Ns: list @ node,M: node,Ns2: list @ node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ Ns2 ) ) )
% 2.42/1.41 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ M @ Ns2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_180_List_Ofinite__set,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] : ( finite_finite @ A @ ( set2 @ A @ Xs ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_181_Cons__prefix__Cons,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.42/1.41 = ( ( X = Y )
% 2.42/1.41 & ( prefix @ A @ Xs @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_182_prefix__code_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] : ( prefix @ A @ ( nil @ A ) @ Xs ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_183_prefix__Nil,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ Xs @ ( nil @ A ) )
% 2.42/1.41 = ( Xs
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_184_prefix__bot_Obot_Oextremum__unique,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ A2 @ ( nil @ A ) )
% 2.42/1.41 = ( A2
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_185_suffix__bot_Obot_Oextremum__unique,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 2.42/1.41 = ( A2
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_186_suffix__Nil,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ Xs @ ( nil @ A ) )
% 2.42/1.41 = ( Xs
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_187_same__prefix__prefix,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ ( append @ A @ Xs @ Ys ) @ ( append @ A @ Xs @ Zs ) )
% 2.42/1.41 = ( prefix @ A @ Ys @ Zs ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_188_same__suffix__suffix,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ ( append @ A @ Zs @ Xs ) )
% 2.42/1.41 = ( suffix @ A @ Ys @ Zs ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_189_old_Oempty__path,axiom,
% 2.42/1.41 ! [N: node,G2: g] :
% 2.42/1.41 ( ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.42/1.41 => ( ( invar @ G2 )
% 2.42/1.41 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( nil @ node ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_190_old_Opath__split_I1_J,axiom,
% 2.42/1.41 ! [G2: g,Ns: list @ node,M: node,Ns2: list @ node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ Ns2 ) ) )
% 2.42/1.41 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( append @ node @ Ns @ ( cons @ node @ M @ ( nil @ node ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_191_old_OCons__path,axiom,
% 2.42/1.41 ! [G2: g,Ns: list @ node,N2: node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 2.42/1.41 => ( ( member @ node @ N2 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns ) ) ) )
% 2.42/1.41 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ns ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_192_old_Opath_Osimps,axiom,
% 2.42/1.41 ! [G2: g,A2: list @ node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ A2 )
% 2.42/1.41 = ( ? [N5: node] :
% 2.42/1.41 ( ( A2
% 2.42/1.41 = ( cons @ node @ N5 @ ( nil @ node ) ) )
% 2.42/1.41 & ( member @ node @ N5 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.42/1.41 & ( invar @ G2 ) )
% 2.42/1.41 | ? [Ns5: list @ node,N6: node] :
% 2.42/1.41 ( ( A2
% 2.42/1.41 = ( cons @ node @ N6 @ Ns5 ) )
% 2.42/1.41 & ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns5 )
% 2.42/1.41 & ( member @ node @ N6 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns5 ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_193_old_Opath_Oinducts,axiom,
% 2.42/1.41 ! [G2: g,X: list @ node,P: ( list @ node ) > $o] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ X )
% 2.42/1.41 => ( ! [N4: node] :
% 2.42/1.41 ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.42/1.41 => ( ( invar @ G2 )
% 2.42/1.41 => ( P @ ( cons @ node @ N4 @ ( nil @ node ) ) ) ) )
% 2.42/1.41 => ( ! [Ns4: list @ node,N3: node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns4 )
% 2.42/1.41 => ( ( P @ Ns4 )
% 2.42/1.41 => ( ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns4 ) ) ) )
% 2.42/1.41 => ( P @ ( cons @ node @ N3 @ Ns4 ) ) ) ) )
% 2.42/1.41 => ( P @ X ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_194_old_Opath_Ocases,axiom,
% 2.42/1.41 ! [G2: g,A2: list @ node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ A2 )
% 2.42/1.41 => ( ! [N4: node] :
% 2.42/1.41 ( ( A2
% 2.42/1.41 = ( cons @ node @ N4 @ ( nil @ node ) ) )
% 2.42/1.41 => ( ( member @ node @ N4 @ ( set2 @ node @ ( alpha_n @ G2 ) ) )
% 2.42/1.41 => ~ ( invar @ G2 ) ) )
% 2.42/1.41 => ~ ! [Ns4: list @ node,N3: node] :
% 2.42/1.41 ( ( A2
% 2.42/1.41 = ( cons @ node @ N3 @ Ns4 ) )
% 2.42/1.41 => ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns4 )
% 2.42/1.41 => ~ ( member @ node @ N3 @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ G2 @ ( hd @ node @ Ns4 ) ) ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_195_same__suffix__nil,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ ( append @ A @ Ys @ Xs ) @ Xs )
% 2.42/1.41 = ( Ys
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_196_hd__append2,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( hd @ A @ Xs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_197_suffix__snoc,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 2.42/1.41 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.42/1.41 = ( ( Xs
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 | ? [Zs3: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Zs3 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.42/1.41 & ( suffix @ A @ Zs3 @ Ys ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_198_snoc__suffix__snoc,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.42/1.41 ( ( suffix @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.42/1.41 = ( ( X = Y )
% 2.42/1.41 & ( suffix @ A @ Xs @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_199_hd__Cons__tl,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 2.42/1.41 = Xs ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_200_list_Ocollapse,axiom,
% 2.42/1.41 ! [A: $tType,List: list @ A] :
% 2.42/1.41 ( ( List
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 2.42/1.41 = List ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_201_in__hd__or__tl__conv,axiom,
% 2.42/1.41 ! [A: $tType,L: list @ A,X: A] :
% 2.42/1.41 ( ( L
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ( X
% 2.42/1.41 = ( hd @ A @ L ) )
% 2.42/1.41 | ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ L ) ) ) )
% 2.42/1.41 = ( member @ A @ X @ ( set2 @ A @ L ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_202_old_Opath__invar,axiom,
% 2.42/1.41 ! [G2: g,Ns: list @ node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 2.42/1.41 => ( invar @ G2 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_203_old_Opath__in___092_060alpha_062n,axiom,
% 2.42/1.41 ! [G2: g,Ns: list @ node,N: node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ Ns )
% 2.42/1.41 => ( ( member @ node @ N @ ( set2 @ node @ Ns ) )
% 2.42/1.41 => ( member @ node @ N @ ( set2 @ node @ ( alpha_n @ G2 ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_204_old_Opath__by__tail,axiom,
% 2.42/1.41 ! [G2: g,N: node,N2: node,Ns: list @ node,Ms: list @ node] :
% 2.42/1.41 ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( cons @ node @ N2 @ Ns ) ) )
% 2.42/1.41 => ( ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ns ) )
% 2.42/1.41 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N2 @ Ms ) ) )
% 2.42/1.41 => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ G2 @ ( cons @ node @ N @ ( cons @ node @ N2 @ Ms ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_205_set__mono__suffix,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ Xs @ Ys )
% 2.42/1.41 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_206_subset__Collect__conv,axiom,
% 2.42/1.41 ! [A: $tType,S: set @ A,P: A > $o] :
% 2.42/1.41 ( ( ord_less_eq @ ( set @ A ) @ S @ ( collect @ A @ P ) )
% 2.42/1.41 = ( ! [X3: A] :
% 2.42/1.41 ( ( member @ A @ X3 @ S )
% 2.42/1.41 => ( P @ X3 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_207_ord__eq__le__eq__trans,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( ord @ A )
% 2.42/1.41 => ! [A2: A,B: A,C: A,D: A] :
% 2.42/1.41 ( ( A2 = B )
% 2.42/1.41 => ( ( ord_less_eq @ A @ B @ C )
% 2.42/1.41 => ( ( C = D )
% 2.42/1.41 => ( ord_less_eq @ A @ A2 @ D ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_208_suffix__ConsD2,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.42/1.41 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_209_suffix__ConsI,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Y: A] :
% 2.42/1.41 ( ( suffix @ A @ Xs @ Ys )
% 2.42/1.41 => ( suffix @ A @ Xs @ ( cons @ A @ Y @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_210_suffix__ConsD,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.42/1.41 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_211_suffix__Cons,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ Xs @ ( cons @ A @ Y @ Ys ) )
% 2.42/1.41 = ( ( Xs
% 2.42/1.41 = ( cons @ A @ Y @ Ys ) )
% 2.42/1.41 | ( suffix @ A @ Xs @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_212_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ A2 @ ( nil @ A ) )
% 2.42/1.41 => ( A2
% 2.42/1.41 = ( nil @ A ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_213_suffix__bot_Obot_Oextremum,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] : ( suffix @ A @ ( nil @ A ) @ A2 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_214_Nil__suffix,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( nil @ A ) @ Xs ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_215_suffixE,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ Xs @ Ys )
% 2.42/1.41 => ~ ! [Zs2: list @ A] :
% 2.42/1.41 ( Ys
% 2.42/1.41 != ( append @ A @ Zs2 @ Xs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_216_suffixI,axiom,
% 2.42/1.41 ! [A: $tType,Ys: list @ A,Zs: list @ A,Xs: list @ A] :
% 2.42/1.41 ( ( Ys
% 2.42/1.41 = ( append @ A @ Zs @ Xs ) )
% 2.42/1.41 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_217_Sublist_Osuffix__def,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( suffix @ A )
% 2.42/1.41 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 2.42/1.41 ? [Zs3: list @ A] :
% 2.42/1.41 ( Ys3
% 2.42/1.41 = ( append @ A @ Zs3 @ Xs3 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_218_suffix__append,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ Xs @ ( append @ A @ Ys @ Zs ) )
% 2.42/1.41 = ( ( suffix @ A @ Xs @ Zs )
% 2.42/1.41 | ? [Xs5: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Xs5 @ Zs ) )
% 2.42/1.41 & ( suffix @ A @ Xs5 @ Ys ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_219_suffix__appendD,axiom,
% 2.42/1.41 ! [A: $tType,Zs: list @ A,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ ( append @ A @ Zs @ Xs ) @ Ys )
% 2.42/1.41 => ( suffix @ A @ Xs @ Ys ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_220_suffix__appendI,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ Xs @ Ys )
% 2.42/1.41 => ( suffix @ A @ Xs @ ( append @ A @ Zs @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_221_suffix__tl,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] : ( suffix @ A @ ( tl @ A @ Xs ) @ Xs ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_222_suffix__same__cases,axiom,
% 2.42/1.41 ! [A: $tType,Xs_1: list @ A,Ys: list @ A,Xs_2: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ Xs_1 @ Ys )
% 2.42/1.41 => ( ( suffix @ A @ Xs_2 @ Ys )
% 2.42/1.41 => ( ( suffix @ A @ Xs_1 @ Xs_2 )
% 2.42/1.41 | ( suffix @ A @ Xs_2 @ Xs_1 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_223_suffix__order_Oeq__iff,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 2.42/1.41 = ( ^ [X3: list @ A,Y3: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ X3 @ Y3 )
% 2.42/1.41 & ( suffix @ A @ Y3 @ X3 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_224_suffix__order_Oantisym,axiom,
% 2.42/1.41 ! [A: $tType,X: list @ A,Y: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ X @ Y )
% 2.42/1.41 => ( ( suffix @ A @ Y @ X )
% 2.42/1.41 => ( X = Y ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_225_suffix__order_Oeq__refl,axiom,
% 2.42/1.41 ! [A: $tType,X: list @ A,Y: list @ A] :
% 2.42/1.41 ( ( X = Y )
% 2.42/1.41 => ( suffix @ A @ X @ Y ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_226_suffix__order_Oorder_Otrans,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ A2 @ B )
% 2.42/1.41 => ( ( suffix @ A @ B @ C )
% 2.42/1.41 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_227_suffix__order_Oorder__trans,axiom,
% 2.42/1.41 ! [A: $tType,X: list @ A,Y: list @ A,Z3: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ X @ Y )
% 2.42/1.41 => ( ( suffix @ A @ Y @ Z3 )
% 2.42/1.41 => ( suffix @ A @ X @ Z3 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_228_suffix__order_Oantisym__conv,axiom,
% 2.42/1.41 ! [A: $tType,Y: list @ A,X: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ Y @ X )
% 2.42/1.41 => ( ( suffix @ A @ X @ Y )
% 2.42/1.41 = ( X = Y ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_229_suffix__order_Oorder_Oeq__iff,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 2.42/1.41 = ( ^ [A5: list @ A,B4: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ A5 @ B4 )
% 2.42/1.41 & ( suffix @ A @ B4 @ A5 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_230_suffix__order_Oorder_Oantisym,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A,B: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ A2 @ B )
% 2.42/1.41 => ( ( suffix @ A @ B @ A2 )
% 2.42/1.41 => ( A2 = B ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_231_suffix__order_Oord__eq__le__trans,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 2.42/1.41 ( ( A2 = B )
% 2.42/1.41 => ( ( suffix @ A @ B @ C )
% 2.42/1.41 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_232_suffix__order_Oord__le__eq__trans,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ A2 @ B )
% 2.42/1.41 => ( ( B = C )
% 2.42/1.41 => ( suffix @ A @ A2 @ C ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_233_suffix__order_Odual__order_Otrans,axiom,
% 2.42/1.41 ! [A: $tType,B: list @ A,A2: list @ A,C: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ B @ A2 )
% 2.42/1.41 => ( ( suffix @ A @ C @ B )
% 2.42/1.41 => ( suffix @ A @ C @ A2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_234_suffix__order_Odual__order_Oeq__iff,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 2.42/1.41 = ( ^ [A5: list @ A,B4: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ B4 @ A5 )
% 2.42/1.41 & ( suffix @ A @ A5 @ B4 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_235_suffix__order_Odual__order_Oantisym,axiom,
% 2.42/1.41 ! [A: $tType,B: list @ A,A2: list @ A] :
% 2.42/1.41 ( ( suffix @ A @ B @ A2 )
% 2.42/1.41 => ( ( suffix @ A @ A2 @ B )
% 2.42/1.41 => ( A2 = B ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_236_list_Osel_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,X21: A,X22: list @ A] :
% 2.42/1.41 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 2.42/1.41 = X21 ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_237_finite__list,axiom,
% 2.42/1.41 ! [A: $tType,A3: set @ A] :
% 2.42/1.41 ( ( finite_finite @ A @ A3 )
% 2.42/1.41 => ? [Xs2: list @ A] :
% 2.42/1.41 ( ( set2 @ A @ Xs2 )
% 2.42/1.41 = A3 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_238_subset__code_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,B5: set @ A] :
% 2.42/1.41 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ B5 )
% 2.42/1.41 = ( ! [X3: A] :
% 2.42/1.41 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.42/1.41 => ( member @ A @ X3 @ B5 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_239_set__mono__prefix,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ Xs @ Ys )
% 2.42/1.41 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_240_list_Oset__sel_I1_J,axiom,
% 2.42/1.41 ! [A: $tType,A2: list @ A] :
% 2.42/1.41 ( ( A2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( member @ A @ ( hd @ A @ A2 ) @ ( set2 @ A @ A2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_241_hd__in__set,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( member @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ Xs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_242_hd__append,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ( ( ( Xs
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( hd @ A @ Ys ) ) )
% 2.42/1.41 & ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.42/1.41 = ( hd @ A @ Xs ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_243_longest__common__prefix,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.42/1.41 ? [Ps: list @ A,Xs6: list @ A,Ys4: list @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 = ( append @ A @ Ps @ Xs6 ) )
% 2.42/1.41 & ( Ys
% 2.42/1.41 = ( append @ A @ Ps @ Ys4 ) )
% 2.42/1.41 & ( ( Xs6
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 | ( Ys4
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 | ( ( hd @ A @ Xs6 )
% 2.42/1.41 != ( hd @ A @ Ys4 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_244_not__suffix__cases,axiom,
% 2.42/1.41 ! [A: $tType,Ps2: list @ A,Ls: list @ A] :
% 2.42/1.41 ( ~ ( suffix @ A @ Ps2 @ Ls )
% 2.42/1.41 => ( ( ( Ps2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( Ls
% 2.42/1.41 != ( nil @ A ) ) )
% 2.42/1.41 => ( ! [A4: A,As: list @ A] :
% 2.42/1.41 ( ( Ps2
% 2.42/1.41 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 2.42/1.41 => ! [X4: A,Xs2: list @ A] :
% 2.42/1.41 ( ( Ls
% 2.42/1.41 = ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 2.42/1.41 => ( ( X4 = A4 )
% 2.42/1.41 => ( suffix @ A @ As @ Xs2 ) ) ) )
% 2.42/1.41 => ~ ! [A4: A] :
% 2.42/1.41 ( ? [As: list @ A] :
% 2.42/1.41 ( Ps2
% 2.42/1.41 = ( append @ A @ As @ ( cons @ A @ A4 @ ( nil @ A ) ) ) )
% 2.42/1.41 => ! [X4: A] :
% 2.42/1.41 ( ? [Xs2: list @ A] :
% 2.42/1.41 ( Ls
% 2.42/1.41 = ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 2.42/1.41 => ( X4 = A4 ) ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_245_not__suffix__induct,axiom,
% 2.42/1.41 ! [A: $tType,Ps2: list @ A,Ls: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.42/1.41 ( ~ ( suffix @ A @ Ps2 @ Ls )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( nil @ A ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.42/1.41 ( ( X4 != Y2 )
% 2.42/1.41 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) )
% 2.42/1.41 => ( ! [X4: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.42/1.41 ( ( X4 = Y2 )
% 2.42/1.41 => ( ~ ( suffix @ A @ Xs2 @ Ys2 )
% 2.42/1.41 => ( ( P @ Xs2 @ Ys2 )
% 2.42/1.41 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) @ ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ) )
% 2.42/1.41 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_246_list_Oexpand,axiom,
% 2.42/1.41 ! [A: $tType,List: list @ A,List2: list @ A] :
% 2.42/1.41 ( ( ( List
% 2.42/1.41 = ( nil @ A ) )
% 2.42/1.41 = ( List2
% 2.42/1.41 = ( nil @ A ) ) )
% 2.42/1.41 => ( ( ( List
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( List2
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ( hd @ A @ List )
% 2.42/1.41 = ( hd @ A @ List2 ) )
% 2.42/1.41 & ( ( tl @ A @ List )
% 2.42/1.41 = ( tl @ A @ List2 ) ) ) ) )
% 2.42/1.41 => ( List = List2 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_247_not__hd__in__tl,axiom,
% 2.42/1.41 ! [A: $tType,X: A,Xs: list @ A] :
% 2.42/1.41 ( ( X
% 2.42/1.41 != ( hd @ A @ Xs ) )
% 2.42/1.41 => ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.42/1.41 => ( member @ A @ X @ ( set2 @ A @ ( tl @ A @ Xs ) ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_248_set__subset__Cons,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,X: A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_249_list_Oexhaust__sel,axiom,
% 2.42/1.41 ! [A: $tType,List: list @ A] :
% 2.42/1.41 ( ( List
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( List
% 2.42/1.41 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_250_tl__subset,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,A3: set @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A3 )
% 2.42/1.41 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( tl @ A @ Xs ) ) @ A3 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_251_butlast__subset,axiom,
% 2.42/1.41 ! [A: $tType,Xs: list @ A,A3: set @ A] :
% 2.42/1.41 ( ( Xs
% 2.42/1.41 != ( nil @ A ) )
% 2.42/1.41 => ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A3 )
% 2.42/1.41 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( butlast @ A @ Xs ) ) @ A3 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_252_prefix__same__cases,axiom,
% 2.42/1.41 ! [A: $tType,Xs_1: list @ A,Ys: list @ A,Xs_2: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ Xs_1 @ Ys )
% 2.42/1.41 => ( ( prefix @ A @ Xs_2 @ Ys )
% 2.42/1.41 => ( ( prefix @ A @ Xs_1 @ Xs_2 )
% 2.42/1.41 | ( prefix @ A @ Xs_2 @ Xs_1 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_253_prefix__order_Oeq__iff,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( ^ [Y4: list @ A,Z: list @ A] : ( Y4 = Z ) )
% 2.42/1.41 = ( ^ [X3: list @ A,Y3: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ X3 @ Y3 )
% 2.42/1.41 & ( prefix @ A @ Y3 @ X3 ) ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(fact_254_prefix__order_Oantisym,axiom,
% 2.42/1.41 ! [A: $tType,X: list @ A,Y: list @ A] :
% 2.42/1.41 ( ( prefix @ A @ X @ Y )
% 2.42/1.41 => ( ( prefix @ A @ Y @ X )
% 2.42/1.41 => ( X = Y ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( linorder @ A )
% 2.42/1.41 => ( type @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 2.42/1.41 ! [A: $tType] :
% 2.42/1.41 ( ( linorder @ A )
% 2.42/1.41 => ( ord @ A ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(tcon_fun___Orderings_Oord,axiom,
% 2.42/1.41 ! [A6: $tType,A7: $tType] :
% 2.42/1.41 ( ( ord @ A7 )
% 2.42/1.41 => ( ord @ ( A6 > A7 ) ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(tcon_Set_Oset___Orderings_Oord_1,axiom,
% 2.42/1.41 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 2.42/1.41
% 2.42/1.41 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.42/1.41 linorder @ $o ).
% 2.42/1.41
% 2.42/1.41 thf(tcon_HOL_Obool___Orderings_Oord_2,axiom,
% 2.42/1.41 ord @ $o ).
% 2.42/1.41
% 2.42/1.41 thf(tfree_0,hypothesis,
% 2.42/1.41 linorder @ val ).
% 2.42/1.41
% 2.42/1.41 thf(tfree_1,hypothesis,
% 2.42/1.41 linorder @ node ).
% 2.42/1.41
% 2.42/1.41 thf(conj_0,conjecture,
% 2.42/1.41 graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append @ node @ ns @ ( tl @ node @ ri ) ) @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 2.42/1.41 ------------------------
% 2.42/1.43 % (28725)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/183Mi)
% 2.42/1.43 % (28726)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_28396 for (2999ds/4Mi)
% 2.42/1.43 % (28727)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_28396 for (2999ds/27Mi)
% 2.42/1.43 % (28728)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/2Mi)
% 2.42/1.43 % (28729)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_28396 for (2999ds/2Mi)
% 2.42/1.43 % (28731)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/18Mi)
% 2.42/1.43 % (28730)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_28396 for (2999ds/275Mi)
% 2.42/1.44 % (28728)Instruction limit reached!
% 2.42/1.44 % (28728)------------------------------
% 2.42/1.44 % (28728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (28728)Termination reason: Unknown
% 2.42/1.44 % (28728)Termination phase: shuffling
% 2.42/1.44
% 2.42/1.44 % (28728)Memory used [KB]: 1407
% 2.42/1.44 % (28728)Time elapsed: 0.002 s
% 2.42/1.44 % (28728)Instructions burned: 2 (million)
% 2.42/1.44 % (28728)------------------------------
% 2.42/1.44 % (28728)------------------------------
% 2.42/1.44 % (28729)Instruction limit reached!
% 2.42/1.44 % (28729)------------------------------
% 2.42/1.44 % (28729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (28729)Termination reason: Unknown
% 2.42/1.44 % (28729)Termination phase: shuffling
% 2.42/1.44
% 2.42/1.44 % (28729)Memory used [KB]: 1407
% 2.42/1.44 % (28729)Time elapsed: 0.002 s
% 2.42/1.44 % (28729)Instructions burned: 2 (million)
% 2.42/1.44 % (28729)------------------------------
% 2.42/1.44 % (28729)------------------------------
% 2.42/1.44 % (28726)Instruction limit reached!
% 2.42/1.44 % (28726)------------------------------
% 2.42/1.44 % (28726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (28726)Termination reason: Unknown
% 2.42/1.44 % (28726)Termination phase: shuffling
% 2.42/1.44
% 2.42/1.44 % (28726)Memory used [KB]: 1407
% 2.42/1.44 % (28726)Time elapsed: 0.003 s
% 2.42/1.44 % (28726)Instructions burned: 5 (million)
% 2.42/1.44 % (28726)------------------------------
% 2.42/1.44 % (28726)------------------------------
% 2.42/1.44 % (28731)Instruction limit reached!
% 2.42/1.44 % (28731)------------------------------
% 2.42/1.44 % (28731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (28731)Termination reason: Unknown
% 2.42/1.44 % (28731)Termination phase: shuffling
% 2.42/1.44
% 2.42/1.44 % (28731)Memory used [KB]: 1535
% 2.42/1.44 % (28731)Time elapsed: 0.008 s
% 2.42/1.44 % (28731)Instructions burned: 20 (million)
% 2.42/1.44 % (28731)------------------------------
% 2.42/1.44 % (28731)------------------------------
% 2.42/1.44 % (28727)Instruction limit reached!
% 2.42/1.44 % (28727)------------------------------
% 2.42/1.44 % (28727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (28727)Termination reason: Unknown
% 2.42/1.44 % (28727)Termination phase: shuffling
% 2.42/1.44
% 2.42/1.44 % (28727)Memory used [KB]: 1791
% 2.42/1.44 % (28727)Time elapsed: 0.010 s
% 2.42/1.44 % (28727)Instructions burned: 27 (million)
% 2.42/1.44 % (28727)------------------------------
% 2.42/1.44 % (28727)------------------------------
% 2.42/1.44 % (28732)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/3Mi)
% 2.42/1.44 % (28733)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_28396 for (2999ds/37Mi)
% 2.42/1.45 % (28734)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_28396 for (2999ds/15Mi)
% 2.42/1.45 % (28732)Instruction limit reached!
% 2.42/1.45 % (28732)------------------------------
% 2.42/1.45 % (28732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.45 % (28732)Termination reason: Unknown
% 2.42/1.45 % (28732)Termination phase: shuffling
% 2.42/1.45
% 2.42/1.45 % (28732)Memory used [KB]: 1407
% 2.42/1.45 % (28732)Time elapsed: 0.002 s
% 2.42/1.45 % (28732)Instructions burned: 3 (million)
% 2.42/1.45 % (28732)------------------------------
% 2.42/1.45 % (28732)------------------------------
% 2.42/1.45 % (28734)Instruction limit reached!
% 2.42/1.45 % (28734)------------------------------
% 2.42/1.45 % (28734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.45 % (28734)Termination reason: Unknown
% 2.42/1.45 % (28734)Termination phase: shuffling
% 2.42/1.45
% 2.42/1.45 % (28734)Memory used [KB]: 1535
% 2.42/1.45 % (28734)Time elapsed: 0.006 s
% 2.42/1.45 % (28734)Instructions burned: 16 (million)
% 2.42/1.45 % (28734)------------------------------
% 2.42/1.45 % (28734)------------------------------
% 2.42/1.45 % (28735)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_28396 for (2999ds/3Mi)
% 2.42/1.45 % (28735)Instruction limit reached!
% 2.42/1.45 % (28735)------------------------------
% 2.42/1.45 % (28735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.45 % (28735)Termination reason: Unknown
% 2.42/1.45 % (28735)Termination phase: shuffling
% 2.42/1.45
% 2.42/1.45 % (28735)Memory used [KB]: 1407
% 2.42/1.45 % (28735)Time elapsed: 0.002 s
% 2.42/1.45 % (28735)Instructions burned: 3 (million)
% 2.42/1.45 % (28735)------------------------------
% 2.42/1.45 % (28735)------------------------------
% 2.42/1.45 % (28736)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_28396 for (2999ds/1041Mi)
% 2.42/1.45 % (28733)Instruction limit reached!
% 2.42/1.45 % (28733)------------------------------
% 2.42/1.45 % (28733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.45 % (28733)Termination reason: Unknown
% 2.42/1.45 % (28733)Termination phase: shuffling
% 2.42/1.45
% 2.42/1.45 % (28733)Memory used [KB]: 2046
% 2.42/1.45 % (28733)Time elapsed: 0.011 s
% 2.42/1.45 % (28733)Instructions burned: 37 (million)
% 2.42/1.45 % (28733)------------------------------
% 2.42/1.45 % (28733)------------------------------
% 2.42/1.45 % (28737)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/7Mi)
% 2.42/1.46 % (28737)Instruction limit reached!
% 2.42/1.46 % (28737)------------------------------
% 2.42/1.46 % (28737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.46 % (28737)Termination reason: Unknown
% 2.42/1.46 % (28737)Termination phase: shuffling
% 2.42/1.46
% 2.42/1.46 % (28737)Memory used [KB]: 1535
% 2.42/1.46 % (28737)Time elapsed: 0.004 s
% 2.42/1.46 % (28737)Instructions burned: 9 (million)
% 2.42/1.46 % (28737)------------------------------
% 2.42/1.46 % (28737)------------------------------
% 2.42/1.46 % (28738)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/16Mi)
% 2.42/1.46 % (28739)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_28396 for (2999ds/3Mi)
% 2.42/1.46 % (28739)Instruction limit reached!
% 2.42/1.46 % (28739)------------------------------
% 2.42/1.46 % (28739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.46 % (28739)Termination reason: Unknown
% 2.42/1.46 % (28739)Termination phase: shuffling
% 2.42/1.46
% 2.42/1.46 % (28739)Memory used [KB]: 1407
% 2.42/1.46 % (28739)Time elapsed: 0.002 s
% 2.42/1.46 % (28739)Instructions burned: 3 (million)
% 2.42/1.46 % (28739)------------------------------
% 2.42/1.46 % (28739)------------------------------
% 2.42/1.46 % (28740)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_28396 for (2999ds/3Mi)
% 2.42/1.47 % (28738)Instruction limit reached!
% 2.42/1.47 % (28738)------------------------------
% 2.42/1.47 % (28738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.47 % (28738)Termination reason: Unknown
% 2.42/1.47 % (28738)Termination phase: shuffling
% 2.42/1.47
% 2.42/1.47 % (28738)Memory used [KB]: 1535
% 2.42/1.47 % (28738)Time elapsed: 0.007 s
% 2.42/1.47 % (28738)Instructions burned: 18 (million)
% 2.42/1.47 % (28738)------------------------------
% 2.42/1.47 % (28738)------------------------------
% 2.42/1.47 % (28740)Instruction limit reached!
% 2.42/1.47 % (28740)------------------------------
% 2.42/1.47 % (28740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.47 % (28740)Termination reason: Unknown
% 2.42/1.47 % (28740)Termination phase: shuffling
% 2.42/1.47
% 2.42/1.47 % (28740)Memory used [KB]: 1407
% 2.42/1.47 % (28740)Time elapsed: 0.003 s
% 2.42/1.47 % (28740)Instructions burned: 5 (million)
% 2.42/1.47 % (28740)------------------------------
% 2.42/1.47 % (28740)------------------------------
% 2.42/1.47 % (28741)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/7Mi)
% 2.42/1.47 % (28741)Instruction limit reached!
% 2.42/1.47 % (28741)------------------------------
% 2.42/1.47 % (28741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.47 % (28741)Termination reason: Unknown
% 2.42/1.47 % (28741)Termination phase: shuffling
% 2.42/1.47
% 2.42/1.47 % (28741)Memory used [KB]: 1535
% 2.42/1.47 % (28741)Time elapsed: 0.004 s
% 2.42/1.47 % (28741)Instructions burned: 9 (million)
% 2.42/1.47 % (28741)------------------------------
% 2.42/1.47 % (28741)------------------------------
% 2.42/1.47 % (28742)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/3Mi)
% 2.42/1.47 % (28742)Instruction limit reached!
% 2.42/1.47 % (28742)------------------------------
% 2.42/1.47 % (28742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.47 % (28742)Termination reason: Unknown
% 2.42/1.47 % (28742)Termination phase: shuffling
% 2.42/1.47
% 2.42/1.47 % (28742)Memory used [KB]: 1407
% 2.42/1.47 % (28742)Time elapsed: 0.002 s
% 2.42/1.47 % (28742)Instructions burned: 3 (million)
% 2.42/1.47 % (28742)------------------------------
% 2.42/1.47 % (28742)------------------------------
% 2.42/1.47 % (28743)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/4Mi)
% 2.42/1.48 % (28744)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/18Mi)
% 2.42/1.48 % (28743)Instruction limit reached!
% 2.42/1.48 % (28743)------------------------------
% 2.42/1.48 % (28743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.48 % (28743)Termination reason: Unknown
% 2.42/1.48 % (28743)Termination phase: shuffling
% 2.42/1.48
% 2.42/1.48 % (28743)Memory used [KB]: 1407
% 2.42/1.48 % (28743)Time elapsed: 0.003 s
% 2.42/1.48 % (28743)Instructions burned: 6 (million)
% 2.42/1.48 % (28743)------------------------------
% 2.42/1.48 % (28743)------------------------------
% 2.42/1.48 % (28745)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/710Mi)
% 2.42/1.48 % (28744)Instruction limit reached!
% 2.42/1.48 % (28744)------------------------------
% 2.42/1.48 % (28744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.48 % (28744)Termination reason: Unknown
% 2.42/1.48 % (28744)Termination phase: shuffling
% 2.42/1.48
% 2.42/1.48 % (28744)Memory used [KB]: 1663
% 2.42/1.48 % (28744)Time elapsed: 0.007 s
% 2.42/1.48 % (28744)Instructions burned: 18 (million)
% 2.42/1.48 % (28744)------------------------------
% 2.42/1.48 % (28744)------------------------------
% 2.42/1.48 % (28746)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/6Mi)
% 2.42/1.48 % (28746)Instruction limit reached!
% 2.42/1.48 % (28746)------------------------------
% 2.42/1.48 % (28746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.48 % (28746)Termination reason: Unknown
% 2.42/1.48 % (28746)Termination phase: shuffling
% 2.42/1.48
% 2.42/1.48 % (28746)Memory used [KB]: 1407
% 2.42/1.48 % (28746)Time elapsed: 0.003 s
% 2.42/1.48 % (28746)Instructions burned: 6 (million)
% 2.42/1.48 % (28746)------------------------------
% 2.42/1.48 % (28746)------------------------------
% 2.42/1.49 % (28725)Instruction limit reached!
% 2.42/1.49 % (28725)------------------------------
% 2.42/1.49 % (28725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.49 % (28725)Termination reason: Unknown
% 2.42/1.49 % (28725)Termination phase: Saturation
% 2.42/1.49
% 2.42/1.49 % (28725)Memory used [KB]: 7291
% 2.42/1.49 % (28725)Time elapsed: 0.053 s
% 2.42/1.49 % (28725)Instructions burned: 183 (million)
% 2.42/1.49 % (28725)------------------------------
% 2.42/1.49 % (28725)------------------------------
% 2.42/1.49 % (28747)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_28396 for (2999ds/902Mi)
% 2.42/1.49 % (28748)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_28396 for (2999ds/21Mi)
% 2.42/1.49 % (28749)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/5Mi)
% 2.42/1.49 % (28749)Instruction limit reached!
% 2.42/1.49 % (28749)------------------------------
% 2.42/1.49 % (28749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.49 % (28749)Termination reason: Unknown
% 2.42/1.49 % (28749)Termination phase: shuffling
% 2.42/1.49
% 2.42/1.49 % (28749)Memory used [KB]: 1535
% 2.42/1.49 % (28749)Time elapsed: 0.003 s
% 2.42/1.49 % (28749)Instructions burned: 8 (million)
% 2.42/1.49 % (28749)------------------------------
% 2.42/1.49 % (28749)------------------------------
% 2.42/1.50 % (28750)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_28396 for (2999ds/6Mi)
% 2.45/1.50 % (28750)Instruction limit reached!
% 2.45/1.50 % (28750)------------------------------
% 2.45/1.50 % (28750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (28750)Termination reason: Unknown
% 2.45/1.50 % (28750)Termination phase: shuffling
% 2.45/1.50
% 2.45/1.50 % (28750)Memory used [KB]: 1535
% 2.45/1.50 % (28750)Time elapsed: 0.003 s
% 2.45/1.50 % (28750)Instructions burned: 7 (million)
% 2.45/1.50 % (28750)------------------------------
% 2.45/1.50 % (28750)------------------------------
% 2.45/1.50 % (28748)Instruction limit reached!
% 2.45/1.50 % (28748)------------------------------
% 2.45/1.50 % (28748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (28748)Termination reason: Unknown
% 2.45/1.50 % (28748)Termination phase: shuffling
% 2.45/1.50
% 2.45/1.50 % (28748)Memory used [KB]: 1663
% 2.45/1.50 % (28748)Time elapsed: 0.008 s
% 2.45/1.50 % (28748)Instructions burned: 22 (million)
% 2.45/1.50 % (28748)------------------------------
% 2.45/1.50 % (28748)------------------------------
% 2.45/1.50 % (28730)First to succeed.
% 2.45/1.50 % (28751)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28396 for (2999ds/377Mi)
% 2.45/1.50 % (28730)Refutation found. Thanks to Tanya!
% 2.45/1.50 % SZS status Theorem for DTF2THF_28396
% 2.45/1.50 % SZS output start Proof for DTF2THF_28396
% 2.45/1.50 thf(type_def_5, type, set: ($tType) > $tType).
% 2.45/1.50 thf(type_def_7, type, list: ($tType) > $tType).
% 2.45/1.50 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 2.45/1.50 thf(type_def_9, type, option: ($tType) > $tType).
% 2.45/1.50 thf(type_def_10, type, g: $tType).
% 2.45/1.50 thf(type_def_11, type, node: $tType).
% 2.45/1.50 thf(type_def_12, type, val: $tType).
% 2.45/1.50 thf(type_def_13, type, edgeD: $tType).
% 2.45/1.50 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 2.45/1.50 thf(func_def_1, type, option: ($tType) > $tType).
% 2.45/1.50 thf(func_def_2, type, list: ($tType) > $tType).
% 2.45/1.50 thf(func_def_3, type, set: ($tType) > $tType).
% 2.45/1.50 thf(func_def_4, type, edgeD: $tType).
% 2.45/1.50 thf(func_def_5, type, node: $tType).
% 2.45/1.50 thf(func_def_6, type, val: $tType).
% 2.45/1.50 thf(func_def_7, type, g: $tType).
% 2.45/1.50 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 2.45/1.50 thf(func_def_9, type, ord: !>[X0: $tType]:($o)).
% 2.45/1.50 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 2.45/1.50 thf(func_def_11, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 2.45/1.50 thf(func_def_12, 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)).
% 2.45/1.50 thf(func_def_13, 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)).
% 2.45/1.50 thf(func_def_14, type, graph_1201503639essors: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1)).
% 2.45/1.50 thf(func_def_15, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_16, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_17, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_18, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.45/1.50 thf(func_def_19, type, hd: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_20, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 2.45/1.50 thf(func_def_21, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_22, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.45/1.50 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)).
% 2.45/1.50 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)).
% 2.45/1.50 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)).
% 2.45/1.50 thf(func_def_26, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.45/1.50 thf(func_def_27, type, prefix: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.45/1.50 thf(func_def_28, type, suffix: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.45/1.50 thf(func_def_29, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.45/1.50 thf(func_def_30, type, alpha_n: g > list @ node).
% 2.45/1.50 thf(func_def_31, type, phi_r: val).
% 2.45/1.50 thf(func_def_32, type, defs: g > node > set @ val).
% 2.45/1.50 thf(func_def_33, type, g2: g).
% 2.45/1.50 thf(func_def_34, type, i: node).
% 2.45/1.50 thf(func_def_35, type, inEdges: g > node > list @ product_prod @ node @ edgeD).
% 2.45/1.50 thf(func_def_36, type, invar: g > $o).
% 2.45/1.50 thf(func_def_37, type, m: node).
% 2.45/1.50 thf(func_def_38, type, ms: list @ node).
% 2.45/1.50 thf(func_def_39, type, ms2: list @ node).
% 2.45/1.50 thf(func_def_40, type, n: node).
% 2.45/1.50 thf(func_def_41, type, ns: list @ node).
% 2.45/1.50 thf(func_def_42, type, phis: g > product_prod @ node @ val > option @ list @ val).
% 2.45/1.50 thf(func_def_43, type, pred_phi_r: node).
% 2.45/1.50 thf(func_def_44, type, r: val).
% 2.45/1.50 thf(func_def_45, type, ri: list @ node).
% 2.45/1.50 thf(func_def_46, type, rs: list @ node).
% 2.45/1.50 thf(func_def_47, type, rs2: list @ node).
% 2.45/1.50 thf(func_def_48, type, s: val).
% 2.45/1.50 thf(func_def_59, type, sP0: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (list @ X1 > list @ X0 > $o) > $o)).
% 2.45/1.50 thf(func_def_60, type, sP1: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > $o)).
% 2.45/1.50 thf(func_def_61, type, sP2: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.45/1.50 thf(func_def_62, type, sP3: !>[X0: $tType]:(X0 > X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0 > $o)).
% 2.45/1.50 thf(func_def_63, type, sK4: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_64, type, sK5: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_65, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (list @ X1 > list @ X0 > $o) > X1)).
% 2.45/1.50 thf(func_def_66, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (list @ X1 > list @ X0 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_67, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (list @ X1 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_68, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (list @ X1 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_69, type, sK10: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_70, type, sK11: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_71, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_72, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_73, type, sK14: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_74, type, sK15: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_75, type, sK16: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_76, type, sK17: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_77, type, sK18: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_78, type, sK19: node > node > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_79, type, sK20: node > node > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_80, type, sK21: node > node > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_81, type, sK22: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_82, type, sK23: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_83, type, sK24: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_84, type, sK25: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_85, type, sK26: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_86, type, sK27: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_87, type, sK28: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_88, type, sK29: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_89, type, sK30: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_90, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 2.45/1.50 thf(func_def_91, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X2)).
% 2.45/1.50 thf(func_def_92, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X2)).
% 2.45/1.50 thf(func_def_93, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 2.45/1.50 thf(func_def_94, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0)).
% 2.45/1.50 thf(func_def_95, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_96, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X2)).
% 2.45/1.50 thf(func_def_97, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X2)).
% 2.45/1.50 thf(func_def_98, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 2.45/1.50 thf(func_def_99, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 2.45/1.50 thf(func_def_100, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0)).
% 2.45/1.50 thf(func_def_101, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_102, type, sK43: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 2.45/1.50 thf(func_def_103, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_104, type, sK45: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_105, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 2.45/1.50 thf(func_def_106, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_107, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_108, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 2.45/1.50 thf(func_def_109, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 2.45/1.50 thf(func_def_110, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_111, type, sK52: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_112, type, sK53: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_113, type, sK54: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_114, type, sK55: node).
% 2.45/1.50 thf(func_def_115, type, sK56: list @ node).
% 2.45/1.50 thf(func_def_116, type, sK57: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_117, type, sK58: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_118, type, sK59: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_119, type, sK60: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_120, type, sK61: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_121, type, sK62: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_122, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.45/1.50 thf(func_def_123, type, sK64: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_124, type, sK65: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.45/1.50 thf(func_def_125, type, sK66: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_126, type, sK67: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_127, type, sK68: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_128, type, sK69: !>[X0: $tType]:(X0 > list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_129, type, sK70: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_130, type, sK71: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_131, type, sK72: node > node > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_132, type, sK73: node > node > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_133, type, sK74: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_134, type, sK75: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_135, type, sK76: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 2.45/1.50 thf(func_def_136, type, sK77: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_137, type, sK78: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 2.45/1.50 thf(func_def_138, type, sK79: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_139, type, sK80: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_140, type, sK81: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 2.45/1.50 thf(func_def_141, type, sK82: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_142, type, sK83: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_143, type, sK84: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_144, type, sK85: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_145, type, sK86: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_146, type, sK87: node > node > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_147, type, sK88: node > node > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_148, type, sK89: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_149, type, sK90: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_150, type, sK91: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > X1)).
% 2.45/1.50 thf(func_def_151, type, sK92: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_152, type, sK93: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_153, type, sK94: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_154, type, sK95: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_155, type, sK96: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_156, type, sK97: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_157, type, sK98: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_158, type, sK99: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_159, type, sK100: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_160, type, sK101: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_161, type, sK102: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_162, type, sK103: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_163, type, sK104: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_164, type, sK105: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_165, type, sK106: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_166, type, sK107: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_167, type, sK108: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_168, type, sK109: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_169, type, sK110: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_170, type, sK111: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_171, type, sK112: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_172, type, sK113: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_173, type, sK114: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_174, type, sK115: node > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_175, type, sK116: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_176, type, sK117: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_177, type, sK118: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_178, type, sK119: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_179, type, sK120: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_180, type, sK121: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_181, type, sK122: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_182, type, sK123: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_183, type, sK124: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_184, type, sK125: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_185, type, sK126: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_186, type, sK127: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_187, type, sK128: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_188, type, sK129: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_189, type, sK130: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_190, type, sK131: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_191, type, sK132: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_192, type, sK133: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_193, type, sK134: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_194, type, sK135: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_195, type, sK136: !>[X0: $tType]:(X0 > list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_196, type, sK137: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_197, type, sK138: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_198, type, sK139: (node > $o) > list @ node > node > g > node).
% 2.45/1.50 thf(func_def_199, type, sK140: (node > $o) > list @ node > node > g > list @ node).
% 2.45/1.50 thf(func_def_200, type, sK141: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 2.45/1.50 thf(func_def_201, type, sK142: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_202, type, sK143: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 2.45/1.50 thf(func_def_203, type, sK144: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_204, type, sK145: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_205, type, sK146: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_206, type, sK147: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 2.45/1.50 thf(func_def_207, type, sK148: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_208, type, sK149: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_209, type, sK150: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_210, type, sK151: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_211, type, sK152: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_212, type, sK153: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_213, type, sK154: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_214, type, sK155: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_215, type, sK156: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_216, type, sK157: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_217, type, sK158: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_218, type, sK159: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_219, type, sK160: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_220, type, sK161: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_221, type, sK162: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_222, type, sK163: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_223, type, sK164: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_224, type, sK165: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_225, type, sK166: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_226, type, sK167: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_227, type, sK168: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_228, type, sK169: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_229, type, sK170: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_230, type, sK171: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_231, type, sK172: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_232, type, sK173: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_233, type, sK174: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_234, type, sK175: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.45/1.50 thf(func_def_235, type, sK176: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.45/1.50 thf(func_def_236, type, sK177: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_237, type, sK178: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_238, type, sK179: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_239, type, sK180: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_240, type, sK181: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_241, type, sK182: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_242, type, sK183: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_243, type, sK184: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_244, type, sK185: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_245, type, sK186: (node > $o) > node > list @ node > g > node).
% 2.45/1.50 thf(func_def_246, type, sK187: (node > $o) > node > list @ node > g > list @ node).
% 2.45/1.50 thf(func_def_247, type, sK188: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_248, type, sK189: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_249, type, sK190: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_250, type, sK191: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_251, type, sK192: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_252, type, sK193: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_253, type, sK194: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_254, type, sK195: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_255, type, sK196: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_256, type, sK197: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_257, type, sK198: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_258, type, sK199: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_259, type, sK200: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_260, type, sK201: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_261, type, sK202: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_262, type, sK203: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_263, type, sK204: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_264, type, sK205: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_265, type, sK206: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_266, type, sK207: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_267, type, sK208: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_268, type, sK209: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_269, type, sK210: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_270, type, sK211: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_271, type, sK212: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_272, type, sK213: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_273, type, sK214: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_274, type, sK215: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.45/1.50 thf(func_def_275, type, sK216: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 2.45/1.50 thf(func_def_276, type, sK217: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_277, type, sK218: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.45/1.50 thf(func_def_278, type, sK219: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_279, type, sK220: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_280, type, sK221: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_281, type, sK222: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_282, type, sK223: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_283, type, sK224: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_284, type, sK225: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_285, type, sK226: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_286, type, sK227: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.45/1.50 thf(func_def_287, type, sK228: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_288, type, sK229: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.45/1.50 thf(func_def_289, type, sK230: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_290, type, sK231: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_291, type, sK232: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_292, type, sK233: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.45/1.50 thf(func_def_293, type, sK234: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.45/1.50 thf(func_def_294, type, sK235: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_295, type, sK236: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_296, type, sK237: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_297, type, sK238: !>[X0: $tType]:(list @ X0 > X0 > X0)).
% 2.45/1.50 thf(func_def_298, type, sK239: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_299, type, sK240: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_300, type, sK241: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_301, type, sK242: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_302, type, sK243: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_303, type, sK244: !>[X0: $tType]:(list @ X0 > X0)).
% 2.45/1.50 thf(func_def_304, type, sK245: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_305, type, sK246: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_306, type, sK247: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_307, type, sK248: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_308, type, sK249: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_309, type, sK250: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_310, type, sK251: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_311, type, sK252: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.45/1.50 thf(func_def_312, type, sK253: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.45/1.50 thf(func_def_313, type, sK254: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_314, type, sK255: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_315, type, sK256: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_316, type, sK257: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_317, type, sK258: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.45/1.50 thf(func_def_318, type, sK259: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_319, type, sK260: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.45/1.50 thf(func_def_320, type, sK261: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.45/1.50 thf(func_def_321, type, sK262: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_322, type, sK263: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.45/1.50 thf(func_def_323, type, sK264: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.45/1.50 thf(func_def_324, type, sK265: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_325, type, sK266: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_326, type, sK267: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_327, type, sK268: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.45/1.50 thf(func_def_329, type, ph270: !>[X0: $tType]:(X0)).
% 2.45/1.50 thf(f1794,plain,(
% 2.45/1.50 $false),
% 2.45/1.50 inference(subsumption_resolution,[status(thm)],[f1793,f1419])).
% 2.45/1.50 thf(f1419,plain,(
% 2.45/1.50 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r)) = $true)),
% 2.45/1.50 inference(cnf_transformation,[status(thm)],[f588])).
% 2.45/1.50 thf(f588,plain,(
% 2.45/1.50 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r)) = $true)),
% 2.45/1.50 inference(fool_elimination,[status(thm)],[f587])).
% 2.45/1.50 thf(f587,plain,(
% 2.45/1.50 (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r))),
% 2.45/1.50 inference(rectify,[status(thm)],[f4])).
% 2.45/1.50 thf(f4,axiom,(
% 2.45/1.50 (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r))),
% 2.45/1.50 file('/export/starexec/sandbox/tmp/tmp.FAhNdHU93a/DTF2THF_28396.p',fact_3_assms_I7_J)).
% 2.45/1.50 thf(f1793,plain,(
% 2.45/1.50 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r)) != $true)),
% 2.45/1.50 inference(trivial_inequality_removal,[status(thm)],[f1792])).
% 2.45/1.50 thf(f1792,plain,(
% 2.45/1.50 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r)) != $true) | ($true != $true)),
% 2.45/1.50 inference(superposition,[status(thm)],[f1791,f1675])).
% 2.45/1.50 thf(f1675,plain,(
% 2.45/1.50 ($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r)))),
% 2.45/1.50 inference(definition_unfolding,[status(thm)],[f1377,f1607])).
% 2.45/1.50 thf(f1607,plain,(
% 2.45/1.50 (i = (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 2.45/1.50 inference(cnf_transformation,[status(thm)],[f2])).
% 2.45/1.50 thf(f2,axiom,(
% 2.45/1.50 (i = (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 2.45/1.50 file('/export/starexec/sandbox/tmp/tmp.FAhNdHU93a/DTF2THF_28396.p',fact_1_ri__is__valid)).
% 2.45/1.50 thf(f1377,plain,(
% 2.45/1.50 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i) = $true)),
% 2.45/1.50 inference(cnf_transformation,[status(thm)],[f626])).
% 2.45/1.50 thf(f626,plain,(
% 2.45/1.50 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i) = $true)),
% 2.45/1.50 inference(fool_elimination,[status(thm)],[f625])).
% 2.45/1.50 thf(f625,plain,(
% 2.45/1.50 (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i)),
% 2.45/1.50 inference(rectify,[status(thm)],[f5])).
% 2.45/1.50 thf(f5,axiom,(
% 2.45/1.50 (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i)),
% 2.45/1.50 file('/export/starexec/sandbox/tmp/tmp.FAhNdHU93a/DTF2THF_28396.p',fact_4_ri__props_I1_J)).
% 2.45/1.50 thf(f1791,plain,(
% 2.45/1.50 ( ! [X0 : node] : (($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ X0 @ ri @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r))) | ($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ X0))) )),
% 2.45/1.50 inference(trivial_inequality_removal,[status(thm)],[f1790])).
% 2.45/1.50 thf(f1790,plain,(
% 2.45/1.50 ( ! [X0 : node] : (($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ X0 @ ri @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r))) | ($true != $true) | ($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ X0))) )),
% 2.45/1.50 inference(superposition,[status(thm)],[f1351,f1265])).
% 2.45/1.50 thf(f1265,plain,(
% 2.45/1.50 ( ! [X2 : list @ node,X3 : node,X0 : g,X1 : node,X4 : list @ node,X5 : node] : (($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (tl @ node @ X4)) @ X5)) | ($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3)) | ($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ X4 @ X5))) )),
% 2.45/1.50 inference(cnf_transformation,[status(thm)],[f838])).
% 2.45/1.50 thf(f838,plain,(
% 2.45/1.50 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node,X4 : list @ node,X5 : node] : (($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (tl @ node @ X4)) @ X5)) | ($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3)) | ($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ X4 @ X5)))),
% 2.45/1.50 inference(flattening,[status(thm)],[f837])).
% 2.45/1.50 thf(f837,plain,(
% 2.45/1.50 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node,X4 : list @ node,X5 : node] : ((($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (tl @ node @ X4)) @ X5)) | ($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ X4 @ X5))) | ($true != (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3)))),
% 2.45/1.50 inference(ennf_transformation,[status(thm)],[f574])).
% 2.45/1.50 thf(f574,plain,(
% 2.45/1.50 ! [X0 : g,X1 : node,X2 : list @ node,X3 : node,X4 : list @ node,X5 : node] : (($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3)) => (($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ X4 @ X5)) => ($true = (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (tl @ node @ X4)) @ X5))))),
% 2.45/1.50 inference(fool_elimination,[status(thm)],[f573])).
% 2.45/1.50 thf(f573,plain,(
% 2.45/1.50 ! [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 @ X2 @ X3) => ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ X4 @ X5) => (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append @ node @ X2 @ (tl @ node @ X4)) @ X5)))),
% 2.45/1.50 inference(rectify,[status(thm)],[f6])).
% 2.45/1.50 thf(f6,axiom,(
% 2.45/1.50 ! [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 @ X7 @ X8) => ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X5 @ X8 @ X9 @ X10) => (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ X5 @ X6 @ (append @ node @ X7 @ (tl @ node @ X9)) @ X10)))),
% 2.45/1.50 file('/export/starexec/sandbox/tmp/tmp.FAhNdHU93a/DTF2THF_28396.p',fact_5_old_Opath2__app)).
% 2.45/1.50 thf(f1351,plain,(
% 2.45/1.50 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append @ node @ ns @ (tl @ node @ ri)) @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r)) != $true)),
% 2.45/1.50 inference(cnf_transformation,[status(thm)],[f695])).
% 2.45/1.50 thf(f695,plain,(
% 2.45/1.50 ((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append @ node @ ns @ (tl @ node @ ri)) @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r)) != $true)),
% 2.45/1.50 inference(flattening,[status(thm)],[f618])).
% 2.45/1.50 thf(f618,plain,(
% 2.45/1.50 ~((graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append @ node @ ns @ (tl @ node @ ri)) @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r)) = $true)),
% 2.45/1.50 inference(fool_elimination,[status(thm)],[f617])).
% 2.45/1.50 thf(f617,plain,(
% 2.45/1.50 ~(graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append @ node @ ns @ (tl @ node @ ri)) @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 2.45/1.50 inference(rectify,[status(thm)],[f265])).
% 2.45/1.50 thf(f265,negated_conjecture,(
% 2.45/1.50 ~(graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append @ node @ ns @ (tl @ node @ ri)) @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 2.45/1.50 inference(negated_conjecture,[status(cth)],[f264])).
% 2.45/1.50 thf(f264,conjecture,(
% 2.45/1.50 (graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ (append @ node @ ns @ (tl @ node @ ri)) @ (sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r))),
% 2.45/1.50 file('/export/starexec/sandbox/tmp/tmp.FAhNdHU93a/DTF2THF_28396.p',conj_0)).
% 2.45/1.50 % SZS output end Proof for DTF2THF_28396
% 2.45/1.50 % (28730)------------------------------
% 2.45/1.50 % (28730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (28730)Termination reason: Refutation
% 2.45/1.50
% 2.45/1.50 % (28730)Memory used [KB]: 7931
% 2.45/1.50 % (28730)Time elapsed: 0.070 s
% 2.45/1.50 % (28730)Instructions burned: 226 (million)
% 2.45/1.50 % (28730)------------------------------
% 2.45/1.50 % (28730)------------------------------
% 2.45/1.50 % (28724)Success in time 0.083 s
%------------------------------------------------------------------------------