%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP082^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 2.90s 1.65s
% Output : Refutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 23 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 302 ( 9 ~; 4 |; 0 &; 286 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 21 con; 0-9 aty)
% Number of variables : 33 ( 0 ^; 33 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
list_node: $tType ).
thf(type_def_8,type,
node: $tType ).
thf(type_def_9,type,
list_P561207620_edgeD: $tType ).
thf(type_def_10,type,
list_list_node: $tType ).
thf(type_def_11,type,
list_val: $tType ).
thf(type_def_12,type,
val: $tType ).
thf(type_def_13,type,
set_list_node: $tType ).
thf(type_def_14,type,
set_node: $tType ).
thf(type_def_15,type,
set_val: $tType ).
thf(type_def_16,type,
produc1432036078de_val: $tType ).
thf(type_def_17,type,
option_list_val: $tType ).
thf(func_def_0,type,
list_P561207620_edgeD: $tType ).
thf(func_def_1,type,
option_list_val: $tType ).
thf(func_def_2,type,
produc1432036078de_val: $tType ).
thf(func_def_3,type,
list_list_node: $tType ).
thf(func_def_4,type,
set_list_node: $tType ).
thf(func_def_5,type,
list_node: $tType ).
thf(func_def_6,type,
list_val: $tType ).
thf(func_def_7,type,
set_node: $tType ).
thf(func_def_8,type,
set_val: $tType ).
thf(func_def_9,type,
node: $tType ).
thf(func_def_10,type,
val: $tType ).
thf(func_def_11,type,
g: $tType ).
thf(func_def_12,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(func_def_13,type,
graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
thf(func_def_14,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(func_def_15,type,
append_list_node: list_list_node > list_list_node > list_list_node ).
thf(func_def_16,type,
append_node: list_node > list_node > list_node ).
thf(func_def_17,type,
append_val: list_val > list_val > list_val ).
thf(func_def_18,type,
butlast_list_node: list_list_node > list_list_node ).
thf(func_def_19,type,
butlast_node: list_node > list_node ).
thf(func_def_20,type,
butlast_val: list_val > list_val ).
thf(func_def_21,type,
cons_list_node: list_node > list_list_node > list_list_node ).
thf(func_def_22,type,
cons_node: node > list_node > list_node ).
thf(func_def_23,type,
cons_val: val > list_val > list_val ).
thf(func_def_24,type,
nil_list_node: list_list_node ).
thf(func_def_25,type,
nil_node: list_node ).
thf(func_def_26,type,
nil_val: list_val ).
thf(func_def_27,type,
hd_list_node: list_list_node > list_node ).
thf(func_def_28,type,
hd_node: list_node > node ).
thf(func_def_29,type,
hd_val: list_val > val ).
thf(func_def_30,type,
set_list_node2: list_list_node > set_list_node ).
thf(func_def_31,type,
set_node2: list_node > set_node ).
thf(func_def_32,type,
set_val2: list_val > set_val ).
thf(func_def_33,type,
tl_list_node: list_list_node > list_list_node ).
thf(func_def_34,type,
tl_node: list_node > list_node ).
thf(func_def_35,type,
tl_val: list_val > list_val ).
thf(func_def_36,type,
graph_2009891965_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > list_node > node > $o ).
thf(func_def_37,type,
ord_less_eq_set_node: set_node > set_node > $o ).
thf(func_def_38,type,
ord_less_eq_set_val: set_val > set_val > $o ).
thf(func_def_39,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_40,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(func_def_41,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(func_def_42,type,
collect_node: ( node > $o ) > set_node ).
thf(func_def_43,type,
collect_val: ( val > $o ) > set_val ).
thf(func_def_44,type,
prefix_node: list_node > list_node > $o ).
thf(func_def_45,type,
suffix_node: list_node > list_node > $o ).
thf(func_def_46,type,
member_list_node: list_node > set_list_node > $o ).
thf(func_def_47,type,
member_node: node > set_node > $o ).
thf(func_def_48,type,
member_val: val > set_val > $o ).
thf(func_def_49,type,
alpha_n: g > list_node ).
thf(func_def_50,type,
phi_r: val ).
thf(func_def_51,type,
defs: g > node > set_val ).
thf(func_def_52,type,
g2: g ).
thf(func_def_53,type,
i: node ).
thf(func_def_54,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(func_def_55,type,
invar: g > $o ).
thf(func_def_56,type,
m: node ).
thf(func_def_57,type,
ms: list_node ).
thf(func_def_58,type,
ms2: list_node ).
thf(func_def_59,type,
n: node ).
thf(func_def_60,type,
ns: list_node ).
thf(func_def_61,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(func_def_62,type,
pred_phi_r: node ).
thf(func_def_63,type,
r: val ).
thf(func_def_64,type,
ri: list_node ).
thf(func_def_65,type,
rs: list_node ).
thf(func_def_66,type,
rs_rest: list_node ).
thf(func_def_67,type,
rs2: list_node ).
thf(func_def_68,type,
s: val ).
thf(func_def_69,type,
tmp: list_node ).
thf(func_def_81,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f961,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f960,f925]) ).
thf(f925,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r )
!= $true ),
inference(cnf_transformation,[status(thm)],[f888]) ).
thf(f888,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r )
!= $true ),
inference(flattening,[status(thm)],[f751]) ).
thf(f751,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r )
!= $true ),
inference(fool_elimination,[status(thm)],[f750]) ).
thf(f750,plain,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r ),
inference(rectify,[status(thm)],[f354]) ).
thf(f354,negated_conjecture,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f353,conjecture,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r,
file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',conj_0) ).
thf(f960,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f959]) ).
thf(f959,plain,
( ( $true != $true )
| ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r )
= $true ) ),
inference(superposition,[status(thm)],[f951,f936]) ).
thf(f936,plain,
( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( append_node @ ri @ rs_rest ) @ pred_phi_r ) ),
inference(backward_demodulation,[status(thm)],[f929,f930]) ).
thf(f930,plain,
( ( append_node @ tmp @ ( cons_node @ i @ rs_rest ) )
= ( append_node @ ri @ rs_rest ) ),
inference(definition_unfolding,[status(thm)],[f924,f907]) ).
thf(f907,plain,
( rs
= ( append_node @ tmp @ ( cons_node @ i @ rs_rest ) ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
( rs
= ( append_node @ tmp @ ( cons_node @ i @ rs_rest ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',fact_1_rs_H__rest__def) ).
thf(f924,plain,
( rs
= ( append_node @ ri @ rs_rest ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,axiom,
( rs
= ( append_node @ ri @ rs_rest ) ),
file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',fact_7_rs_H__rest__prop) ).
thf(f929,plain,
( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( append_node @ tmp @ ( cons_node @ i @ rs_rest ) ) @ pred_phi_r ) ),
inference(definition_unfolding,[status(thm)],[f914,f907]) ).
thf(f914,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r )
= $true ),
inference(cnf_transformation,[status(thm)],[f449]) ).
thf(f449,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r )
= $true ),
inference(fool_elimination,[status(thm)],[f448]) ).
thf(f448,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',fact_5_rs_H__props_I1_J) ).
thf(f951,plain,
! [X2: node,X0: g,X1: node] :
( ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ ( append_node @ ri @ rs_rest ) @ X2 ) )
| ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ i @ ( cons_node @ i @ rs_rest ) @ X2 ) ) ),
inference(superposition,[status(thm)],[f906,f930]) ).
thf(f906,plain,
! [X2: g,X3: list_node,X0: node,X1: list_node,X4: node,X5: node] :
( ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X4 @ ( append_node @ X1 @ ( cons_node @ X5 @ X3 ) ) @ X0 ) )
| ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X5 @ ( cons_node @ X5 @ X3 ) @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f903]) ).
thf(f903,plain,
! [X0: node,X1: list_node,X2: g,X3: list_node,X4: node,X5: node] :
( ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X5 @ ( cons_node @ X5 @ X3 ) @ X0 ) )
| ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X4 @ ( append_node @ X1 @ ( cons_node @ X5 @ X3 ) ) @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f749]) ).
thf(f749,plain,
! [X0: node,X1: list_node,X2: g,X3: list_node,X4: node,X5: node] :
( ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X4 @ ( append_node @ X1 @ ( cons_node @ X5 @ X3 ) ) @ X0 ) )
=> ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X5 @ ( cons_node @ X5 @ X3 ) @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f748]) ).
thf(f748,plain,
! [X0: node,X1: list_node,X2: g,X3: list_node,X4: node,X5: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X4 @ ( append_node @ X1 @ ( cons_node @ X5 @ X3 ) ) @ X0 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X5 @ ( cons_node @ X5 @ X3 ) @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X5: node,X2: list_node,X0: g,X4: list_node,X1: node,X3: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ ( append_node @ X2 @ ( cons_node @ X3 @ X4 ) ) @ X5 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ ( cons_node @ X3 @ X4 ) @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',fact_3_old_Opath2__split_I2_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP082^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:25:32 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : ITP082^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.44 % Domain : Interactive Theorem Proving
% 0.19/0.44 % Problem : Sledgehammer Irreducible problem prob_559__6628256_1
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Des21]
% 0.19/0.44 % Names : Irreducible/prob_559__6628256_1 [Des21]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0
% 0.19/0.44 % Syntax : Number of formulae : 423 ( 153 unt; 70 typ; 0 def)
% 0.19/0.44 % Number of atoms : 1084 ( 638 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 14 ( 3 avg)
% 0.19/0.44 % Number of connectives : 3833 ( 215 ~; 24 |; 113 &;3023 @)
% 0.19/0.44 % ( 0 <=>; 458 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 26 ( 7 avg)
% 0.19/0.44 % Number of types : 13 ( 12 usr)
% 0.19/0.44 % Number of type conns : 229 ( 229 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 59 ( 58 usr; 19 con; 0-9 aty)
% 0.19/0.44 % Number of variables : 1148 ( 19 ^;1052 !; 77 ?;1148 :)
% 0.19/0.44 % SPC : TH0_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 15:42:19.440
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % Could-be-implicit typings (12)
% 0.19/0.44 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 0.19/0.44 list_P561207620_edgeD: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__val_J_J,type,
% 0.19/0.44 option_list_val: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 0.19/0.44 produc1432036078de_val: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_t__List__Olist_It__List__Olist_Itf__node_J_J,type,
% 0.19/0.44 list_list_node: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__node_J_J,type,
% 0.19/0.44 set_list_node: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_t__List__Olist_Itf__node_J,type,
% 0.19/0.44 list_node: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_t__List__Olist_Itf__val_J,type,
% 0.19/0.44 list_val: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_t__Set__Oset_Itf__node_J,type,
% 0.19/0.44 set_node: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 0.19/0.44 set_val: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_tf__node,type,
% 0.19/0.44 node: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_tf__val,type,
% 0.19/0.44 val: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(ty_n_tf__g,type,
% 0.19/0.44 g: $tType ).
% 0.19/0.44
% 0.19/0.44 % Explicit typings (58)
% 0.19/0.44 thf(sy_c_Graph__path_Ograph__path__base_Opath2_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.44 graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Graph__path_Ograph__path__base_Opath_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.44 graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.44 graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Oappend_001t__List__Olist_Itf__node_J,type,
% 0.19/0.44 append_list_node: list_list_node > list_list_node > list_list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Oappend_001tf__node,type,
% 0.19/0.44 append_node: list_node > list_node > list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Oappend_001tf__val,type,
% 0.19/0.44 append_val: list_val > list_val > list_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__node_J,type,
% 0.19/0.44 butlast_list_node: list_list_node > list_list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Obutlast_001tf__node,type,
% 0.19/0.44 butlast_node: list_node > list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Obutlast_001tf__val,type,
% 0.19/0.44 butlast_val: list_val > list_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__node_J,type,
% 0.19/0.44 cons_list_node: list_node > list_list_node > list_list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_OCons_001tf__node,type,
% 0.19/0.44 cons_node: node > list_node > list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_OCons_001tf__val,type,
% 0.19/0.44 cons_val: val > list_val > list_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__node_J,type,
% 0.19/0.44 nil_list_node: list_list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_ONil_001tf__node,type,
% 0.19/0.44 nil_node: list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_ONil_001tf__val,type,
% 0.19/0.44 nil_val: list_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Ohd_001t__List__Olist_Itf__node_J,type,
% 0.19/0.44 hd_list_node: list_list_node > list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Ohd_001tf__node,type,
% 0.19/0.44 hd_node: list_node > node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Ohd_001tf__val,type,
% 0.19/0.44 hd_val: list_val > val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__node_J,type,
% 0.19/0.44 set_list_node2: list_list_node > set_list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Oset_001tf__node,type,
% 0.19/0.44 set_node2: list_node > set_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Oset_001tf__val,type,
% 0.19/0.44 set_val2: list_val > set_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Otl_001t__List__Olist_Itf__node_J,type,
% 0.19/0.44 tl_list_node: list_list_node > list_list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Otl_001tf__node,type,
% 0.19/0.44 tl_node: list_node > list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_List_Olist_Otl_001tf__val,type,
% 0.19/0.44 tl_val: list_val > list_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Minimality_Ograph__path_OpathsConverge_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.44 graph_2009891965_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > list_node > node > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__node_J,type,
% 0.19/0.44 ord_less_eq_set_node: set_node > set_node > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__val_J,type,
% 0.19/0.44 ord_less_eq_set_val: set_val > set_val > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 0.19/0.44 sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode_001tf__g_001tf__node_001tf__val,type,
% 0.19/0.44 sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg_001tf__g_001tf__node_001tf__val,type,
% 0.19/0.44 sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Set_OCollect_001tf__node,type,
% 0.19/0.44 collect_node: ( node > $o ) > set_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Set_OCollect_001tf__val,type,
% 0.19/0.44 collect_val: ( val > $o ) > set_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Sublist_Oprefix_001tf__node,type,
% 0.19/0.44 prefix_node: list_node > list_node > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_Sublist_Osuffix_001tf__node,type,
% 0.19/0.44 suffix_node: list_node > list_node > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_member_001t__List__Olist_Itf__node_J,type,
% 0.19/0.44 member_list_node: list_node > set_list_node > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_member_001tf__node,type,
% 0.19/0.44 member_node: node > set_node > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_c_member_001tf__val,type,
% 0.19/0.44 member_val: val > set_val > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v__092_060alpha_062n,type,
% 0.19/0.44 alpha_n: g > list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 0.19/0.44 phi_r: val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_defs,type,
% 0.19/0.44 defs: g > node > set_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_g,type,
% 0.19/0.44 g2: g ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_i____,type,
% 0.19/0.44 i: node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_inEdges_H,type,
% 0.19/0.44 inEdges: g > node > list_P561207620_edgeD ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_invar,type,
% 0.19/0.44 invar: g > $o ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_m,type,
% 0.19/0.44 m: node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_ms,type,
% 0.19/0.44 ms: list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_ms_H____,type,
% 0.19/0.44 ms2: list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_n,type,
% 0.19/0.44 n: node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_ns,type,
% 0.19/0.44 ns: list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_phis,type,
% 0.19/0.44 phis: g > produc1432036078de_val > option_list_val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 0.19/0.44 pred_phi_r: node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_r,type,
% 0.19/0.44 r: val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_ri____,type,
% 0.19/0.44 ri: list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_rs_H____,type,
% 0.19/0.44 rs: list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_rs_H__rest____,type,
% 0.19/0.44 rs_rest: list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_rs____,type,
% 0.19/0.44 rs2: list_node ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_s,type,
% 0.19/0.44 s: val ).
% 0.19/0.44
% 0.19/0.44 thf(sy_v_tmp____,type,
% 0.19/0.44 tmp: list_node ).
% 0.19/0.44
% 0.19/0.44 % Relevant facts (352)
% 0.19/0.44 thf(fact_0_m__i__differ_I2_J,axiom,
% 0.19/0.44 m != i ).
% 0.19/0.44
% 0.19/0.44 % m_i_differ(2)
% 0.19/0.44 thf(fact_1_rs_H__rest__def,axiom,
% 0.19/0.44 ( rs
% 0.19/0.44 = ( append_node @ tmp @ ( cons_node @ i @ rs_rest ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % rs'_rest_def
% 0.19/0.44 thf(fact_2_old_Oinvar,axiom,
% 0.19/0.44 ! [G: g] : ( invar @ G ) ).
% 0.19/0.44
% 0.19/0.44 % old.invar
% 0.19/0.44 thf(fact_3_old_Opath2__split_I2_J,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 0.19/0.44 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns2 ) @ M ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_split(2)
% 0.19/0.44 thf(fact_4_False,axiom,
% 0.19/0.44 r != phi_r ).
% 0.19/0.44
% 0.19/0.44 % False
% 0.19/0.44 thf(fact_5_rs_H__props_I1_J,axiom,
% 0.19/0.44 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 0.19/0.44
% 0.19/0.44 % rs'_props(1)
% 0.19/0.44 thf(fact_6_ms_H__props_I1_J,axiom,
% 0.19/0.44 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 0.19/0.44
% 0.19/0.44 % ms'_props(1)
% 0.19/0.44 thf(fact_7_rs_H__rest__prop,axiom,
% 0.19/0.44 ( rs
% 0.19/0.44 = ( append_node @ ri @ rs_rest ) ) ).
% 0.19/0.44
% 0.19/0.44 % rs'_rest_prop
% 0.19/0.44 thf(fact_8_rs_H__props_I3_J,axiom,
% 0.19/0.44 member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 0.19/0.44
% 0.19/0.44 % rs'_props(3)
% 0.19/0.44 thf(fact_9_old_Opath2__not__Nil,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( Ns != nil_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_not_Nil
% 0.19/0.44 thf(fact_10_old_Opath2__not__Nil2,axiom,
% 0.19/0.44 ! [G: g,N: node,M: node] :
% 0.19/0.44 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ nil_node @ M ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_not_Nil2
% 0.19/0.44 thf(fact_11_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_hd_in_\<alpha>n
% 0.19/0.44 thf(fact_12_old_Opath2__hd__in__ns,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( member_node @ N @ ( set_node2 @ Ns ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_hd_in_ns
% 0.19/0.44 thf(fact_13_old_Opath2__in___092_060alpha_062n,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,L: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( member_node @ L @ ( set_node2 @ Ns ) )
% 0.19/0.44 => ( member_node @ L @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_in_\<alpha>n
% 0.19/0.44 thf(fact_14_old_Opath2__last__in__ns,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( member_node @ M @ ( set_node2 @ Ns ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_last_in_ns
% 0.19/0.44 thf(fact_15_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_tl_in_\<alpha>n
% 0.19/0.44 thf(fact_16_old_Opath2__forget__hd,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ Ns ) @ Ns @ M ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_forget_hd
% 0.19/0.44 thf(fact_17_old_Opath2__hd,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( N
% 0.19/0.44 = ( hd_node @ Ns ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_hd
% 0.19/0.44 thf(fact_18__092_060open_062ri_A_061_Atmp_A_064_A_091i_093_092_060close_062,axiom,
% 0.19/0.44 ( ri
% 0.19/0.44 = ( append_node @ tmp @ ( cons_node @ i @ nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % \<open>ri = tmp @ [i]\<close>
% 0.19/0.44 thf(fact_19__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H__rest_O_Ars_H_A_061_Ari_A_064_Ars_H__rest_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.19/0.44 ~ ! [Rs_rest: list_node] :
% 0.19/0.44 ( rs
% 0.19/0.44 != ( append_node @ ri @ Rs_rest ) ) ).
% 0.19/0.44
% 0.19/0.44 % \<open>\<And>thesis. (\<And>rs'_rest. rs' = ri @ rs'_rest \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.19/0.44 thf(fact_20_ri__props_I2_J,axiom,
% 0.19/0.44 member_node @ i @ ( set_node2 @ ms ) ).
% 0.19/0.44
% 0.19/0.44 % ri_props(2)
% 0.19/0.44 thf(fact_21_m__i__differ_I1_J,axiom,
% 0.19/0.44 ( i
% 0.19/0.44 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 0.19/0.44
% 0.19/0.44 % m_i_differ(1)
% 0.19/0.44 thf(fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tmp_O_Ari_A_061_Atmp_A_064_A_091i_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.19/0.44 ~ ! [Tmp: list_node] :
% 0.19/0.44 ( ri
% 0.19/0.44 != ( append_node @ Tmp @ ( cons_node @ i @ nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % \<open>\<And>thesis. (\<And>tmp. ri = tmp @ [i] \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.19/0.44 thf(fact_23_ri__props_I1_J,axiom,
% 0.19/0.44 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 0.19/0.44
% 0.19/0.44 % ri_props(1)
% 0.19/0.44 thf(fact_24_old_Opath2__split_I1_J,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 0.19/0.44 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ nil_node ) ) @ N2 ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_split(1)
% 0.19/0.44 thf(fact_25__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 0.19/0.44 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 0.19/0.44 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 0.19/0.44
% 0.19/0.44 % \<open>defNode g \<phi>\<^sub>r \<noteq> defNode g r\<close>
% 0.19/0.44 thf(fact_26__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.19/0.44 ( ( i
% 0.19/0.44 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.19/0.44 => ( ( ( i
% 0.19/0.44 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.19/0.44 => ( m != i ) )
% 0.19/0.44 => ~ ( ( i
% 0.19/0.44 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.19/0.44 => ( m = i ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % \<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>
% 0.19/0.44 thf(fact_27_old_Oempty__path2,axiom,
% 0.19/0.44 ! [N: node,G: g] :
% 0.19/0.44 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.44 => ( ( invar @ G )
% 0.19/0.44 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( cons_node @ N @ nil_node ) @ N ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.empty_path2
% 0.19/0.44 thf(fact_28_ms_H__props_I3_J,axiom,
% 0.19/0.44 ~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ms'_props(3)
% 0.19/0.44 thf(fact_29_assms_I10_J,axiom,
% 0.19/0.44 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 0.19/0.44
% 0.19/0.44 % assms(10)
% 0.19/0.44 thf(fact_30_rs_H__props_I4_J,axiom,
% 0.19/0.44 member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % rs'_props(4)
% 0.19/0.44 thf(fact_31_assms_I7_J,axiom,
% 0.19/0.44 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 0.19/0.44
% 0.19/0.44 % assms(7)
% 0.19/0.44 thf(fact_32_rs__props_I1_J,axiom,
% 0.19/0.44 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 0.19/0.44
% 0.19/0.44 % rs_props(1)
% 0.19/0.44 thf(fact_33_rs__def,axiom,
% 0.19/0.44 ( rs2
% 0.19/0.44 = ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % rs_def
% 0.19/0.44 thf(fact_34_assms_I8_J,axiom,
% 0.19/0.44 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 0.19/0.44
% 0.19/0.44 % assms(8)
% 0.19/0.44 thf(fact_35_rs_H__loopfree,axiom,
% 0.19/0.44 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % rs'_loopfree
% 0.19/0.44 thf(fact_36_hd__append2,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val] :
% 0.19/0.44 ( ( Xs != nil_val )
% 0.19/0.44 => ( ( hd_val @ ( append_val @ Xs @ Ys ) )
% 0.19/0.44 = ( hd_val @ Xs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % hd_append2
% 0.19/0.44 thf(fact_37_hd__append2,axiom,
% 0.19/0.44 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.19/0.44 ( ( Xs != nil_list_node )
% 0.19/0.44 => ( ( hd_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.19/0.44 = ( hd_list_node @ Xs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % hd_append2
% 0.19/0.44 thf(fact_38_hd__append2,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.44 ( ( Xs != nil_node )
% 0.19/0.44 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.19/0.44 = ( hd_node @ Xs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % hd_append2
% 0.19/0.44 thf(fact_39_append1__eq__conv,axiom,
% 0.19/0.44 ! [Xs: list_val,X: val,Ys: list_val,Y: val] :
% 0.19/0.44 ( ( ( append_val @ Xs @ ( cons_val @ X @ nil_val ) )
% 0.19/0.44 = ( append_val @ Ys @ ( cons_val @ Y @ nil_val ) ) )
% 0.19/0.44 = ( ( Xs = Ys )
% 0.19/0.44 & ( X = Y ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append1_eq_conv
% 0.19/0.44 thf(fact_40_append1__eq__conv,axiom,
% 0.19/0.44 ! [Xs: list_list_node,X: list_node,Ys: list_list_node,Y: list_node] :
% 0.19/0.44 ( ( ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) )
% 0.19/0.44 = ( append_list_node @ Ys @ ( cons_list_node @ Y @ nil_list_node ) ) )
% 0.19/0.44 = ( ( Xs = Ys )
% 0.19/0.44 & ( X = Y ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append1_eq_conv
% 0.19/0.44 thf(fact_41_append1__eq__conv,axiom,
% 0.19/0.44 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 0.19/0.44 ( ( ( append_node @ Xs @ ( cons_node @ X @ nil_node ) )
% 0.19/0.44 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.19/0.44 = ( ( Xs = Ys )
% 0.19/0.44 & ( X = Y ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append1_eq_conv
% 0.19/0.44 thf(fact_42_list__ee__eq__leel_I1_J,axiom,
% 0.19/0.44 ! [E1: val,E2: val,L1: list_val,E12: val,E22: val,L2: list_val] :
% 0.19/0.44 ( ( ( cons_val @ E1 @ ( cons_val @ E2 @ nil_val ) )
% 0.19/0.44 = ( append_val @ L1 @ ( cons_val @ E12 @ ( cons_val @ E22 @ L2 ) ) ) )
% 0.19/0.44 = ( ( L1 = nil_val )
% 0.19/0.44 & ( E1 = E12 )
% 0.19/0.44 & ( E2 = E22 )
% 0.19/0.44 & ( L2 = nil_val ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_ee_eq_leel(1)
% 0.19/0.44 thf(fact_43_list__ee__eq__leel_I1_J,axiom,
% 0.19/0.44 ! [E1: list_node,E2: list_node,L1: list_list_node,E12: list_node,E22: list_node,L2: list_list_node] :
% 0.19/0.44 ( ( ( cons_list_node @ E1 @ ( cons_list_node @ E2 @ nil_list_node ) )
% 0.19/0.44 = ( append_list_node @ L1 @ ( cons_list_node @ E12 @ ( cons_list_node @ E22 @ L2 ) ) ) )
% 0.19/0.44 = ( ( L1 = nil_list_node )
% 0.19/0.44 & ( E1 = E12 )
% 0.19/0.44 & ( E2 = E22 )
% 0.19/0.44 & ( L2 = nil_list_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_ee_eq_leel(1)
% 0.19/0.44 thf(fact_44_list__ee__eq__leel_I1_J,axiom,
% 0.19/0.44 ! [E1: node,E2: node,L1: list_node,E12: node,E22: node,L2: list_node] :
% 0.19/0.44 ( ( ( cons_node @ E1 @ ( cons_node @ E2 @ nil_node ) )
% 0.19/0.44 = ( append_node @ L1 @ ( cons_node @ E12 @ ( cons_node @ E22 @ L2 ) ) ) )
% 0.19/0.44 = ( ( L1 = nil_node )
% 0.19/0.44 & ( E1 = E12 )
% 0.19/0.44 & ( E2 = E22 )
% 0.19/0.44 & ( L2 = nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_ee_eq_leel(1)
% 0.19/0.44 thf(fact_45_list__ee__eq__leel_I2_J,axiom,
% 0.19/0.44 ! [L1: list_val,E12: val,E22: val,L2: list_val,E1: val,E2: val] :
% 0.19/0.44 ( ( ( append_val @ L1 @ ( cons_val @ E12 @ ( cons_val @ E22 @ L2 ) ) )
% 0.19/0.44 = ( cons_val @ E1 @ ( cons_val @ E2 @ nil_val ) ) )
% 0.19/0.44 = ( ( L1 = nil_val )
% 0.19/0.44 & ( E1 = E12 )
% 0.19/0.44 & ( E2 = E22 )
% 0.19/0.44 & ( L2 = nil_val ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_ee_eq_leel(2)
% 0.19/0.44 thf(fact_46_list__ee__eq__leel_I2_J,axiom,
% 0.19/0.44 ! [L1: list_list_node,E12: list_node,E22: list_node,L2: list_list_node,E1: list_node,E2: list_node] :
% 0.19/0.44 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E12 @ ( cons_list_node @ E22 @ L2 ) ) )
% 0.19/0.44 = ( cons_list_node @ E1 @ ( cons_list_node @ E2 @ nil_list_node ) ) )
% 0.19/0.44 = ( ( L1 = nil_list_node )
% 0.19/0.44 & ( E1 = E12 )
% 0.19/0.44 & ( E2 = E22 )
% 0.19/0.44 & ( L2 = nil_list_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_ee_eq_leel(2)
% 0.19/0.44 thf(fact_47_list__ee__eq__leel_I2_J,axiom,
% 0.19/0.44 ! [L1: list_node,E12: node,E22: node,L2: list_node,E1: node,E2: node] :
% 0.19/0.44 ( ( ( append_node @ L1 @ ( cons_node @ E12 @ ( cons_node @ E22 @ L2 ) ) )
% 0.19/0.44 = ( cons_node @ E1 @ ( cons_node @ E2 @ nil_node ) ) )
% 0.19/0.44 = ( ( L1 = nil_node )
% 0.19/0.44 & ( E1 = E12 )
% 0.19/0.44 & ( E2 = E22 )
% 0.19/0.44 & ( L2 = nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_ee_eq_leel(2)
% 0.19/0.44 thf(fact_48_list__se__match_I1_J,axiom,
% 0.19/0.44 ! [L1: list_val,L2: list_val,A: val] :
% 0.19/0.44 ( ( L1 != nil_val )
% 0.19/0.44 => ( ( ( append_val @ L1 @ L2 )
% 0.19/0.44 = ( cons_val @ A @ nil_val ) )
% 0.19/0.44 = ( ( L1
% 0.19/0.44 = ( cons_val @ A @ nil_val ) )
% 0.19/0.44 & ( L2 = nil_val ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(1)
% 0.19/0.44 thf(fact_49_list__se__match_I1_J,axiom,
% 0.19/0.44 ! [L1: list_list_node,L2: list_list_node,A: list_node] :
% 0.19/0.44 ( ( L1 != nil_list_node )
% 0.19/0.44 => ( ( ( append_list_node @ L1 @ L2 )
% 0.19/0.44 = ( cons_list_node @ A @ nil_list_node ) )
% 0.19/0.44 = ( ( L1
% 0.19/0.44 = ( cons_list_node @ A @ nil_list_node ) )
% 0.19/0.44 & ( L2 = nil_list_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(1)
% 0.19/0.44 thf(fact_50_list__se__match_I1_J,axiom,
% 0.19/0.44 ! [L1: list_node,L2: list_node,A: node] :
% 0.19/0.44 ( ( L1 != nil_node )
% 0.19/0.44 => ( ( ( append_node @ L1 @ L2 )
% 0.19/0.44 = ( cons_node @ A @ nil_node ) )
% 0.19/0.44 = ( ( L1
% 0.19/0.44 = ( cons_node @ A @ nil_node ) )
% 0.19/0.44 & ( L2 = nil_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(1)
% 0.19/0.44 thf(fact_51_ri__props_I3_J,axiom,
% 0.19/0.44 ! [X2: node] :
% 0.19/0.44 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ ri ) ) )
% 0.19/0.44 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % ri_props(3)
% 0.19/0.44 thf(fact_52_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.19/0.44 ! [X: list_node,Xs: list_list_node,Ys: list_list_node,Y: list_node] :
% 0.19/0.44 ( ( member_list_node @ X @ ( set_list_node2 @ Xs ) )
% 0.19/0.44 => ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ ( append_list_node @ Ys @ ( cons_list_node @ Y @ Xs ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.elem_set_implies_elem_tl_app_cons
% 0.19/0.44 thf(fact_53_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.19/0.44 ! [X: val,Xs: list_val,Ys: list_val,Y: val] :
% 0.19/0.44 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.44 => ( member_val @ X @ ( set_val2 @ ( tl_val @ ( append_val @ Ys @ ( cons_val @ Y @ Xs ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.elem_set_implies_elem_tl_app_cons
% 0.19/0.44 thf(fact_54_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.19/0.44 ! [X: node,Xs: list_node,Ys: list_node,Y: node] :
% 0.19/0.44 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.44 => ( member_node @ X @ ( set_node2 @ ( tl_node @ ( append_node @ Ys @ ( cons_node @ Y @ Xs ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.elem_set_implies_elem_tl_app_cons
% 0.19/0.44 thf(fact_55_list_Oinject,axiom,
% 0.19/0.44 ! [X21: val,X22: list_val,Y21: val,Y22: list_val] :
% 0.19/0.44 ( ( ( cons_val @ X21 @ X22 )
% 0.19/0.44 = ( cons_val @ Y21 @ Y22 ) )
% 0.19/0.44 = ( ( X21 = Y21 )
% 0.19/0.44 & ( X22 = Y22 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.inject
% 0.19/0.44 thf(fact_56_list_Oinject,axiom,
% 0.19/0.44 ! [X21: list_node,X22: list_list_node,Y21: list_node,Y22: list_list_node] :
% 0.19/0.44 ( ( ( cons_list_node @ X21 @ X22 )
% 0.19/0.44 = ( cons_list_node @ Y21 @ Y22 ) )
% 0.19/0.44 = ( ( X21 = Y21 )
% 0.19/0.44 & ( X22 = Y22 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.inject
% 0.19/0.44 thf(fact_57_list_Oinject,axiom,
% 0.19/0.44 ! [X21: node,X22: list_node,Y21: node,Y22: list_node] :
% 0.19/0.44 ( ( ( cons_node @ X21 @ X22 )
% 0.19/0.44 = ( cons_node @ Y21 @ Y22 ) )
% 0.19/0.44 = ( ( X21 = Y21 )
% 0.19/0.44 & ( X22 = Y22 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.inject
% 0.19/0.44 thf(fact_58_same__append__eq,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 0.19/0.44 ( ( ( append_val @ Xs @ Ys )
% 0.19/0.44 = ( append_val @ Xs @ Zs ) )
% 0.19/0.44 = ( Ys = Zs ) ) ).
% 0.19/0.44
% 0.19/0.44 % same_append_eq
% 0.19/0.44 thf(fact_59_same__append__eq,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.19/0.44 ( ( ( append_node @ Xs @ Ys )
% 0.19/0.44 = ( append_node @ Xs @ Zs ) )
% 0.19/0.44 = ( Ys = Zs ) ) ).
% 0.19/0.44
% 0.19/0.44 % same_append_eq
% 0.19/0.44 thf(fact_60_mem__Collect__eq,axiom,
% 0.19/0.44 ! [A: val,P: val > $o] :
% 0.19/0.44 ( ( member_val @ A @ ( collect_val @ P ) )
% 0.19/0.44 = ( P @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % mem_Collect_eq
% 0.19/0.44 thf(fact_61_mem__Collect__eq,axiom,
% 0.19/0.44 ! [A: node,P: node > $o] :
% 0.19/0.44 ( ( member_node @ A @ ( collect_node @ P ) )
% 0.19/0.44 = ( P @ A ) ) ).
% 0.19/0.44
% 0.19/0.44 % mem_Collect_eq
% 0.19/0.44 thf(fact_62_Collect__mem__eq,axiom,
% 0.19/0.44 ! [A2: set_val] :
% 0.19/0.44 ( ( collect_val
% 0.19/0.44 @ ^ [X3: val] : ( member_val @ X3 @ A2 ) )
% 0.19/0.44 = A2 ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mem_eq
% 0.19/0.44 thf(fact_63_Collect__mem__eq,axiom,
% 0.19/0.44 ! [A2: set_node] :
% 0.19/0.44 ( ( collect_node
% 0.19/0.44 @ ^ [X3: node] : ( member_node @ X3 @ A2 ) )
% 0.19/0.44 = A2 ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_mem_eq
% 0.19/0.44 thf(fact_64_Collect__cong,axiom,
% 0.19/0.44 ! [P: node > $o,Q: node > $o] :
% 0.19/0.44 ( ! [X4: node] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 = ( Q @ X4 ) )
% 0.19/0.44 => ( ( collect_node @ P )
% 0.19/0.44 = ( collect_node @ Q ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_cong
% 0.19/0.44 thf(fact_65_Collect__cong,axiom,
% 0.19/0.44 ! [P: val > $o,Q: val > $o] :
% 0.19/0.44 ( ! [X4: val] :
% 0.19/0.44 ( ( P @ X4 )
% 0.19/0.44 = ( Q @ X4 ) )
% 0.19/0.44 => ( ( collect_val @ P )
% 0.19/0.44 = ( collect_val @ Q ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Collect_cong
% 0.19/0.44 thf(fact_66_append__same__eq,axiom,
% 0.19/0.44 ! [Ys: list_val,Xs: list_val,Zs: list_val] :
% 0.19/0.44 ( ( ( append_val @ Ys @ Xs )
% 0.19/0.44 = ( append_val @ Zs @ Xs ) )
% 0.19/0.44 = ( Ys = Zs ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_same_eq
% 0.19/0.44 thf(fact_67_append__same__eq,axiom,
% 0.19/0.44 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.19/0.44 ( ( ( append_node @ Ys @ Xs )
% 0.19/0.44 = ( append_node @ Zs @ Xs ) )
% 0.19/0.44 = ( Ys = Zs ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_same_eq
% 0.19/0.44 thf(fact_68_append__assoc,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 0.19/0.44 ( ( append_val @ ( append_val @ Xs @ Ys ) @ Zs )
% 0.19/0.44 = ( append_val @ Xs @ ( append_val @ Ys @ Zs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_assoc
% 0.19/0.44 thf(fact_69_append__assoc,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.19/0.44 ( ( append_node @ ( append_node @ Xs @ Ys ) @ Zs )
% 0.19/0.44 = ( append_node @ Xs @ ( append_node @ Ys @ Zs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_assoc
% 0.19/0.44 thf(fact_70_append_Oassoc,axiom,
% 0.19/0.44 ! [A: list_val,B: list_val,C: list_val] :
% 0.19/0.44 ( ( append_val @ ( append_val @ A @ B ) @ C )
% 0.19/0.44 = ( append_val @ A @ ( append_val @ B @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append.assoc
% 0.19/0.44 thf(fact_71_append_Oassoc,axiom,
% 0.19/0.44 ! [A: list_node,B: list_node,C: list_node] :
% 0.19/0.44 ( ( append_node @ ( append_node @ A @ B ) @ C )
% 0.19/0.44 = ( append_node @ A @ ( append_node @ B @ C ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append.assoc
% 0.19/0.44 thf(fact_72_old_Opredecessor__is__node,axiom,
% 0.19/0.44 ! [N: node,G: g,N2: node] :
% 0.19/0.44 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 0.19/0.44 => ( ( invar @ G )
% 0.19/0.44 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.predecessor_is_node
% 0.19/0.44 thf(fact_73_old_Osuccessor__is__node,axiom,
% 0.19/0.44 ! [N: node,G: g,N2: node] :
% 0.19/0.44 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 0.19/0.44 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.44 => ( ( invar @ G )
% 0.19/0.44 => ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.successor_is_node
% 0.19/0.44 thf(fact_74_old_Osuccessor__in___092_060alpha_062n,axiom,
% 0.19/0.44 ! [G: g,N: node] :
% 0.19/0.44 ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 0.19/0.44 != nil_node )
% 0.19/0.44 => ( ( invar @ G )
% 0.19/0.44 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.successor_in_\<alpha>n
% 0.19/0.44 thf(fact_75_old_Opath2__app_H,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 0.19/0.44 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ ( butlast_node @ Ns ) @ Ms ) @ L ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_app'
% 0.19/0.44 thf(fact_76_old_Opath2__app,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 0.19/0.44 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( tl_node @ Ms ) ) @ L ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_app
% 0.19/0.44 thf(fact_77_append_Oright__neutral,axiom,
% 0.19/0.44 ! [A: list_val] :
% 0.19/0.44 ( ( append_val @ A @ nil_val )
% 0.19/0.44 = A ) ).
% 0.19/0.44
% 0.19/0.44 % append.right_neutral
% 0.19/0.44 thf(fact_78_append_Oright__neutral,axiom,
% 0.19/0.44 ! [A: list_list_node] :
% 0.19/0.44 ( ( append_list_node @ A @ nil_list_node )
% 0.19/0.44 = A ) ).
% 0.19/0.44
% 0.19/0.44 % append.right_neutral
% 0.19/0.44 thf(fact_79_append_Oright__neutral,axiom,
% 0.19/0.44 ! [A: list_node] :
% 0.19/0.44 ( ( append_node @ A @ nil_node )
% 0.19/0.44 = A ) ).
% 0.19/0.44
% 0.19/0.44 % append.right_neutral
% 0.19/0.44 thf(fact_80_empty__append__eq__id,axiom,
% 0.19/0.44 ( ( append_val @ nil_val )
% 0.19/0.44 = ( ^ [X3: list_val] : X3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % empty_append_eq_id
% 0.19/0.44 thf(fact_81_empty__append__eq__id,axiom,
% 0.19/0.44 ( ( append_list_node @ nil_list_node )
% 0.19/0.44 = ( ^ [X3: list_list_node] : X3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % empty_append_eq_id
% 0.19/0.44 thf(fact_82_empty__append__eq__id,axiom,
% 0.19/0.44 ( ( append_node @ nil_node )
% 0.19/0.44 = ( ^ [X3: list_node] : X3 ) ) ).
% 0.19/0.44
% 0.19/0.44 % empty_append_eq_id
% 0.19/0.44 thf(fact_83_append__is__Nil__conv,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val] :
% 0.19/0.44 ( ( ( append_val @ Xs @ Ys )
% 0.19/0.44 = nil_val )
% 0.19/0.44 = ( ( Xs = nil_val )
% 0.19/0.44 & ( Ys = nil_val ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_is_Nil_conv
% 0.19/0.44 thf(fact_84_append__is__Nil__conv,axiom,
% 0.19/0.44 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.19/0.44 ( ( ( append_list_node @ Xs @ Ys )
% 0.19/0.44 = nil_list_node )
% 0.19/0.44 = ( ( Xs = nil_list_node )
% 0.19/0.44 & ( Ys = nil_list_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_is_Nil_conv
% 0.19/0.44 thf(fact_85_append__is__Nil__conv,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.44 ( ( ( append_node @ Xs @ Ys )
% 0.19/0.44 = nil_node )
% 0.19/0.44 = ( ( Xs = nil_node )
% 0.19/0.44 & ( Ys = nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_is_Nil_conv
% 0.19/0.44 thf(fact_86_Nil__is__append__conv,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val] :
% 0.19/0.44 ( ( nil_val
% 0.19/0.44 = ( append_val @ Xs @ Ys ) )
% 0.19/0.44 = ( ( Xs = nil_val )
% 0.19/0.44 & ( Ys = nil_val ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Nil_is_append_conv
% 0.19/0.44 thf(fact_87_Nil__is__append__conv,axiom,
% 0.19/0.44 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.19/0.44 ( ( nil_list_node
% 0.19/0.44 = ( append_list_node @ Xs @ Ys ) )
% 0.19/0.44 = ( ( Xs = nil_list_node )
% 0.19/0.44 & ( Ys = nil_list_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Nil_is_append_conv
% 0.19/0.44 thf(fact_88_Nil__is__append__conv,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.44 ( ( nil_node
% 0.19/0.44 = ( append_node @ Xs @ Ys ) )
% 0.19/0.44 = ( ( Xs = nil_node )
% 0.19/0.44 & ( Ys = nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Nil_is_append_conv
% 0.19/0.44 thf(fact_89_self__append__conv2,axiom,
% 0.19/0.44 ! [Ys: list_val,Xs: list_val] :
% 0.19/0.44 ( ( Ys
% 0.19/0.44 = ( append_val @ Xs @ Ys ) )
% 0.19/0.44 = ( Xs = nil_val ) ) ).
% 0.19/0.44
% 0.19/0.44 % self_append_conv2
% 0.19/0.44 thf(fact_90_self__append__conv2,axiom,
% 0.19/0.44 ! [Ys: list_list_node,Xs: list_list_node] :
% 0.19/0.44 ( ( Ys
% 0.19/0.44 = ( append_list_node @ Xs @ Ys ) )
% 0.19/0.44 = ( Xs = nil_list_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % self_append_conv2
% 0.19/0.44 thf(fact_91_self__append__conv2,axiom,
% 0.19/0.44 ! [Ys: list_node,Xs: list_node] :
% 0.19/0.44 ( ( Ys
% 0.19/0.44 = ( append_node @ Xs @ Ys ) )
% 0.19/0.44 = ( Xs = nil_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % self_append_conv2
% 0.19/0.44 thf(fact_92_append__self__conv2,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val] :
% 0.19/0.44 ( ( ( append_val @ Xs @ Ys )
% 0.19/0.44 = Ys )
% 0.19/0.44 = ( Xs = nil_val ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_self_conv2
% 0.19/0.44 thf(fact_93_append__self__conv2,axiom,
% 0.19/0.44 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.19/0.44 ( ( ( append_list_node @ Xs @ Ys )
% 0.19/0.44 = Ys )
% 0.19/0.44 = ( Xs = nil_list_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_self_conv2
% 0.19/0.44 thf(fact_94_append__self__conv2,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.44 ( ( ( append_node @ Xs @ Ys )
% 0.19/0.44 = Ys )
% 0.19/0.44 = ( Xs = nil_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_self_conv2
% 0.19/0.44 thf(fact_95_self__append__conv,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val] :
% 0.19/0.44 ( ( Xs
% 0.19/0.44 = ( append_val @ Xs @ Ys ) )
% 0.19/0.44 = ( Ys = nil_val ) ) ).
% 0.19/0.44
% 0.19/0.44 % self_append_conv
% 0.19/0.44 thf(fact_96_self__append__conv,axiom,
% 0.19/0.44 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.19/0.44 ( ( Xs
% 0.19/0.44 = ( append_list_node @ Xs @ Ys ) )
% 0.19/0.44 = ( Ys = nil_list_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % self_append_conv
% 0.19/0.44 thf(fact_97_self__append__conv,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.44 ( ( Xs
% 0.19/0.44 = ( append_node @ Xs @ Ys ) )
% 0.19/0.44 = ( Ys = nil_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % self_append_conv
% 0.19/0.44 thf(fact_98_append__self__conv,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val] :
% 0.19/0.44 ( ( ( append_val @ Xs @ Ys )
% 0.19/0.44 = Xs )
% 0.19/0.44 = ( Ys = nil_val ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_self_conv
% 0.19/0.44 thf(fact_99_append__self__conv,axiom,
% 0.19/0.44 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.19/0.44 ( ( ( append_list_node @ Xs @ Ys )
% 0.19/0.44 = Xs )
% 0.19/0.44 = ( Ys = nil_list_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_self_conv
% 0.19/0.44 thf(fact_100_append__self__conv,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.44 ( ( ( append_node @ Xs @ Ys )
% 0.19/0.44 = Xs )
% 0.19/0.44 = ( Ys = nil_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_self_conv
% 0.19/0.44 thf(fact_101_append__Nil2,axiom,
% 0.19/0.44 ! [Xs: list_val] :
% 0.19/0.44 ( ( append_val @ Xs @ nil_val )
% 0.19/0.44 = Xs ) ).
% 0.19/0.44
% 0.19/0.44 % append_Nil2
% 0.19/0.44 thf(fact_102_append__Nil2,axiom,
% 0.19/0.44 ! [Xs: list_list_node] :
% 0.19/0.44 ( ( append_list_node @ Xs @ nil_list_node )
% 0.19/0.44 = Xs ) ).
% 0.19/0.44
% 0.19/0.44 % append_Nil2
% 0.19/0.44 thf(fact_103_append__Nil2,axiom,
% 0.19/0.44 ! [Xs: list_node] :
% 0.19/0.44 ( ( append_node @ Xs @ nil_node )
% 0.19/0.44 = Xs ) ).
% 0.19/0.44
% 0.19/0.44 % append_Nil2
% 0.19/0.44 thf(fact_104_old_Opath2__split__ex_H,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.19/0.44 => ~ ! [Ns_1: list_node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 0.19/0.44 => ! [Ns_2: list_node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 0.19/0.44 => ( Ns
% 0.19/0.44 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_split_ex'
% 0.19/0.44 thf(fact_105_old_Opath2__induct,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( ( invar @ G )
% 0.19/0.44 => ( P @ M @ ( cons_node @ M @ nil_node ) @ M ) )
% 0.19/0.44 => ( ! [Ns3: list_node,N3: node,N4: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N4 @ Ns3 @ M )
% 0.19/0.44 => ( ( P @ N4 @ Ns3 @ M )
% 0.19/0.44 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N4 ) ) )
% 0.19/0.44 => ( P @ N3 @ ( cons_node @ N3 @ Ns3 ) @ M ) ) ) )
% 0.19/0.44 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_induct
% 0.19/0.44 thf(fact_106_old_Opath2__split__ex,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.19/0.44 => ~ ! [Ns_1: list_node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 0.19/0.44 => ! [Ns_2: list_node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 0.19/0.44 => ( ( Ns
% 0.19/0.44 = ( append_node @ Ns_1 @ ( tl_node @ Ns_2 ) ) )
% 0.19/0.44 => ( Ns
% 0.19/0.44 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_split_ex
% 0.19/0.44 thf(fact_107_old_Opath2__rev__induct,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.44 => ( P @ N @ ( cons_node @ N @ nil_node ) @ N ) )
% 0.19/0.44 => ( ! [Ns3: list_node,M2: node,M3: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ M2 )
% 0.19/0.44 => ( ( P @ N @ Ns3 @ M2 )
% 0.19/0.44 => ( ( member_node @ M2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M3 ) ) )
% 0.19/0.44 => ( P @ N @ ( append_node @ Ns3 @ ( cons_node @ M3 @ nil_node ) ) @ M3 ) ) ) )
% 0.19/0.44 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_rev_induct
% 0.19/0.44 thf(fact_108_old_Opath2__snoc,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,M4: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M4 ) ) )
% 0.19/0.44 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ M4 @ nil_node ) ) @ M4 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_snoc
% 0.19/0.44 thf(fact_109_list__e__eq__lel_I2_J,axiom,
% 0.19/0.44 ! [L1: list_val,E: val,L2: list_val,E3: val] :
% 0.19/0.44 ( ( ( append_val @ L1 @ ( cons_val @ E @ L2 ) )
% 0.19/0.44 = ( cons_val @ E3 @ nil_val ) )
% 0.19/0.44 = ( ( L1 = nil_val )
% 0.19/0.44 & ( E = E3 )
% 0.19/0.44 & ( L2 = nil_val ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_e_eq_lel(2)
% 0.19/0.44 thf(fact_110_list__e__eq__lel_I2_J,axiom,
% 0.19/0.44 ! [L1: list_list_node,E: list_node,L2: list_list_node,E3: list_node] :
% 0.19/0.44 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) )
% 0.19/0.44 = ( cons_list_node @ E3 @ nil_list_node ) )
% 0.19/0.44 = ( ( L1 = nil_list_node )
% 0.19/0.44 & ( E = E3 )
% 0.19/0.44 & ( L2 = nil_list_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_e_eq_lel(2)
% 0.19/0.44 thf(fact_111_list__e__eq__lel_I2_J,axiom,
% 0.19/0.44 ! [L1: list_node,E: node,L2: list_node,E3: node] :
% 0.19/0.44 ( ( ( append_node @ L1 @ ( cons_node @ E @ L2 ) )
% 0.19/0.44 = ( cons_node @ E3 @ nil_node ) )
% 0.19/0.44 = ( ( L1 = nil_node )
% 0.19/0.44 & ( E = E3 )
% 0.19/0.44 & ( L2 = nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_e_eq_lel(2)
% 0.19/0.44 thf(fact_112_list__e__eq__lel_I1_J,axiom,
% 0.19/0.44 ! [E3: val,L1: list_val,E: val,L2: list_val] :
% 0.19/0.44 ( ( ( cons_val @ E3 @ nil_val )
% 0.19/0.44 = ( append_val @ L1 @ ( cons_val @ E @ L2 ) ) )
% 0.19/0.44 = ( ( L1 = nil_val )
% 0.19/0.44 & ( E = E3 )
% 0.19/0.44 & ( L2 = nil_val ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_e_eq_lel(1)
% 0.19/0.44 thf(fact_113_list__e__eq__lel_I1_J,axiom,
% 0.19/0.44 ! [E3: list_node,L1: list_list_node,E: list_node,L2: list_list_node] :
% 0.19/0.44 ( ( ( cons_list_node @ E3 @ nil_list_node )
% 0.19/0.44 = ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) ) )
% 0.19/0.44 = ( ( L1 = nil_list_node )
% 0.19/0.44 & ( E = E3 )
% 0.19/0.44 & ( L2 = nil_list_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_e_eq_lel(1)
% 0.19/0.44 thf(fact_114_list__e__eq__lel_I1_J,axiom,
% 0.19/0.44 ! [E3: node,L1: list_node,E: node,L2: list_node] :
% 0.19/0.44 ( ( ( cons_node @ E3 @ nil_node )
% 0.19/0.44 = ( append_node @ L1 @ ( cons_node @ E @ L2 ) ) )
% 0.19/0.44 = ( ( L1 = nil_node )
% 0.19/0.44 & ( E = E3 )
% 0.19/0.44 & ( L2 = nil_node ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_e_eq_lel(1)
% 0.19/0.44 thf(fact_115_list__se__match_I4_J,axiom,
% 0.19/0.44 ! [L2: list_val,A: val,L1: list_val] :
% 0.19/0.44 ( ( L2 != nil_val )
% 0.19/0.44 => ( ( ( cons_val @ A @ nil_val )
% 0.19/0.44 = ( append_val @ L1 @ L2 ) )
% 0.19/0.44 = ( ( L1 = nil_val )
% 0.19/0.44 & ( L2
% 0.19/0.44 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(4)
% 0.19/0.44 thf(fact_116_list__se__match_I4_J,axiom,
% 0.19/0.44 ! [L2: list_list_node,A: list_node,L1: list_list_node] :
% 0.19/0.44 ( ( L2 != nil_list_node )
% 0.19/0.44 => ( ( ( cons_list_node @ A @ nil_list_node )
% 0.19/0.44 = ( append_list_node @ L1 @ L2 ) )
% 0.19/0.44 = ( ( L1 = nil_list_node )
% 0.19/0.44 & ( L2
% 0.19/0.44 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(4)
% 0.19/0.44 thf(fact_117_list__se__match_I4_J,axiom,
% 0.19/0.44 ! [L2: list_node,A: node,L1: list_node] :
% 0.19/0.44 ( ( L2 != nil_node )
% 0.19/0.44 => ( ( ( cons_node @ A @ nil_node )
% 0.19/0.44 = ( append_node @ L1 @ L2 ) )
% 0.19/0.44 = ( ( L1 = nil_node )
% 0.19/0.44 & ( L2
% 0.19/0.44 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(4)
% 0.19/0.44 thf(fact_118_list__se__match_I3_J,axiom,
% 0.19/0.44 ! [L1: list_val,A: val,L2: list_val] :
% 0.19/0.44 ( ( L1 != nil_val )
% 0.19/0.44 => ( ( ( cons_val @ A @ nil_val )
% 0.19/0.44 = ( append_val @ L1 @ L2 ) )
% 0.19/0.44 = ( ( L1
% 0.19/0.44 = ( cons_val @ A @ nil_val ) )
% 0.19/0.44 & ( L2 = nil_val ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(3)
% 0.19/0.44 thf(fact_119_list__se__match_I3_J,axiom,
% 0.19/0.44 ! [L1: list_list_node,A: list_node,L2: list_list_node] :
% 0.19/0.44 ( ( L1 != nil_list_node )
% 0.19/0.44 => ( ( ( cons_list_node @ A @ nil_list_node )
% 0.19/0.44 = ( append_list_node @ L1 @ L2 ) )
% 0.19/0.44 = ( ( L1
% 0.19/0.44 = ( cons_list_node @ A @ nil_list_node ) )
% 0.19/0.44 & ( L2 = nil_list_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(3)
% 0.19/0.44 thf(fact_120_list__se__match_I3_J,axiom,
% 0.19/0.44 ! [L1: list_node,A: node,L2: list_node] :
% 0.19/0.44 ( ( L1 != nil_node )
% 0.19/0.44 => ( ( ( cons_node @ A @ nil_node )
% 0.19/0.44 = ( append_node @ L1 @ L2 ) )
% 0.19/0.44 = ( ( L1
% 0.19/0.44 = ( cons_node @ A @ nil_node ) )
% 0.19/0.44 & ( L2 = nil_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(3)
% 0.19/0.44 thf(fact_121_list__se__match_I2_J,axiom,
% 0.19/0.44 ! [L2: list_val,L1: list_val,A: val] :
% 0.19/0.44 ( ( L2 != nil_val )
% 0.19/0.44 => ( ( ( append_val @ L1 @ L2 )
% 0.19/0.44 = ( cons_val @ A @ nil_val ) )
% 0.19/0.44 = ( ( L1 = nil_val )
% 0.19/0.44 & ( L2
% 0.19/0.44 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(2)
% 0.19/0.44 thf(fact_122_list__se__match_I2_J,axiom,
% 0.19/0.44 ! [L2: list_list_node,L1: list_list_node,A: list_node] :
% 0.19/0.44 ( ( L2 != nil_list_node )
% 0.19/0.44 => ( ( ( append_list_node @ L1 @ L2 )
% 0.19/0.44 = ( cons_list_node @ A @ nil_list_node ) )
% 0.19/0.44 = ( ( L1 = nil_list_node )
% 0.19/0.44 & ( L2
% 0.19/0.44 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(2)
% 0.19/0.44 thf(fact_123_list__se__match_I2_J,axiom,
% 0.19/0.44 ! [L2: list_node,L1: list_node,A: node] :
% 0.19/0.44 ( ( L2 != nil_node )
% 0.19/0.44 => ( ( ( append_node @ L1 @ L2 )
% 0.19/0.44 = ( cons_node @ A @ nil_node ) )
% 0.19/0.44 = ( ( L1 = nil_node )
% 0.19/0.44 & ( L2
% 0.19/0.44 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_se_match(2)
% 0.19/0.44 thf(fact_124_tl__append2,axiom,
% 0.19/0.44 ! [Xs: list_val,Ys: list_val] :
% 0.19/0.44 ( ( Xs != nil_val )
% 0.19/0.44 => ( ( tl_val @ ( append_val @ Xs @ Ys ) )
% 0.19/0.44 = ( append_val @ ( tl_val @ Xs ) @ Ys ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_append2
% 0.19/0.44 thf(fact_125_tl__append2,axiom,
% 0.19/0.44 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.19/0.44 ( ( Xs != nil_list_node )
% 0.19/0.44 => ( ( tl_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.19/0.44 = ( append_list_node @ ( tl_list_node @ Xs ) @ Ys ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_append2
% 0.19/0.44 thf(fact_126_tl__append2,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.44 ( ( Xs != nil_node )
% 0.19/0.44 => ( ( tl_node @ ( append_node @ Xs @ Ys ) )
% 0.19/0.44 = ( append_node @ ( tl_node @ Xs ) @ Ys ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_append2
% 0.19/0.44 thf(fact_127_old_Opath2__cases,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( ( Ns
% 0.19/0.44 = ( cons_node @ N @ nil_node ) )
% 0.19/0.44 => ( M != N ) )
% 0.19/0.44 => ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) @ ( tl_node @ Ns ) @ M )
% 0.19/0.44 => ~ ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.path2_cases
% 0.19/0.44 thf(fact_128_rs__props_I3_J,axiom,
% 0.19/0.44 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % rs_props(3)
% 0.19/0.44 thf(fact_129_butlast__snoc,axiom,
% 0.19/0.44 ! [Xs: list_val,X: val] :
% 0.19/0.44 ( ( butlast_val @ ( append_val @ Xs @ ( cons_val @ X @ nil_val ) ) )
% 0.19/0.44 = Xs ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_snoc
% 0.19/0.44 thf(fact_130_butlast__snoc,axiom,
% 0.19/0.44 ! [Xs: list_list_node,X: list_node] :
% 0.19/0.44 ( ( butlast_list_node @ ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) ) )
% 0.19/0.44 = Xs ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_snoc
% 0.19/0.44 thf(fact_131_butlast__snoc,axiom,
% 0.19/0.44 ! [Xs: list_node,X: node] :
% 0.19/0.44 ( ( butlast_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) )
% 0.19/0.44 = Xs ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_snoc
% 0.19/0.44 thf(fact_132_list_Ocollapse,axiom,
% 0.19/0.44 ! [List: list_val] :
% 0.19/0.44 ( ( List != nil_val )
% 0.19/0.44 => ( ( cons_val @ ( hd_val @ List ) @ ( tl_val @ List ) )
% 0.19/0.44 = List ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.collapse
% 0.19/0.44 thf(fact_133_list_Ocollapse,axiom,
% 0.19/0.44 ! [List: list_list_node] :
% 0.19/0.44 ( ( List != nil_list_node )
% 0.19/0.44 => ( ( cons_list_node @ ( hd_list_node @ List ) @ ( tl_list_node @ List ) )
% 0.19/0.44 = List ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.collapse
% 0.19/0.44 thf(fact_134_list_Ocollapse,axiom,
% 0.19/0.44 ! [List: list_node] :
% 0.19/0.44 ( ( List != nil_node )
% 0.19/0.44 => ( ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) )
% 0.19/0.44 = List ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.collapse
% 0.19/0.44 thf(fact_135_hd__Cons__tl,axiom,
% 0.19/0.44 ! [Xs: list_val] :
% 0.19/0.44 ( ( Xs != nil_val )
% 0.19/0.44 => ( ( cons_val @ ( hd_val @ Xs ) @ ( tl_val @ Xs ) )
% 0.19/0.44 = Xs ) ) ).
% 0.19/0.44
% 0.19/0.44 % hd_Cons_tl
% 0.19/0.44 thf(fact_136_hd__Cons__tl,axiom,
% 0.19/0.44 ! [Xs: list_list_node] :
% 0.19/0.44 ( ( Xs != nil_list_node )
% 0.19/0.44 => ( ( cons_list_node @ ( hd_list_node @ Xs ) @ ( tl_list_node @ Xs ) )
% 0.19/0.44 = Xs ) ) ).
% 0.19/0.44
% 0.19/0.44 % hd_Cons_tl
% 0.19/0.44 thf(fact_137_hd__Cons__tl,axiom,
% 0.19/0.44 ! [Xs: list_node] :
% 0.19/0.44 ( ( Xs != nil_node )
% 0.19/0.44 => ( ( cons_node @ ( hd_node @ Xs ) @ ( tl_node @ Xs ) )
% 0.19/0.44 = Xs ) ) ).
% 0.19/0.44
% 0.19/0.44 % hd_Cons_tl
% 0.19/0.44 thf(fact_138_in__hd__or__tl__conv,axiom,
% 0.19/0.44 ! [L: list_list_node,X: list_node] :
% 0.19/0.44 ( ( L != nil_list_node )
% 0.19/0.44 => ( ( ( X
% 0.19/0.44 = ( hd_list_node @ L ) )
% 0.19/0.44 | ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ L ) ) ) )
% 0.19/0.44 = ( member_list_node @ X @ ( set_list_node2 @ L ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_hd_or_tl_conv
% 0.19/0.44 thf(fact_139_in__hd__or__tl__conv,axiom,
% 0.19/0.44 ! [L: list_val,X: val] :
% 0.19/0.44 ( ( L != nil_val )
% 0.19/0.44 => ( ( ( X
% 0.19/0.44 = ( hd_val @ L ) )
% 0.19/0.44 | ( member_val @ X @ ( set_val2 @ ( tl_val @ L ) ) ) )
% 0.19/0.44 = ( member_val @ X @ ( set_val2 @ L ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_hd_or_tl_conv
% 0.19/0.44 thf(fact_140_in__hd__or__tl__conv,axiom,
% 0.19/0.44 ! [L: list_node,X: node] :
% 0.19/0.44 ( ( L != nil_node )
% 0.19/0.44 => ( ( ( X
% 0.19/0.44 = ( hd_node @ L ) )
% 0.19/0.44 | ( member_node @ X @ ( set_node2 @ ( tl_node @ L ) ) ) )
% 0.19/0.44 = ( member_node @ X @ ( set_node2 @ L ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_hd_or_tl_conv
% 0.19/0.44 thf(fact_141_ri__props_I4_J,axiom,
% 0.19/0.44 prefix_node @ ri @ rs2 ).
% 0.19/0.44
% 0.19/0.44 % ri_props(4)
% 0.19/0.44 thf(fact_142_ms_H__props_I2_J,axiom,
% 0.19/0.44 prefix_node @ ms2 @ ms ).
% 0.19/0.44
% 0.19/0.44 % ms'_props(2)
% 0.19/0.44 thf(fact_143_old_OCons__path2,axiom,
% 0.19/0.44 ! [G: g,N: node,Ns: list_node,M: node,N2: node] :
% 0.19/0.44 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.44 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 0.19/0.44 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns ) @ M ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % old.Cons_path2
% 0.19/0.44 thf(fact_144_butlast__tl,axiom,
% 0.19/0.44 ! [Xs: list_val] :
% 0.19/0.44 ( ( butlast_val @ ( tl_val @ Xs ) )
% 0.19/0.44 = ( tl_val @ ( butlast_val @ Xs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_tl
% 0.19/0.44 thf(fact_145_butlast__tl,axiom,
% 0.19/0.44 ! [Xs: list_node] :
% 0.19/0.44 ( ( butlast_node @ ( tl_node @ Xs ) )
% 0.19/0.44 = ( tl_node @ ( butlast_node @ Xs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_tl
% 0.19/0.44 thf(fact_146_butlast_Osimps_I1_J,axiom,
% 0.19/0.44 ( ( butlast_val @ nil_val )
% 0.19/0.44 = nil_val ) ).
% 0.19/0.44
% 0.19/0.44 % butlast.simps(1)
% 0.19/0.44 thf(fact_147_butlast_Osimps_I1_J,axiom,
% 0.19/0.44 ( ( butlast_list_node @ nil_list_node )
% 0.19/0.44 = nil_list_node ) ).
% 0.19/0.44
% 0.19/0.44 % butlast.simps(1)
% 0.19/0.44 thf(fact_148_butlast_Osimps_I1_J,axiom,
% 0.19/0.44 ( ( butlast_node @ nil_node )
% 0.19/0.44 = nil_node ) ).
% 0.19/0.44
% 0.19/0.44 % butlast.simps(1)
% 0.19/0.44 thf(fact_149_list_Osel_I3_J,axiom,
% 0.19/0.44 ! [X21: val,X22: list_val] :
% 0.19/0.44 ( ( tl_val @ ( cons_val @ X21 @ X22 ) )
% 0.19/0.44 = X22 ) ).
% 0.19/0.44
% 0.19/0.44 % list.sel(3)
% 0.19/0.44 thf(fact_150_list_Osel_I3_J,axiom,
% 0.19/0.44 ! [X21: list_node,X22: list_list_node] :
% 0.19/0.44 ( ( tl_list_node @ ( cons_list_node @ X21 @ X22 ) )
% 0.19/0.44 = X22 ) ).
% 0.19/0.44
% 0.19/0.44 % list.sel(3)
% 0.19/0.44 thf(fact_151_list_Osel_I3_J,axiom,
% 0.19/0.44 ! [X21: node,X22: list_node] :
% 0.19/0.44 ( ( tl_node @ ( cons_node @ X21 @ X22 ) )
% 0.19/0.44 = X22 ) ).
% 0.19/0.44
% 0.19/0.44 % list.sel(3)
% 0.19/0.44 thf(fact_152_in__set__butlastD,axiom,
% 0.19/0.44 ! [X: val,Xs: list_val] :
% 0.19/0.44 ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 0.19/0.44 => ( member_val @ X @ ( set_val2 @ Xs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_set_butlastD
% 0.19/0.44 thf(fact_153_in__set__butlastD,axiom,
% 0.19/0.44 ! [X: node,Xs: list_node] :
% 0.19/0.44 ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 0.19/0.44 => ( member_node @ X @ ( set_node2 @ Xs ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_set_butlastD
% 0.19/0.44 thf(fact_154_list_Osel_I2_J,axiom,
% 0.19/0.44 ( ( tl_val @ nil_val )
% 0.19/0.44 = nil_val ) ).
% 0.19/0.44
% 0.19/0.44 % list.sel(2)
% 0.19/0.44 thf(fact_155_list_Osel_I2_J,axiom,
% 0.19/0.44 ( ( tl_list_node @ nil_list_node )
% 0.19/0.44 = nil_list_node ) ).
% 0.19/0.44
% 0.19/0.44 % list.sel(2)
% 0.19/0.44 thf(fact_156_list_Osel_I2_J,axiom,
% 0.19/0.44 ( ( tl_node @ nil_node )
% 0.19/0.44 = nil_node ) ).
% 0.19/0.44
% 0.19/0.44 % list.sel(2)
% 0.19/0.44 thf(fact_157_butlast_Osimps_I2_J,axiom,
% 0.19/0.44 ! [Xs: list_val,X: val] :
% 0.19/0.44 ( ( ( Xs = nil_val )
% 0.19/0.44 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 0.19/0.44 = nil_val ) )
% 0.19/0.44 & ( ( Xs != nil_val )
% 0.19/0.44 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 0.19/0.44 = ( cons_val @ X @ ( butlast_val @ Xs ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast.simps(2)
% 0.19/0.44 thf(fact_158_butlast_Osimps_I2_J,axiom,
% 0.19/0.44 ! [Xs: list_list_node,X: list_node] :
% 0.19/0.44 ( ( ( Xs = nil_list_node )
% 0.19/0.44 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 0.19/0.44 = nil_list_node ) )
% 0.19/0.44 & ( ( Xs != nil_list_node )
% 0.19/0.44 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 0.19/0.44 = ( cons_list_node @ X @ ( butlast_list_node @ Xs ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast.simps(2)
% 0.19/0.44 thf(fact_159_butlast_Osimps_I2_J,axiom,
% 0.19/0.44 ! [Xs: list_node,X: node] :
% 0.19/0.44 ( ( ( Xs = nil_node )
% 0.19/0.44 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 0.19/0.44 = nil_node ) )
% 0.19/0.44 & ( ( Xs != nil_node )
% 0.19/0.44 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 0.19/0.44 = ( cons_node @ X @ ( butlast_node @ Xs ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast.simps(2)
% 0.19/0.44 thf(fact_160_tl__obtain__elem,axiom,
% 0.19/0.44 ! [Xs: list_val] :
% 0.19/0.44 ( ( Xs != nil_val )
% 0.19/0.44 => ( ( ( tl_val @ Xs )
% 0.19/0.44 = nil_val )
% 0.19/0.44 => ~ ! [E4: val] :
% 0.19/0.44 ( Xs
% 0.19/0.44 != ( cons_val @ E4 @ nil_val ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_obtain_elem
% 0.19/0.44 thf(fact_161_tl__obtain__elem,axiom,
% 0.19/0.44 ! [Xs: list_list_node] :
% 0.19/0.44 ( ( Xs != nil_list_node )
% 0.19/0.44 => ( ( ( tl_list_node @ Xs )
% 0.19/0.44 = nil_list_node )
% 0.19/0.44 => ~ ! [E4: list_node] :
% 0.19/0.44 ( Xs
% 0.19/0.44 != ( cons_list_node @ E4 @ nil_list_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_obtain_elem
% 0.19/0.44 thf(fact_162_tl__obtain__elem,axiom,
% 0.19/0.44 ! [Xs: list_node] :
% 0.19/0.44 ( ( Xs != nil_node )
% 0.19/0.44 => ( ( ( tl_node @ Xs )
% 0.19/0.44 = nil_node )
% 0.19/0.44 => ~ ! [E4: node] :
% 0.19/0.44 ( Xs
% 0.19/0.44 != ( cons_node @ E4 @ nil_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_obtain_elem
% 0.19/0.44 thf(fact_163_tl__Nil,axiom,
% 0.19/0.44 ! [Xs: list_val] :
% 0.19/0.44 ( ( ( tl_val @ Xs )
% 0.19/0.44 = nil_val )
% 0.19/0.44 = ( ( Xs = nil_val )
% 0.19/0.44 | ? [X3: val] :
% 0.19/0.44 ( Xs
% 0.19/0.44 = ( cons_val @ X3 @ nil_val ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_Nil
% 0.19/0.44 thf(fact_164_tl__Nil,axiom,
% 0.19/0.44 ! [Xs: list_list_node] :
% 0.19/0.44 ( ( ( tl_list_node @ Xs )
% 0.19/0.44 = nil_list_node )
% 0.19/0.44 = ( ( Xs = nil_list_node )
% 0.19/0.44 | ? [X3: list_node] :
% 0.19/0.44 ( Xs
% 0.19/0.44 = ( cons_list_node @ X3 @ nil_list_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_Nil
% 0.19/0.44 thf(fact_165_tl__Nil,axiom,
% 0.19/0.44 ! [Xs: list_node] :
% 0.19/0.44 ( ( ( tl_node @ Xs )
% 0.19/0.44 = nil_node )
% 0.19/0.44 = ( ( Xs = nil_node )
% 0.19/0.44 | ? [X3: node] :
% 0.19/0.44 ( Xs
% 0.19/0.44 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % tl_Nil
% 0.19/0.44 thf(fact_166_Nil__tl,axiom,
% 0.19/0.44 ! [Xs: list_val] :
% 0.19/0.44 ( ( nil_val
% 0.19/0.44 = ( tl_val @ Xs ) )
% 0.19/0.44 = ( ( Xs = nil_val )
% 0.19/0.44 | ? [X3: val] :
% 0.19/0.44 ( Xs
% 0.19/0.44 = ( cons_val @ X3 @ nil_val ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Nil_tl
% 0.19/0.44 thf(fact_167_Nil__tl,axiom,
% 0.19/0.44 ! [Xs: list_list_node] :
% 0.19/0.44 ( ( nil_list_node
% 0.19/0.44 = ( tl_list_node @ Xs ) )
% 0.19/0.44 = ( ( Xs = nil_list_node )
% 0.19/0.44 | ? [X3: list_node] :
% 0.19/0.44 ( Xs
% 0.19/0.44 = ( cons_list_node @ X3 @ nil_list_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Nil_tl
% 0.19/0.44 thf(fact_168_Nil__tl,axiom,
% 0.19/0.44 ! [Xs: list_node] :
% 0.19/0.44 ( ( nil_node
% 0.19/0.44 = ( tl_node @ Xs ) )
% 0.19/0.44 = ( ( Xs = nil_node )
% 0.19/0.44 | ? [X3: node] :
% 0.19/0.44 ( Xs
% 0.19/0.44 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % Nil_tl
% 0.19/0.44 thf(fact_169_butlast__append,axiom,
% 0.19/0.44 ! [Ys: list_val,Xs: list_val] :
% 0.19/0.44 ( ( ( Ys = nil_val )
% 0.19/0.44 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 0.19/0.44 = ( butlast_val @ Xs ) ) )
% 0.19/0.44 & ( ( Ys != nil_val )
% 0.19/0.44 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 0.19/0.44 = ( append_val @ Xs @ ( butlast_val @ Ys ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_append
% 0.19/0.44 thf(fact_170_butlast__append,axiom,
% 0.19/0.44 ! [Ys: list_list_node,Xs: list_list_node] :
% 0.19/0.44 ( ( ( Ys = nil_list_node )
% 0.19/0.44 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.19/0.44 = ( butlast_list_node @ Xs ) ) )
% 0.19/0.44 & ( ( Ys != nil_list_node )
% 0.19/0.44 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.19/0.44 = ( append_list_node @ Xs @ ( butlast_list_node @ Ys ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_append
% 0.19/0.44 thf(fact_171_butlast__append,axiom,
% 0.19/0.44 ! [Ys: list_node,Xs: list_node] :
% 0.19/0.44 ( ( ( Ys = nil_node )
% 0.19/0.44 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 0.19/0.44 = ( butlast_node @ Xs ) ) )
% 0.19/0.44 & ( ( Ys != nil_node )
% 0.19/0.44 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 0.19/0.44 = ( append_node @ Xs @ ( butlast_node @ Ys ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_append
% 0.19/0.44 thf(fact_172_list_Oset__sel_I2_J,axiom,
% 0.19/0.44 ! [A: list_list_node,X: list_node] :
% 0.19/0.44 ( ( A != nil_list_node )
% 0.19/0.44 => ( ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ A ) ) )
% 0.19/0.44 => ( member_list_node @ X @ ( set_list_node2 @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.set_sel(2)
% 0.19/0.44 thf(fact_173_list_Oset__sel_I2_J,axiom,
% 0.19/0.44 ! [A: list_val,X: val] :
% 0.19/0.44 ( ( A != nil_val )
% 0.19/0.44 => ( ( member_val @ X @ ( set_val2 @ ( tl_val @ A ) ) )
% 0.19/0.44 => ( member_val @ X @ ( set_val2 @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.set_sel(2)
% 0.19/0.44 thf(fact_174_list_Oset__sel_I2_J,axiom,
% 0.19/0.44 ! [A: list_node,X: node] :
% 0.19/0.44 ( ( A != nil_node )
% 0.19/0.44 => ( ( member_node @ X @ ( set_node2 @ ( tl_node @ A ) ) )
% 0.19/0.44 => ( member_node @ X @ ( set_node2 @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.set_sel(2)
% 0.19/0.44 thf(fact_175_in__set__butlast__appendI,axiom,
% 0.19/0.44 ! [X: val,Xs: list_val,Ys: list_val] :
% 0.19/0.44 ( ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 0.19/0.44 | ( member_val @ X @ ( set_val2 @ ( butlast_val @ Ys ) ) ) )
% 0.19/0.44 => ( member_val @ X @ ( set_val2 @ ( butlast_val @ ( append_val @ Xs @ Ys ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_set_butlast_appendI
% 0.19/0.44 thf(fact_176_in__set__butlast__appendI,axiom,
% 0.19/0.44 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.19/0.44 ( ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 0.19/0.44 | ( member_node @ X @ ( set_node2 @ ( butlast_node @ Ys ) ) ) )
% 0.19/0.44 => ( member_node @ X @ ( set_node2 @ ( butlast_node @ ( append_node @ Xs @ Ys ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % in_set_butlast_appendI
% 0.19/0.44 thf(fact_177_list_Oexpand,axiom,
% 0.19/0.44 ! [List: list_val,List2: list_val] :
% 0.19/0.44 ( ( ( List = nil_val )
% 0.19/0.44 = ( List2 = nil_val ) )
% 0.19/0.44 => ( ( ( List != nil_val )
% 0.19/0.44 => ( ( List2 != nil_val )
% 0.19/0.44 => ( ( ( hd_val @ List )
% 0.19/0.44 = ( hd_val @ List2 ) )
% 0.19/0.44 & ( ( tl_val @ List )
% 0.19/0.44 = ( tl_val @ List2 ) ) ) ) )
% 0.19/0.44 => ( List = List2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.expand
% 0.19/0.44 thf(fact_178_list_Oexpand,axiom,
% 0.19/0.44 ! [List: list_list_node,List2: list_list_node] :
% 0.19/0.44 ( ( ( List = nil_list_node )
% 0.19/0.44 = ( List2 = nil_list_node ) )
% 0.19/0.44 => ( ( ( List != nil_list_node )
% 0.19/0.44 => ( ( List2 != nil_list_node )
% 0.19/0.44 => ( ( ( hd_list_node @ List )
% 0.19/0.44 = ( hd_list_node @ List2 ) )
% 0.19/0.44 & ( ( tl_list_node @ List )
% 0.19/0.44 = ( tl_list_node @ List2 ) ) ) ) )
% 0.19/0.44 => ( List = List2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.expand
% 0.19/0.44 thf(fact_179_list_Oexpand,axiom,
% 0.19/0.44 ! [List: list_node,List2: list_node] :
% 0.19/0.44 ( ( ( List = nil_node )
% 0.19/0.44 = ( List2 = nil_node ) )
% 0.19/0.44 => ( ( ( List != nil_node )
% 0.19/0.44 => ( ( List2 != nil_node )
% 0.19/0.44 => ( ( ( hd_node @ List )
% 0.19/0.44 = ( hd_node @ List2 ) )
% 0.19/0.44 & ( ( tl_node @ List )
% 0.19/0.44 = ( tl_node @ List2 ) ) ) ) )
% 0.19/0.44 => ( List = List2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.expand
% 0.19/0.44 thf(fact_180_not__hd__in__tl,axiom,
% 0.19/0.44 ! [X: val,Xs: list_val] :
% 0.19/0.44 ( ( X
% 0.19/0.44 != ( hd_val @ Xs ) )
% 0.19/0.44 => ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.44 => ( member_val @ X @ ( set_val2 @ ( tl_val @ Xs ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % not_hd_in_tl
% 0.19/0.44 thf(fact_181_not__hd__in__tl,axiom,
% 0.19/0.44 ! [X: node,Xs: list_node] :
% 0.19/0.44 ( ( X
% 0.19/0.44 != ( hd_node @ Xs ) )
% 0.19/0.44 => ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.44 => ( member_node @ X @ ( set_node2 @ ( tl_node @ Xs ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % not_hd_in_tl
% 0.19/0.44 thf(fact_182_butlast__eq__cons__conv,axiom,
% 0.19/0.44 ! [L: list_list_node,X: list_node,Xs: list_list_node] :
% 0.19/0.44 ( ( ( butlast_list_node @ L )
% 0.19/0.44 = ( cons_list_node @ X @ Xs ) )
% 0.19/0.44 = ( ? [Xl: list_node] :
% 0.19/0.44 ( L
% 0.19/0.44 = ( cons_list_node @ X @ ( append_list_node @ Xs @ ( cons_list_node @ Xl @ nil_list_node ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_eq_cons_conv
% 0.19/0.44 thf(fact_183_butlast__eq__cons__conv,axiom,
% 0.19/0.44 ! [L: list_node,X: node,Xs: list_node] :
% 0.19/0.44 ( ( ( butlast_node @ L )
% 0.19/0.44 = ( cons_node @ X @ Xs ) )
% 0.19/0.44 = ( ? [Xl: node] :
% 0.19/0.44 ( L
% 0.19/0.44 = ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl @ nil_node ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_eq_cons_conv
% 0.19/0.44 thf(fact_184_butlast__eq__consE,axiom,
% 0.19/0.44 ! [L: list_node,X: node,Xs: list_node] :
% 0.19/0.44 ( ( ( butlast_node @ L )
% 0.19/0.44 = ( cons_node @ X @ Xs ) )
% 0.19/0.44 => ~ ! [Xl2: node] :
% 0.19/0.44 ( L
% 0.19/0.44 != ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl2 @ nil_node ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % butlast_eq_consE
% 0.19/0.44 thf(fact_185_list_Oexhaust__sel,axiom,
% 0.19/0.44 ! [List: list_node] :
% 0.19/0.44 ( ( List != nil_node )
% 0.19/0.44 => ( List
% 0.19/0.44 = ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.exhaust_sel
% 0.19/0.44 thf(fact_186_not__Cons__self2,axiom,
% 0.19/0.44 ! [X: node,Xs: list_node] :
% 0.19/0.44 ( ( cons_node @ X @ Xs )
% 0.19/0.44 != Xs ) ).
% 0.19/0.44
% 0.19/0.44 % not_Cons_self2
% 0.19/0.44 thf(fact_187_list__tail__coinc,axiom,
% 0.19/0.44 ! [N1: node,R1: list_node,N22: node,R2: list_node] :
% 0.19/0.44 ( ( ( cons_node @ N1 @ R1 )
% 0.19/0.44 = ( cons_node @ N22 @ R2 ) )
% 0.19/0.44 => ( ( N1 = N22 )
% 0.19/0.44 & ( R1 = R2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % list_tail_coinc
% 0.19/0.44 thf(fact_188_append__eq__append__conv2,axiom,
% 0.19/0.44 ! [Xs: list_node,Ys: list_node,Zs: list_node,Ts: list_node] :
% 0.19/0.44 ( ( ( append_node @ Xs @ Ys )
% 0.19/0.44 = ( append_node @ Zs @ Ts ) )
% 0.19/0.44 = ( ? [Us: list_node] :
% 0.19/0.44 ( ( ( Xs
% 0.19/0.44 = ( append_node @ Zs @ Us ) )
% 0.19/0.44 & ( ( append_node @ Us @ Ys )
% 0.19/0.44 = Ts ) )
% 0.19/0.44 | ( ( ( append_node @ Xs @ Us )
% 0.19/0.44 = Zs )
% 0.19/0.44 & ( Ys
% 0.19/0.44 = ( append_node @ Us @ Ts ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_eq_append_conv2
% 0.19/0.44 thf(fact_189_append__eq__appendI,axiom,
% 0.19/0.44 ! [Xs: list_node,Xs1: list_node,Zs: list_node,Ys: list_node,Us2: list_node] :
% 0.19/0.44 ( ( ( append_node @ Xs @ Xs1 )
% 0.19/0.44 = Zs )
% 0.19/0.44 => ( ( Ys
% 0.19/0.44 = ( append_node @ Xs1 @ Us2 ) )
% 0.19/0.44 => ( ( append_node @ Xs @ Ys )
% 0.19/0.44 = ( append_node @ Zs @ Us2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % append_eq_appendI
% 0.19/0.44 thf(fact_190_list_Odistinct_I1_J,axiom,
% 0.19/0.44 ! [X21: node,X22: list_node] :
% 0.19/0.44 ( nil_node
% 0.19/0.44 != ( cons_node @ X21 @ X22 ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.distinct(1)
% 0.19/0.44 thf(fact_191_neq__NilE,axiom,
% 0.19/0.44 ! [L: list_node] :
% 0.19/0.44 ( ( L != nil_node )
% 0.19/0.44 => ~ ! [X4: node,Xs2: list_node] :
% 0.19/0.44 ( L
% 0.19/0.44 != ( cons_node @ X4 @ Xs2 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % neq_NilE
% 0.19/0.44 thf(fact_192_list_OdiscI,axiom,
% 0.19/0.44 ! [List: list_node,X21: node,X22: list_node] :
% 0.19/0.44 ( ( List
% 0.19/0.44 = ( cons_node @ X21 @ X22 ) )
% 0.19/0.44 => ( List != nil_node ) ) ).
% 0.19/0.44
% 0.19/0.44 % list.discI
% 0.19/0.44 thf(fact_193_revg_Oinduct,axiom,
% 0.19/0.44 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.19/0.44 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.19/0.44 => ( ! [A3: node,As: list_node,B2: list_node] :
% 0.19/0.44 ( ( P @ As @ ( cons_node @ A3 @ B2 ) )
% 0.19/0.44 => ( P @ ( cons_node @ A3 @ As ) @ B2 ) )
% 0.19/0.44 => ( P @ A0 @ A1 ) ) ) ).
% 0.19/0.44
% 0.19/0.44 % revg.induct
% 0.19/0.44 thf(fact_194_list_Oexhaust,axiom,
% 0.19/0.44 ! [Y: list_node] :
% 0.19/0.44 ( ( Y != nil_node )
% 0.19/0.44 => ~ ! [X212: node,X222: list_node] :
% 0.19/0.44 ( Y
% 0.19/0.44 != ( cons_node @ X212 @ X222 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.exhaust
% 0.19/0.45 thf(fact_195_list_Oinducts,axiom,
% 0.19/0.45 ! [P: list_node > $o,List: list_node] :
% 0.19/0.45 ( ( P @ nil_node )
% 0.19/0.45 => ( ! [X1: node,X23: list_node] :
% 0.19/0.45 ( ( P @ X23 )
% 0.19/0.45 => ( P @ ( cons_node @ X1 @ X23 ) ) )
% 0.19/0.45 => ( P @ List ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.inducts
% 0.19/0.45 thf(fact_196_neq__Nil__conv,axiom,
% 0.19/0.45 ! [Xs: list_node] :
% 0.19/0.45 ( ( Xs != nil_node )
% 0.19/0.45 = ( ? [Y2: node,Ys2: list_node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( cons_node @ Y2 @ Ys2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % neq_Nil_conv
% 0.19/0.45 thf(fact_197_list__induct2_H,axiom,
% 0.19/0.45 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ( P @ nil_node @ nil_node )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node] : ( P @ ( cons_node @ X4 @ Xs2 ) @ nil_node )
% 0.19/0.45 => ( ! [Y3: node,Ys3: list_node] : ( P @ nil_node @ ( cons_node @ Y3 @ Ys3 ) )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) )
% 0.19/0.45 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_induct2'
% 0.19/0.45 thf(fact_198_splice_Oinduct,axiom,
% 0.19/0.45 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.19/0.45 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Ys3: list_node] :
% 0.19/0.45 ( ( P @ Ys3 @ Xs2 )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys3 ) )
% 0.19/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % splice.induct
% 0.19/0.45 thf(fact_199_induct__list012,axiom,
% 0.19/0.45 ! [P: list_node > $o,Xs: list_node] :
% 0.19/0.45 ( ( P @ nil_node )
% 0.19/0.45 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.19/0.45 => ( ! [X4: node,Y3: node,Zs2: list_node] :
% 0.19/0.45 ( ( P @ Zs2 )
% 0.19/0.45 => ( ( P @ ( cons_node @ Y3 @ Zs2 ) )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y3 @ Zs2 ) ) ) ) )
% 0.19/0.45 => ( P @ Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % induct_list012
% 0.19/0.45 thf(fact_200_min__list_Ocases,axiom,
% 0.19/0.45 ! [X: list_node] :
% 0.19/0.45 ( ! [X4: node,Xs2: list_node] :
% 0.19/0.45 ( X
% 0.19/0.45 != ( cons_node @ X4 @ Xs2 ) )
% 0.19/0.45 => ( X = nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % min_list.cases
% 0.19/0.45 thf(fact_201_min__list_Oinduct,axiom,
% 0.19/0.45 ! [P: list_node > $o,A0: list_node] :
% 0.19/0.45 ( ! [X4: node,Xs2: list_node] :
% 0.19/0.45 ( ! [X213: node,X223: list_node] :
% 0.19/0.45 ( ( Xs2
% 0.19/0.45 = ( cons_node @ X213 @ X223 ) )
% 0.19/0.45 => ( P @ Xs2 ) )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 0.19/0.45 => ( ( P @ nil_node )
% 0.19/0.45 => ( P @ A0 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % min_list.induct
% 0.19/0.45 thf(fact_202_shuffles_Oinduct,axiom,
% 0.19/0.45 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.19/0.45 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.19/0.45 => ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( P @ Xs2 @ ( cons_node @ Y3 @ Ys3 ) )
% 0.19/0.45 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys3 )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) ) )
% 0.19/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % shuffles.induct
% 0.19/0.45 thf(fact_203_list__2pre__induct,axiom,
% 0.19/0.45 ! [P: list_node > list_node > $o,W1: list_node,W2: list_node] :
% 0.19/0.45 ( ( P @ nil_node @ nil_node )
% 0.19/0.45 => ( ! [E4: node,W12: list_node,W22: list_node] :
% 0.19/0.45 ( ( P @ W12 @ W22 )
% 0.19/0.45 => ( P @ ( cons_node @ E4 @ W12 ) @ W22 ) )
% 0.19/0.45 => ( ! [E4: node,W13: list_node,W23: list_node] :
% 0.19/0.45 ( ( P @ W13 @ W23 )
% 0.19/0.45 => ( P @ W13 @ ( cons_node @ E4 @ W23 ) ) )
% 0.19/0.45 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_2pre_induct
% 0.19/0.45 thf(fact_204_remdups__adj_Ocases,axiom,
% 0.19/0.45 ! [X: list_node] :
% 0.19/0.45 ( ( X != nil_node )
% 0.19/0.45 => ( ! [X4: node] :
% 0.19/0.45 ( X
% 0.19/0.45 != ( cons_node @ X4 @ nil_node ) )
% 0.19/0.45 => ~ ! [X4: node,Y3: node,Xs2: list_node] :
% 0.19/0.45 ( X
% 0.19/0.45 != ( cons_node @ X4 @ ( cons_node @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % remdups_adj.cases
% 0.19/0.45 thf(fact_205_sorted__wrt_Oinduct,axiom,
% 0.19/0.45 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 0.19/0.45 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 0.19/0.45 => ( ! [P2: node > node > $o,X4: node,Ys3: list_node] :
% 0.19/0.45 ( ( P @ P2 @ Ys3 )
% 0.19/0.45 => ( P @ P2 @ ( cons_node @ X4 @ Ys3 ) ) )
% 0.19/0.45 => ( P @ A0 @ A1 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % sorted_wrt.induct
% 0.19/0.45 thf(fact_206_remdups__adj_Oinduct,axiom,
% 0.19/0.45 ! [P: list_node > $o,A0: list_node] :
% 0.19/0.45 ( ( P @ nil_node )
% 0.19/0.45 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.19/0.45 => ( ! [X4: node,Y3: node,Xs2: list_node] :
% 0.19/0.45 ( ( ( X4 = Y3 )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 0.19/0.45 => ( ( ( X4 != Y3 )
% 0.19/0.45 => ( P @ ( cons_node @ Y3 @ Xs2 ) ) )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y3 @ Xs2 ) ) ) ) )
% 0.19/0.45 => ( P @ A0 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % remdups_adj.induct
% 0.19/0.45 thf(fact_207_list__induct__first2,axiom,
% 0.19/0.45 ! [P: list_node > $o,Xs: list_node] :
% 0.19/0.45 ( ( P @ nil_node )
% 0.19/0.45 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.19/0.45 => ( ! [X1: node,X23: node,Xs2: list_node] :
% 0.19/0.45 ( ( P @ Xs2 )
% 0.19/0.45 => ( P @ ( cons_node @ X1 @ ( cons_node @ X23 @ Xs2 ) ) ) )
% 0.19/0.45 => ( P @ Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_induct_first2
% 0.19/0.45 thf(fact_208_successively_Oinduct,axiom,
% 0.19/0.45 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 0.19/0.45 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 0.19/0.45 => ( ! [P2: node > node > $o,X4: node] : ( P @ P2 @ ( cons_node @ X4 @ nil_node ) )
% 0.19/0.45 => ( ! [P2: node > node > $o,X4: node,Y3: node,Xs2: list_node] :
% 0.19/0.45 ( ( P @ P2 @ ( cons_node @ Y3 @ Xs2 ) )
% 0.19/0.45 => ( P @ P2 @ ( cons_node @ X4 @ ( cons_node @ Y3 @ Xs2 ) ) ) )
% 0.19/0.45 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % successively.induct
% 0.19/0.45 thf(fact_209_list__all__zip_Oinduct,axiom,
% 0.19/0.45 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 0.19/0.45 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node @ nil_node )
% 0.19/0.45 => ( ! [P2: node > node > $o,A3: node,As: list_node,B2: node,Bs: list_node] :
% 0.19/0.45 ( ( P @ P2 @ As @ Bs )
% 0.19/0.45 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 0.19/0.45 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V @ Va ) @ nil_node )
% 0.19/0.45 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ nil_node @ ( cons_node @ V @ Va ) )
% 0.19/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_all_zip.induct
% 0.19/0.45 thf(fact_210_list__nonempty__induct,axiom,
% 0.19/0.45 ! [Xs: list_node,P: list_node > $o] :
% 0.19/0.45 ( ( Xs != nil_node )
% 0.19/0.45 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node] :
% 0.19/0.45 ( ( Xs2 != nil_node )
% 0.19/0.45 => ( ( P @ Xs2 )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Xs2 ) ) ) )
% 0.19/0.45 => ( P @ Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_nonempty_induct
% 0.19/0.45 thf(fact_211_map__tailrec__rev_Oinduct,axiom,
% 0.19/0.45 ! [P: ( node > node ) > list_node > list_node > $o,A0: node > node,A1: list_node,A22: list_node] :
% 0.19/0.45 ( ! [F: node > node,X_1: list_node] : ( P @ F @ nil_node @ X_1 )
% 0.19/0.45 => ( ! [F: node > node,A3: node,As: list_node,Bs: list_node] :
% 0.19/0.45 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 0.19/0.45 => ( P @ F @ ( cons_node @ A3 @ As ) @ Bs ) )
% 0.19/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % map_tailrec_rev.induct
% 0.19/0.45 thf(fact_212_mergesort__by__rel__merge_Oinduct,axiom,
% 0.19/0.45 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 0.19/0.45 ( ! [R: node > node > $o,X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( ( R @ X4 @ Y3 )
% 0.19/0.45 => ( P @ R @ Xs2 @ ( cons_node @ Y3 @ Ys3 ) ) )
% 0.19/0.45 => ( ( ~ ( R @ X4 @ Y3 )
% 0.19/0.45 => ( P @ R @ ( cons_node @ X4 @ Xs2 ) @ Ys3 ) )
% 0.19/0.45 => ( P @ R @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) ) )
% 0.19/0.45 => ( ! [R: node > node > $o,Xs2: list_node] : ( P @ R @ Xs2 @ nil_node )
% 0.19/0.45 => ( ! [R: node > node > $o,V: node,Va: list_node] : ( P @ R @ nil_node @ ( cons_node @ V @ Va ) )
% 0.19/0.45 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % mergesort_by_rel_merge.induct
% 0.19/0.45 thf(fact_213_mergesort__by__rel__merge__induct,axiom,
% 0.19/0.45 ! [P: list_node > list_node > $o,R3: node > node > $o,Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 0.19/0.45 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( R3 @ X4 @ Y3 )
% 0.19/0.45 => ( ( P @ Xs2 @ ( cons_node @ Y3 @ Ys3 ) )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) ) )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ~ ( R3 @ X4 @ Y3 )
% 0.19/0.45 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys3 )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) ) )
% 0.19/0.45 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % mergesort_by_rel_merge_induct
% 0.19/0.45 thf(fact_214_strict__sorted_Oinduct,axiom,
% 0.19/0.45 ! [P: list_node > $o,A0: list_node] :
% 0.19/0.45 ( ( P @ nil_node )
% 0.19/0.45 => ( ! [X4: node,Ys3: list_node] :
% 0.19/0.45 ( ( P @ Ys3 )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ Ys3 ) ) )
% 0.19/0.45 => ( P @ A0 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % strict_sorted.induct
% 0.19/0.45 thf(fact_215_transpose_Ocases,axiom,
% 0.19/0.45 ! [X: list_list_node] :
% 0.19/0.45 ( ( X != nil_list_node )
% 0.19/0.45 => ( ! [Xss: list_list_node] :
% 0.19/0.45 ( X
% 0.19/0.45 != ( cons_list_node @ nil_node @ Xss ) )
% 0.19/0.45 => ~ ! [X4: node,Xs2: list_node,Xss: list_list_node] :
% 0.19/0.45 ( X
% 0.19/0.45 != ( cons_list_node @ ( cons_node @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transpose.cases
% 0.19/0.45 thf(fact_216_list_Oset__intros_I2_J,axiom,
% 0.19/0.45 ! [Y: val,X22: list_val,X21: val] :
% 0.19/0.45 ( ( member_val @ Y @ ( set_val2 @ X22 ) )
% 0.19/0.45 => ( member_val @ Y @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.set_intros(2)
% 0.19/0.45 thf(fact_217_list_Oset__intros_I2_J,axiom,
% 0.19/0.45 ! [Y: node,X22: list_node,X21: node] :
% 0.19/0.45 ( ( member_node @ Y @ ( set_node2 @ X22 ) )
% 0.19/0.45 => ( member_node @ Y @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.set_intros(2)
% 0.19/0.45 thf(fact_218_list_Oset__intros_I1_J,axiom,
% 0.19/0.45 ! [X21: val,X22: list_val] : ( member_val @ X21 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.set_intros(1)
% 0.19/0.45 thf(fact_219_list_Oset__intros_I1_J,axiom,
% 0.19/0.45 ! [X21: node,X22: list_node] : ( member_node @ X21 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.set_intros(1)
% 0.19/0.45 thf(fact_220_set__ConsD,axiom,
% 0.19/0.45 ! [Y: val,X: val,Xs: list_val] :
% 0.19/0.45 ( ( member_val @ Y @ ( set_val2 @ ( cons_val @ X @ Xs ) ) )
% 0.19/0.45 => ( ( Y = X )
% 0.19/0.45 | ( member_val @ Y @ ( set_val2 @ Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_ConsD
% 0.19/0.45 thf(fact_221_set__ConsD,axiom,
% 0.19/0.45 ! [Y: node,X: node,Xs: list_node] :
% 0.19/0.45 ( ( member_node @ Y @ ( set_node2 @ ( cons_node @ X @ Xs ) ) )
% 0.19/0.45 => ( ( Y = X )
% 0.19/0.45 | ( member_node @ Y @ ( set_node2 @ Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_ConsD
% 0.19/0.45 thf(fact_222_list_Oset__cases,axiom,
% 0.19/0.45 ! [E3: val,A: list_val] :
% 0.19/0.45 ( ( member_val @ E3 @ ( set_val2 @ A ) )
% 0.19/0.45 => ( ! [Z2: list_val] :
% 0.19/0.45 ( A
% 0.19/0.45 != ( cons_val @ E3 @ Z2 ) )
% 0.19/0.45 => ~ ! [Z1: val,Z2: list_val] :
% 0.19/0.45 ( ( A
% 0.19/0.45 = ( cons_val @ Z1 @ Z2 ) )
% 0.19/0.45 => ~ ( member_val @ E3 @ ( set_val2 @ Z2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.set_cases
% 0.19/0.45 thf(fact_223_list_Oset__cases,axiom,
% 0.19/0.45 ! [E3: node,A: list_node] :
% 0.19/0.45 ( ( member_node @ E3 @ ( set_node2 @ A ) )
% 0.19/0.45 => ( ! [Z2: list_node] :
% 0.19/0.45 ( A
% 0.19/0.45 != ( cons_node @ E3 @ Z2 ) )
% 0.19/0.45 => ~ ! [Z1: node,Z2: list_node] :
% 0.19/0.45 ( ( A
% 0.19/0.45 = ( cons_node @ Z1 @ Z2 ) )
% 0.19/0.45 => ~ ( member_node @ E3 @ ( set_node2 @ Z2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.set_cases
% 0.19/0.45 thf(fact_224_Cons__eq__appendI,axiom,
% 0.19/0.45 ! [X: node,Xs1: list_node,Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.19/0.45 ( ( ( cons_node @ X @ Xs1 )
% 0.19/0.45 = Ys )
% 0.19/0.45 => ( ( Xs
% 0.19/0.45 = ( append_node @ Xs1 @ Zs ) )
% 0.19/0.45 => ( ( cons_node @ X @ Xs )
% 0.19/0.45 = ( append_node @ Ys @ Zs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Cons_eq_appendI
% 0.19/0.45 thf(fact_225_append__Cons,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ( append_node @ ( cons_node @ X @ Xs ) @ Ys )
% 0.19/0.45 = ( cons_node @ X @ ( append_node @ Xs @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % append_Cons
% 0.19/0.45 thf(fact_226_list__match__lel__lel,axiom,
% 0.19/0.45 ! [C1: list_node,Qs: node,C2: list_node,C12: list_node,Qs2: node,C22: list_node] :
% 0.19/0.45 ( ( ( append_node @ C1 @ ( cons_node @ Qs @ C2 ) )
% 0.19/0.45 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C22 ) ) )
% 0.19/0.45 => ( ! [C21: list_node] :
% 0.19/0.45 ( ( C1
% 0.19/0.45 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C21 ) ) )
% 0.19/0.45 => ( C22
% 0.19/0.45 != ( append_node @ C21 @ ( cons_node @ Qs @ C2 ) ) ) )
% 0.19/0.45 => ( ( ( C12 = C1 )
% 0.19/0.45 => ( ( Qs2 = Qs )
% 0.19/0.45 => ( C22 != C2 ) ) )
% 0.19/0.45 => ~ ! [C212: list_node] :
% 0.19/0.45 ( ( C12
% 0.19/0.45 = ( append_node @ C1 @ ( cons_node @ Qs @ C212 ) ) )
% 0.19/0.45 => ( C2
% 0.19/0.45 != ( append_node @ C212 @ ( cons_node @ Qs2 @ C22 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_match_lel_lel
% 0.19/0.45 thf(fact_227_append_Oleft__neutral,axiom,
% 0.19/0.45 ! [A: list_node] :
% 0.19/0.45 ( ( append_node @ nil_node @ A )
% 0.19/0.45 = A ) ).
% 0.19/0.45
% 0.19/0.45 % append.left_neutral
% 0.19/0.45 thf(fact_228_append__Nil,axiom,
% 0.19/0.45 ! [Ys: list_node] :
% 0.19/0.45 ( ( append_node @ nil_node @ Ys )
% 0.19/0.45 = Ys ) ).
% 0.19/0.45
% 0.19/0.45 % append_Nil
% 0.19/0.45 thf(fact_229_eq__Nil__appendI,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ( Xs = Ys )
% 0.19/0.45 => ( Xs
% 0.19/0.45 = ( append_node @ nil_node @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eq_Nil_appendI
% 0.19/0.45 thf(fact_230_list_Osel_I1_J,axiom,
% 0.19/0.45 ! [X21: node,X22: list_node] :
% 0.19/0.45 ( ( hd_node @ ( cons_node @ X21 @ X22 ) )
% 0.19/0.45 = X21 ) ).
% 0.19/0.45
% 0.19/0.45 % list.sel(1)
% 0.19/0.45 thf(fact_231_rev__induct,axiom,
% 0.19/0.45 ! [P: list_node > $o,Xs: list_node] :
% 0.19/0.45 ( ( P @ nil_node )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node] :
% 0.19/0.45 ( ( P @ Xs2 )
% 0.19/0.45 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) )
% 0.19/0.45 => ( P @ Xs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rev_induct
% 0.19/0.45 thf(fact_232_rev__exhaust,axiom,
% 0.19/0.45 ! [Xs: list_node] :
% 0.19/0.45 ( ( Xs != nil_node )
% 0.19/0.45 => ~ ! [Ys3: list_node,Y3: node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 != ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rev_exhaust
% 0.19/0.45 thf(fact_233_neq__Nil__revE,axiom,
% 0.19/0.45 ! [L: list_node] :
% 0.19/0.45 ( ( L != nil_node )
% 0.19/0.45 => ~ ! [Ll: list_node,E4: node] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_node @ Ll @ ( cons_node @ E4 @ nil_node ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % neq_Nil_revE
% 0.19/0.45 thf(fact_234_rev__induct2_H,axiom,
% 0.19/0.45 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ( P @ nil_node @ nil_node )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 0.19/0.45 => ( ! [Y3: node,Ys3: list_node] : ( P @ nil_node @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.19/0.45 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) )
% 0.19/0.45 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rev_induct2'
% 0.19/0.45 thf(fact_235_neq__Nil__rev__conv,axiom,
% 0.19/0.45 ! [L: list_node] :
% 0.19/0.45 ( ( L != nil_node )
% 0.19/0.45 = ( ? [Xs3: list_node,X3: node] :
% 0.19/0.45 ( L
% 0.19/0.45 = ( append_node @ Xs3 @ ( cons_node @ X3 @ nil_node ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % neq_Nil_rev_conv
% 0.19/0.45 thf(fact_236_Cons__eq__append__conv,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.19/0.45 ( ( ( cons_node @ X @ Xs )
% 0.19/0.45 = ( append_node @ Ys @ Zs ) )
% 0.19/0.45 = ( ( ( Ys = nil_node )
% 0.19/0.45 & ( ( cons_node @ X @ Xs )
% 0.19/0.45 = Zs ) )
% 0.19/0.45 | ? [Ys4: list_node] :
% 0.19/0.45 ( ( ( cons_node @ X @ Ys4 )
% 0.19/0.45 = Ys )
% 0.19/0.45 & ( Xs
% 0.19/0.45 = ( append_node @ Ys4 @ Zs ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Cons_eq_append_conv
% 0.19/0.45 thf(fact_237_append__eq__Cons__conv,axiom,
% 0.19/0.45 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 0.19/0.45 ( ( ( append_node @ Ys @ Zs )
% 0.19/0.45 = ( cons_node @ X @ Xs ) )
% 0.19/0.45 = ( ( ( Ys = nil_node )
% 0.19/0.45 & ( Zs
% 0.19/0.45 = ( cons_node @ X @ Xs ) ) )
% 0.19/0.45 | ? [Ys4: list_node] :
% 0.19/0.45 ( ( Ys
% 0.19/0.45 = ( cons_node @ X @ Ys4 ) )
% 0.19/0.45 & ( ( append_node @ Ys4 @ Zs )
% 0.19/0.45 = Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % append_eq_Cons_conv
% 0.19/0.45 thf(fact_238_rev__nonempty__induct,axiom,
% 0.19/0.45 ! [Xs: list_node,P: list_node > $o] :
% 0.19/0.45 ( ( Xs != nil_node )
% 0.19/0.45 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node] :
% 0.19/0.45 ( ( Xs2 != nil_node )
% 0.19/0.45 => ( ( P @ Xs2 )
% 0.19/0.45 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) ) )
% 0.19/0.45 => ( P @ Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rev_nonempty_induct
% 0.19/0.45 thf(fact_239_rev__nonempty__induct2_H,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node,P: list_node > list_node > $o] :
% 0.19/0.45 ( ( Xs != nil_node )
% 0.19/0.45 => ( ( Ys != nil_node )
% 0.19/0.45 => ( ! [X4: node,Y3: node] : ( P @ ( cons_node @ X4 @ nil_node ) @ ( cons_node @ Y3 @ nil_node ) )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node] :
% 0.19/0.45 ( ( Xs2 != nil_node )
% 0.19/0.45 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( cons_node @ Y3 @ nil_node ) ) )
% 0.19/0.45 => ( ! [X4: node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( Ys3 != nil_node )
% 0.19/0.45 => ( P @ ( cons_node @ X4 @ nil_node ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( P @ Xs2 @ Ys3 )
% 0.19/0.45 => ( ( Xs2 != nil_node )
% 0.19/0.45 => ( ( Ys3 != nil_node )
% 0.19/0.45 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) ) ) )
% 0.19/0.45 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rev_nonempty_induct2'
% 0.19/0.45 thf(fact_240_list__Cons__eq__append__cases,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.19/0.45 ( ( ( cons_node @ X @ Xs )
% 0.19/0.45 = ( append_node @ Ys @ Zs ) )
% 0.19/0.45 => ( ( ( Ys = nil_node )
% 0.19/0.45 => ( Zs
% 0.19/0.45 != ( cons_node @ X @ Xs ) ) )
% 0.19/0.45 => ~ ! [Ys5: list_node] :
% 0.19/0.45 ( ( Ys
% 0.19/0.45 = ( cons_node @ X @ Ys5 ) )
% 0.19/0.45 => ( ( append_node @ Ys5 @ Zs )
% 0.19/0.45 != Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_Cons_eq_append_cases
% 0.19/0.45 thf(fact_241_list__append__eq__Cons__cases,axiom,
% 0.19/0.45 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 0.19/0.45 ( ( ( append_node @ Ys @ Zs )
% 0.19/0.45 = ( cons_node @ X @ Xs ) )
% 0.19/0.45 => ( ( ( Ys = nil_node )
% 0.19/0.45 => ( Zs
% 0.19/0.45 != ( cons_node @ X @ Xs ) ) )
% 0.19/0.45 => ~ ! [Ys5: list_node] :
% 0.19/0.45 ( ( Ys
% 0.19/0.45 = ( cons_node @ X @ Ys5 ) )
% 0.19/0.45 => ( ( append_node @ Ys5 @ Zs )
% 0.19/0.45 != Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list_append_eq_Cons_cases
% 0.19/0.45 thf(fact_242_split__list,axiom,
% 0.19/0.45 ! [X: val,Xs: list_val] :
% 0.19/0.45 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.45 => ? [Ys3: list_val,Zs2: list_val] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list
% 0.19/0.45 thf(fact_243_split__list,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node] :
% 0.19/0.45 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.45 => ? [Ys3: list_node,Zs2: list_node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list
% 0.19/0.45 thf(fact_244_split__list__last,axiom,
% 0.19/0.45 ! [X: val,Xs: list_val] :
% 0.19/0.45 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.45 => ? [Ys3: list_val,Zs2: list_val] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs2 ) ) )
% 0.19/0.45 & ~ ( member_val @ X @ ( set_val2 @ Zs2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_last
% 0.19/0.45 thf(fact_245_split__list__last,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node] :
% 0.19/0.45 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.45 => ? [Ys3: list_node,Zs2: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs2 ) ) )
% 0.19/0.45 & ~ ( member_node @ X @ ( set_node2 @ Zs2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_last
% 0.19/0.45 thf(fact_246_split__list__prop,axiom,
% 0.19/0.45 ! [Xs: list_node,P: node > $o] :
% 0.19/0.45 ( ? [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.19/0.45 & ( P @ X2 ) )
% 0.19/0.45 => ? [Ys3: list_node,X4: node] :
% 0.19/0.45 ( ? [Zs2: list_node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.19/0.45 & ( P @ X4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_prop
% 0.19/0.45 thf(fact_247_xy__in__set__cases,axiom,
% 0.19/0.45 ! [X: val,L: list_val,Y: val] :
% 0.19/0.45 ( ( member_val @ X @ ( set_val2 @ L ) )
% 0.19/0.45 => ( ( member_val @ Y @ ( set_val2 @ L ) )
% 0.19/0.45 => ( ( ( X = Y )
% 0.19/0.45 => ! [L12: list_val,L22: list_val] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_val @ L12 @ ( cons_val @ Y @ L22 ) ) ) )
% 0.19/0.45 => ( ( ( X != Y )
% 0.19/0.45 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_val @ L12 @ ( cons_val @ X @ ( append_val @ L22 @ ( cons_val @ Y @ L3 ) ) ) ) ) )
% 0.19/0.45 => ~ ( ( X != Y )
% 0.19/0.45 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_val @ L12 @ ( cons_val @ Y @ ( append_val @ L22 @ ( cons_val @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % xy_in_set_cases
% 0.19/0.45 thf(fact_248_xy__in__set__cases,axiom,
% 0.19/0.45 ! [X: node,L: list_node,Y: node] :
% 0.19/0.45 ( ( member_node @ X @ ( set_node2 @ L ) )
% 0.19/0.45 => ( ( member_node @ Y @ ( set_node2 @ L ) )
% 0.19/0.45 => ( ( ( X = Y )
% 0.19/0.45 => ! [L12: list_node,L22: list_node] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_node @ L12 @ ( cons_node @ Y @ L22 ) ) ) )
% 0.19/0.45 => ( ( ( X != Y )
% 0.19/0.45 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_node @ L12 @ ( cons_node @ X @ ( append_node @ L22 @ ( cons_node @ Y @ L3 ) ) ) ) ) )
% 0.19/0.45 => ~ ( ( X != Y )
% 0.19/0.45 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_node @ L12 @ ( cons_node @ Y @ ( append_node @ L22 @ ( cons_node @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % xy_in_set_cases
% 0.19/0.45 thf(fact_249_split__list__first,axiom,
% 0.19/0.45 ! [X: val,Xs: list_val] :
% 0.19/0.45 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.45 => ? [Ys3: list_val,Zs2: list_val] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs2 ) ) )
% 0.19/0.45 & ~ ( member_val @ X @ ( set_val2 @ Ys3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_first
% 0.19/0.45 thf(fact_250_split__list__first,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node] :
% 0.19/0.45 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.45 => ? [Ys3: list_node,Zs2: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs2 ) ) )
% 0.19/0.45 & ~ ( member_node @ X @ ( set_node2 @ Ys3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_first
% 0.19/0.45 thf(fact_251_split__list__propE,axiom,
% 0.19/0.45 ! [Xs: list_node,P: node > $o] :
% 0.19/0.45 ( ? [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.19/0.45 & ( P @ X2 ) )
% 0.19/0.45 => ~ ! [Ys3: list_node,X4: node] :
% 0.19/0.45 ( ? [Zs2: list_node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.19/0.45 => ~ ( P @ X4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_propE
% 0.19/0.45 thf(fact_252_append__Cons__eq__iff,axiom,
% 0.19/0.45 ! [X: val,Xs: list_val,Ys: list_val,Xs4: list_val,Ys6: list_val] :
% 0.19/0.45 ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.45 => ( ~ ( member_val @ X @ ( set_val2 @ Ys ) )
% 0.19/0.45 => ( ( ( append_val @ Xs @ ( cons_val @ X @ Ys ) )
% 0.19/0.45 = ( append_val @ Xs4 @ ( cons_val @ X @ Ys6 ) ) )
% 0.19/0.45 = ( ( Xs = Xs4 )
% 0.19/0.45 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % append_Cons_eq_iff
% 0.19/0.45 thf(fact_253_append__Cons__eq__iff,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node,Ys: list_node,Xs4: list_node,Ys6: list_node] :
% 0.19/0.45 ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.45 => ( ~ ( member_node @ X @ ( set_node2 @ Ys ) )
% 0.19/0.45 => ( ( ( append_node @ Xs @ ( cons_node @ X @ Ys ) )
% 0.19/0.45 = ( append_node @ Xs4 @ ( cons_node @ X @ Ys6 ) ) )
% 0.19/0.45 = ( ( Xs = Xs4 )
% 0.19/0.45 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % append_Cons_eq_iff
% 0.19/0.45 thf(fact_254_in__set__conv__decomp,axiom,
% 0.19/0.45 ! [X: val,Xs: list_val] :
% 0.19/0.45 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.45 = ( ? [Ys2: list_val,Zs3: list_val] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_set_conv_decomp
% 0.19/0.45 thf(fact_255_in__set__conv__decomp,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node] :
% 0.19/0.45 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.45 = ( ? [Ys2: list_node,Zs3: list_node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_set_conv_decomp
% 0.19/0.45 thf(fact_256_in__set__list__format,axiom,
% 0.19/0.45 ! [E3: val,L: list_val] :
% 0.19/0.45 ( ( member_val @ E3 @ ( set_val2 @ L ) )
% 0.19/0.45 => ~ ! [L12: list_val,L22: list_val] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_val @ L12 @ ( cons_val @ E3 @ L22 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_set_list_format
% 0.19/0.45 thf(fact_257_in__set__list__format,axiom,
% 0.19/0.45 ! [E3: node,L: list_node] :
% 0.19/0.45 ( ( member_node @ E3 @ ( set_node2 @ L ) )
% 0.19/0.45 => ~ ! [L12: list_node,L22: list_node] :
% 0.19/0.45 ( L
% 0.19/0.45 != ( append_node @ L12 @ ( cons_node @ E3 @ L22 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_set_list_format
% 0.19/0.45 thf(fact_258_split__list__last__prop,axiom,
% 0.19/0.45 ! [Xs: list_node,P: node > $o] :
% 0.19/0.45 ( ? [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.19/0.45 & ( P @ X2 ) )
% 0.19/0.45 => ? [Ys3: list_node,X4: node,Zs2: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.19/0.45 & ( P @ X4 )
% 0.19/0.45 & ! [Xa: node] :
% 0.19/0.45 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 0.19/0.45 => ~ ( P @ Xa ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_last_prop
% 0.19/0.45 thf(fact_259_split__list__first__prop,axiom,
% 0.19/0.45 ! [Xs: list_node,P: node > $o] :
% 0.19/0.45 ( ? [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.19/0.45 & ( P @ X2 ) )
% 0.19/0.45 => ? [Ys3: list_node,X4: node] :
% 0.19/0.45 ( ? [Zs2: list_node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.19/0.45 & ( P @ X4 )
% 0.19/0.45 & ! [Xa: node] :
% 0.19/0.45 ( ( member_node @ Xa @ ( set_node2 @ Ys3 ) )
% 0.19/0.45 => ~ ( P @ Xa ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_first_prop
% 0.19/0.45 thf(fact_260_split__list__last__propE,axiom,
% 0.19/0.45 ! [Xs: list_node,P: node > $o] :
% 0.19/0.45 ( ? [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.19/0.45 & ( P @ X2 ) )
% 0.19/0.45 => ~ ! [Ys3: list_node,X4: node,Zs2: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.19/0.45 => ( ( P @ X4 )
% 0.19/0.45 => ~ ! [Xa: node] :
% 0.19/0.45 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 0.19/0.45 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_last_propE
% 0.19/0.45 thf(fact_261_split__list__first__propE,axiom,
% 0.19/0.45 ! [Xs: list_node,P: node > $o] :
% 0.19/0.45 ( ? [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.19/0.45 & ( P @ X2 ) )
% 0.19/0.45 => ~ ! [Ys3: list_node,X4: node] :
% 0.19/0.45 ( ? [Zs2: list_node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.19/0.45 => ( ( P @ X4 )
% 0.19/0.45 => ~ ! [Xa: node] :
% 0.19/0.45 ( ( member_node @ Xa @ ( set_node2 @ Ys3 ) )
% 0.19/0.45 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_first_propE
% 0.19/0.45 thf(fact_262_in__set__conv__decomp__last,axiom,
% 0.19/0.45 ! [X: val,Xs: list_val] :
% 0.19/0.45 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.45 = ( ? [Ys2: list_val,Zs3: list_val] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs3 ) ) )
% 0.19/0.45 & ~ ( member_val @ X @ ( set_val2 @ Zs3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_set_conv_decomp_last
% 0.19/0.45 thf(fact_263_in__set__conv__decomp__last,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node] :
% 0.19/0.45 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.45 = ( ? [Ys2: list_node,Zs3: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs3 ) ) )
% 0.19/0.45 & ~ ( member_node @ X @ ( set_node2 @ Zs3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_set_conv_decomp_last
% 0.19/0.45 thf(fact_264_in__set__conv__decomp__first,axiom,
% 0.19/0.45 ! [X: val,Xs: list_val] :
% 0.19/0.45 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.45 = ( ? [Ys2: list_val,Zs3: list_val] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs3 ) ) )
% 0.19/0.45 & ~ ( member_val @ X @ ( set_val2 @ Ys2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_set_conv_decomp_first
% 0.19/0.45 thf(fact_265_in__set__conv__decomp__first,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node] :
% 0.19/0.45 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.45 = ( ? [Ys2: list_node,Zs3: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs3 ) ) )
% 0.19/0.45 & ~ ( member_node @ X @ ( set_node2 @ Ys2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_set_conv_decomp_first
% 0.19/0.45 thf(fact_266_split__list__last__prop__iff,axiom,
% 0.19/0.45 ! [Xs: list_node,P: node > $o] :
% 0.19/0.45 ( ( ? [X3: node] :
% 0.19/0.45 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.19/0.45 & ( P @ X3 ) ) )
% 0.19/0.45 = ( ? [Ys2: list_node,X3: node,Zs3: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Ys2 @ ( cons_node @ X3 @ Zs3 ) ) )
% 0.19/0.45 & ( P @ X3 )
% 0.19/0.45 & ! [Y2: node] :
% 0.19/0.45 ( ( member_node @ Y2 @ ( set_node2 @ Zs3 ) )
% 0.19/0.45 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_last_prop_iff
% 0.19/0.45 thf(fact_267_split__list__first__prop__iff,axiom,
% 0.19/0.45 ! [Xs: list_node,P: node > $o] :
% 0.19/0.45 ( ( ? [X3: node] :
% 0.19/0.45 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.19/0.45 & ( P @ X3 ) ) )
% 0.19/0.45 = ( ? [Ys2: list_node,X3: node] :
% 0.19/0.45 ( ? [Zs3: list_node] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( append_node @ Ys2 @ ( cons_node @ X3 @ Zs3 ) ) )
% 0.19/0.45 & ( P @ X3 )
% 0.19/0.45 & ! [Y2: node] :
% 0.19/0.45 ( ( member_node @ Y2 @ ( set_node2 @ Ys2 ) )
% 0.19/0.45 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % split_list_first_prop_iff
% 0.19/0.45 thf(fact_268_hd__in__set,axiom,
% 0.19/0.45 ! [Xs: list_val] :
% 0.19/0.45 ( ( Xs != nil_val )
% 0.19/0.45 => ( member_val @ ( hd_val @ Xs ) @ ( set_val2 @ Xs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % hd_in_set
% 0.19/0.45 thf(fact_269_hd__in__set,axiom,
% 0.19/0.45 ! [Xs: list_node] :
% 0.19/0.45 ( ( Xs != nil_node )
% 0.19/0.45 => ( member_node @ ( hd_node @ Xs ) @ ( set_node2 @ Xs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % hd_in_set
% 0.19/0.45 thf(fact_270_list_Oset__sel_I1_J,axiom,
% 0.19/0.45 ! [A: list_val] :
% 0.19/0.45 ( ( A != nil_val )
% 0.19/0.45 => ( member_val @ ( hd_val @ A ) @ ( set_val2 @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.set_sel(1)
% 0.19/0.45 thf(fact_271_list_Oset__sel_I1_J,axiom,
% 0.19/0.45 ! [A: list_node] :
% 0.19/0.45 ( ( A != nil_node )
% 0.19/0.45 => ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % list.set_sel(1)
% 0.19/0.45 thf(fact_272_longest__common__prefix,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.45 ? [Ps: list_node,Xs5: list_node,Ys5: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Ps @ Xs5 ) )
% 0.19/0.45 & ( Ys
% 0.19/0.45 = ( append_node @ Ps @ Ys5 ) )
% 0.19/0.45 & ( ( Xs5 = nil_node )
% 0.19/0.45 | ( Ys5 = nil_node )
% 0.19/0.45 | ( ( hd_node @ Xs5 )
% 0.19/0.45 != ( hd_node @ Ys5 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % longest_common_prefix
% 0.19/0.45 thf(fact_273_hd__append,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ( ( Xs = nil_node )
% 0.19/0.45 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.19/0.45 = ( hd_node @ Ys ) ) )
% 0.19/0.45 & ( ( Xs != nil_node )
% 0.19/0.45 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.19/0.45 = ( hd_node @ Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % hd_append
% 0.19/0.45 thf(fact_274__092_060open_062old_OpathsConverge_Ag_Am_Ams_H_An_A_Ins_A_064_Atl_Ari_J_Ai_092_060close_062,axiom,
% 0.19/0.45 graph_2009891965_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ i ).
% 0.19/0.45
% 0.19/0.45 % \<open>old.pathsConverge g m ms' n (ns @ tl ri) i\<close>
% 0.19/0.45 thf(fact_275__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,
% 0.19/0.45 ~ ! [I: node,Ri: list_node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 0.19/0.45 => ( ( member_node @ I @ ( set_node2 @ ms ) )
% 0.19/0.45 => ( ! [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ri ) ) )
% 0.19/0.45 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) )
% 0.19/0.45 => ~ ( prefix_node @ Ri @ rs2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<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>
% 0.19/0.45 thf(fact_276__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,
% 0.19/0.45 ~ ! [Ms2: list_node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 0.19/0.45 => ( ( prefix_node @ Ms2 @ ms )
% 0.19/0.45 => ( member_node @ i @ ( set_node2 @ ( butlast_node @ Ms2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<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>
% 0.19/0.45 thf(fact_277_old_Opath2__simple__loop,axiom,
% 0.19/0.45 ! [G: g,N: node,Ns: list_node,N2: node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ N )
% 0.19/0.45 => ( ( member_node @ N2 @ ( set_node2 @ Ns ) )
% 0.19/0.45 => ~ ! [Ns4: list_node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ N )
% 0.19/0.45 => ( ( member_node @ N2 @ ( set_node2 @ Ns4 ) )
% 0.19/0.45 => ( ~ ( member_node @ N @ ( set_node2 @ ( tl_node @ ( butlast_node @ Ns4 ) ) ) )
% 0.19/0.45 => ~ ( ord_less_eq_set_node @ ( set_node2 @ Ns4 ) @ ( set_node2 @ Ns ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path2_simple_loop
% 0.19/0.45 thf(fact_278_old_Opath_Ocases,axiom,
% 0.19/0.45 ! [G: g,A: list_node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 0.19/0.45 => ( ! [N4: node] :
% 0.19/0.45 ( ( A
% 0.19/0.45 = ( cons_node @ N4 @ nil_node ) )
% 0.19/0.45 => ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.45 => ~ ( invar @ G ) ) )
% 0.19/0.45 => ~ ! [Ns3: list_node,N3: node] :
% 0.19/0.45 ( ( A
% 0.19/0.45 = ( cons_node @ N3 @ Ns3 ) )
% 0.19/0.45 => ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns3 )
% 0.19/0.45 => ~ ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns3 ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path.cases
% 0.19/0.45 thf(fact_279_old_Opath_Oinducts,axiom,
% 0.19/0.45 ! [G: g,X: list_node,P: list_node > $o] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ X )
% 0.19/0.45 => ( ! [N4: node] :
% 0.19/0.45 ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.45 => ( ( invar @ G )
% 0.19/0.45 => ( P @ ( cons_node @ N4 @ nil_node ) ) ) )
% 0.19/0.45 => ( ! [Ns3: list_node,N3: node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns3 )
% 0.19/0.45 => ( ( P @ Ns3 )
% 0.19/0.45 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns3 ) ) ) )
% 0.19/0.45 => ( P @ ( cons_node @ N3 @ Ns3 ) ) ) ) )
% 0.19/0.45 => ( P @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path.inducts
% 0.19/0.45 thf(fact_280_old_Opath_Osimps,axiom,
% 0.19/0.45 ! [G: g,A: list_node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 0.19/0.45 = ( ? [N5: node] :
% 0.19/0.45 ( ( A
% 0.19/0.45 = ( cons_node @ N5 @ nil_node ) )
% 0.19/0.45 & ( member_node @ N5 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.45 & ( invar @ G ) )
% 0.19/0.45 | ? [Ns5: list_node,N6: node] :
% 0.19/0.45 ( ( A
% 0.19/0.45 = ( cons_node @ N6 @ Ns5 ) )
% 0.19/0.45 & ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns5 )
% 0.19/0.45 & ( member_node @ N6 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns5 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path.simps
% 0.19/0.45 thf(fact_281_old_Opath__snoc,axiom,
% 0.19/0.45 ! [G: g,Ns: list_node,N: node,M: node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ nil_node ) ) )
% 0.19/0.45 => ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M ) ) )
% 0.19/0.45 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ ( cons_node @ M @ nil_node ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path_snoc
% 0.19/0.45 thf(fact_282_ri__rs_H__prefix,axiom,
% 0.19/0.45 prefix_node @ ri @ rs ).
% 0.19/0.45
% 0.19/0.45 % ri_rs'_prefix
% 0.19/0.45 thf(fact_283_old_Opath__not__Nil,axiom,
% 0.19/0.45 ! [G: g,Ns: list_node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.19/0.45 => ( Ns != nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path_not_Nil
% 0.19/0.45 thf(fact_284_old_Opath__hd,axiom,
% 0.19/0.45 ! [G: g,N: node,Ns: list_node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ Ns ) )
% 0.19/0.45 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path_hd
% 0.19/0.45 thf(fact_285_old_Opath__split_I2_J,axiom,
% 0.19/0.45 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 0.19/0.45 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ M @ Ns2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path_split(2)
% 0.19/0.45 thf(fact_286_old_Oempty__path,axiom,
% 0.19/0.45 ! [N: node,G: g] :
% 0.19/0.45 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.45 => ( ( invar @ G )
% 0.19/0.45 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.empty_path
% 0.19/0.45 thf(fact_287_old_Opath__split_I1_J,axiom,
% 0.19/0.45 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 0.19/0.45 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ nil_node ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path_split(1)
% 0.19/0.45 thf(fact_288_old_Opath2__split__first__prop,axiom,
% 0.19/0.45 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.45 => ( ? [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 0.19/0.45 & ( P @ X2 ) )
% 0.19/0.45 => ~ ! [M2: node,Ns4: list_node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ M2 )
% 0.19/0.45 => ( ( P @ M2 )
% 0.19/0.45 => ( ! [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ns4 ) ) )
% 0.19/0.45 => ~ ( P @ X2 ) )
% 0.19/0.45 => ~ ( prefix_node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path2_split_first_prop
% 0.19/0.45 thf(fact_289_old_Opath2__prefix__ex,axiom,
% 0.19/0.45 ! [G: g,N: node,Ns: list_node,M: node,M4: node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.45 => ( ( member_node @ M4 @ ( set_node2 @ Ns ) )
% 0.19/0.45 => ~ ! [Ns4: list_node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ M4 )
% 0.19/0.45 => ( ( prefix_node @ Ns4 @ Ns )
% 0.19/0.45 => ( member_node @ M4 @ ( set_node2 @ ( butlast_node @ Ns4 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path2_prefix_ex
% 0.19/0.45 thf(fact_290_old_OCons__path,axiom,
% 0.19/0.45 ! [G: g,Ns: list_node,N2: node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.19/0.45 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns ) ) ) )
% 0.19/0.45 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.Cons_path
% 0.19/0.45 thf(fact_291_old_Opath2__prefix,axiom,
% 0.19/0.45 ! [G: g,N: node,Ns: list_node,M: node,Ns2: list_node,M4: node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.45 => ( ( prefix_node @ ( append_node @ Ns2 @ ( cons_node @ M4 @ nil_node ) ) @ Ns )
% 0.19/0.45 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns2 @ ( cons_node @ M4 @ nil_node ) ) @ M4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path2_prefix
% 0.19/0.45 thf(fact_292_old_Opath__invar,axiom,
% 0.19/0.45 ! [G: g,Ns: list_node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.19/0.45 => ( invar @ G ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path_invar
% 0.19/0.45 thf(fact_293_old_Opath__in___092_060alpha_062n,axiom,
% 0.19/0.45 ! [G: g,Ns: list_node,N: node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.19/0.45 => ( ( member_node @ N @ ( set_node2 @ Ns ) )
% 0.19/0.45 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path_in_\<alpha>n
% 0.19/0.45 thf(fact_294_old_Opath__by__tail,axiom,
% 0.19/0.45 ! [G: g,N: node,N2: node,Ns: list_node,Ms: list_node] :
% 0.19/0.45 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ns ) ) )
% 0.19/0.45 => ( ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) )
% 0.19/0.45 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ms ) ) )
% 0.19/0.45 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ms ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path_by_tail
% 0.19/0.45 thf(fact_295_subset__Collect__conv,axiom,
% 0.19/0.45 ! [S: set_node,P: node > $o] :
% 0.19/0.45 ( ( ord_less_eq_set_node @ S @ ( collect_node @ P ) )
% 0.19/0.45 = ( ! [X3: node] :
% 0.19/0.45 ( ( member_node @ X3 @ S )
% 0.19/0.45 => ( P @ X3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_Collect_conv
% 0.19/0.45 thf(fact_296_ord__eq__le__eq__trans,axiom,
% 0.19/0.45 ! [A: set_node,B: set_node,C: set_node,D: set_node] :
% 0.19/0.45 ( ( A = B )
% 0.19/0.45 => ( ( ord_less_eq_set_node @ B @ C )
% 0.19/0.45 => ( ( C = D )
% 0.19/0.45 => ( ord_less_eq_set_node @ A @ D ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_eq_le_eq_trans
% 0.19/0.45 thf(fact_297_subset__code_I1_J,axiom,
% 0.19/0.45 ! [Xs: list_val,B3: set_val] :
% 0.19/0.45 ( ( ord_less_eq_set_val @ ( set_val2 @ Xs ) @ B3 )
% 0.19/0.45 = ( ! [X3: val] :
% 0.19/0.45 ( ( member_val @ X3 @ ( set_val2 @ Xs ) )
% 0.19/0.45 => ( member_val @ X3 @ B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_code(1)
% 0.19/0.45 thf(fact_298_subset__code_I1_J,axiom,
% 0.19/0.45 ! [Xs: list_node,B3: set_node] :
% 0.19/0.45 ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ B3 )
% 0.19/0.45 = ( ! [X3: node] :
% 0.19/0.45 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.19/0.45 => ( member_node @ X3 @ B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_code(1)
% 0.19/0.45 thf(fact_299_set__subset__Cons,axiom,
% 0.19/0.45 ! [Xs: list_node,X: node] : ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ ( cons_node @ X @ Xs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_subset_Cons
% 0.19/0.45 thf(fact_300_tl__subset,axiom,
% 0.19/0.45 ! [Xs: list_node,A2: set_node] :
% 0.19/0.45 ( ( Xs != nil_node )
% 0.19/0.45 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 0.19/0.45 => ( ord_less_eq_set_node @ ( set_node2 @ ( tl_node @ Xs ) ) @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % tl_subset
% 0.19/0.45 thf(fact_301_butlast__subset,axiom,
% 0.19/0.45 ! [Xs: list_node,A2: set_node] :
% 0.19/0.45 ( ( Xs != nil_node )
% 0.19/0.45 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 0.19/0.45 => ( ord_less_eq_set_node @ ( set_node2 @ ( butlast_node @ Xs ) ) @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % butlast_subset
% 0.19/0.45 thf(fact_302_prefix__snoc,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.19/0.45 ( ( prefix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.19/0.45 = ( ( Xs
% 0.19/0.45 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.19/0.45 | ( prefix_node @ Xs @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % prefix_snoc
% 0.19/0.45 thf(fact_303_old_Opath2__split__first__last,axiom,
% 0.19/0.45 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.45 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.19/0.45 => ~ ! [Ns_1: list_node,Ns_3: list_node,Ns_2: list_node] :
% 0.19/0.45 ( ( Ns
% 0.19/0.45 = ( append_node @ Ns_1 @ ( append_node @ Ns_3 @ Ns_2 ) ) )
% 0.19/0.45 => ( ( prefix_node @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ Ns )
% 0.19/0.45 => ( ( suffix_node @ ( cons_node @ X @ Ns_2 ) @ Ns )
% 0.19/0.45 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ X )
% 0.19/0.45 => ( ~ ( member_node @ X @ ( set_node2 @ Ns_1 ) )
% 0.19/0.45 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_3 @ X )
% 0.19/0.45 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ ( cons_node @ X @ Ns_2 ) @ M )
% 0.19/0.45 => ( member_node @ X @ ( set_node2 @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path2_split_first_last
% 0.19/0.45 thf(fact_304_same__prefix__nil,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ Xs )
% 0.19/0.45 = ( Ys = nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % same_prefix_nil
% 0.19/0.45 thf(fact_305_prefix__order_Odual__order_Orefl,axiom,
% 0.19/0.45 ! [A: list_node] : ( prefix_node @ A @ A ) ).
% 0.19/0.45
% 0.19/0.45 % prefix_order.dual_order.refl
% 0.19/0.45 thf(fact_306_prefix__order_Oorder__refl,axiom,
% 0.19/0.45 ! [X: list_node] : ( prefix_node @ X @ X ) ).
% 0.19/0.45
% 0.19/0.45 % prefix_order.order_refl
% 0.19/0.45 thf(fact_307_suffix__order_Odual__order_Orefl,axiom,
% 0.19/0.45 ! [A: list_node] : ( suffix_node @ A @ A ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_order.dual_order.refl
% 0.19/0.45 thf(fact_308_suffix__order_Oorder__refl,axiom,
% 0.19/0.45 ! [X: list_node] : ( suffix_node @ X @ X ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_order.order_refl
% 0.19/0.45 thf(fact_309_Cons__prefix__Cons,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 0.19/0.45 ( ( prefix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 0.19/0.45 = ( ( X = Y )
% 0.19/0.45 & ( prefix_node @ Xs @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Cons_prefix_Cons
% 0.19/0.45 thf(fact_310_prefix__code_I1_J,axiom,
% 0.19/0.45 ! [Xs: list_node] : ( prefix_node @ nil_node @ Xs ) ).
% 0.19/0.45
% 0.19/0.45 % prefix_code(1)
% 0.19/0.45 thf(fact_311_prefix__Nil,axiom,
% 0.19/0.45 ! [Xs: list_node] :
% 0.19/0.45 ( ( prefix_node @ Xs @ nil_node )
% 0.19/0.45 = ( Xs = nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % prefix_Nil
% 0.19/0.45 thf(fact_312_prefix__bot_Obot_Oextremum__unique,axiom,
% 0.19/0.45 ! [A: list_node] :
% 0.19/0.45 ( ( prefix_node @ A @ nil_node )
% 0.19/0.45 = ( A = nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % prefix_bot.bot.extremum_unique
% 0.19/0.45 thf(fact_313_suffix__bot_Obot_Oextremum__unique,axiom,
% 0.19/0.45 ! [A: list_node] :
% 0.19/0.45 ( ( suffix_node @ A @ nil_node )
% 0.19/0.45 = ( A = nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_bot.bot.extremum_unique
% 0.19/0.45 thf(fact_314_suffix__Nil,axiom,
% 0.19/0.45 ! [Xs: list_node] :
% 0.19/0.45 ( ( suffix_node @ Xs @ nil_node )
% 0.19/0.45 = ( Xs = nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_Nil
% 0.19/0.45 thf(fact_315_same__prefix__prefix,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.19/0.45 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ ( append_node @ Xs @ Zs ) )
% 0.19/0.45 = ( prefix_node @ Ys @ Zs ) ) ).
% 0.19/0.45
% 0.19/0.45 % same_prefix_prefix
% 0.19/0.45 thf(fact_316_same__suffix__suffix,axiom,
% 0.19/0.45 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.19/0.45 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ ( append_node @ Zs @ Xs ) )
% 0.19/0.45 = ( suffix_node @ Ys @ Zs ) ) ).
% 0.19/0.45
% 0.19/0.45 % same_suffix_suffix
% 0.19/0.45 thf(fact_317_old_Opath2__split__last__prop,axiom,
% 0.19/0.45 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.45 => ( ? [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 0.19/0.45 & ( P @ X2 ) )
% 0.19/0.45 => ~ ! [N3: node,Ns4: list_node] :
% 0.19/0.45 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N3 @ Ns4 @ M )
% 0.19/0.45 => ( ( P @ N3 )
% 0.19/0.45 => ( ! [X2: node] :
% 0.19/0.45 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns4 ) ) )
% 0.19/0.45 => ~ ( P @ X2 ) )
% 0.19/0.45 => ~ ( suffix_node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.path2_split_last_prop
% 0.19/0.45 thf(fact_318_same__suffix__nil,axiom,
% 0.19/0.45 ! [Ys: list_node,Xs: list_node] :
% 0.19/0.45 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ Xs )
% 0.19/0.45 = ( Ys = nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % same_suffix_nil
% 0.19/0.45 thf(fact_319_snoc__suffix__snoc,axiom,
% 0.19/0.45 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 0.19/0.45 ( ( suffix_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.19/0.45 = ( ( X = Y )
% 0.19/0.45 & ( suffix_node @ Xs @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % snoc_suffix_snoc
% 0.19/0.45 thf(fact_320_suffix__snoc,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.19/0.45 ( ( suffix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.19/0.45 = ( ( Xs = nil_node )
% 0.19/0.45 | ? [Zs3: list_node] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( append_node @ Zs3 @ ( cons_node @ Y @ nil_node ) ) )
% 0.19/0.45 & ( suffix_node @ Zs3 @ Ys ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_snoc
% 0.19/0.45 thf(fact_321_suffix__tl,axiom,
% 0.19/0.45 ! [Xs: list_node] : ( suffix_node @ ( tl_node @ Xs ) @ Xs ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_tl
% 0.19/0.45 thf(fact_322_suffix__Cons,axiom,
% 0.19/0.45 ! [Xs: list_node,Y: node,Ys: list_node] :
% 0.19/0.45 ( ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) )
% 0.19/0.45 = ( ( Xs
% 0.19/0.45 = ( cons_node @ Y @ Ys ) )
% 0.19/0.45 | ( suffix_node @ Xs @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_Cons
% 0.19/0.45 thf(fact_323_suffix__ConsD,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ Ys )
% 0.19/0.45 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_ConsD
% 0.19/0.45 thf(fact_324_suffix__ConsI,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.19/0.45 ( ( suffix_node @ Xs @ Ys )
% 0.19/0.45 => ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_ConsI
% 0.19/0.45 thf(fact_325_suffix__ConsD2,axiom,
% 0.19/0.45 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 0.19/0.45 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 0.19/0.45 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_ConsD2
% 0.19/0.45 thf(fact_326_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 0.19/0.45 ! [A: list_node] :
% 0.19/0.45 ( ( suffix_node @ A @ nil_node )
% 0.19/0.45 => ( A = nil_node ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_bot.bot.extremum_uniqueI
% 0.19/0.45 thf(fact_327_suffix__bot_Obot_Oextremum,axiom,
% 0.19/0.45 ! [A: list_node] : ( suffix_node @ nil_node @ A ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_bot.bot.extremum
% 0.19/0.45 thf(fact_328_Nil__suffix,axiom,
% 0.19/0.45 ! [Xs: list_node] : ( suffix_node @ nil_node @ Xs ) ).
% 0.19/0.45
% 0.19/0.45 % Nil_suffix
% 0.19/0.45 thf(fact_329_set__mono__suffix,axiom,
% 0.19/0.45 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.45 ( ( suffix_node @ Xs @ Ys )
% 0.19/0.45 => ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_mono_suffix
% 0.19/0.45 thf(fact_330_not__suffix__cases,axiom,
% 0.19/0.45 ! [Ps2: list_node,Ls: list_node] :
% 0.19/0.45 ( ~ ( suffix_node @ Ps2 @ Ls )
% 0.19/0.45 => ( ( ( Ps2 != nil_node )
% 0.19/0.45 => ( Ls != nil_node ) )
% 0.19/0.45 => ( ! [A3: node,As: list_node] :
% 0.19/0.45 ( ( Ps2
% 0.19/0.45 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 0.19/0.45 => ! [X4: node,Xs2: list_node] :
% 0.19/0.45 ( ( Ls
% 0.19/0.45 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 0.19/0.45 => ( ( X4 = A3 )
% 0.19/0.45 => ( suffix_node @ As @ Xs2 ) ) ) )
% 0.19/0.45 => ~ ! [A3: node] :
% 0.19/0.45 ( ? [As: list_node] :
% 0.19/0.45 ( Ps2
% 0.19/0.45 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 0.19/0.45 => ! [X4: node] :
% 0.19/0.45 ( ? [Xs2: list_node] :
% 0.19/0.45 ( Ls
% 0.19/0.45 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 0.19/0.45 => ( X4 = A3 ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_suffix_cases
% 0.19/0.45 thf(fact_331_not__suffix__induct,axiom,
% 0.19/0.45 ! [Ps2: list_node,Ls: list_node,P: list_node > list_node > $o] :
% 0.19/0.45 ( ~ ( suffix_node @ Ps2 @ Ls )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( X4 != Y3 )
% 0.19/0.45 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) )
% 0.19/0.45 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 0.19/0.45 ( ( X4 = Y3 )
% 0.19/0.45 => ( ~ ( suffix_node @ Xs2 @ Ys3 )
% 0.19/0.45 => ( ( P @ Xs2 @ Ys3 )
% 0.19/0.45 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) ) ) )
% 0.19/0.45 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_suffix_induct
% 0.19/0.45 thf(fact_332_suffix__order_Odual__order_Oantisym,axiom,
% 0.19/0.45 ! [B: list_node,A: list_node] :
% 0.19/0.45 ( ( suffix_node @ B @ A )
% 0.19/0.45 => ( ( suffix_node @ A @ B )
% 0.19/0.45 => ( A = B ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % suffix_order.dual_order.antisym
% 0.19/0.45 thf(fact_333_suffix__order_Odual__order_Oeq__iff,axiom,
% 0.19/0.45 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.19/0.45 = ( ^ [A4: list_node,B4: list_node] :
% 0.19/0.45 ( ( suffix_node @ B4 @ A4 )
% 0.19/0.45 & ( suffix_node @ A4 @ B4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.dual_order.eq_iff
% 0.29/0.45 thf(fact_334_suffix__order_Odual__order_Otrans,axiom,
% 0.29/0.45 ! [B: list_node,A: list_node,C: list_node] :
% 0.29/0.45 ( ( suffix_node @ B @ A )
% 0.29/0.45 => ( ( suffix_node @ C @ B )
% 0.29/0.45 => ( suffix_node @ C @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.dual_order.trans
% 0.29/0.45 thf(fact_335_suffix__order_Oord__le__eq__trans,axiom,
% 0.29/0.45 ! [A: list_node,B: list_node,C: list_node] :
% 0.29/0.45 ( ( suffix_node @ A @ B )
% 0.29/0.45 => ( ( B = C )
% 0.29/0.45 => ( suffix_node @ A @ C ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.ord_le_eq_trans
% 0.29/0.45 thf(fact_336_suffix__order_Oord__eq__le__trans,axiom,
% 0.29/0.45 ! [A: list_node,B: list_node,C: list_node] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( ( suffix_node @ B @ C )
% 0.29/0.45 => ( suffix_node @ A @ C ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.ord_eq_le_trans
% 0.29/0.45 thf(fact_337_suffix__order_Oorder_Oantisym,axiom,
% 0.29/0.45 ! [A: list_node,B: list_node] :
% 0.29/0.45 ( ( suffix_node @ A @ B )
% 0.29/0.45 => ( ( suffix_node @ B @ A )
% 0.29/0.45 => ( A = B ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.order.antisym
% 0.29/0.45 thf(fact_338_suffix__order_Oorder_Oeq__iff,axiom,
% 0.29/0.45 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.29/0.45 = ( ^ [A4: list_node,B4: list_node] :
% 0.29/0.45 ( ( suffix_node @ A4 @ B4 )
% 0.29/0.45 & ( suffix_node @ B4 @ A4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.order.eq_iff
% 0.29/0.45 thf(fact_339_suffix__order_Oantisym__conv,axiom,
% 0.29/0.45 ! [Y: list_node,X: list_node] :
% 0.29/0.45 ( ( suffix_node @ Y @ X )
% 0.29/0.45 => ( ( suffix_node @ X @ Y )
% 0.29/0.45 = ( X = Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.antisym_conv
% 0.29/0.45 thf(fact_340_suffix__order_Oorder__trans,axiom,
% 0.29/0.45 ! [X: list_node,Y: list_node,Z3: list_node] :
% 0.29/0.45 ( ( suffix_node @ X @ Y )
% 0.29/0.45 => ( ( suffix_node @ Y @ Z3 )
% 0.29/0.45 => ( suffix_node @ X @ Z3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.order_trans
% 0.29/0.45 thf(fact_341_suffix__order_Oorder_Otrans,axiom,
% 0.29/0.45 ! [A: list_node,B: list_node,C: list_node] :
% 0.29/0.45 ( ( suffix_node @ A @ B )
% 0.29/0.45 => ( ( suffix_node @ B @ C )
% 0.29/0.45 => ( suffix_node @ A @ C ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.order.trans
% 0.29/0.45 thf(fact_342_suffix__order_Oeq__refl,axiom,
% 0.29/0.45 ! [X: list_node,Y: list_node] :
% 0.29/0.45 ( ( X = Y )
% 0.29/0.45 => ( suffix_node @ X @ Y ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.eq_refl
% 0.29/0.45 thf(fact_343_suffix__order_Oantisym,axiom,
% 0.29/0.45 ! [X: list_node,Y: list_node] :
% 0.29/0.45 ( ( suffix_node @ X @ Y )
% 0.29/0.45 => ( ( suffix_node @ Y @ X )
% 0.29/0.45 => ( X = Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.antisym
% 0.29/0.45 thf(fact_344_suffix__order_Oeq__iff,axiom,
% 0.29/0.45 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.29/0.45 = ( ^ [X3: list_node,Y2: list_node] :
% 0.29/0.45 ( ( suffix_node @ X3 @ Y2 )
% 0.29/0.45 & ( suffix_node @ Y2 @ X3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_order.eq_iff
% 0.29/0.45 thf(fact_345_suffix__same__cases,axiom,
% 0.29/0.45 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 0.29/0.45 ( ( suffix_node @ Xs_1 @ Ys )
% 0.29/0.45 => ( ( suffix_node @ Xs_2 @ Ys )
% 0.29/0.45 => ( ( suffix_node @ Xs_1 @ Xs_2 )
% 0.29/0.45 | ( suffix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_same_cases
% 0.29/0.45 thf(fact_346_suffixE,axiom,
% 0.29/0.45 ! [Xs: list_node,Ys: list_node] :
% 0.29/0.45 ( ( suffix_node @ Xs @ Ys )
% 0.29/0.45 => ~ ! [Zs2: list_node] :
% 0.29/0.45 ( Ys
% 0.29/0.45 != ( append_node @ Zs2 @ Xs ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffixE
% 0.29/0.45 thf(fact_347_suffixI,axiom,
% 0.29/0.45 ! [Ys: list_node,Zs: list_node,Xs: list_node] :
% 0.29/0.45 ( ( Ys
% 0.29/0.45 = ( append_node @ Zs @ Xs ) )
% 0.29/0.45 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffixI
% 0.29/0.45 thf(fact_348_Sublist_Osuffix__def,axiom,
% 0.29/0.45 ( suffix_node
% 0.29/0.45 = ( ^ [Xs3: list_node,Ys2: list_node] :
% 0.29/0.45 ? [Zs3: list_node] :
% 0.29/0.45 ( Ys2
% 0.29/0.45 = ( append_node @ Zs3 @ Xs3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Sublist.suffix_def
% 0.29/0.45 thf(fact_349_suffix__append,axiom,
% 0.29/0.45 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.29/0.45 ( ( suffix_node @ Xs @ ( append_node @ Ys @ Zs ) )
% 0.29/0.45 = ( ( suffix_node @ Xs @ Zs )
% 0.29/0.45 | ? [Xs6: list_node] :
% 0.29/0.45 ( ( Xs
% 0.29/0.45 = ( append_node @ Xs6 @ Zs ) )
% 0.29/0.45 & ( suffix_node @ Xs6 @ Ys ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_append
% 0.29/0.45 thf(fact_350_suffix__appendD,axiom,
% 0.29/0.45 ! [Zs: list_node,Xs: list_node,Ys: list_node] :
% 0.29/0.45 ( ( suffix_node @ ( append_node @ Zs @ Xs ) @ Ys )
% 0.29/0.45 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_appendD
% 0.29/0.45 thf(fact_351_suffix__appendI,axiom,
% 0.29/0.45 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.29/0.45 ( ( suffix_node @ Xs @ Ys )
% 0.29/0.45 => ( suffix_node @ Xs @ ( append_node @ Zs @ Ys ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % suffix_appendI
% 0.29/0.45
% 0.29/0.45 % Conjectures (1)
% 0.29/0.45 thf(conj_0,conjecture,
% 0.29/0.45 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 2.65/1.48 ---- Embedded in THF ---
% 2.65/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.65/1.48 %%% Generated on Tue Feb 24 08:25:33 EST 2026
% 2.65/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.65/1.48 %%% Logic specification used:
% 2.65/1.48 %%% thf(spec, logic, $$dhol).
% 2.65/1.48
% 2.65/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2DTF26027.p
% See solution above
% 2.65/1.48 ------------------------
% 2.87/1.51 ---- Cleaned THF ---
% 2.87/1.51 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 2.87/1.51 list_P561207620_edgeD: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__val_J_J,type,
% 2.87/1.51 option_list_val: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 2.87/1.51 produc1432036078de_val: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_t__List__Olist_It__List__Olist_Itf__node_J_J,type,
% 2.87/1.51 list_list_node: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__node_J_J,type,
% 2.87/1.51 set_list_node: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_t__List__Olist_Itf__node_J,type,
% 2.87/1.51 list_node: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_t__List__Olist_Itf__val_J,type,
% 2.87/1.51 list_val: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_t__Set__Oset_Itf__node_J,type,
% 2.87/1.51 set_node: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 2.87/1.51 set_val: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_tf__node,type,
% 2.87/1.51 node: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_tf__val,type,
% 2.87/1.51 val: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(ty_n_tf__g,type,
% 2.87/1.51 g: $tType ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Graph__path_Ograph__path__base_Opath2_001tf__g_001tf__node_001tf__edgeD,type,
% 2.87/1.51 graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Graph__path_Ograph__path__base_Opath_001tf__g_001tf__node_001tf__edgeD,type,
% 2.87/1.51 graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors_001tf__g_001tf__node_001tf__edgeD,type,
% 2.87/1.51 graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Oappend_001t__List__Olist_Itf__node_J,type,
% 2.87/1.51 append_list_node: list_list_node > list_list_node > list_list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Oappend_001tf__node,type,
% 2.87/1.51 append_node: list_node > list_node > list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Oappend_001tf__val,type,
% 2.87/1.51 append_val: list_val > list_val > list_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__node_J,type,
% 2.87/1.51 butlast_list_node: list_list_node > list_list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Obutlast_001tf__node,type,
% 2.87/1.51 butlast_node: list_node > list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Obutlast_001tf__val,type,
% 2.87/1.51 butlast_val: list_val > list_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__node_J,type,
% 2.87/1.51 cons_list_node: list_node > list_list_node > list_list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_OCons_001tf__node,type,
% 2.87/1.51 cons_node: node > list_node > list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_OCons_001tf__val,type,
% 2.87/1.51 cons_val: val > list_val > list_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__node_J,type,
% 2.87/1.51 nil_list_node: list_list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_ONil_001tf__node,type,
% 2.87/1.51 nil_node: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_ONil_001tf__val,type,
% 2.87/1.51 nil_val: list_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Ohd_001t__List__Olist_Itf__node_J,type,
% 2.87/1.51 hd_list_node: list_list_node > list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Ohd_001tf__node,type,
% 2.87/1.51 hd_node: list_node > node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Ohd_001tf__val,type,
% 2.87/1.51 hd_val: list_val > val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__node_J,type,
% 2.87/1.51 set_list_node2: list_list_node > set_list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Oset_001tf__node,type,
% 2.87/1.51 set_node2: list_node > set_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Oset_001tf__val,type,
% 2.87/1.51 set_val2: list_val > set_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Otl_001t__List__Olist_Itf__node_J,type,
% 2.87/1.51 tl_list_node: list_list_node > list_list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Otl_001tf__node,type,
% 2.87/1.51 tl_node: list_node > list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_List_Olist_Otl_001tf__val,type,
% 2.87/1.51 tl_val: list_val > list_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Minimality_Ograph__path_OpathsConverge_001tf__g_001tf__node_001tf__edgeD,type,
% 2.87/1.51 graph_2009891965_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > list_node > node > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__node_J,type,
% 2.87/1.51 ord_less_eq_set_node: set_node > set_node > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__val_J,type,
% 2.87/1.51 ord_less_eq_set_val: set_val > set_val > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.87/1.51 sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode_001tf__g_001tf__node_001tf__val,type,
% 2.87/1.51 sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg_001tf__g_001tf__node_001tf__val,type,
% 2.87/1.51 sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Set_OCollect_001tf__node,type,
% 2.87/1.51 collect_node: ( node > $o ) > set_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Set_OCollect_001tf__val,type,
% 2.87/1.51 collect_val: ( val > $o ) > set_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Sublist_Oprefix_001tf__node,type,
% 2.87/1.51 prefix_node: list_node > list_node > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_Sublist_Osuffix_001tf__node,type,
% 2.87/1.51 suffix_node: list_node > list_node > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_member_001t__List__Olist_Itf__node_J,type,
% 2.87/1.51 member_list_node: list_node > set_list_node > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_member_001tf__node,type,
% 2.87/1.51 member_node: node > set_node > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_c_member_001tf__val,type,
% 2.87/1.51 member_val: val > set_val > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v__092_060alpha_062n,type,
% 2.87/1.51 alpha_n: g > list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 2.87/1.51 phi_r: val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_defs,type,
% 2.87/1.51 defs: g > node > set_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_g,type,
% 2.87/1.51 g2: g ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_i____,type,
% 2.87/1.51 i: node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_inEdges_H,type,
% 2.87/1.51 inEdges: g > node > list_P561207620_edgeD ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_invar,type,
% 2.87/1.51 invar: g > $o ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_m,type,
% 2.87/1.51 m: node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_ms,type,
% 2.87/1.51 ms: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_ms_H____,type,
% 2.87/1.51 ms2: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_n,type,
% 2.87/1.51 n: node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_ns,type,
% 2.87/1.51 ns: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_phis,type,
% 2.87/1.51 phis: g > produc1432036078de_val > option_list_val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 2.87/1.51 pred_phi_r: node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_r,type,
% 2.87/1.51 r: val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_ri____,type,
% 2.87/1.51 ri: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_rs_H____,type,
% 2.87/1.51 rs: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_rs_H__rest____,type,
% 2.87/1.51 rs_rest: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_rs____,type,
% 2.87/1.51 rs2: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_s,type,
% 2.87/1.51 s: val ).
% 2.87/1.51
% 2.87/1.51 thf(sy_v_tmp____,type,
% 2.87/1.51 tmp: list_node ).
% 2.87/1.51
% 2.87/1.51 thf(fact_0_m__i__differ_I2_J,axiom,
% 2.87/1.51 m != i ).
% 2.87/1.51
% 2.87/1.51 thf(fact_1_rs_H__rest__def,axiom,
% 2.87/1.51 ( rs
% 2.87/1.51 = ( append_node @ tmp @ ( cons_node @ i @ rs_rest ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_2_old_Oinvar,axiom,
% 2.87/1.51 ! [G: g] : ( invar @ G ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_3_old_Opath2__split_I2_J,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 2.87/1.51 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns2 ) @ M ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_4_False,axiom,
% 2.87/1.51 r != phi_r ).
% 2.87/1.51
% 2.87/1.51 thf(fact_5_rs_H__props_I1_J,axiom,
% 2.87/1.51 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 2.87/1.51
% 2.87/1.51 thf(fact_6_ms_H__props_I1_J,axiom,
% 2.87/1.51 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 2.87/1.51
% 2.87/1.51 thf(fact_7_rs_H__rest__prop,axiom,
% 2.87/1.51 ( rs
% 2.87/1.51 = ( append_node @ ri @ rs_rest ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_8_rs_H__props_I3_J,axiom,
% 2.87/1.51 member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_9_old_Opath2__not__Nil,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( Ns != nil_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_10_old_Opath2__not__Nil2,axiom,
% 2.87/1.51 ! [G: g,N: node,M: node] :
% 2.87/1.51 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ nil_node @ M ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_11_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_12_old_Opath2__hd__in__ns,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( member_node @ N @ ( set_node2 @ Ns ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_13_old_Opath2__in___092_060alpha_062n,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,L: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( member_node @ L @ ( set_node2 @ Ns ) )
% 2.87/1.51 => ( member_node @ L @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_14_old_Opath2__last__in__ns,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( member_node @ M @ ( set_node2 @ Ns ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_15_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_16_old_Opath2__forget__hd,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ Ns ) @ Ns @ M ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_17_old_Opath2__hd,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( N
% 2.87/1.51 = ( hd_node @ Ns ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_18__092_060open_062ri_A_061_Atmp_A_064_A_091i_093_092_060close_062,axiom,
% 2.87/1.51 ( ri
% 2.87/1.51 = ( append_node @ tmp @ ( cons_node @ i @ nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_19__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H__rest_O_Ars_H_A_061_Ari_A_064_Ars_H__rest_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.87/1.51 ~ ! [Rs_rest: list_node] :
% 2.87/1.51 ( rs
% 2.87/1.51 != ( append_node @ ri @ Rs_rest ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_20_ri__props_I2_J,axiom,
% 2.87/1.51 member_node @ i @ ( set_node2 @ ms ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_21_m__i__differ_I1_J,axiom,
% 2.87/1.51 ( i
% 2.87/1.51 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tmp_O_Ari_A_061_Atmp_A_064_A_091i_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.87/1.51 ~ ! [Tmp: list_node] :
% 2.87/1.51 ( ri
% 2.87/1.51 != ( append_node @ Tmp @ ( cons_node @ i @ nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_23_ri__props_I1_J,axiom,
% 2.87/1.51 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 2.87/1.51
% 2.87/1.51 thf(fact_24_old_Opath2__split_I1_J,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 2.87/1.51 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ nil_node ) ) @ N2 ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_25__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 2.87/1.51 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 2.87/1.51 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_26__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.87/1.51 ( ( i
% 2.87/1.51 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.87/1.51 => ( ( ( i
% 2.87/1.51 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.87/1.51 => ( m != i ) )
% 2.87/1.51 => ~ ( ( i
% 2.87/1.51 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 2.87/1.51 => ( m = i ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_27_old_Oempty__path2,axiom,
% 2.87/1.51 ! [N: node,G: g] :
% 2.87/1.51 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.87/1.51 => ( ( invar @ G )
% 2.87/1.51 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( cons_node @ N @ nil_node ) @ N ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_28_ms_H__props_I3_J,axiom,
% 2.87/1.51 ~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_29_assms_I10_J,axiom,
% 2.87/1.51 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 2.87/1.51
% 2.87/1.51 thf(fact_30_rs_H__props_I4_J,axiom,
% 2.87/1.51 member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_31_assms_I7_J,axiom,
% 2.87/1.51 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_32_rs__props_I1_J,axiom,
% 2.87/1.51 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_33_rs__def,axiom,
% 2.87/1.51 ( rs2
% 2.87/1.51 = ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_34_assms_I8_J,axiom,
% 2.87/1.51 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_35_rs_H__loopfree,axiom,
% 2.87/1.51 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_36_hd__append2,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val] :
% 2.87/1.51 ( ( Xs != nil_val )
% 2.87/1.51 => ( ( hd_val @ ( append_val @ Xs @ Ys ) )
% 2.87/1.51 = ( hd_val @ Xs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_37_hd__append2,axiom,
% 2.87/1.51 ! [Xs: list_list_node,Ys: list_list_node] :
% 2.87/1.51 ( ( Xs != nil_list_node )
% 2.87/1.51 => ( ( hd_list_node @ ( append_list_node @ Xs @ Ys ) )
% 2.87/1.51 = ( hd_list_node @ Xs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_38_hd__append2,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 2.87/1.51 = ( hd_node @ Xs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_39_append1__eq__conv,axiom,
% 2.87/1.51 ! [Xs: list_val,X: val,Ys: list_val,Y: val] :
% 2.87/1.51 ( ( ( append_val @ Xs @ ( cons_val @ X @ nil_val ) )
% 2.87/1.51 = ( append_val @ Ys @ ( cons_val @ Y @ nil_val ) ) )
% 2.87/1.51 = ( ( Xs = Ys )
% 2.87/1.51 & ( X = Y ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_40_append1__eq__conv,axiom,
% 2.87/1.51 ! [Xs: list_list_node,X: list_node,Ys: list_list_node,Y: list_node] :
% 2.87/1.51 ( ( ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) )
% 2.87/1.51 = ( append_list_node @ Ys @ ( cons_list_node @ Y @ nil_list_node ) ) )
% 2.87/1.51 = ( ( Xs = Ys )
% 2.87/1.51 & ( X = Y ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_41_append1__eq__conv,axiom,
% 2.87/1.51 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 2.87/1.51 ( ( ( append_node @ Xs @ ( cons_node @ X @ nil_node ) )
% 2.87/1.51 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 2.87/1.51 = ( ( Xs = Ys )
% 2.87/1.51 & ( X = Y ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_42_list__ee__eq__leel_I1_J,axiom,
% 2.87/1.51 ! [E1: val,E2: val,L1: list_val,E12: val,E22: val,L2: list_val] :
% 2.87/1.51 ( ( ( cons_val @ E1 @ ( cons_val @ E2 @ nil_val ) )
% 2.87/1.51 = ( append_val @ L1 @ ( cons_val @ E12 @ ( cons_val @ E22 @ L2 ) ) ) )
% 2.87/1.51 = ( ( L1 = nil_val )
% 2.87/1.51 & ( E1 = E12 )
% 2.87/1.51 & ( E2 = E22 )
% 2.87/1.51 & ( L2 = nil_val ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_43_list__ee__eq__leel_I1_J,axiom,
% 2.87/1.51 ! [E1: list_node,E2: list_node,L1: list_list_node,E12: list_node,E22: list_node,L2: list_list_node] :
% 2.87/1.51 ( ( ( cons_list_node @ E1 @ ( cons_list_node @ E2 @ nil_list_node ) )
% 2.87/1.51 = ( append_list_node @ L1 @ ( cons_list_node @ E12 @ ( cons_list_node @ E22 @ L2 ) ) ) )
% 2.87/1.51 = ( ( L1 = nil_list_node )
% 2.87/1.51 & ( E1 = E12 )
% 2.87/1.51 & ( E2 = E22 )
% 2.87/1.51 & ( L2 = nil_list_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_44_list__ee__eq__leel_I1_J,axiom,
% 2.87/1.51 ! [E1: node,E2: node,L1: list_node,E12: node,E22: node,L2: list_node] :
% 2.87/1.51 ( ( ( cons_node @ E1 @ ( cons_node @ E2 @ nil_node ) )
% 2.87/1.51 = ( append_node @ L1 @ ( cons_node @ E12 @ ( cons_node @ E22 @ L2 ) ) ) )
% 2.87/1.51 = ( ( L1 = nil_node )
% 2.87/1.51 & ( E1 = E12 )
% 2.87/1.51 & ( E2 = E22 )
% 2.87/1.51 & ( L2 = nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_45_list__ee__eq__leel_I2_J,axiom,
% 2.87/1.51 ! [L1: list_val,E12: val,E22: val,L2: list_val,E1: val,E2: val] :
% 2.87/1.51 ( ( ( append_val @ L1 @ ( cons_val @ E12 @ ( cons_val @ E22 @ L2 ) ) )
% 2.87/1.51 = ( cons_val @ E1 @ ( cons_val @ E2 @ nil_val ) ) )
% 2.87/1.51 = ( ( L1 = nil_val )
% 2.87/1.51 & ( E1 = E12 )
% 2.87/1.51 & ( E2 = E22 )
% 2.87/1.51 & ( L2 = nil_val ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_46_list__ee__eq__leel_I2_J,axiom,
% 2.87/1.51 ! [L1: list_list_node,E12: list_node,E22: list_node,L2: list_list_node,E1: list_node,E2: list_node] :
% 2.87/1.51 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E12 @ ( cons_list_node @ E22 @ L2 ) ) )
% 2.87/1.51 = ( cons_list_node @ E1 @ ( cons_list_node @ E2 @ nil_list_node ) ) )
% 2.87/1.51 = ( ( L1 = nil_list_node )
% 2.87/1.51 & ( E1 = E12 )
% 2.87/1.51 & ( E2 = E22 )
% 2.87/1.51 & ( L2 = nil_list_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_47_list__ee__eq__leel_I2_J,axiom,
% 2.87/1.51 ! [L1: list_node,E12: node,E22: node,L2: list_node,E1: node,E2: node] :
% 2.87/1.51 ( ( ( append_node @ L1 @ ( cons_node @ E12 @ ( cons_node @ E22 @ L2 ) ) )
% 2.87/1.51 = ( cons_node @ E1 @ ( cons_node @ E2 @ nil_node ) ) )
% 2.87/1.51 = ( ( L1 = nil_node )
% 2.87/1.51 & ( E1 = E12 )
% 2.87/1.51 & ( E2 = E22 )
% 2.87/1.51 & ( L2 = nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_48_list__se__match_I1_J,axiom,
% 2.87/1.51 ! [L1: list_val,L2: list_val,A: val] :
% 2.87/1.51 ( ( L1 != nil_val )
% 2.87/1.51 => ( ( ( append_val @ L1 @ L2 )
% 2.87/1.51 = ( cons_val @ A @ nil_val ) )
% 2.87/1.51 = ( ( L1
% 2.87/1.51 = ( cons_val @ A @ nil_val ) )
% 2.87/1.51 & ( L2 = nil_val ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_49_list__se__match_I1_J,axiom,
% 2.87/1.51 ! [L1: list_list_node,L2: list_list_node,A: list_node] :
% 2.87/1.51 ( ( L1 != nil_list_node )
% 2.87/1.51 => ( ( ( append_list_node @ L1 @ L2 )
% 2.87/1.51 = ( cons_list_node @ A @ nil_list_node ) )
% 2.87/1.51 = ( ( L1
% 2.87/1.51 = ( cons_list_node @ A @ nil_list_node ) )
% 2.87/1.51 & ( L2 = nil_list_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_50_list__se__match_I1_J,axiom,
% 2.87/1.51 ! [L1: list_node,L2: list_node,A: node] :
% 2.87/1.51 ( ( L1 != nil_node )
% 2.87/1.51 => ( ( ( append_node @ L1 @ L2 )
% 2.87/1.51 = ( cons_node @ A @ nil_node ) )
% 2.87/1.51 = ( ( L1
% 2.87/1.51 = ( cons_node @ A @ nil_node ) )
% 2.87/1.51 & ( L2 = nil_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_51_ri__props_I3_J,axiom,
% 2.87/1.51 ! [X2: node] :
% 2.87/1.51 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ ri ) ) )
% 2.87/1.51 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_52_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 2.87/1.51 ! [X: list_node,Xs: list_list_node,Ys: list_list_node,Y: list_node] :
% 2.87/1.51 ( ( member_list_node @ X @ ( set_list_node2 @ Xs ) )
% 2.87/1.51 => ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ ( append_list_node @ Ys @ ( cons_list_node @ Y @ Xs ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_53_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val,Ys: list_val,Y: val] :
% 2.87/1.51 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.51 => ( member_val @ X @ ( set_val2 @ ( tl_val @ ( append_val @ Ys @ ( cons_val @ Y @ Xs ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_54_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node,Ys: list_node,Y: node] :
% 2.87/1.51 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.51 => ( member_node @ X @ ( set_node2 @ ( tl_node @ ( append_node @ Ys @ ( cons_node @ Y @ Xs ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_55_list_Oinject,axiom,
% 2.87/1.51 ! [X21: val,X22: list_val,Y21: val,Y22: list_val] :
% 2.87/1.51 ( ( ( cons_val @ X21 @ X22 )
% 2.87/1.51 = ( cons_val @ Y21 @ Y22 ) )
% 2.87/1.51 = ( ( X21 = Y21 )
% 2.87/1.51 & ( X22 = Y22 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_56_list_Oinject,axiom,
% 2.87/1.51 ! [X21: list_node,X22: list_list_node,Y21: list_node,Y22: list_list_node] :
% 2.87/1.51 ( ( ( cons_list_node @ X21 @ X22 )
% 2.87/1.51 = ( cons_list_node @ Y21 @ Y22 ) )
% 2.87/1.51 = ( ( X21 = Y21 )
% 2.87/1.51 & ( X22 = Y22 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_57_list_Oinject,axiom,
% 2.87/1.51 ! [X21: node,X22: list_node,Y21: node,Y22: list_node] :
% 2.87/1.51 ( ( ( cons_node @ X21 @ X22 )
% 2.87/1.51 = ( cons_node @ Y21 @ Y22 ) )
% 2.87/1.51 = ( ( X21 = Y21 )
% 2.87/1.51 & ( X22 = Y22 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_58_same__append__eq,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 2.87/1.51 ( ( ( append_val @ Xs @ Ys )
% 2.87/1.51 = ( append_val @ Xs @ Zs ) )
% 2.87/1.51 = ( Ys = Zs ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_59_same__append__eq,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.87/1.51 ( ( ( append_node @ Xs @ Ys )
% 2.87/1.51 = ( append_node @ Xs @ Zs ) )
% 2.87/1.51 = ( Ys = Zs ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_60_mem__Collect__eq,axiom,
% 2.87/1.51 ! [A: val,P: val > $o] :
% 2.87/1.51 ( ( member_val @ A @ ( collect_val @ P ) )
% 2.87/1.51 = ( P @ A ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_61_mem__Collect__eq,axiom,
% 2.87/1.51 ! [A: node,P: node > $o] :
% 2.87/1.51 ( ( member_node @ A @ ( collect_node @ P ) )
% 2.87/1.51 = ( P @ A ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_62_Collect__mem__eq,axiom,
% 2.87/1.51 ! [A2: set_val] :
% 2.87/1.51 ( ( collect_val
% 2.87/1.51 @ ^ [X3: val] : ( member_val @ X3 @ A2 ) )
% 2.87/1.51 = A2 ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_63_Collect__mem__eq,axiom,
% 2.87/1.51 ! [A2: set_node] :
% 2.87/1.51 ( ( collect_node
% 2.87/1.51 @ ^ [X3: node] : ( member_node @ X3 @ A2 ) )
% 2.87/1.51 = A2 ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_64_Collect__cong,axiom,
% 2.87/1.51 ! [P: node > $o,Q: node > $o] :
% 2.87/1.51 ( ! [X4: node] :
% 2.87/1.51 ( ( P @ X4 )
% 2.87/1.51 = ( Q @ X4 ) )
% 2.87/1.51 => ( ( collect_node @ P )
% 2.87/1.51 = ( collect_node @ Q ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_65_Collect__cong,axiom,
% 2.87/1.51 ! [P: val > $o,Q: val > $o] :
% 2.87/1.51 ( ! [X4: val] :
% 2.87/1.51 ( ( P @ X4 )
% 2.87/1.51 = ( Q @ X4 ) )
% 2.87/1.51 => ( ( collect_val @ P )
% 2.87/1.51 = ( collect_val @ Q ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_66_append__same__eq,axiom,
% 2.87/1.51 ! [Ys: list_val,Xs: list_val,Zs: list_val] :
% 2.87/1.51 ( ( ( append_val @ Ys @ Xs )
% 2.87/1.51 = ( append_val @ Zs @ Xs ) )
% 2.87/1.51 = ( Ys = Zs ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_67_append__same__eq,axiom,
% 2.87/1.51 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 2.87/1.51 ( ( ( append_node @ Ys @ Xs )
% 2.87/1.51 = ( append_node @ Zs @ Xs ) )
% 2.87/1.51 = ( Ys = Zs ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_68_append__assoc,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 2.87/1.51 ( ( append_val @ ( append_val @ Xs @ Ys ) @ Zs )
% 2.87/1.51 = ( append_val @ Xs @ ( append_val @ Ys @ Zs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_69_append__assoc,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.87/1.51 ( ( append_node @ ( append_node @ Xs @ Ys ) @ Zs )
% 2.87/1.51 = ( append_node @ Xs @ ( append_node @ Ys @ Zs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_70_append_Oassoc,axiom,
% 2.87/1.51 ! [A: list_val,B: list_val,C: list_val] :
% 2.87/1.51 ( ( append_val @ ( append_val @ A @ B ) @ C )
% 2.87/1.51 = ( append_val @ A @ ( append_val @ B @ C ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_71_append_Oassoc,axiom,
% 2.87/1.51 ! [A: list_node,B: list_node,C: list_node] :
% 2.87/1.51 ( ( append_node @ ( append_node @ A @ B ) @ C )
% 2.87/1.51 = ( append_node @ A @ ( append_node @ B @ C ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_72_old_Opredecessor__is__node,axiom,
% 2.87/1.51 ! [N: node,G: g,N2: node] :
% 2.87/1.51 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 2.87/1.51 => ( ( invar @ G )
% 2.87/1.51 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_73_old_Osuccessor__is__node,axiom,
% 2.87/1.51 ! [N: node,G: g,N2: node] :
% 2.87/1.51 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 2.87/1.51 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.87/1.51 => ( ( invar @ G )
% 2.87/1.51 => ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_74_old_Osuccessor__in___092_060alpha_062n,axiom,
% 2.87/1.51 ! [G: g,N: node] :
% 2.87/1.51 ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 2.87/1.51 != nil_node )
% 2.87/1.51 => ( ( invar @ G )
% 2.87/1.51 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_75_old_Opath2__app_H,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 2.87/1.51 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ ( butlast_node @ Ns ) @ Ms ) @ L ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_76_old_Opath2__app,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 2.87/1.51 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( tl_node @ Ms ) ) @ L ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_77_append_Oright__neutral,axiom,
% 2.87/1.51 ! [A: list_val] :
% 2.87/1.51 ( ( append_val @ A @ nil_val )
% 2.87/1.51 = A ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_78_append_Oright__neutral,axiom,
% 2.87/1.51 ! [A: list_list_node] :
% 2.87/1.51 ( ( append_list_node @ A @ nil_list_node )
% 2.87/1.51 = A ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_79_append_Oright__neutral,axiom,
% 2.87/1.51 ! [A: list_node] :
% 2.87/1.51 ( ( append_node @ A @ nil_node )
% 2.87/1.51 = A ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_80_empty__append__eq__id,axiom,
% 2.87/1.51 ( ( append_val @ nil_val )
% 2.87/1.51 = ( ^ [X3: list_val] : X3 ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_81_empty__append__eq__id,axiom,
% 2.87/1.51 ( ( append_list_node @ nil_list_node )
% 2.87/1.51 = ( ^ [X3: list_list_node] : X3 ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_82_empty__append__eq__id,axiom,
% 2.87/1.51 ( ( append_node @ nil_node )
% 2.87/1.51 = ( ^ [X3: list_node] : X3 ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_83_append__is__Nil__conv,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val] :
% 2.87/1.51 ( ( ( append_val @ Xs @ Ys )
% 2.87/1.51 = nil_val )
% 2.87/1.51 = ( ( Xs = nil_val )
% 2.87/1.51 & ( Ys = nil_val ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_84_append__is__Nil__conv,axiom,
% 2.87/1.51 ! [Xs: list_list_node,Ys: list_list_node] :
% 2.87/1.51 ( ( ( append_list_node @ Xs @ Ys )
% 2.87/1.51 = nil_list_node )
% 2.87/1.51 = ( ( Xs = nil_list_node )
% 2.87/1.51 & ( Ys = nil_list_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_85_append__is__Nil__conv,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( ( append_node @ Xs @ Ys )
% 2.87/1.51 = nil_node )
% 2.87/1.51 = ( ( Xs = nil_node )
% 2.87/1.51 & ( Ys = nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_86_Nil__is__append__conv,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val] :
% 2.87/1.51 ( ( nil_val
% 2.87/1.51 = ( append_val @ Xs @ Ys ) )
% 2.87/1.51 = ( ( Xs = nil_val )
% 2.87/1.51 & ( Ys = nil_val ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_87_Nil__is__append__conv,axiom,
% 2.87/1.51 ! [Xs: list_list_node,Ys: list_list_node] :
% 2.87/1.51 ( ( nil_list_node
% 2.87/1.51 = ( append_list_node @ Xs @ Ys ) )
% 2.87/1.51 = ( ( Xs = nil_list_node )
% 2.87/1.51 & ( Ys = nil_list_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_88_Nil__is__append__conv,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( nil_node
% 2.87/1.51 = ( append_node @ Xs @ Ys ) )
% 2.87/1.51 = ( ( Xs = nil_node )
% 2.87/1.51 & ( Ys = nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_89_self__append__conv2,axiom,
% 2.87/1.51 ! [Ys: list_val,Xs: list_val] :
% 2.87/1.51 ( ( Ys
% 2.87/1.51 = ( append_val @ Xs @ Ys ) )
% 2.87/1.51 = ( Xs = nil_val ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_90_self__append__conv2,axiom,
% 2.87/1.51 ! [Ys: list_list_node,Xs: list_list_node] :
% 2.87/1.51 ( ( Ys
% 2.87/1.51 = ( append_list_node @ Xs @ Ys ) )
% 2.87/1.51 = ( Xs = nil_list_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_91_self__append__conv2,axiom,
% 2.87/1.51 ! [Ys: list_node,Xs: list_node] :
% 2.87/1.51 ( ( Ys
% 2.87/1.51 = ( append_node @ Xs @ Ys ) )
% 2.87/1.51 = ( Xs = nil_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_92_append__self__conv2,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val] :
% 2.87/1.51 ( ( ( append_val @ Xs @ Ys )
% 2.87/1.51 = Ys )
% 2.87/1.51 = ( Xs = nil_val ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_93_append__self__conv2,axiom,
% 2.87/1.51 ! [Xs: list_list_node,Ys: list_list_node] :
% 2.87/1.51 ( ( ( append_list_node @ Xs @ Ys )
% 2.87/1.51 = Ys )
% 2.87/1.51 = ( Xs = nil_list_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_94_append__self__conv2,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( ( append_node @ Xs @ Ys )
% 2.87/1.51 = Ys )
% 2.87/1.51 = ( Xs = nil_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_95_self__append__conv,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_val @ Xs @ Ys ) )
% 2.87/1.51 = ( Ys = nil_val ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_96_self__append__conv,axiom,
% 2.87/1.51 ! [Xs: list_list_node,Ys: list_list_node] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_list_node @ Xs @ Ys ) )
% 2.87/1.51 = ( Ys = nil_list_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_97_self__append__conv,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_node @ Xs @ Ys ) )
% 2.87/1.51 = ( Ys = nil_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_98_append__self__conv,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val] :
% 2.87/1.51 ( ( ( append_val @ Xs @ Ys )
% 2.87/1.51 = Xs )
% 2.87/1.51 = ( Ys = nil_val ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_99_append__self__conv,axiom,
% 2.87/1.51 ! [Xs: list_list_node,Ys: list_list_node] :
% 2.87/1.51 ( ( ( append_list_node @ Xs @ Ys )
% 2.87/1.51 = Xs )
% 2.87/1.51 = ( Ys = nil_list_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_100_append__self__conv,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( ( append_node @ Xs @ Ys )
% 2.87/1.51 = Xs )
% 2.87/1.51 = ( Ys = nil_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_101_append__Nil2,axiom,
% 2.87/1.51 ! [Xs: list_val] :
% 2.87/1.51 ( ( append_val @ Xs @ nil_val )
% 2.87/1.51 = Xs ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_102_append__Nil2,axiom,
% 2.87/1.51 ! [Xs: list_list_node] :
% 2.87/1.51 ( ( append_list_node @ Xs @ nil_list_node )
% 2.87/1.51 = Xs ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_103_append__Nil2,axiom,
% 2.87/1.51 ! [Xs: list_node] :
% 2.87/1.51 ( ( append_node @ Xs @ nil_node )
% 2.87/1.51 = Xs ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_104_old_Opath2__split__ex_H,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 2.87/1.51 => ~ ! [Ns_1: list_node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 2.87/1.51 => ! [Ns_2: list_node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 2.87/1.51 => ( Ns
% 2.87/1.51 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_105_old_Opath2__induct,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( ( invar @ G )
% 2.87/1.51 => ( P @ M @ ( cons_node @ M @ nil_node ) @ M ) )
% 2.87/1.51 => ( ! [Ns3: list_node,N3: node,N4: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N4 @ Ns3 @ M )
% 2.87/1.51 => ( ( P @ N4 @ Ns3 @ M )
% 2.87/1.51 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N4 ) ) )
% 2.87/1.51 => ( P @ N3 @ ( cons_node @ N3 @ Ns3 ) @ M ) ) ) )
% 2.87/1.51 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_106_old_Opath2__split__ex,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 2.87/1.51 => ~ ! [Ns_1: list_node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 2.87/1.51 => ! [Ns_2: list_node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 2.87/1.51 => ( ( Ns
% 2.87/1.51 = ( append_node @ Ns_1 @ ( tl_node @ Ns_2 ) ) )
% 2.87/1.51 => ( Ns
% 2.87/1.51 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_107_old_Opath2__rev__induct,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.87/1.51 => ( P @ N @ ( cons_node @ N @ nil_node ) @ N ) )
% 2.87/1.51 => ( ! [Ns3: list_node,M2: node,M3: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ M2 )
% 2.87/1.51 => ( ( P @ N @ Ns3 @ M2 )
% 2.87/1.51 => ( ( member_node @ M2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M3 ) ) )
% 2.87/1.51 => ( P @ N @ ( append_node @ Ns3 @ ( cons_node @ M3 @ nil_node ) ) @ M3 ) ) ) )
% 2.87/1.51 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_108_old_Opath2__snoc,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,M4: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M4 ) ) )
% 2.87/1.51 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ M4 @ nil_node ) ) @ M4 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_109_list__e__eq__lel_I2_J,axiom,
% 2.87/1.51 ! [L1: list_val,E: val,L2: list_val,E3: val] :
% 2.87/1.51 ( ( ( append_val @ L1 @ ( cons_val @ E @ L2 ) )
% 2.87/1.51 = ( cons_val @ E3 @ nil_val ) )
% 2.87/1.51 = ( ( L1 = nil_val )
% 2.87/1.51 & ( E = E3 )
% 2.87/1.51 & ( L2 = nil_val ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_110_list__e__eq__lel_I2_J,axiom,
% 2.87/1.51 ! [L1: list_list_node,E: list_node,L2: list_list_node,E3: list_node] :
% 2.87/1.51 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) )
% 2.87/1.51 = ( cons_list_node @ E3 @ nil_list_node ) )
% 2.87/1.51 = ( ( L1 = nil_list_node )
% 2.87/1.51 & ( E = E3 )
% 2.87/1.51 & ( L2 = nil_list_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_111_list__e__eq__lel_I2_J,axiom,
% 2.87/1.51 ! [L1: list_node,E: node,L2: list_node,E3: node] :
% 2.87/1.51 ( ( ( append_node @ L1 @ ( cons_node @ E @ L2 ) )
% 2.87/1.51 = ( cons_node @ E3 @ nil_node ) )
% 2.87/1.51 = ( ( L1 = nil_node )
% 2.87/1.51 & ( E = E3 )
% 2.87/1.51 & ( L2 = nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_112_list__e__eq__lel_I1_J,axiom,
% 2.87/1.51 ! [E3: val,L1: list_val,E: val,L2: list_val] :
% 2.87/1.51 ( ( ( cons_val @ E3 @ nil_val )
% 2.87/1.51 = ( append_val @ L1 @ ( cons_val @ E @ L2 ) ) )
% 2.87/1.51 = ( ( L1 = nil_val )
% 2.87/1.51 & ( E = E3 )
% 2.87/1.51 & ( L2 = nil_val ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_113_list__e__eq__lel_I1_J,axiom,
% 2.87/1.51 ! [E3: list_node,L1: list_list_node,E: list_node,L2: list_list_node] :
% 2.87/1.51 ( ( ( cons_list_node @ E3 @ nil_list_node )
% 2.87/1.51 = ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) ) )
% 2.87/1.51 = ( ( L1 = nil_list_node )
% 2.87/1.51 & ( E = E3 )
% 2.87/1.51 & ( L2 = nil_list_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_114_list__e__eq__lel_I1_J,axiom,
% 2.87/1.51 ! [E3: node,L1: list_node,E: node,L2: list_node] :
% 2.87/1.51 ( ( ( cons_node @ E3 @ nil_node )
% 2.87/1.51 = ( append_node @ L1 @ ( cons_node @ E @ L2 ) ) )
% 2.87/1.51 = ( ( L1 = nil_node )
% 2.87/1.51 & ( E = E3 )
% 2.87/1.51 & ( L2 = nil_node ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_115_list__se__match_I4_J,axiom,
% 2.87/1.51 ! [L2: list_val,A: val,L1: list_val] :
% 2.87/1.51 ( ( L2 != nil_val )
% 2.87/1.51 => ( ( ( cons_val @ A @ nil_val )
% 2.87/1.51 = ( append_val @ L1 @ L2 ) )
% 2.87/1.51 = ( ( L1 = nil_val )
% 2.87/1.51 & ( L2
% 2.87/1.51 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_116_list__se__match_I4_J,axiom,
% 2.87/1.51 ! [L2: list_list_node,A: list_node,L1: list_list_node] :
% 2.87/1.51 ( ( L2 != nil_list_node )
% 2.87/1.51 => ( ( ( cons_list_node @ A @ nil_list_node )
% 2.87/1.51 = ( append_list_node @ L1 @ L2 ) )
% 2.87/1.51 = ( ( L1 = nil_list_node )
% 2.87/1.51 & ( L2
% 2.87/1.51 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_117_list__se__match_I4_J,axiom,
% 2.87/1.51 ! [L2: list_node,A: node,L1: list_node] :
% 2.87/1.51 ( ( L2 != nil_node )
% 2.87/1.51 => ( ( ( cons_node @ A @ nil_node )
% 2.87/1.51 = ( append_node @ L1 @ L2 ) )
% 2.87/1.51 = ( ( L1 = nil_node )
% 2.87/1.51 & ( L2
% 2.87/1.51 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_118_list__se__match_I3_J,axiom,
% 2.87/1.51 ! [L1: list_val,A: val,L2: list_val] :
% 2.87/1.51 ( ( L1 != nil_val )
% 2.87/1.51 => ( ( ( cons_val @ A @ nil_val )
% 2.87/1.51 = ( append_val @ L1 @ L2 ) )
% 2.87/1.51 = ( ( L1
% 2.87/1.51 = ( cons_val @ A @ nil_val ) )
% 2.87/1.51 & ( L2 = nil_val ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_119_list__se__match_I3_J,axiom,
% 2.87/1.51 ! [L1: list_list_node,A: list_node,L2: list_list_node] :
% 2.87/1.51 ( ( L1 != nil_list_node )
% 2.87/1.51 => ( ( ( cons_list_node @ A @ nil_list_node )
% 2.87/1.51 = ( append_list_node @ L1 @ L2 ) )
% 2.87/1.51 = ( ( L1
% 2.87/1.51 = ( cons_list_node @ A @ nil_list_node ) )
% 2.87/1.51 & ( L2 = nil_list_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_120_list__se__match_I3_J,axiom,
% 2.87/1.51 ! [L1: list_node,A: node,L2: list_node] :
% 2.87/1.51 ( ( L1 != nil_node )
% 2.87/1.51 => ( ( ( cons_node @ A @ nil_node )
% 2.87/1.51 = ( append_node @ L1 @ L2 ) )
% 2.87/1.51 = ( ( L1
% 2.87/1.51 = ( cons_node @ A @ nil_node ) )
% 2.87/1.51 & ( L2 = nil_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_121_list__se__match_I2_J,axiom,
% 2.87/1.51 ! [L2: list_val,L1: list_val,A: val] :
% 2.87/1.51 ( ( L2 != nil_val )
% 2.87/1.51 => ( ( ( append_val @ L1 @ L2 )
% 2.87/1.51 = ( cons_val @ A @ nil_val ) )
% 2.87/1.51 = ( ( L1 = nil_val )
% 2.87/1.51 & ( L2
% 2.87/1.51 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_122_list__se__match_I2_J,axiom,
% 2.87/1.51 ! [L2: list_list_node,L1: list_list_node,A: list_node] :
% 2.87/1.51 ( ( L2 != nil_list_node )
% 2.87/1.51 => ( ( ( append_list_node @ L1 @ L2 )
% 2.87/1.51 = ( cons_list_node @ A @ nil_list_node ) )
% 2.87/1.51 = ( ( L1 = nil_list_node )
% 2.87/1.51 & ( L2
% 2.87/1.51 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_123_list__se__match_I2_J,axiom,
% 2.87/1.51 ! [L2: list_node,L1: list_node,A: node] :
% 2.87/1.51 ( ( L2 != nil_node )
% 2.87/1.51 => ( ( ( append_node @ L1 @ L2 )
% 2.87/1.51 = ( cons_node @ A @ nil_node ) )
% 2.87/1.51 = ( ( L1 = nil_node )
% 2.87/1.51 & ( L2
% 2.87/1.51 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_124_tl__append2,axiom,
% 2.87/1.51 ! [Xs: list_val,Ys: list_val] :
% 2.87/1.51 ( ( Xs != nil_val )
% 2.87/1.51 => ( ( tl_val @ ( append_val @ Xs @ Ys ) )
% 2.87/1.51 = ( append_val @ ( tl_val @ Xs ) @ Ys ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_125_tl__append2,axiom,
% 2.87/1.51 ! [Xs: list_list_node,Ys: list_list_node] :
% 2.87/1.51 ( ( Xs != nil_list_node )
% 2.87/1.51 => ( ( tl_list_node @ ( append_list_node @ Xs @ Ys ) )
% 2.87/1.51 = ( append_list_node @ ( tl_list_node @ Xs ) @ Ys ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_126_tl__append2,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 => ( ( tl_node @ ( append_node @ Xs @ Ys ) )
% 2.87/1.51 = ( append_node @ ( tl_node @ Xs ) @ Ys ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_127_old_Opath2__cases,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( ( Ns
% 2.87/1.51 = ( cons_node @ N @ nil_node ) )
% 2.87/1.51 => ( M != N ) )
% 2.87/1.51 => ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) @ ( tl_node @ Ns ) @ M )
% 2.87/1.51 => ~ ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_128_rs__props_I3_J,axiom,
% 2.87/1.51 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_129_butlast__snoc,axiom,
% 2.87/1.51 ! [Xs: list_val,X: val] :
% 2.87/1.51 ( ( butlast_val @ ( append_val @ Xs @ ( cons_val @ X @ nil_val ) ) )
% 2.87/1.51 = Xs ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_130_butlast__snoc,axiom,
% 2.87/1.51 ! [Xs: list_list_node,X: list_node] :
% 2.87/1.51 ( ( butlast_list_node @ ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) ) )
% 2.87/1.51 = Xs ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_131_butlast__snoc,axiom,
% 2.87/1.51 ! [Xs: list_node,X: node] :
% 2.87/1.51 ( ( butlast_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) )
% 2.87/1.51 = Xs ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_132_list_Ocollapse,axiom,
% 2.87/1.51 ! [List: list_val] :
% 2.87/1.51 ( ( List != nil_val )
% 2.87/1.51 => ( ( cons_val @ ( hd_val @ List ) @ ( tl_val @ List ) )
% 2.87/1.51 = List ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_133_list_Ocollapse,axiom,
% 2.87/1.51 ! [List: list_list_node] :
% 2.87/1.51 ( ( List != nil_list_node )
% 2.87/1.51 => ( ( cons_list_node @ ( hd_list_node @ List ) @ ( tl_list_node @ List ) )
% 2.87/1.51 = List ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_134_list_Ocollapse,axiom,
% 2.87/1.51 ! [List: list_node] :
% 2.87/1.51 ( ( List != nil_node )
% 2.87/1.51 => ( ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) )
% 2.87/1.51 = List ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_135_hd__Cons__tl,axiom,
% 2.87/1.51 ! [Xs: list_val] :
% 2.87/1.51 ( ( Xs != nil_val )
% 2.87/1.51 => ( ( cons_val @ ( hd_val @ Xs ) @ ( tl_val @ Xs ) )
% 2.87/1.51 = Xs ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_136_hd__Cons__tl,axiom,
% 2.87/1.51 ! [Xs: list_list_node] :
% 2.87/1.51 ( ( Xs != nil_list_node )
% 2.87/1.51 => ( ( cons_list_node @ ( hd_list_node @ Xs ) @ ( tl_list_node @ Xs ) )
% 2.87/1.51 = Xs ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_137_hd__Cons__tl,axiom,
% 2.87/1.51 ! [Xs: list_node] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 => ( ( cons_node @ ( hd_node @ Xs ) @ ( tl_node @ Xs ) )
% 2.87/1.51 = Xs ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_138_in__hd__or__tl__conv,axiom,
% 2.87/1.51 ! [L: list_list_node,X: list_node] :
% 2.87/1.51 ( ( L != nil_list_node )
% 2.87/1.51 => ( ( ( X
% 2.87/1.51 = ( hd_list_node @ L ) )
% 2.87/1.51 | ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ L ) ) ) )
% 2.87/1.51 = ( member_list_node @ X @ ( set_list_node2 @ L ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_139_in__hd__or__tl__conv,axiom,
% 2.87/1.51 ! [L: list_val,X: val] :
% 2.87/1.51 ( ( L != nil_val )
% 2.87/1.51 => ( ( ( X
% 2.87/1.51 = ( hd_val @ L ) )
% 2.87/1.51 | ( member_val @ X @ ( set_val2 @ ( tl_val @ L ) ) ) )
% 2.87/1.51 = ( member_val @ X @ ( set_val2 @ L ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_140_in__hd__or__tl__conv,axiom,
% 2.87/1.51 ! [L: list_node,X: node] :
% 2.87/1.51 ( ( L != nil_node )
% 2.87/1.51 => ( ( ( X
% 2.87/1.51 = ( hd_node @ L ) )
% 2.87/1.51 | ( member_node @ X @ ( set_node2 @ ( tl_node @ L ) ) ) )
% 2.87/1.51 = ( member_node @ X @ ( set_node2 @ L ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_141_ri__props_I4_J,axiom,
% 2.87/1.51 prefix_node @ ri @ rs2 ).
% 2.87/1.51
% 2.87/1.51 thf(fact_142_ms_H__props_I2_J,axiom,
% 2.87/1.51 prefix_node @ ms2 @ ms ).
% 2.87/1.51
% 2.87/1.51 thf(fact_143_old_OCons__path2,axiom,
% 2.87/1.51 ! [G: g,N: node,Ns: list_node,M: node,N2: node] :
% 2.87/1.51 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.51 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 2.87/1.51 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns ) @ M ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_144_butlast__tl,axiom,
% 2.87/1.51 ! [Xs: list_val] :
% 2.87/1.51 ( ( butlast_val @ ( tl_val @ Xs ) )
% 2.87/1.51 = ( tl_val @ ( butlast_val @ Xs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_145_butlast__tl,axiom,
% 2.87/1.51 ! [Xs: list_node] :
% 2.87/1.51 ( ( butlast_node @ ( tl_node @ Xs ) )
% 2.87/1.51 = ( tl_node @ ( butlast_node @ Xs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_146_butlast_Osimps_I1_J,axiom,
% 2.87/1.51 ( ( butlast_val @ nil_val )
% 2.87/1.51 = nil_val ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_147_butlast_Osimps_I1_J,axiom,
% 2.87/1.51 ( ( butlast_list_node @ nil_list_node )
% 2.87/1.51 = nil_list_node ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_148_butlast_Osimps_I1_J,axiom,
% 2.87/1.51 ( ( butlast_node @ nil_node )
% 2.87/1.51 = nil_node ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_149_list_Osel_I3_J,axiom,
% 2.87/1.51 ! [X21: val,X22: list_val] :
% 2.87/1.51 ( ( tl_val @ ( cons_val @ X21 @ X22 ) )
% 2.87/1.51 = X22 ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_150_list_Osel_I3_J,axiom,
% 2.87/1.51 ! [X21: list_node,X22: list_list_node] :
% 2.87/1.51 ( ( tl_list_node @ ( cons_list_node @ X21 @ X22 ) )
% 2.87/1.51 = X22 ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_151_list_Osel_I3_J,axiom,
% 2.87/1.51 ! [X21: node,X22: list_node] :
% 2.87/1.51 ( ( tl_node @ ( cons_node @ X21 @ X22 ) )
% 2.87/1.51 = X22 ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_152_in__set__butlastD,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val] :
% 2.87/1.51 ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 2.87/1.51 => ( member_val @ X @ ( set_val2 @ Xs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_153_in__set__butlastD,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node] :
% 2.87/1.51 ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 2.87/1.51 => ( member_node @ X @ ( set_node2 @ Xs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_154_list_Osel_I2_J,axiom,
% 2.87/1.51 ( ( tl_val @ nil_val )
% 2.87/1.51 = nil_val ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_155_list_Osel_I2_J,axiom,
% 2.87/1.51 ( ( tl_list_node @ nil_list_node )
% 2.87/1.51 = nil_list_node ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_156_list_Osel_I2_J,axiom,
% 2.87/1.51 ( ( tl_node @ nil_node )
% 2.87/1.51 = nil_node ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_157_butlast_Osimps_I2_J,axiom,
% 2.87/1.51 ! [Xs: list_val,X: val] :
% 2.87/1.51 ( ( ( Xs = nil_val )
% 2.87/1.51 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 2.87/1.51 = nil_val ) )
% 2.87/1.51 & ( ( Xs != nil_val )
% 2.87/1.51 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 2.87/1.51 = ( cons_val @ X @ ( butlast_val @ Xs ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_158_butlast_Osimps_I2_J,axiom,
% 2.87/1.51 ! [Xs: list_list_node,X: list_node] :
% 2.87/1.51 ( ( ( Xs = nil_list_node )
% 2.87/1.51 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 2.87/1.51 = nil_list_node ) )
% 2.87/1.51 & ( ( Xs != nil_list_node )
% 2.87/1.51 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 2.87/1.51 = ( cons_list_node @ X @ ( butlast_list_node @ Xs ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_159_butlast_Osimps_I2_J,axiom,
% 2.87/1.51 ! [Xs: list_node,X: node] :
% 2.87/1.51 ( ( ( Xs = nil_node )
% 2.87/1.51 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 2.87/1.51 = nil_node ) )
% 2.87/1.51 & ( ( Xs != nil_node )
% 2.87/1.51 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 2.87/1.51 = ( cons_node @ X @ ( butlast_node @ Xs ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_160_tl__obtain__elem,axiom,
% 2.87/1.51 ! [Xs: list_val] :
% 2.87/1.51 ( ( Xs != nil_val )
% 2.87/1.51 => ( ( ( tl_val @ Xs )
% 2.87/1.51 = nil_val )
% 2.87/1.51 => ~ ! [E4: val] :
% 2.87/1.51 ( Xs
% 2.87/1.51 != ( cons_val @ E4 @ nil_val ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_161_tl__obtain__elem,axiom,
% 2.87/1.51 ! [Xs: list_list_node] :
% 2.87/1.51 ( ( Xs != nil_list_node )
% 2.87/1.51 => ( ( ( tl_list_node @ Xs )
% 2.87/1.51 = nil_list_node )
% 2.87/1.51 => ~ ! [E4: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 != ( cons_list_node @ E4 @ nil_list_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_162_tl__obtain__elem,axiom,
% 2.87/1.51 ! [Xs: list_node] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 => ( ( ( tl_node @ Xs )
% 2.87/1.51 = nil_node )
% 2.87/1.51 => ~ ! [E4: node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 != ( cons_node @ E4 @ nil_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_163_tl__Nil,axiom,
% 2.87/1.51 ! [Xs: list_val] :
% 2.87/1.51 ( ( ( tl_val @ Xs )
% 2.87/1.51 = nil_val )
% 2.87/1.51 = ( ( Xs = nil_val )
% 2.87/1.51 | ? [X3: val] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( cons_val @ X3 @ nil_val ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_164_tl__Nil,axiom,
% 2.87/1.51 ! [Xs: list_list_node] :
% 2.87/1.51 ( ( ( tl_list_node @ Xs )
% 2.87/1.51 = nil_list_node )
% 2.87/1.51 = ( ( Xs = nil_list_node )
% 2.87/1.51 | ? [X3: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( cons_list_node @ X3 @ nil_list_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_165_tl__Nil,axiom,
% 2.87/1.51 ! [Xs: list_node] :
% 2.87/1.51 ( ( ( tl_node @ Xs )
% 2.87/1.51 = nil_node )
% 2.87/1.51 = ( ( Xs = nil_node )
% 2.87/1.51 | ? [X3: node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_166_Nil__tl,axiom,
% 2.87/1.51 ! [Xs: list_val] :
% 2.87/1.51 ( ( nil_val
% 2.87/1.51 = ( tl_val @ Xs ) )
% 2.87/1.51 = ( ( Xs = nil_val )
% 2.87/1.51 | ? [X3: val] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( cons_val @ X3 @ nil_val ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_167_Nil__tl,axiom,
% 2.87/1.51 ! [Xs: list_list_node] :
% 2.87/1.51 ( ( nil_list_node
% 2.87/1.51 = ( tl_list_node @ Xs ) )
% 2.87/1.51 = ( ( Xs = nil_list_node )
% 2.87/1.51 | ? [X3: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( cons_list_node @ X3 @ nil_list_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_168_Nil__tl,axiom,
% 2.87/1.51 ! [Xs: list_node] :
% 2.87/1.51 ( ( nil_node
% 2.87/1.51 = ( tl_node @ Xs ) )
% 2.87/1.51 = ( ( Xs = nil_node )
% 2.87/1.51 | ? [X3: node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_169_butlast__append,axiom,
% 2.87/1.51 ! [Ys: list_val,Xs: list_val] :
% 2.87/1.51 ( ( ( Ys = nil_val )
% 2.87/1.51 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 2.87/1.51 = ( butlast_val @ Xs ) ) )
% 2.87/1.51 & ( ( Ys != nil_val )
% 2.87/1.51 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 2.87/1.51 = ( append_val @ Xs @ ( butlast_val @ Ys ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_170_butlast__append,axiom,
% 2.87/1.51 ! [Ys: list_list_node,Xs: list_list_node] :
% 2.87/1.51 ( ( ( Ys = nil_list_node )
% 2.87/1.51 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 2.87/1.51 = ( butlast_list_node @ Xs ) ) )
% 2.87/1.51 & ( ( Ys != nil_list_node )
% 2.87/1.51 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 2.87/1.51 = ( append_list_node @ Xs @ ( butlast_list_node @ Ys ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_171_butlast__append,axiom,
% 2.87/1.51 ! [Ys: list_node,Xs: list_node] :
% 2.87/1.51 ( ( ( Ys = nil_node )
% 2.87/1.51 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 2.87/1.51 = ( butlast_node @ Xs ) ) )
% 2.87/1.51 & ( ( Ys != nil_node )
% 2.87/1.51 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 2.87/1.51 = ( append_node @ Xs @ ( butlast_node @ Ys ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_172_list_Oset__sel_I2_J,axiom,
% 2.87/1.51 ! [A: list_list_node,X: list_node] :
% 2.87/1.51 ( ( A != nil_list_node )
% 2.87/1.51 => ( ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ A ) ) )
% 2.87/1.51 => ( member_list_node @ X @ ( set_list_node2 @ A ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_173_list_Oset__sel_I2_J,axiom,
% 2.87/1.51 ! [A: list_val,X: val] :
% 2.87/1.51 ( ( A != nil_val )
% 2.87/1.51 => ( ( member_val @ X @ ( set_val2 @ ( tl_val @ A ) ) )
% 2.87/1.51 => ( member_val @ X @ ( set_val2 @ A ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_174_list_Oset__sel_I2_J,axiom,
% 2.87/1.51 ! [A: list_node,X: node] :
% 2.87/1.51 ( ( A != nil_node )
% 2.87/1.51 => ( ( member_node @ X @ ( set_node2 @ ( tl_node @ A ) ) )
% 2.87/1.51 => ( member_node @ X @ ( set_node2 @ A ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_175_in__set__butlast__appendI,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val,Ys: list_val] :
% 2.87/1.51 ( ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 2.87/1.51 | ( member_val @ X @ ( set_val2 @ ( butlast_val @ Ys ) ) ) )
% 2.87/1.51 => ( member_val @ X @ ( set_val2 @ ( butlast_val @ ( append_val @ Xs @ Ys ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_176_in__set__butlast__appendI,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 2.87/1.51 | ( member_node @ X @ ( set_node2 @ ( butlast_node @ Ys ) ) ) )
% 2.87/1.51 => ( member_node @ X @ ( set_node2 @ ( butlast_node @ ( append_node @ Xs @ Ys ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_177_list_Oexpand,axiom,
% 2.87/1.51 ! [List: list_val,List2: list_val] :
% 2.87/1.51 ( ( ( List = nil_val )
% 2.87/1.51 = ( List2 = nil_val ) )
% 2.87/1.51 => ( ( ( List != nil_val )
% 2.87/1.51 => ( ( List2 != nil_val )
% 2.87/1.51 => ( ( ( hd_val @ List )
% 2.87/1.51 = ( hd_val @ List2 ) )
% 2.87/1.51 & ( ( tl_val @ List )
% 2.87/1.51 = ( tl_val @ List2 ) ) ) ) )
% 2.87/1.51 => ( List = List2 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_178_list_Oexpand,axiom,
% 2.87/1.51 ! [List: list_list_node,List2: list_list_node] :
% 2.87/1.51 ( ( ( List = nil_list_node )
% 2.87/1.51 = ( List2 = nil_list_node ) )
% 2.87/1.51 => ( ( ( List != nil_list_node )
% 2.87/1.51 => ( ( List2 != nil_list_node )
% 2.87/1.51 => ( ( ( hd_list_node @ List )
% 2.87/1.51 = ( hd_list_node @ List2 ) )
% 2.87/1.51 & ( ( tl_list_node @ List )
% 2.87/1.51 = ( tl_list_node @ List2 ) ) ) ) )
% 2.87/1.51 => ( List = List2 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_179_list_Oexpand,axiom,
% 2.87/1.51 ! [List: list_node,List2: list_node] :
% 2.87/1.51 ( ( ( List = nil_node )
% 2.87/1.51 = ( List2 = nil_node ) )
% 2.87/1.51 => ( ( ( List != nil_node )
% 2.87/1.51 => ( ( List2 != nil_node )
% 2.87/1.51 => ( ( ( hd_node @ List )
% 2.87/1.51 = ( hd_node @ List2 ) )
% 2.87/1.51 & ( ( tl_node @ List )
% 2.87/1.51 = ( tl_node @ List2 ) ) ) ) )
% 2.87/1.51 => ( List = List2 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_180_not__hd__in__tl,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val] :
% 2.87/1.51 ( ( X
% 2.87/1.51 != ( hd_val @ Xs ) )
% 2.87/1.51 => ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.51 => ( member_val @ X @ ( set_val2 @ ( tl_val @ Xs ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_181_not__hd__in__tl,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node] :
% 2.87/1.51 ( ( X
% 2.87/1.51 != ( hd_node @ Xs ) )
% 2.87/1.51 => ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.51 => ( member_node @ X @ ( set_node2 @ ( tl_node @ Xs ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_182_butlast__eq__cons__conv,axiom,
% 2.87/1.51 ! [L: list_list_node,X: list_node,Xs: list_list_node] :
% 2.87/1.51 ( ( ( butlast_list_node @ L )
% 2.87/1.51 = ( cons_list_node @ X @ Xs ) )
% 2.87/1.51 = ( ? [Xl: list_node] :
% 2.87/1.51 ( L
% 2.87/1.51 = ( cons_list_node @ X @ ( append_list_node @ Xs @ ( cons_list_node @ Xl @ nil_list_node ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_183_butlast__eq__cons__conv,axiom,
% 2.87/1.51 ! [L: list_node,X: node,Xs: list_node] :
% 2.87/1.51 ( ( ( butlast_node @ L )
% 2.87/1.51 = ( cons_node @ X @ Xs ) )
% 2.87/1.51 = ( ? [Xl: node] :
% 2.87/1.51 ( L
% 2.87/1.51 = ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl @ nil_node ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_184_butlast__eq__consE,axiom,
% 2.87/1.51 ! [L: list_node,X: node,Xs: list_node] :
% 2.87/1.51 ( ( ( butlast_node @ L )
% 2.87/1.51 = ( cons_node @ X @ Xs ) )
% 2.87/1.51 => ~ ! [Xl2: node] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl2 @ nil_node ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_185_list_Oexhaust__sel,axiom,
% 2.87/1.51 ! [List: list_node] :
% 2.87/1.51 ( ( List != nil_node )
% 2.87/1.51 => ( List
% 2.87/1.51 = ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_186_not__Cons__self2,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node] :
% 2.87/1.51 ( ( cons_node @ X @ Xs )
% 2.87/1.51 != Xs ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_187_list__tail__coinc,axiom,
% 2.87/1.51 ! [N1: node,R1: list_node,N22: node,R2: list_node] :
% 2.87/1.51 ( ( ( cons_node @ N1 @ R1 )
% 2.87/1.51 = ( cons_node @ N22 @ R2 ) )
% 2.87/1.51 => ( ( N1 = N22 )
% 2.87/1.51 & ( R1 = R2 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_188_append__eq__append__conv2,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node,Zs: list_node,Ts: list_node] :
% 2.87/1.51 ( ( ( append_node @ Xs @ Ys )
% 2.87/1.51 = ( append_node @ Zs @ Ts ) )
% 2.87/1.51 = ( ? [Us: list_node] :
% 2.87/1.51 ( ( ( Xs
% 2.87/1.51 = ( append_node @ Zs @ Us ) )
% 2.87/1.51 & ( ( append_node @ Us @ Ys )
% 2.87/1.51 = Ts ) )
% 2.87/1.51 | ( ( ( append_node @ Xs @ Us )
% 2.87/1.51 = Zs )
% 2.87/1.51 & ( Ys
% 2.87/1.51 = ( append_node @ Us @ Ts ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_189_append__eq__appendI,axiom,
% 2.87/1.51 ! [Xs: list_node,Xs1: list_node,Zs: list_node,Ys: list_node,Us2: list_node] :
% 2.87/1.51 ( ( ( append_node @ Xs @ Xs1 )
% 2.87/1.51 = Zs )
% 2.87/1.51 => ( ( Ys
% 2.87/1.51 = ( append_node @ Xs1 @ Us2 ) )
% 2.87/1.51 => ( ( append_node @ Xs @ Ys )
% 2.87/1.51 = ( append_node @ Zs @ Us2 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_190_list_Odistinct_I1_J,axiom,
% 2.87/1.51 ! [X21: node,X22: list_node] :
% 2.87/1.51 ( nil_node
% 2.87/1.51 != ( cons_node @ X21 @ X22 ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_191_neq__NilE,axiom,
% 2.87/1.51 ! [L: list_node] :
% 2.87/1.51 ( ( L != nil_node )
% 2.87/1.51 => ~ ! [X4: node,Xs2: list_node] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( cons_node @ X4 @ Xs2 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_192_list_OdiscI,axiom,
% 2.87/1.51 ! [List: list_node,X21: node,X22: list_node] :
% 2.87/1.51 ( ( List
% 2.87/1.51 = ( cons_node @ X21 @ X22 ) )
% 2.87/1.51 => ( List != nil_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_193_revg_Oinduct,axiom,
% 2.87/1.51 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 2.87/1.51 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.87/1.51 => ( ! [A3: node,As: list_node,B2: list_node] :
% 2.87/1.51 ( ( P @ As @ ( cons_node @ A3 @ B2 ) )
% 2.87/1.51 => ( P @ ( cons_node @ A3 @ As ) @ B2 ) )
% 2.87/1.51 => ( P @ A0 @ A1 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_194_list_Oexhaust,axiom,
% 2.87/1.51 ! [Y: list_node] :
% 2.87/1.51 ( ( Y != nil_node )
% 2.87/1.51 => ~ ! [X212: node,X222: list_node] :
% 2.87/1.51 ( Y
% 2.87/1.51 != ( cons_node @ X212 @ X222 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_195_list_Oinducts,axiom,
% 2.87/1.51 ! [P: list_node > $o,List: list_node] :
% 2.87/1.51 ( ( P @ nil_node )
% 2.87/1.51 => ( ! [X1: node,X23: list_node] :
% 2.87/1.51 ( ( P @ X23 )
% 2.87/1.51 => ( P @ ( cons_node @ X1 @ X23 ) ) )
% 2.87/1.51 => ( P @ List ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_196_neq__Nil__conv,axiom,
% 2.87/1.51 ! [Xs: list_node] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 = ( ? [Y2: node,Ys2: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( cons_node @ Y2 @ Ys2 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_197_list__induct2_H,axiom,
% 2.87/1.51 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( P @ nil_node @ nil_node )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node] : ( P @ ( cons_node @ X4 @ Xs2 ) @ nil_node )
% 2.87/1.51 => ( ! [Y3: node,Ys3: list_node] : ( P @ nil_node @ ( cons_node @ Y3 @ Ys3 ) )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.51 ( ( P @ Xs2 @ Ys3 )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) )
% 2.87/1.51 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_198_splice_Oinduct,axiom,
% 2.87/1.51 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 2.87/1.51 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node,Ys3: list_node] :
% 2.87/1.51 ( ( P @ Ys3 @ Xs2 )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys3 ) )
% 2.87/1.51 => ( P @ A0 @ A1 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_199_induct__list012,axiom,
% 2.87/1.51 ! [P: list_node > $o,Xs: list_node] :
% 2.87/1.51 ( ( P @ nil_node )
% 2.87/1.51 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 2.87/1.51 => ( ! [X4: node,Y3: node,Zs2: list_node] :
% 2.87/1.51 ( ( P @ Zs2 )
% 2.87/1.51 => ( ( P @ ( cons_node @ Y3 @ Zs2 ) )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y3 @ Zs2 ) ) ) ) )
% 2.87/1.51 => ( P @ Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_200_min__list_Ocases,axiom,
% 2.87/1.51 ! [X: list_node] :
% 2.87/1.51 ( ! [X4: node,Xs2: list_node] :
% 2.87/1.51 ( X
% 2.87/1.51 != ( cons_node @ X4 @ Xs2 ) )
% 2.87/1.51 => ( X = nil_node ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_201_min__list_Oinduct,axiom,
% 2.87/1.51 ! [P: list_node > $o,A0: list_node] :
% 2.87/1.51 ( ! [X4: node,Xs2: list_node] :
% 2.87/1.51 ( ! [X213: node,X223: list_node] :
% 2.87/1.51 ( ( Xs2
% 2.87/1.51 = ( cons_node @ X213 @ X223 ) )
% 2.87/1.51 => ( P @ Xs2 ) )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 2.87/1.51 => ( ( P @ nil_node )
% 2.87/1.51 => ( P @ A0 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_202_shuffles_Oinduct,axiom,
% 2.87/1.51 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 2.87/1.51 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.87/1.51 => ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.51 ( ( P @ Xs2 @ ( cons_node @ Y3 @ Ys3 ) )
% 2.87/1.51 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys3 )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) ) )
% 2.87/1.51 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_203_list__2pre__induct,axiom,
% 2.87/1.51 ! [P: list_node > list_node > $o,W1: list_node,W2: list_node] :
% 2.87/1.51 ( ( P @ nil_node @ nil_node )
% 2.87/1.51 => ( ! [E4: node,W12: list_node,W22: list_node] :
% 2.87/1.51 ( ( P @ W12 @ W22 )
% 2.87/1.51 => ( P @ ( cons_node @ E4 @ W12 ) @ W22 ) )
% 2.87/1.51 => ( ! [E4: node,W13: list_node,W23: list_node] :
% 2.87/1.51 ( ( P @ W13 @ W23 )
% 2.87/1.51 => ( P @ W13 @ ( cons_node @ E4 @ W23 ) ) )
% 2.87/1.51 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_204_remdups__adj_Ocases,axiom,
% 2.87/1.51 ! [X: list_node] :
% 2.87/1.51 ( ( X != nil_node )
% 2.87/1.51 => ( ! [X4: node] :
% 2.87/1.51 ( X
% 2.87/1.51 != ( cons_node @ X4 @ nil_node ) )
% 2.87/1.51 => ~ ! [X4: node,Y3: node,Xs2: list_node] :
% 2.87/1.51 ( X
% 2.87/1.51 != ( cons_node @ X4 @ ( cons_node @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_205_sorted__wrt_Oinduct,axiom,
% 2.87/1.51 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 2.87/1.51 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 2.87/1.51 => ( ! [P2: node > node > $o,X4: node,Ys3: list_node] :
% 2.87/1.51 ( ( P @ P2 @ Ys3 )
% 2.87/1.51 => ( P @ P2 @ ( cons_node @ X4 @ Ys3 ) ) )
% 2.87/1.51 => ( P @ A0 @ A1 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_206_remdups__adj_Oinduct,axiom,
% 2.87/1.51 ! [P: list_node > $o,A0: list_node] :
% 2.87/1.51 ( ( P @ nil_node )
% 2.87/1.51 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 2.87/1.51 => ( ! [X4: node,Y3: node,Xs2: list_node] :
% 2.87/1.51 ( ( ( X4 = Y3 )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 2.87/1.51 => ( ( ( X4 != Y3 )
% 2.87/1.51 => ( P @ ( cons_node @ Y3 @ Xs2 ) ) )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y3 @ Xs2 ) ) ) ) )
% 2.87/1.51 => ( P @ A0 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_207_list__induct__first2,axiom,
% 2.87/1.51 ! [P: list_node > $o,Xs: list_node] :
% 2.87/1.51 ( ( P @ nil_node )
% 2.87/1.51 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 2.87/1.51 => ( ! [X1: node,X23: node,Xs2: list_node] :
% 2.87/1.51 ( ( P @ Xs2 )
% 2.87/1.51 => ( P @ ( cons_node @ X1 @ ( cons_node @ X23 @ Xs2 ) ) ) )
% 2.87/1.51 => ( P @ Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_208_successively_Oinduct,axiom,
% 2.87/1.51 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 2.87/1.51 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 2.87/1.51 => ( ! [P2: node > node > $o,X4: node] : ( P @ P2 @ ( cons_node @ X4 @ nil_node ) )
% 2.87/1.51 => ( ! [P2: node > node > $o,X4: node,Y3: node,Xs2: list_node] :
% 2.87/1.51 ( ( P @ P2 @ ( cons_node @ Y3 @ Xs2 ) )
% 2.87/1.51 => ( P @ P2 @ ( cons_node @ X4 @ ( cons_node @ Y3 @ Xs2 ) ) ) )
% 2.87/1.51 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_209_list__all__zip_Oinduct,axiom,
% 2.87/1.51 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 2.87/1.51 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node @ nil_node )
% 2.87/1.51 => ( ! [P2: node > node > $o,A3: node,As: list_node,B2: node,Bs: list_node] :
% 2.87/1.51 ( ( P @ P2 @ As @ Bs )
% 2.87/1.51 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 2.87/1.51 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V @ Va ) @ nil_node )
% 2.87/1.51 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ nil_node @ ( cons_node @ V @ Va ) )
% 2.87/1.51 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_210_list__nonempty__induct,axiom,
% 2.87/1.51 ! [Xs: list_node,P: list_node > $o] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node] :
% 2.87/1.51 ( ( Xs2 != nil_node )
% 2.87/1.51 => ( ( P @ Xs2 )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Xs2 ) ) ) )
% 2.87/1.51 => ( P @ Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_211_map__tailrec__rev_Oinduct,axiom,
% 2.87/1.51 ! [P: ( node > node ) > list_node > list_node > $o,A0: node > node,A1: list_node,A22: list_node] :
% 2.87/1.51 ( ! [F: node > node,X_1: list_node] : ( P @ F @ nil_node @ X_1 )
% 2.87/1.51 => ( ! [F: node > node,A3: node,As: list_node,Bs: list_node] :
% 2.87/1.51 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 2.87/1.51 => ( P @ F @ ( cons_node @ A3 @ As ) @ Bs ) )
% 2.87/1.51 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_212_mergesort__by__rel__merge_Oinduct,axiom,
% 2.87/1.51 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 2.87/1.51 ( ! [R: node > node > $o,X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.51 ( ( ( R @ X4 @ Y3 )
% 2.87/1.51 => ( P @ R @ Xs2 @ ( cons_node @ Y3 @ Ys3 ) ) )
% 2.87/1.51 => ( ( ~ ( R @ X4 @ Y3 )
% 2.87/1.51 => ( P @ R @ ( cons_node @ X4 @ Xs2 ) @ Ys3 ) )
% 2.87/1.51 => ( P @ R @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) ) )
% 2.87/1.51 => ( ! [R: node > node > $o,Xs2: list_node] : ( P @ R @ Xs2 @ nil_node )
% 2.87/1.51 => ( ! [R: node > node > $o,V: node,Va: list_node] : ( P @ R @ nil_node @ ( cons_node @ V @ Va ) )
% 2.87/1.51 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_213_mergesort__by__rel__merge__induct,axiom,
% 2.87/1.51 ! [P: list_node > list_node > $o,R3: node > node > $o,Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 2.87/1.51 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.51 ( ( R3 @ X4 @ Y3 )
% 2.87/1.51 => ( ( P @ Xs2 @ ( cons_node @ Y3 @ Ys3 ) )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) ) )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.51 ( ~ ( R3 @ X4 @ Y3 )
% 2.87/1.51 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys3 )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y3 @ Ys3 ) ) ) )
% 2.87/1.51 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_214_strict__sorted_Oinduct,axiom,
% 2.87/1.51 ! [P: list_node > $o,A0: list_node] :
% 2.87/1.51 ( ( P @ nil_node )
% 2.87/1.51 => ( ! [X4: node,Ys3: list_node] :
% 2.87/1.51 ( ( P @ Ys3 )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ Ys3 ) ) )
% 2.87/1.51 => ( P @ A0 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_215_transpose_Ocases,axiom,
% 2.87/1.51 ! [X: list_list_node] :
% 2.87/1.51 ( ( X != nil_list_node )
% 2.87/1.51 => ( ! [Xss: list_list_node] :
% 2.87/1.51 ( X
% 2.87/1.51 != ( cons_list_node @ nil_node @ Xss ) )
% 2.87/1.51 => ~ ! [X4: node,Xs2: list_node,Xss: list_list_node] :
% 2.87/1.51 ( X
% 2.87/1.51 != ( cons_list_node @ ( cons_node @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_216_list_Oset__intros_I2_J,axiom,
% 2.87/1.51 ! [Y: val,X22: list_val,X21: val] :
% 2.87/1.51 ( ( member_val @ Y @ ( set_val2 @ X22 ) )
% 2.87/1.51 => ( member_val @ Y @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_217_list_Oset__intros_I2_J,axiom,
% 2.87/1.51 ! [Y: node,X22: list_node,X21: node] :
% 2.87/1.51 ( ( member_node @ Y @ ( set_node2 @ X22 ) )
% 2.87/1.51 => ( member_node @ Y @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_218_list_Oset__intros_I1_J,axiom,
% 2.87/1.51 ! [X21: val,X22: list_val] : ( member_val @ X21 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_219_list_Oset__intros_I1_J,axiom,
% 2.87/1.51 ! [X21: node,X22: list_node] : ( member_node @ X21 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_220_set__ConsD,axiom,
% 2.87/1.51 ! [Y: val,X: val,Xs: list_val] :
% 2.87/1.51 ( ( member_val @ Y @ ( set_val2 @ ( cons_val @ X @ Xs ) ) )
% 2.87/1.51 => ( ( Y = X )
% 2.87/1.51 | ( member_val @ Y @ ( set_val2 @ Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_221_set__ConsD,axiom,
% 2.87/1.51 ! [Y: node,X: node,Xs: list_node] :
% 2.87/1.51 ( ( member_node @ Y @ ( set_node2 @ ( cons_node @ X @ Xs ) ) )
% 2.87/1.51 => ( ( Y = X )
% 2.87/1.51 | ( member_node @ Y @ ( set_node2 @ Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_222_list_Oset__cases,axiom,
% 2.87/1.51 ! [E3: val,A: list_val] :
% 2.87/1.51 ( ( member_val @ E3 @ ( set_val2 @ A ) )
% 2.87/1.51 => ( ! [Z2: list_val] :
% 2.87/1.51 ( A
% 2.87/1.51 != ( cons_val @ E3 @ Z2 ) )
% 2.87/1.51 => ~ ! [Z1: val,Z2: list_val] :
% 2.87/1.51 ( ( A
% 2.87/1.51 = ( cons_val @ Z1 @ Z2 ) )
% 2.87/1.51 => ~ ( member_val @ E3 @ ( set_val2 @ Z2 ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_223_list_Oset__cases,axiom,
% 2.87/1.51 ! [E3: node,A: list_node] :
% 2.87/1.51 ( ( member_node @ E3 @ ( set_node2 @ A ) )
% 2.87/1.51 => ( ! [Z2: list_node] :
% 2.87/1.51 ( A
% 2.87/1.51 != ( cons_node @ E3 @ Z2 ) )
% 2.87/1.51 => ~ ! [Z1: node,Z2: list_node] :
% 2.87/1.51 ( ( A
% 2.87/1.51 = ( cons_node @ Z1 @ Z2 ) )
% 2.87/1.51 => ~ ( member_node @ E3 @ ( set_node2 @ Z2 ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_224_Cons__eq__appendI,axiom,
% 2.87/1.51 ! [X: node,Xs1: list_node,Ys: list_node,Xs: list_node,Zs: list_node] :
% 2.87/1.51 ( ( ( cons_node @ X @ Xs1 )
% 2.87/1.51 = Ys )
% 2.87/1.51 => ( ( Xs
% 2.87/1.51 = ( append_node @ Xs1 @ Zs ) )
% 2.87/1.51 => ( ( cons_node @ X @ Xs )
% 2.87/1.51 = ( append_node @ Ys @ Zs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_225_append__Cons,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( append_node @ ( cons_node @ X @ Xs ) @ Ys )
% 2.87/1.51 = ( cons_node @ X @ ( append_node @ Xs @ Ys ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_226_list__match__lel__lel,axiom,
% 2.87/1.51 ! [C1: list_node,Qs: node,C2: list_node,C12: list_node,Qs2: node,C22: list_node] :
% 2.87/1.51 ( ( ( append_node @ C1 @ ( cons_node @ Qs @ C2 ) )
% 2.87/1.51 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C22 ) ) )
% 2.87/1.51 => ( ! [C21: list_node] :
% 2.87/1.51 ( ( C1
% 2.87/1.51 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C21 ) ) )
% 2.87/1.51 => ( C22
% 2.87/1.51 != ( append_node @ C21 @ ( cons_node @ Qs @ C2 ) ) ) )
% 2.87/1.51 => ( ( ( C12 = C1 )
% 2.87/1.51 => ( ( Qs2 = Qs )
% 2.87/1.51 => ( C22 != C2 ) ) )
% 2.87/1.51 => ~ ! [C212: list_node] :
% 2.87/1.51 ( ( C12
% 2.87/1.51 = ( append_node @ C1 @ ( cons_node @ Qs @ C212 ) ) )
% 2.87/1.51 => ( C2
% 2.87/1.51 != ( append_node @ C212 @ ( cons_node @ Qs2 @ C22 ) ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_227_append_Oleft__neutral,axiom,
% 2.87/1.51 ! [A: list_node] :
% 2.87/1.51 ( ( append_node @ nil_node @ A )
% 2.87/1.51 = A ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_228_append__Nil,axiom,
% 2.87/1.51 ! [Ys: list_node] :
% 2.87/1.51 ( ( append_node @ nil_node @ Ys )
% 2.87/1.51 = Ys ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_229_eq__Nil__appendI,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( Xs = Ys )
% 2.87/1.51 => ( Xs
% 2.87/1.51 = ( append_node @ nil_node @ Ys ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_230_list_Osel_I1_J,axiom,
% 2.87/1.51 ! [X21: node,X22: list_node] :
% 2.87/1.51 ( ( hd_node @ ( cons_node @ X21 @ X22 ) )
% 2.87/1.51 = X21 ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_231_rev__induct,axiom,
% 2.87/1.51 ! [P: list_node > $o,Xs: list_node] :
% 2.87/1.51 ( ( P @ nil_node )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node] :
% 2.87/1.51 ( ( P @ Xs2 )
% 2.87/1.51 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) )
% 2.87/1.51 => ( P @ Xs ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_232_rev__exhaust,axiom,
% 2.87/1.51 ! [Xs: list_node] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 => ~ ! [Ys3: list_node,Y3: node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 != ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_233_neq__Nil__revE,axiom,
% 2.87/1.51 ! [L: list_node] :
% 2.87/1.51 ( ( L != nil_node )
% 2.87/1.51 => ~ ! [Ll: list_node,E4: node] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_node @ Ll @ ( cons_node @ E4 @ nil_node ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_234_rev__induct2_H,axiom,
% 2.87/1.51 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 2.87/1.51 ( ( P @ nil_node @ nil_node )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 2.87/1.51 => ( ! [Y3: node,Ys3: list_node] : ( P @ nil_node @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.51 ( ( P @ Xs2 @ Ys3 )
% 2.87/1.51 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) )
% 2.87/1.51 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_235_neq__Nil__rev__conv,axiom,
% 2.87/1.51 ! [L: list_node] :
% 2.87/1.51 ( ( L != nil_node )
% 2.87/1.51 = ( ? [Xs3: list_node,X3: node] :
% 2.87/1.51 ( L
% 2.87/1.51 = ( append_node @ Xs3 @ ( cons_node @ X3 @ nil_node ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_236_Cons__eq__append__conv,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.87/1.51 ( ( ( cons_node @ X @ Xs )
% 2.87/1.51 = ( append_node @ Ys @ Zs ) )
% 2.87/1.51 = ( ( ( Ys = nil_node )
% 2.87/1.51 & ( ( cons_node @ X @ Xs )
% 2.87/1.51 = Zs ) )
% 2.87/1.51 | ? [Ys4: list_node] :
% 2.87/1.51 ( ( ( cons_node @ X @ Ys4 )
% 2.87/1.51 = Ys )
% 2.87/1.51 & ( Xs
% 2.87/1.51 = ( append_node @ Ys4 @ Zs ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_237_append__eq__Cons__conv,axiom,
% 2.87/1.51 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 2.87/1.51 ( ( ( append_node @ Ys @ Zs )
% 2.87/1.51 = ( cons_node @ X @ Xs ) )
% 2.87/1.51 = ( ( ( Ys = nil_node )
% 2.87/1.51 & ( Zs
% 2.87/1.51 = ( cons_node @ X @ Xs ) ) )
% 2.87/1.51 | ? [Ys4: list_node] :
% 2.87/1.51 ( ( Ys
% 2.87/1.51 = ( cons_node @ X @ Ys4 ) )
% 2.87/1.51 & ( ( append_node @ Ys4 @ Zs )
% 2.87/1.51 = Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_238_rev__nonempty__induct,axiom,
% 2.87/1.51 ! [Xs: list_node,P: list_node > $o] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node] :
% 2.87/1.51 ( ( Xs2 != nil_node )
% 2.87/1.51 => ( ( P @ Xs2 )
% 2.87/1.51 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) ) )
% 2.87/1.51 => ( P @ Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_239_rev__nonempty__induct2_H,axiom,
% 2.87/1.51 ! [Xs: list_node,Ys: list_node,P: list_node > list_node > $o] :
% 2.87/1.51 ( ( Xs != nil_node )
% 2.87/1.51 => ( ( Ys != nil_node )
% 2.87/1.51 => ( ! [X4: node,Y3: node] : ( P @ ( cons_node @ X4 @ nil_node ) @ ( cons_node @ Y3 @ nil_node ) )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node,Y3: node] :
% 2.87/1.51 ( ( Xs2 != nil_node )
% 2.87/1.51 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( cons_node @ Y3 @ nil_node ) ) )
% 2.87/1.51 => ( ! [X4: node,Y3: node,Ys3: list_node] :
% 2.87/1.51 ( ( Ys3 != nil_node )
% 2.87/1.51 => ( P @ ( cons_node @ X4 @ nil_node ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) )
% 2.87/1.51 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.51 ( ( P @ Xs2 @ Ys3 )
% 2.87/1.51 => ( ( Xs2 != nil_node )
% 2.87/1.51 => ( ( Ys3 != nil_node )
% 2.87/1.51 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) ) ) )
% 2.87/1.51 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_240_list__Cons__eq__append__cases,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.87/1.51 ( ( ( cons_node @ X @ Xs )
% 2.87/1.51 = ( append_node @ Ys @ Zs ) )
% 2.87/1.51 => ( ( ( Ys = nil_node )
% 2.87/1.51 => ( Zs
% 2.87/1.51 != ( cons_node @ X @ Xs ) ) )
% 2.87/1.51 => ~ ! [Ys5: list_node] :
% 2.87/1.51 ( ( Ys
% 2.87/1.51 = ( cons_node @ X @ Ys5 ) )
% 2.87/1.51 => ( ( append_node @ Ys5 @ Zs )
% 2.87/1.51 != Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_241_list__append__eq__Cons__cases,axiom,
% 2.87/1.51 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 2.87/1.51 ( ( ( append_node @ Ys @ Zs )
% 2.87/1.51 = ( cons_node @ X @ Xs ) )
% 2.87/1.51 => ( ( ( Ys = nil_node )
% 2.87/1.51 => ( Zs
% 2.87/1.51 != ( cons_node @ X @ Xs ) ) )
% 2.87/1.51 => ~ ! [Ys5: list_node] :
% 2.87/1.51 ( ( Ys
% 2.87/1.51 = ( cons_node @ X @ Ys5 ) )
% 2.87/1.51 => ( ( append_node @ Ys5 @ Zs )
% 2.87/1.51 != Xs ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_242_split__list,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val] :
% 2.87/1.51 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.51 => ? [Ys3: list_val,Zs2: list_val] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs2 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_243_split__list,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node] :
% 2.87/1.51 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.51 => ? [Ys3: list_node,Zs2: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs2 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_244_split__list__last,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val] :
% 2.87/1.51 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.51 => ? [Ys3: list_val,Zs2: list_val] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs2 ) ) )
% 2.87/1.51 & ~ ( member_val @ X @ ( set_val2 @ Zs2 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_245_split__list__last,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node] :
% 2.87/1.51 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.51 => ? [Ys3: list_node,Zs2: list_node] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs2 ) ) )
% 2.87/1.51 & ~ ( member_node @ X @ ( set_node2 @ Zs2 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_246_split__list__prop,axiom,
% 2.87/1.51 ! [Xs: list_node,P: node > $o] :
% 2.87/1.51 ( ? [X2: node] :
% 2.87/1.51 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.87/1.51 & ( P @ X2 ) )
% 2.87/1.51 => ? [Ys3: list_node,X4: node] :
% 2.87/1.51 ( ? [Zs2: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 2.87/1.51 & ( P @ X4 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_247_xy__in__set__cases,axiom,
% 2.87/1.51 ! [X: val,L: list_val,Y: val] :
% 2.87/1.51 ( ( member_val @ X @ ( set_val2 @ L ) )
% 2.87/1.51 => ( ( member_val @ Y @ ( set_val2 @ L ) )
% 2.87/1.51 => ( ( ( X = Y )
% 2.87/1.51 => ! [L12: list_val,L22: list_val] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_val @ L12 @ ( cons_val @ Y @ L22 ) ) ) )
% 2.87/1.51 => ( ( ( X != Y )
% 2.87/1.51 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_val @ L12 @ ( cons_val @ X @ ( append_val @ L22 @ ( cons_val @ Y @ L3 ) ) ) ) ) )
% 2.87/1.51 => ~ ( ( X != Y )
% 2.87/1.51 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_val @ L12 @ ( cons_val @ Y @ ( append_val @ L22 @ ( cons_val @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_248_xy__in__set__cases,axiom,
% 2.87/1.51 ! [X: node,L: list_node,Y: node] :
% 2.87/1.51 ( ( member_node @ X @ ( set_node2 @ L ) )
% 2.87/1.51 => ( ( member_node @ Y @ ( set_node2 @ L ) )
% 2.87/1.51 => ( ( ( X = Y )
% 2.87/1.51 => ! [L12: list_node,L22: list_node] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_node @ L12 @ ( cons_node @ Y @ L22 ) ) ) )
% 2.87/1.51 => ( ( ( X != Y )
% 2.87/1.51 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_node @ L12 @ ( cons_node @ X @ ( append_node @ L22 @ ( cons_node @ Y @ L3 ) ) ) ) ) )
% 2.87/1.51 => ~ ( ( X != Y )
% 2.87/1.51 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_node @ L12 @ ( cons_node @ Y @ ( append_node @ L22 @ ( cons_node @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_249_split__list__first,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val] :
% 2.87/1.51 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.51 => ? [Ys3: list_val,Zs2: list_val] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs2 ) ) )
% 2.87/1.51 & ~ ( member_val @ X @ ( set_val2 @ Ys3 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_250_split__list__first,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node] :
% 2.87/1.51 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.51 => ? [Ys3: list_node,Zs2: list_node] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs2 ) ) )
% 2.87/1.51 & ~ ( member_node @ X @ ( set_node2 @ Ys3 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_251_split__list__propE,axiom,
% 2.87/1.51 ! [Xs: list_node,P: node > $o] :
% 2.87/1.51 ( ? [X2: node] :
% 2.87/1.51 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.87/1.51 & ( P @ X2 ) )
% 2.87/1.51 => ~ ! [Ys3: list_node,X4: node] :
% 2.87/1.51 ( ? [Zs2: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 2.87/1.51 => ~ ( P @ X4 ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_252_append__Cons__eq__iff,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val,Ys: list_val,Xs4: list_val,Ys6: list_val] :
% 2.87/1.51 ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.51 => ( ~ ( member_val @ X @ ( set_val2 @ Ys ) )
% 2.87/1.51 => ( ( ( append_val @ Xs @ ( cons_val @ X @ Ys ) )
% 2.87/1.51 = ( append_val @ Xs4 @ ( cons_val @ X @ Ys6 ) ) )
% 2.87/1.51 = ( ( Xs = Xs4 )
% 2.87/1.51 & ( Ys = Ys6 ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_253_append__Cons__eq__iff,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node,Ys: list_node,Xs4: list_node,Ys6: list_node] :
% 2.87/1.51 ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.51 => ( ~ ( member_node @ X @ ( set_node2 @ Ys ) )
% 2.87/1.51 => ( ( ( append_node @ Xs @ ( cons_node @ X @ Ys ) )
% 2.87/1.51 = ( append_node @ Xs4 @ ( cons_node @ X @ Ys6 ) ) )
% 2.87/1.51 = ( ( Xs = Xs4 )
% 2.87/1.51 & ( Ys = Ys6 ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_254_in__set__conv__decomp,axiom,
% 2.87/1.51 ! [X: val,Xs: list_val] :
% 2.87/1.51 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.51 = ( ? [Ys2: list_val,Zs3: list_val] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs3 ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_255_in__set__conv__decomp,axiom,
% 2.87/1.51 ! [X: node,Xs: list_node] :
% 2.87/1.51 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.51 = ( ? [Ys2: list_node,Zs3: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs3 ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_256_in__set__list__format,axiom,
% 2.87/1.51 ! [E3: val,L: list_val] :
% 2.87/1.51 ( ( member_val @ E3 @ ( set_val2 @ L ) )
% 2.87/1.51 => ~ ! [L12: list_val,L22: list_val] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_val @ L12 @ ( cons_val @ E3 @ L22 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_257_in__set__list__format,axiom,
% 2.87/1.51 ! [E3: node,L: list_node] :
% 2.87/1.51 ( ( member_node @ E3 @ ( set_node2 @ L ) )
% 2.87/1.51 => ~ ! [L12: list_node,L22: list_node] :
% 2.87/1.51 ( L
% 2.87/1.51 != ( append_node @ L12 @ ( cons_node @ E3 @ L22 ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_258_split__list__last__prop,axiom,
% 2.87/1.51 ! [Xs: list_node,P: node > $o] :
% 2.87/1.51 ( ? [X2: node] :
% 2.87/1.51 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.87/1.51 & ( P @ X2 ) )
% 2.87/1.51 => ? [Ys3: list_node,X4: node,Zs2: list_node] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 2.87/1.51 & ( P @ X4 )
% 2.87/1.51 & ! [Xa: node] :
% 2.87/1.51 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 2.87/1.51 => ~ ( P @ Xa ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_259_split__list__first__prop,axiom,
% 2.87/1.51 ! [Xs: list_node,P: node > $o] :
% 2.87/1.51 ( ? [X2: node] :
% 2.87/1.51 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.87/1.51 & ( P @ X2 ) )
% 2.87/1.51 => ? [Ys3: list_node,X4: node] :
% 2.87/1.51 ( ? [Zs2: list_node] :
% 2.87/1.51 ( Xs
% 2.87/1.51 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 2.87/1.51 & ( P @ X4 )
% 2.87/1.51 & ! [Xa: node] :
% 2.87/1.51 ( ( member_node @ Xa @ ( set_node2 @ Ys3 ) )
% 2.87/1.51 => ~ ( P @ Xa ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_260_split__list__last__propE,axiom,
% 2.87/1.51 ! [Xs: list_node,P: node > $o] :
% 2.87/1.51 ( ? [X2: node] :
% 2.87/1.51 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.87/1.51 & ( P @ X2 ) )
% 2.87/1.51 => ~ ! [Ys3: list_node,X4: node,Zs2: list_node] :
% 2.87/1.51 ( ( Xs
% 2.87/1.51 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 2.87/1.51 => ( ( P @ X4 )
% 2.87/1.51 => ~ ! [Xa: node] :
% 2.87/1.51 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 2.87/1.51 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.87/1.51
% 2.87/1.51 thf(fact_261_split__list__first__propE,axiom,
% 2.87/1.51 ! [Xs: list_node,P: node > $o] :
% 2.87/1.51 ( ? [X2: node] :
% 2.87/1.51 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.87/1.51 & ( P @ X2 ) )
% 2.87/1.51 => ~ ! [Ys3: list_node,X4: node] :
% 2.87/1.52 ( ? [Zs2: list_node] :
% 2.87/1.52 ( Xs
% 2.87/1.52 = ( append_node @ Ys3 @ ( cons_node @ X4 @ Zs2 ) ) )
% 2.87/1.52 => ( ( P @ X4 )
% 2.87/1.52 => ~ ! [Xa: node] :
% 2.87/1.52 ( ( member_node @ Xa @ ( set_node2 @ Ys3 ) )
% 2.87/1.52 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_262_in__set__conv__decomp__last,axiom,
% 2.87/1.52 ! [X: val,Xs: list_val] :
% 2.87/1.52 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.52 = ( ? [Ys2: list_val,Zs3: list_val] :
% 2.87/1.52 ( ( Xs
% 2.87/1.52 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs3 ) ) )
% 2.87/1.52 & ~ ( member_val @ X @ ( set_val2 @ Zs3 ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_263_in__set__conv__decomp__last,axiom,
% 2.87/1.52 ! [X: node,Xs: list_node] :
% 2.87/1.52 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.52 = ( ? [Ys2: list_node,Zs3: list_node] :
% 2.87/1.52 ( ( Xs
% 2.87/1.52 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs3 ) ) )
% 2.87/1.52 & ~ ( member_node @ X @ ( set_node2 @ Zs3 ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_264_in__set__conv__decomp__first,axiom,
% 2.87/1.52 ! [X: val,Xs: list_val] :
% 2.87/1.52 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.87/1.52 = ( ? [Ys2: list_val,Zs3: list_val] :
% 2.87/1.52 ( ( Xs
% 2.87/1.52 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs3 ) ) )
% 2.87/1.52 & ~ ( member_val @ X @ ( set_val2 @ Ys2 ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_265_in__set__conv__decomp__first,axiom,
% 2.87/1.52 ! [X: node,Xs: list_node] :
% 2.87/1.52 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.87/1.52 = ( ? [Ys2: list_node,Zs3: list_node] :
% 2.87/1.52 ( ( Xs
% 2.87/1.52 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs3 ) ) )
% 2.87/1.52 & ~ ( member_node @ X @ ( set_node2 @ Ys2 ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_266_split__list__last__prop__iff,axiom,
% 2.87/1.52 ! [Xs: list_node,P: node > $o] :
% 2.87/1.52 ( ( ? [X3: node] :
% 2.87/1.52 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 2.87/1.52 & ( P @ X3 ) ) )
% 2.87/1.52 = ( ? [Ys2: list_node,X3: node,Zs3: list_node] :
% 2.87/1.52 ( ( Xs
% 2.87/1.52 = ( append_node @ Ys2 @ ( cons_node @ X3 @ Zs3 ) ) )
% 2.87/1.52 & ( P @ X3 )
% 2.87/1.52 & ! [Y2: node] :
% 2.87/1.52 ( ( member_node @ Y2 @ ( set_node2 @ Zs3 ) )
% 2.87/1.52 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_267_split__list__first__prop__iff,axiom,
% 2.87/1.52 ! [Xs: list_node,P: node > $o] :
% 2.87/1.52 ( ( ? [X3: node] :
% 2.87/1.52 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 2.87/1.52 & ( P @ X3 ) ) )
% 2.87/1.52 = ( ? [Ys2: list_node,X3: node] :
% 2.87/1.52 ( ? [Zs3: list_node] :
% 2.87/1.52 ( Xs
% 2.87/1.52 = ( append_node @ Ys2 @ ( cons_node @ X3 @ Zs3 ) ) )
% 2.87/1.52 & ( P @ X3 )
% 2.87/1.52 & ! [Y2: node] :
% 2.87/1.52 ( ( member_node @ Y2 @ ( set_node2 @ Ys2 ) )
% 2.87/1.52 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_268_hd__in__set,axiom,
% 2.87/1.52 ! [Xs: list_val] :
% 2.87/1.52 ( ( Xs != nil_val )
% 2.87/1.52 => ( member_val @ ( hd_val @ Xs ) @ ( set_val2 @ Xs ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_269_hd__in__set,axiom,
% 2.87/1.52 ! [Xs: list_node] :
% 2.87/1.52 ( ( Xs != nil_node )
% 2.87/1.52 => ( member_node @ ( hd_node @ Xs ) @ ( set_node2 @ Xs ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_270_list_Oset__sel_I1_J,axiom,
% 2.87/1.52 ! [A: list_val] :
% 2.87/1.52 ( ( A != nil_val )
% 2.87/1.52 => ( member_val @ ( hd_val @ A ) @ ( set_val2 @ A ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_271_list_Oset__sel_I1_J,axiom,
% 2.87/1.52 ! [A: list_node] :
% 2.87/1.52 ( ( A != nil_node )
% 2.87/1.52 => ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_272_longest__common__prefix,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.52 ? [Ps: list_node,Xs5: list_node,Ys5: list_node] :
% 2.87/1.52 ( ( Xs
% 2.87/1.52 = ( append_node @ Ps @ Xs5 ) )
% 2.87/1.52 & ( Ys
% 2.87/1.52 = ( append_node @ Ps @ Ys5 ) )
% 2.87/1.52 & ( ( Xs5 = nil_node )
% 2.87/1.52 | ( Ys5 = nil_node )
% 2.87/1.52 | ( ( hd_node @ Xs5 )
% 2.87/1.52 != ( hd_node @ Ys5 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_273_hd__append,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.52 ( ( ( Xs = nil_node )
% 2.87/1.52 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 2.87/1.52 = ( hd_node @ Ys ) ) )
% 2.87/1.52 & ( ( Xs != nil_node )
% 2.87/1.52 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 2.87/1.52 = ( hd_node @ Xs ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_274__092_060open_062old_OpathsConverge_Ag_Am_Ams_H_An_A_Ins_A_064_Atl_Ari_J_Ai_092_060close_062,axiom,
% 2.87/1.52 graph_2009891965_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ i ).
% 2.87/1.52
% 2.87/1.52 thf(fact_275__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,
% 2.87/1.52 ~ ! [I: node,Ri: list_node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 2.87/1.52 => ( ( member_node @ I @ ( set_node2 @ ms ) )
% 2.87/1.52 => ( ! [X2: node] :
% 2.87/1.52 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ri ) ) )
% 2.87/1.52 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) )
% 2.87/1.52 => ~ ( prefix_node @ Ri @ rs2 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_276__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,
% 2.87/1.52 ~ ! [Ms2: list_node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 2.87/1.52 => ( ( prefix_node @ Ms2 @ ms )
% 2.87/1.52 => ( member_node @ i @ ( set_node2 @ ( butlast_node @ Ms2 ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_277_old_Opath2__simple__loop,axiom,
% 2.87/1.52 ! [G: g,N: node,Ns: list_node,N2: node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ N )
% 2.87/1.52 => ( ( member_node @ N2 @ ( set_node2 @ Ns ) )
% 2.87/1.52 => ~ ! [Ns4: list_node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ N )
% 2.87/1.52 => ( ( member_node @ N2 @ ( set_node2 @ Ns4 ) )
% 2.87/1.52 => ( ~ ( member_node @ N @ ( set_node2 @ ( tl_node @ ( butlast_node @ Ns4 ) ) ) )
% 2.87/1.52 => ~ ( ord_less_eq_set_node @ ( set_node2 @ Ns4 ) @ ( set_node2 @ Ns ) ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_278_old_Opath_Ocases,axiom,
% 2.87/1.52 ! [G: g,A: list_node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 2.87/1.52 => ( ! [N4: node] :
% 2.87/1.52 ( ( A
% 2.87/1.52 = ( cons_node @ N4 @ nil_node ) )
% 2.87/1.52 => ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.87/1.52 => ~ ( invar @ G ) ) )
% 2.87/1.52 => ~ ! [Ns3: list_node,N3: node] :
% 2.87/1.52 ( ( A
% 2.87/1.52 = ( cons_node @ N3 @ Ns3 ) )
% 2.87/1.52 => ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns3 )
% 2.87/1.52 => ~ ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns3 ) ) ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_279_old_Opath_Oinducts,axiom,
% 2.87/1.52 ! [G: g,X: list_node,P: list_node > $o] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ X )
% 2.87/1.52 => ( ! [N4: node] :
% 2.87/1.52 ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.87/1.52 => ( ( invar @ G )
% 2.87/1.52 => ( P @ ( cons_node @ N4 @ nil_node ) ) ) )
% 2.87/1.52 => ( ! [Ns3: list_node,N3: node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns3 )
% 2.87/1.52 => ( ( P @ Ns3 )
% 2.87/1.52 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns3 ) ) ) )
% 2.87/1.52 => ( P @ ( cons_node @ N3 @ Ns3 ) ) ) ) )
% 2.87/1.52 => ( P @ X ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_280_old_Opath_Osimps,axiom,
% 2.87/1.52 ! [G: g,A: list_node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 2.87/1.52 = ( ? [N5: node] :
% 2.87/1.52 ( ( A
% 2.87/1.52 = ( cons_node @ N5 @ nil_node ) )
% 2.87/1.52 & ( member_node @ N5 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.87/1.52 & ( invar @ G ) )
% 2.87/1.52 | ? [Ns5: list_node,N6: node] :
% 2.87/1.52 ( ( A
% 2.87/1.52 = ( cons_node @ N6 @ Ns5 ) )
% 2.87/1.52 & ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns5 )
% 2.87/1.52 & ( member_node @ N6 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns5 ) ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_281_old_Opath__snoc,axiom,
% 2.87/1.52 ! [G: g,Ns: list_node,N: node,M: node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ nil_node ) ) )
% 2.87/1.52 => ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M ) ) )
% 2.87/1.52 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ ( cons_node @ M @ nil_node ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_282_ri__rs_H__prefix,axiom,
% 2.87/1.52 prefix_node @ ri @ rs ).
% 2.87/1.52
% 2.87/1.52 thf(fact_283_old_Opath__not__Nil,axiom,
% 2.87/1.52 ! [G: g,Ns: list_node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 2.87/1.52 => ( Ns != nil_node ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_284_old_Opath__hd,axiom,
% 2.87/1.52 ! [G: g,N: node,Ns: list_node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ Ns ) )
% 2.87/1.52 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_285_old_Opath__split_I2_J,axiom,
% 2.87/1.52 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 2.87/1.52 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ M @ Ns2 ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_286_old_Oempty__path,axiom,
% 2.87/1.52 ! [N: node,G: g] :
% 2.87/1.52 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.87/1.52 => ( ( invar @ G )
% 2.87/1.52 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_287_old_Opath__split_I1_J,axiom,
% 2.87/1.52 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 2.87/1.52 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ nil_node ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_288_old_Opath2__split__first__prop,axiom,
% 2.87/1.52 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.52 => ( ? [X2: node] :
% 2.87/1.52 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 2.87/1.52 & ( P @ X2 ) )
% 2.87/1.52 => ~ ! [M2: node,Ns4: list_node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ M2 )
% 2.87/1.52 => ( ( P @ M2 )
% 2.87/1.52 => ( ! [X2: node] :
% 2.87/1.52 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ns4 ) ) )
% 2.87/1.52 => ~ ( P @ X2 ) )
% 2.87/1.52 => ~ ( prefix_node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_289_old_Opath2__prefix__ex,axiom,
% 2.87/1.52 ! [G: g,N: node,Ns: list_node,M: node,M4: node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.52 => ( ( member_node @ M4 @ ( set_node2 @ Ns ) )
% 2.87/1.52 => ~ ! [Ns4: list_node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ M4 )
% 2.87/1.52 => ( ( prefix_node @ Ns4 @ Ns )
% 2.87/1.52 => ( member_node @ M4 @ ( set_node2 @ ( butlast_node @ Ns4 ) ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_290_old_OCons__path,axiom,
% 2.87/1.52 ! [G: g,Ns: list_node,N2: node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 2.87/1.52 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns ) ) ) )
% 2.87/1.52 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_291_old_Opath2__prefix,axiom,
% 2.87/1.52 ! [G: g,N: node,Ns: list_node,M: node,Ns2: list_node,M4: node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.52 => ( ( prefix_node @ ( append_node @ Ns2 @ ( cons_node @ M4 @ nil_node ) ) @ Ns )
% 2.87/1.52 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns2 @ ( cons_node @ M4 @ nil_node ) ) @ M4 ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_292_old_Opath__invar,axiom,
% 2.87/1.52 ! [G: g,Ns: list_node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 2.87/1.52 => ( invar @ G ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_293_old_Opath__in___092_060alpha_062n,axiom,
% 2.87/1.52 ! [G: g,Ns: list_node,N: node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 2.87/1.52 => ( ( member_node @ N @ ( set_node2 @ Ns ) )
% 2.87/1.52 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_294_old_Opath__by__tail,axiom,
% 2.87/1.52 ! [G: g,N: node,N2: node,Ns: list_node,Ms: list_node] :
% 2.87/1.52 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ns ) ) )
% 2.87/1.52 => ( ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) )
% 2.87/1.52 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ms ) ) )
% 2.87/1.52 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ms ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_295_subset__Collect__conv,axiom,
% 2.87/1.52 ! [S: set_node,P: node > $o] :
% 2.87/1.52 ( ( ord_less_eq_set_node @ S @ ( collect_node @ P ) )
% 2.87/1.52 = ( ! [X3: node] :
% 2.87/1.52 ( ( member_node @ X3 @ S )
% 2.87/1.52 => ( P @ X3 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_296_ord__eq__le__eq__trans,axiom,
% 2.87/1.52 ! [A: set_node,B: set_node,C: set_node,D: set_node] :
% 2.87/1.52 ( ( A = B )
% 2.87/1.52 => ( ( ord_less_eq_set_node @ B @ C )
% 2.87/1.52 => ( ( C = D )
% 2.87/1.52 => ( ord_less_eq_set_node @ A @ D ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_297_subset__code_I1_J,axiom,
% 2.87/1.52 ! [Xs: list_val,B3: set_val] :
% 2.87/1.52 ( ( ord_less_eq_set_val @ ( set_val2 @ Xs ) @ B3 )
% 2.87/1.52 = ( ! [X3: val] :
% 2.87/1.52 ( ( member_val @ X3 @ ( set_val2 @ Xs ) )
% 2.87/1.52 => ( member_val @ X3 @ B3 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_298_subset__code_I1_J,axiom,
% 2.87/1.52 ! [Xs: list_node,B3: set_node] :
% 2.87/1.52 ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ B3 )
% 2.87/1.52 = ( ! [X3: node] :
% 2.87/1.52 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 2.87/1.52 => ( member_node @ X3 @ B3 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_299_set__subset__Cons,axiom,
% 2.87/1.52 ! [Xs: list_node,X: node] : ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ ( cons_node @ X @ Xs ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_300_tl__subset,axiom,
% 2.87/1.52 ! [Xs: list_node,A2: set_node] :
% 2.87/1.52 ( ( Xs != nil_node )
% 2.87/1.52 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 2.87/1.52 => ( ord_less_eq_set_node @ ( set_node2 @ ( tl_node @ Xs ) ) @ A2 ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_301_butlast__subset,axiom,
% 2.87/1.52 ! [Xs: list_node,A2: set_node] :
% 2.87/1.52 ( ( Xs != nil_node )
% 2.87/1.52 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 2.87/1.52 => ( ord_less_eq_set_node @ ( set_node2 @ ( butlast_node @ Xs ) ) @ A2 ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_302_prefix__snoc,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node,Y: node] :
% 2.87/1.52 ( ( prefix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 2.87/1.52 = ( ( Xs
% 2.87/1.52 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 2.87/1.52 | ( prefix_node @ Xs @ Ys ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_303_old_Opath2__split__first__last,axiom,
% 2.87/1.52 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.52 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 2.87/1.52 => ~ ! [Ns_1: list_node,Ns_3: list_node,Ns_2: list_node] :
% 2.87/1.52 ( ( Ns
% 2.87/1.52 = ( append_node @ Ns_1 @ ( append_node @ Ns_3 @ Ns_2 ) ) )
% 2.87/1.52 => ( ( prefix_node @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ Ns )
% 2.87/1.52 => ( ( suffix_node @ ( cons_node @ X @ Ns_2 ) @ Ns )
% 2.87/1.52 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ X )
% 2.87/1.52 => ( ~ ( member_node @ X @ ( set_node2 @ Ns_1 ) )
% 2.87/1.52 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_3 @ X )
% 2.87/1.52 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ ( cons_node @ X @ Ns_2 ) @ M )
% 2.87/1.52 => ( member_node @ X @ ( set_node2 @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_304_same__prefix__nil,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.52 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ Xs )
% 2.87/1.52 = ( Ys = nil_node ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_305_prefix__order_Odual__order_Orefl,axiom,
% 2.87/1.52 ! [A: list_node] : ( prefix_node @ A @ A ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_306_prefix__order_Oorder__refl,axiom,
% 2.87/1.52 ! [X: list_node] : ( prefix_node @ X @ X ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_307_suffix__order_Odual__order_Orefl,axiom,
% 2.87/1.52 ! [A: list_node] : ( suffix_node @ A @ A ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_308_suffix__order_Oorder__refl,axiom,
% 2.87/1.52 ! [X: list_node] : ( suffix_node @ X @ X ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_309_Cons__prefix__Cons,axiom,
% 2.87/1.52 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 2.87/1.52 ( ( prefix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 2.87/1.52 = ( ( X = Y )
% 2.87/1.52 & ( prefix_node @ Xs @ Ys ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_310_prefix__code_I1_J,axiom,
% 2.87/1.52 ! [Xs: list_node] : ( prefix_node @ nil_node @ Xs ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_311_prefix__Nil,axiom,
% 2.87/1.52 ! [Xs: list_node] :
% 2.87/1.52 ( ( prefix_node @ Xs @ nil_node )
% 2.87/1.52 = ( Xs = nil_node ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_312_prefix__bot_Obot_Oextremum__unique,axiom,
% 2.87/1.52 ! [A: list_node] :
% 2.87/1.52 ( ( prefix_node @ A @ nil_node )
% 2.87/1.52 = ( A = nil_node ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_313_suffix__bot_Obot_Oextremum__unique,axiom,
% 2.87/1.52 ! [A: list_node] :
% 2.87/1.52 ( ( suffix_node @ A @ nil_node )
% 2.87/1.52 = ( A = nil_node ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_314_suffix__Nil,axiom,
% 2.87/1.52 ! [Xs: list_node] :
% 2.87/1.52 ( ( suffix_node @ Xs @ nil_node )
% 2.87/1.52 = ( Xs = nil_node ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_315_same__prefix__prefix,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.87/1.52 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ ( append_node @ Xs @ Zs ) )
% 2.87/1.52 = ( prefix_node @ Ys @ Zs ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_316_same__suffix__suffix,axiom,
% 2.87/1.52 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 2.87/1.52 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ ( append_node @ Zs @ Xs ) )
% 2.87/1.52 = ( suffix_node @ Ys @ Zs ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_317_old_Opath2__split__last__prop,axiom,
% 2.87/1.52 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.87/1.52 => ( ? [X2: node] :
% 2.87/1.52 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 2.87/1.52 & ( P @ X2 ) )
% 2.87/1.52 => ~ ! [N3: node,Ns4: list_node] :
% 2.87/1.52 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N3 @ Ns4 @ M )
% 2.87/1.52 => ( ( P @ N3 )
% 2.87/1.52 => ( ! [X2: node] :
% 2.87/1.52 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns4 ) ) )
% 2.87/1.52 => ~ ( P @ X2 ) )
% 2.87/1.52 => ~ ( suffix_node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_318_same__suffix__nil,axiom,
% 2.87/1.52 ! [Ys: list_node,Xs: list_node] :
% 2.87/1.52 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ Xs )
% 2.87/1.52 = ( Ys = nil_node ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_319_snoc__suffix__snoc,axiom,
% 2.87/1.52 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 2.87/1.52 ( ( suffix_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 2.87/1.52 = ( ( X = Y )
% 2.87/1.52 & ( suffix_node @ Xs @ Ys ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_320_suffix__snoc,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node,Y: node] :
% 2.87/1.52 ( ( suffix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 2.87/1.52 = ( ( Xs = nil_node )
% 2.87/1.52 | ? [Zs3: list_node] :
% 2.87/1.52 ( ( Xs
% 2.87/1.52 = ( append_node @ Zs3 @ ( cons_node @ Y @ nil_node ) ) )
% 2.87/1.52 & ( suffix_node @ Zs3 @ Ys ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_321_suffix__tl,axiom,
% 2.87/1.52 ! [Xs: list_node] : ( suffix_node @ ( tl_node @ Xs ) @ Xs ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_322_suffix__Cons,axiom,
% 2.87/1.52 ! [Xs: list_node,Y: node,Ys: list_node] :
% 2.87/1.52 ( ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) )
% 2.87/1.52 = ( ( Xs
% 2.87/1.52 = ( cons_node @ Y @ Ys ) )
% 2.87/1.52 | ( suffix_node @ Xs @ Ys ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_323_suffix__ConsD,axiom,
% 2.87/1.52 ! [X: node,Xs: list_node,Ys: list_node] :
% 2.87/1.52 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ Ys )
% 2.87/1.52 => ( suffix_node @ Xs @ Ys ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_324_suffix__ConsI,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node,Y: node] :
% 2.87/1.52 ( ( suffix_node @ Xs @ Ys )
% 2.87/1.52 => ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_325_suffix__ConsD2,axiom,
% 2.87/1.52 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 2.87/1.52 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 2.87/1.52 => ( suffix_node @ Xs @ Ys ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_326_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 2.87/1.52 ! [A: list_node] :
% 2.87/1.52 ( ( suffix_node @ A @ nil_node )
% 2.87/1.52 => ( A = nil_node ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_327_suffix__bot_Obot_Oextremum,axiom,
% 2.87/1.52 ! [A: list_node] : ( suffix_node @ nil_node @ A ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_328_Nil__suffix,axiom,
% 2.87/1.52 ! [Xs: list_node] : ( suffix_node @ nil_node @ Xs ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_329_set__mono__suffix,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.52 ( ( suffix_node @ Xs @ Ys )
% 2.87/1.52 => ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ Ys ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_330_not__suffix__cases,axiom,
% 2.87/1.52 ! [Ps2: list_node,Ls: list_node] :
% 2.87/1.52 ( ~ ( suffix_node @ Ps2 @ Ls )
% 2.87/1.52 => ( ( ( Ps2 != nil_node )
% 2.87/1.52 => ( Ls != nil_node ) )
% 2.87/1.52 => ( ! [A3: node,As: list_node] :
% 2.87/1.52 ( ( Ps2
% 2.87/1.52 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 2.87/1.52 => ! [X4: node,Xs2: list_node] :
% 2.87/1.52 ( ( Ls
% 2.87/1.52 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 2.87/1.52 => ( ( X4 = A3 )
% 2.87/1.52 => ( suffix_node @ As @ Xs2 ) ) ) )
% 2.87/1.52 => ~ ! [A3: node] :
% 2.87/1.52 ( ? [As: list_node] :
% 2.87/1.52 ( Ps2
% 2.87/1.52 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 2.87/1.52 => ! [X4: node] :
% 2.87/1.52 ( ? [Xs2: list_node] :
% 2.87/1.52 ( Ls
% 2.87/1.52 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 2.87/1.52 => ( X4 = A3 ) ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_331_not__suffix__induct,axiom,
% 2.87/1.52 ! [Ps2: list_node,Ls: list_node,P: list_node > list_node > $o] :
% 2.87/1.52 ( ~ ( suffix_node @ Ps2 @ Ls )
% 2.87/1.52 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 2.87/1.52 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.52 ( ( X4 != Y3 )
% 2.87/1.52 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) )
% 2.87/1.52 => ( ! [X4: node,Xs2: list_node,Y3: node,Ys3: list_node] :
% 2.87/1.52 ( ( X4 = Y3 )
% 2.87/1.52 => ( ~ ( suffix_node @ Xs2 @ Ys3 )
% 2.87/1.52 => ( ( P @ Xs2 @ Ys3 )
% 2.87/1.52 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y3 @ nil_node ) ) ) ) ) )
% 2.87/1.52 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_332_suffix__order_Odual__order_Oantisym,axiom,
% 2.87/1.52 ! [B: list_node,A: list_node] :
% 2.87/1.52 ( ( suffix_node @ B @ A )
% 2.87/1.52 => ( ( suffix_node @ A @ B )
% 2.87/1.52 => ( A = B ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_333_suffix__order_Odual__order_Oeq__iff,axiom,
% 2.87/1.52 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 2.87/1.52 = ( ^ [A4: list_node,B4: list_node] :
% 2.87/1.52 ( ( suffix_node @ B4 @ A4 )
% 2.87/1.52 & ( suffix_node @ A4 @ B4 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_334_suffix__order_Odual__order_Otrans,axiom,
% 2.87/1.52 ! [B: list_node,A: list_node,C: list_node] :
% 2.87/1.52 ( ( suffix_node @ B @ A )
% 2.87/1.52 => ( ( suffix_node @ C @ B )
% 2.87/1.52 => ( suffix_node @ C @ A ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_335_suffix__order_Oord__le__eq__trans,axiom,
% 2.87/1.52 ! [A: list_node,B: list_node,C: list_node] :
% 2.87/1.52 ( ( suffix_node @ A @ B )
% 2.87/1.52 => ( ( B = C )
% 2.87/1.52 => ( suffix_node @ A @ C ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_336_suffix__order_Oord__eq__le__trans,axiom,
% 2.87/1.52 ! [A: list_node,B: list_node,C: list_node] :
% 2.87/1.52 ( ( A = B )
% 2.87/1.52 => ( ( suffix_node @ B @ C )
% 2.87/1.52 => ( suffix_node @ A @ C ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_337_suffix__order_Oorder_Oantisym,axiom,
% 2.87/1.52 ! [A: list_node,B: list_node] :
% 2.87/1.52 ( ( suffix_node @ A @ B )
% 2.87/1.52 => ( ( suffix_node @ B @ A )
% 2.87/1.52 => ( A = B ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_338_suffix__order_Oorder_Oeq__iff,axiom,
% 2.87/1.52 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 2.87/1.52 = ( ^ [A4: list_node,B4: list_node] :
% 2.87/1.52 ( ( suffix_node @ A4 @ B4 )
% 2.87/1.52 & ( suffix_node @ B4 @ A4 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_339_suffix__order_Oantisym__conv,axiom,
% 2.87/1.52 ! [Y: list_node,X: list_node] :
% 2.87/1.52 ( ( suffix_node @ Y @ X )
% 2.87/1.52 => ( ( suffix_node @ X @ Y )
% 2.87/1.52 = ( X = Y ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_340_suffix__order_Oorder__trans,axiom,
% 2.87/1.52 ! [X: list_node,Y: list_node,Z3: list_node] :
% 2.87/1.52 ( ( suffix_node @ X @ Y )
% 2.87/1.52 => ( ( suffix_node @ Y @ Z3 )
% 2.87/1.52 => ( suffix_node @ X @ Z3 ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_341_suffix__order_Oorder_Otrans,axiom,
% 2.87/1.52 ! [A: list_node,B: list_node,C: list_node] :
% 2.87/1.52 ( ( suffix_node @ A @ B )
% 2.87/1.52 => ( ( suffix_node @ B @ C )
% 2.87/1.52 => ( suffix_node @ A @ C ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_342_suffix__order_Oeq__refl,axiom,
% 2.87/1.52 ! [X: list_node,Y: list_node] :
% 2.87/1.52 ( ( X = Y )
% 2.87/1.52 => ( suffix_node @ X @ Y ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_343_suffix__order_Oantisym,axiom,
% 2.87/1.52 ! [X: list_node,Y: list_node] :
% 2.87/1.52 ( ( suffix_node @ X @ Y )
% 2.87/1.52 => ( ( suffix_node @ Y @ X )
% 2.87/1.52 => ( X = Y ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_344_suffix__order_Oeq__iff,axiom,
% 2.87/1.52 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 2.87/1.52 = ( ^ [X3: list_node,Y2: list_node] :
% 2.87/1.52 ( ( suffix_node @ X3 @ Y2 )
% 2.87/1.52 & ( suffix_node @ Y2 @ X3 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_345_suffix__same__cases,axiom,
% 2.87/1.52 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 2.87/1.52 ( ( suffix_node @ Xs_1 @ Ys )
% 2.87/1.52 => ( ( suffix_node @ Xs_2 @ Ys )
% 2.87/1.52 => ( ( suffix_node @ Xs_1 @ Xs_2 )
% 2.87/1.52 | ( suffix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_346_suffixE,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node] :
% 2.87/1.52 ( ( suffix_node @ Xs @ Ys )
% 2.87/1.52 => ~ ! [Zs2: list_node] :
% 2.87/1.52 ( Ys
% 2.87/1.52 != ( append_node @ Zs2 @ Xs ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_347_suffixI,axiom,
% 2.87/1.52 ! [Ys: list_node,Zs: list_node,Xs: list_node] :
% 2.87/1.52 ( ( Ys
% 2.87/1.52 = ( append_node @ Zs @ Xs ) )
% 2.87/1.52 => ( suffix_node @ Xs @ Ys ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_348_Sublist_Osuffix__def,axiom,
% 2.87/1.52 ( suffix_node
% 2.87/1.52 = ( ^ [Xs3: list_node,Ys2: list_node] :
% 2.87/1.52 ? [Zs3: list_node] :
% 2.87/1.52 ( Ys2
% 2.87/1.52 = ( append_node @ Zs3 @ Xs3 ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_349_suffix__append,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.87/1.52 ( ( suffix_node @ Xs @ ( append_node @ Ys @ Zs ) )
% 2.87/1.52 = ( ( suffix_node @ Xs @ Zs )
% 2.87/1.52 | ? [Xs6: list_node] :
% 2.87/1.52 ( ( Xs
% 2.87/1.52 = ( append_node @ Xs6 @ Zs ) )
% 2.87/1.52 & ( suffix_node @ Xs6 @ Ys ) ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_350_suffix__appendD,axiom,
% 2.87/1.52 ! [Zs: list_node,Xs: list_node,Ys: list_node] :
% 2.87/1.52 ( ( suffix_node @ ( append_node @ Zs @ Xs ) @ Ys )
% 2.87/1.52 => ( suffix_node @ Xs @ Ys ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(fact_351_suffix__appendI,axiom,
% 2.87/1.52 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.87/1.52 ( ( suffix_node @ Xs @ Ys )
% 2.87/1.52 => ( suffix_node @ Xs @ ( append_node @ Zs @ Ys ) ) ) ).
% 2.87/1.52
% 2.87/1.52 thf(conj_0,conjecture,
% 2.87/1.52 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ ( cons_node @ i @ rs_rest ) @ pred_phi_r ).
% 2.87/1.52 ------------------------
% 2.87/1.55 % (26251)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_26027 for (2999ds/275Mi)
% 2.87/1.55 % (26250)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_26027 for (2999ds/2Mi)
% 2.87/1.55 % (26246)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/183Mi)
% 2.87/1.56 % (26252)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/18Mi)
% 2.87/1.56 % (26250)Instruction limit reached!
% 2.87/1.56 % (26250)------------------------------
% 2.87/1.56 % (26250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.56 % (26250)Termination reason: Unknown
% 2.87/1.56 % (26250)Termination phase: shuffling
% 2.87/1.56
% 2.87/1.56 % (26250)Memory used [KB]: 1535
% 2.87/1.56 % (26250)Time elapsed: 0.002 s
% 2.87/1.56 % (26250)Instructions burned: 3 (million)
% 2.87/1.56 % (26250)------------------------------
% 2.87/1.56 % (26250)------------------------------
% 2.87/1.56 % (26247)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_26027 for (2999ds/4Mi)
% 2.87/1.56 % (26249)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/2Mi)
% 2.87/1.56 % (26248)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_26027 for (2999ds/27Mi)
% 2.87/1.56 % (26252)Instruction limit reached!
% 2.87/1.56 % (26252)------------------------------
% 2.87/1.56 % (26252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.56 % (26252)Termination reason: Unknown
% 2.87/1.56 % (26252)Termination phase: shuffling
% 2.87/1.56
% 2.87/1.56 % (26252)Memory used [KB]: 1791
% 2.87/1.56 % (26252)Time elapsed: 0.009 s
% 2.87/1.56 % (26252)Instructions burned: 18 (million)
% 2.87/1.56 % (26252)------------------------------
% 2.87/1.56 % (26252)------------------------------
% 2.87/1.56 % (26249)Instruction limit reached!
% 2.87/1.56 % (26249)------------------------------
% 2.87/1.56 % (26249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.56 % (26249)Termination reason: Unknown
% 2.87/1.56 % (26249)Termination phase: shuffling
% 2.87/1.56
% 2.87/1.56 % (26249)Memory used [KB]: 1407
% 2.87/1.56 % (26249)Time elapsed: 0.004 s
% 2.87/1.56 % (26249)Instructions burned: 2 (million)
% 2.87/1.56 % (26249)------------------------------
% 2.87/1.56 % (26249)------------------------------
% 2.87/1.56 % (26247)Instruction limit reached!
% 2.87/1.56 % (26247)------------------------------
% 2.87/1.56 % (26247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.56 % (26247)Termination reason: Unknown
% 2.87/1.56 % (26247)Termination phase: shuffling
% 2.87/1.56
% 2.87/1.56 % (26247)Memory used [KB]: 1535
% 2.87/1.56 % (26247)Time elapsed: 0.005 s
% 2.87/1.56 % (26247)Instructions burned: 4 (million)
% 2.87/1.56 % (26247)------------------------------
% 2.87/1.56 % (26247)------------------------------
% 2.87/1.57 % (26253)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/3Mi)
% 2.87/1.57 % (26253)Instruction limit reached!
% 2.87/1.57 % (26253)------------------------------
% 2.87/1.57 % (26253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.57 % (26253)Termination reason: Unknown
% 2.87/1.57 % (26253)Termination phase: shuffling
% 2.87/1.57
% 2.87/1.57 % (26253)Memory used [KB]: 1407
% 2.87/1.57 % (26253)Time elapsed: 0.002 s
% 2.87/1.57 % (26253)Instructions burned: 3 (million)
% 2.87/1.57 % (26253)------------------------------
% 2.87/1.57 % (26253)------------------------------
% 2.87/1.57 % (26254)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_26027 for (2999ds/37Mi)
% 2.87/1.58 % (26257)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_26027 for (2999ds/1041Mi)
% 2.87/1.58 % (26248)Instruction limit reached!
% 2.87/1.58 % (26248)------------------------------
% 2.87/1.58 % (26248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.58 % (26248)Termination reason: Unknown
% 2.87/1.58 % (26248)Termination phase: shuffling
% 2.87/1.58
% 2.87/1.58 % (26248)Memory used [KB]: 1918
% 2.87/1.58 % (26248)Time elapsed: 0.019 s
% 2.87/1.58 % (26248)Instructions burned: 27 (million)
% 2.87/1.58 % (26248)------------------------------
% 2.87/1.58 % (26248)------------------------------
% 2.87/1.58 % (26255)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_26027 for (2999ds/15Mi)
% 2.87/1.58 % (26256)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_26027 for (2999ds/3Mi)
% 2.87/1.58 % (26256)Instruction limit reached!
% 2.87/1.58 % (26256)------------------------------
% 2.87/1.58 % (26256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.58 % (26256)Termination reason: Unknown
% 2.87/1.58 % (26256)Termination phase: shuffling
% 2.87/1.58
% 2.87/1.58 % (26256)Memory used [KB]: 1407
% 2.87/1.58 % (26256)Time elapsed: 0.004 s
% 2.87/1.58 % (26256)Instructions burned: 3 (million)
% 2.87/1.58 % (26256)------------------------------
% 2.87/1.58 % (26256)------------------------------
% 2.87/1.58 % (26254)Instruction limit reached!
% 2.87/1.58 % (26254)------------------------------
% 2.87/1.58 % (26254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.58 % (26254)Termination reason: Unknown
% 2.87/1.58 % (26254)Termination phase: shuffling
% 2.87/1.58
% 2.87/1.58 % (26254)Memory used [KB]: 2174
% 2.87/1.58 % (26254)Time elapsed: 0.012 s
% 2.87/1.58 % (26254)Instructions burned: 37 (million)
% 2.87/1.58 % (26254)------------------------------
% 2.87/1.58 % (26254)------------------------------
% 2.87/1.59 % (26255)Instruction limit reached!
% 2.87/1.59 % (26255)------------------------------
% 2.87/1.59 % (26255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.59 % (26255)Termination reason: Unknown
% 2.87/1.59 % (26255)Termination phase: shuffling
% 2.87/1.59
% 2.87/1.59 % (26255)Memory used [KB]: 1663
% 2.87/1.59 % (26255)Time elapsed: 0.011 s
% 2.87/1.59 % (26255)Instructions burned: 15 (million)
% 2.87/1.59 % (26255)------------------------------
% 2.87/1.59 % (26255)------------------------------
% 2.87/1.59 % (26260)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_26027 for (2999ds/3Mi)
% 2.87/1.60 % (26260)Instruction limit reached!
% 2.87/1.60 % (26260)------------------------------
% 2.87/1.60 % (26260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.60 % (26260)Termination reason: Unknown
% 2.87/1.60 % (26260)Termination phase: shuffling
% 2.87/1.60
% 2.87/1.60 % (26260)Memory used [KB]: 1535
% 2.87/1.60 % (26260)Time elapsed: 0.003 s
% 2.87/1.60 % (26260)Instructions burned: 3 (million)
% 2.87/1.60 % (26260)------------------------------
% 2.87/1.60 % (26260)------------------------------
% 2.90/1.60 % (26258)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/7Mi)
% 2.90/1.60 % (26251)Refutation not found, incomplete strategy
% 2.90/1.60 % (26251)------------------------------
% 2.90/1.60 % (26251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (26251)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.60
% 2.90/1.60
% 2.90/1.60 % (26251)Memory used [KB]: 7547
% 2.90/1.60 % (26251)Time elapsed: 0.046 s
% 2.90/1.60 % (26251)Instructions burned: 149 (million)
% 2.90/1.60 % (26251)------------------------------
% 2.90/1.60 % (26251)------------------------------
% 2.90/1.60 % (26258)Instruction limit reached!
% 2.90/1.60 % (26258)------------------------------
% 2.90/1.60 % (26258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (26258)Termination reason: Unknown
% 2.90/1.60 % (26258)Termination phase: shuffling
% 2.90/1.60
% 2.90/1.60 % (26258)Memory used [KB]: 1535
% 2.90/1.60 % (26258)Time elapsed: 0.007 s
% 2.90/1.60 % (26258)Instructions burned: 8 (million)
% 2.90/1.60 % (26258)------------------------------
% 2.90/1.60 % (26258)------------------------------
% 2.90/1.60 % (26259)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/16Mi)
% 2.90/1.61 % (26262)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/7Mi)
% 2.90/1.61 % (26261)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_26027 for (2999ds/3Mi)
% 2.90/1.61 % (26263)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/3Mi)
% 2.90/1.61 % (26262)Instruction limit reached!
% 2.90/1.61 % (26262)------------------------------
% 2.90/1.61 % (26262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26262)Termination reason: Unknown
% 2.90/1.61 % (26262)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (26262)Memory used [KB]: 1663
% 2.90/1.61 % (26262)Time elapsed: 0.005 s
% 2.90/1.61 % (26262)Instructions burned: 9 (million)
% 2.90/1.61 % (26262)------------------------------
% 2.90/1.61 % (26262)------------------------------
% 2.90/1.61 % (26246)Instruction limit reached!
% 2.90/1.61 % (26246)------------------------------
% 2.90/1.61 % (26246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26246)Termination reason: Unknown
% 2.90/1.61 % (26246)Termination phase: Saturation
% 2.90/1.61
% 2.90/1.61 % (26246)Memory used [KB]: 7419
% 2.90/1.61 % (26246)Time elapsed: 0.056 s
% 2.90/1.61 % (26246)Instructions burned: 184 (million)
% 2.90/1.61 % (26246)------------------------------
% 2.90/1.61 % (26246)------------------------------
% 2.90/1.61 % (26261)Instruction limit reached!
% 2.90/1.61 % (26261)------------------------------
% 2.90/1.61 % (26261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26261)Termination reason: Unknown
% 2.90/1.61 % (26261)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (26261)Memory used [KB]: 1535
% 2.90/1.61 % (26261)Time elapsed: 0.004 s
% 2.90/1.61 % (26261)Instructions burned: 4 (million)
% 2.90/1.61 % (26261)------------------------------
% 2.90/1.61 % (26261)------------------------------
% 2.90/1.61 % (26263)Instruction limit reached!
% 2.90/1.61 % (26263)------------------------------
% 2.90/1.61 % (26263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26263)Termination reason: Unknown
% 2.90/1.61 % (26263)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (26263)Memory used [KB]: 1535
% 2.90/1.61 % (26263)Time elapsed: 0.002 s
% 2.90/1.61 % (26263)Instructions burned: 3 (million)
% 2.90/1.61 % (26263)------------------------------
% 2.90/1.61 % (26263)------------------------------
% 2.90/1.61 % (26259)Instruction limit reached!
% 2.90/1.61 % (26259)------------------------------
% 2.90/1.61 % (26259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26259)Termination reason: Unknown
% 2.90/1.61 % (26259)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (26259)Memory used [KB]: 1791
% 2.90/1.61 % (26259)Time elapsed: 0.012 s
% 2.90/1.61 % (26259)Instructions burned: 16 (million)
% 2.90/1.61 % (26259)------------------------------
% 2.90/1.61 % (26259)------------------------------
% 2.90/1.62 % (26264)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/4Mi)
% 2.90/1.62 % (26265)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/18Mi)
% 2.90/1.62 % (26268)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_26027 for (2999ds/902Mi)
% 2.90/1.62 % (26266)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/710Mi)
% 2.90/1.62 % (26264)Instruction limit reached!
% 2.90/1.62 % (26264)------------------------------
% 2.90/1.62 % (26264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (26264)Termination reason: Unknown
% 2.90/1.62 % (26264)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (26264)Memory used [KB]: 1535
% 2.90/1.62 % (26264)Time elapsed: 0.005 s
% 2.90/1.62 % (26264)Instructions burned: 5 (million)
% 2.90/1.62 % (26264)------------------------------
% 2.90/1.62 % (26264)------------------------------
% 2.90/1.63 % (26265)Instruction limit reached!
% 2.90/1.63 % (26265)------------------------------
% 2.90/1.63 % (26265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (26265)Termination reason: Unknown
% 2.90/1.63 % (26265)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (26265)Memory used [KB]: 1791
% 2.90/1.63 % (26265)Time elapsed: 0.008 s
% 2.90/1.63 % (26265)Instructions burned: 18 (million)
% 2.90/1.63 % (26265)------------------------------
% 2.90/1.63 % (26265)------------------------------
% 2.90/1.63 % (26267)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/6Mi)
% 2.90/1.63 % (26269)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_26027 for (2999ds/21Mi)
% 2.90/1.63 % (26267)Instruction limit reached!
% 2.90/1.63 % (26267)------------------------------
% 2.90/1.63 % (26267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (26267)Termination reason: Unknown
% 2.90/1.63 % (26267)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (26267)Memory used [KB]: 1535
% 2.90/1.63 % (26267)Time elapsed: 0.006 s
% 2.90/1.63 % (26267)Instructions burned: 6 (million)
% 2.90/1.63 % (26267)------------------------------
% 2.90/1.63 % (26267)------------------------------
% 2.90/1.64 % (26271)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_26027 for (2999ds/6Mi)
% 2.90/1.64 % (26271)Instruction limit reached!
% 2.90/1.64 % (26271)------------------------------
% 2.90/1.64 % (26271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.64 % (26271)Termination reason: Unknown
% 2.90/1.64 % (26271)Termination phase: shuffling
% 2.90/1.64
% 2.90/1.64 % (26271)Memory used [KB]: 1663
% 2.90/1.64 % (26271)Time elapsed: 0.004 s
% 2.90/1.64 % (26271)Instructions burned: 7 (million)
% 2.90/1.64 % (26271)------------------------------
% 2.90/1.64 % (26271)------------------------------
% 2.90/1.64 % (26270)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26027 for (2999ds/5Mi)
% 2.90/1.64 % (26269)Instruction limit reached!
% 2.90/1.64 % (26269)------------------------------
% 2.90/1.64 % (26269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.64 % (26269)Termination reason: Unknown
% 2.90/1.64 % (26269)Termination phase: shuffling
% 2.90/1.64
% 2.90/1.64 % (26269)Memory used [KB]: 1791
% 2.90/1.64 % (26269)Time elapsed: 0.015 s
% 2.90/1.64 % (26269)Instructions burned: 22 (million)
% 2.90/1.64 % (26269)------------------------------
% 2.90/1.64 % (26269)------------------------------
% 2.90/1.64 % (26270)Instruction limit reached!
% 2.90/1.64 % (26270)------------------------------
% 2.90/1.64 % (26270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.64 % (26270)Termination reason: Unknown
% 2.90/1.64 % (26270)Termination phase: shuffling
% 2.90/1.64
% 2.90/1.64 % (26270)Memory used [KB]: 1535
% 2.90/1.64 % (26270)Time elapsed: 0.005 s
% 2.90/1.64 % (26270)Instructions burned: 5 (million)
% 2.90/1.64 % (26270)------------------------------
% 2.90/1.64 % (26270)------------------------------
% 2.90/1.65 % (26266)First to succeed.
% 2.90/1.65 % (26273)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_26027 for (2998ds/779Mi)
% 2.90/1.65 % (26272)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26027 for (2998ds/377Mi)
% 2.90/1.65 % (26266)Refutation found. Thanks to Tanya!
% 2.90/1.65 % SZS status Theorem for DTF2THF_26027
% 2.90/1.65 % SZS output start Proof for DTF2THF_26027
% 2.90/1.65 thf(type_def_5, type, g: $tType).
% 2.90/1.65 thf(type_def_6, type, list_node: $tType).
% 2.90/1.65 thf(type_def_8, type, node: $tType).
% 2.90/1.65 thf(type_def_9, type, list_P561207620_edgeD: $tType).
% 2.90/1.65 thf(type_def_10, type, list_list_node: $tType).
% 2.90/1.65 thf(type_def_11, type, list_val: $tType).
% 2.90/1.65 thf(type_def_12, type, val: $tType).
% 2.90/1.65 thf(type_def_13, type, set_list_node: $tType).
% 2.90/1.65 thf(type_def_14, type, set_node: $tType).
% 2.90/1.65 thf(type_def_15, type, set_val: $tType).
% 2.90/1.65 thf(type_def_16, type, produc1432036078de_val: $tType).
% 2.90/1.65 thf(type_def_17, type, option_list_val: $tType).
% 2.90/1.65 thf(func_def_0, type, list_P561207620_edgeD: $tType).
% 2.90/1.65 thf(func_def_1, type, option_list_val: $tType).
% 2.90/1.65 thf(func_def_2, type, produc1432036078de_val: $tType).
% 2.90/1.65 thf(func_def_3, type, list_list_node: $tType).
% 2.90/1.65 thf(func_def_4, type, set_list_node: $tType).
% 2.90/1.65 thf(func_def_5, type, list_node: $tType).
% 2.90/1.65 thf(func_def_6, type, list_val: $tType).
% 2.90/1.65 thf(func_def_7, type, set_node: $tType).
% 2.90/1.65 thf(func_def_8, type, set_val: $tType).
% 2.90/1.65 thf(func_def_9, type, node: $tType).
% 2.90/1.65 thf(func_def_10, type, val: $tType).
% 2.90/1.65 thf(func_def_11, type, g: $tType).
% 2.90/1.65 thf(func_def_12, type, graph_1012773594_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > g > node > list_node > node > $o).
% 2.90/1.65 thf(func_def_13, type, graph_435229452_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > g > list_node > $o).
% 2.90/1.65 thf(func_def_14, type, graph_272749361_edgeD: (g > node > list_P561207620_edgeD) > g > node > list_node).
% 2.90/1.65 thf(func_def_15, type, append_list_node: list_list_node > list_list_node > list_list_node).
% 2.90/1.65 thf(func_def_16, type, append_node: list_node > list_node > list_node).
% 2.90/1.65 thf(func_def_17, type, append_val: list_val > list_val > list_val).
% 2.90/1.65 thf(func_def_18, type, butlast_list_node: list_list_node > list_list_node).
% 2.90/1.65 thf(func_def_19, type, butlast_node: list_node > list_node).
% 2.90/1.65 thf(func_def_20, type, butlast_val: list_val > list_val).
% 2.90/1.65 thf(func_def_21, type, cons_list_node: list_node > list_list_node > list_list_node).
% 2.90/1.65 thf(func_def_22, type, cons_node: node > list_node > list_node).
% 2.90/1.65 thf(func_def_23, type, cons_val: val > list_val > list_val).
% 2.90/1.65 thf(func_def_24, type, nil_list_node: list_list_node).
% 2.90/1.65 thf(func_def_25, type, nil_node: list_node).
% 2.90/1.65 thf(func_def_26, type, nil_val: list_val).
% 2.90/1.65 thf(func_def_27, type, hd_list_node: list_list_node > list_node).
% 2.90/1.65 thf(func_def_28, type, hd_node: list_node > node).
% 2.90/1.65 thf(func_def_29, type, hd_val: list_val > val).
% 2.90/1.65 thf(func_def_30, type, set_list_node2: list_list_node > set_list_node).
% 2.90/1.65 thf(func_def_31, type, set_node2: list_node > set_node).
% 2.90/1.65 thf(func_def_32, type, set_val2: list_val > set_val).
% 2.90/1.65 thf(func_def_33, type, tl_list_node: list_list_node > list_list_node).
% 2.90/1.65 thf(func_def_34, type, tl_node: list_node > list_node).
% 2.90/1.65 thf(func_def_35, type, tl_val: list_val > list_val).
% 2.90/1.65 thf(func_def_36, type, graph_2009891965_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > g > node > list_node > node > list_node > node > $o).
% 2.90/1.65 thf(func_def_37, type, ord_less_eq_set_node: set_node > set_node > $o).
% 2.90/1.65 thf(func_def_38, type, ord_less_eq_set_val: set_val > set_val > $o).
% 2.90/1.65 thf(func_def_39, type, sSA_CF848637139eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 2.90/1.65 thf(func_def_40, type, sSA_CF551432799de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > node).
% 2.90/1.65 thf(func_def_41, type, sSA_CF1252180629de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > val > $o).
% 2.90/1.65 thf(func_def_42, type, collect_node: (node > $o) > set_node).
% 2.90/1.65 thf(func_def_43, type, collect_val: (val > $o) > set_val).
% 2.90/1.65 thf(func_def_44, type, prefix_node: list_node > list_node > $o).
% 2.90/1.65 thf(func_def_45, type, suffix_node: list_node > list_node > $o).
% 2.90/1.65 thf(func_def_46, type, member_list_node: list_node > set_list_node > $o).
% 2.90/1.65 thf(func_def_47, type, member_node: node > set_node > $o).
% 2.90/1.65 thf(func_def_48, type, member_val: val > set_val > $o).
% 2.90/1.65 thf(func_def_49, type, alpha_n: g > list_node).
% 2.90/1.65 thf(func_def_50, type, phi_r: val).
% 2.90/1.65 thf(func_def_51, type, defs: g > node > set_val).
% 2.90/1.65 thf(func_def_52, type, g2: g).
% 2.90/1.65 thf(func_def_53, type, i: node).
% 2.90/1.65 thf(func_def_54, type, inEdges: g > node > list_P561207620_edgeD).
% 2.90/1.65 thf(func_def_55, type, invar: g > $o).
% 2.90/1.65 thf(func_def_56, type, m: node).
% 2.90/1.65 thf(func_def_57, type, ms: list_node).
% 2.90/1.65 thf(func_def_58, type, ms2: list_node).
% 2.90/1.65 thf(func_def_59, type, n: node).
% 2.90/1.65 thf(func_def_60, type, ns: list_node).
% 2.90/1.65 thf(func_def_61, type, phis: g > produc1432036078de_val > option_list_val).
% 2.90/1.65 thf(func_def_62, type, pred_phi_r: node).
% 2.90/1.65 thf(func_def_63, type, r: val).
% 2.90/1.65 thf(func_def_64, type, ri: list_node).
% 2.90/1.65 thf(func_def_65, type, rs: list_node).
% 2.90/1.65 thf(func_def_66, type, rs_rest: list_node).
% 2.90/1.65 thf(func_def_67, type, rs2: list_node).
% 2.90/1.65 thf(func_def_68, type, s: val).
% 2.90/1.65 thf(func_def_69, type, tmp: list_node).
% 2.90/1.65 thf(func_def_81, type, ph1: !>[X0: $tType]:(X0)).
% 2.90/1.65 thf(f961,plain,(
% 2.90/1.65 $false),
% 2.90/1.65 inference(subsumption_resolution,[status(thm)],[f960,f925])).
% 2.90/1.65 thf(f925,plain,(
% 2.90/1.65 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r) != $true)),
% 2.90/1.65 inference(cnf_transformation,[status(thm)],[f888])).
% 2.90/1.65 thf(f888,plain,(
% 2.90/1.65 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r) != $true)),
% 2.90/1.65 inference(flattening,[status(thm)],[f751])).
% 2.90/1.65 thf(f751,plain,(
% 2.90/1.65 ~((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r) = $true)),
% 2.90/1.65 inference(fool_elimination,[status(thm)],[f750])).
% 2.90/1.65 thf(f750,plain,(
% 2.90/1.65 ~(graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r)),
% 2.90/1.65 inference(rectify,[status(thm)],[f354])).
% 2.90/1.65 thf(f354,negated_conjecture,(
% 2.90/1.65 ~(graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r)),
% 2.90/1.65 inference(negated_conjecture,[status(cth)],[f353])).
% 2.90/1.65 thf(f353,conjecture,(
% 2.90/1.65 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r)),
% 2.90/1.65 file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',conj_0)).
% 2.90/1.65 thf(f960,plain,(
% 2.90/1.65 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r) = $true)),
% 2.90/1.65 inference(trivial_inequality_removal,[status(thm)],[f959])).
% 2.90/1.65 thf(f959,plain,(
% 2.90/1.65 ($true != $true) | ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r) = $true)),
% 2.90/1.65 inference(superposition,[status(thm)],[f951,f936])).
% 2.90/1.65 thf(f936,plain,(
% 2.90/1.65 ($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (append_node @ ri @ rs_rest) @ pred_phi_r))),
% 2.90/1.65 inference(backward_demodulation,[status(thm)],[f929,f930])).
% 2.90/1.65 thf(f930,plain,(
% 2.90/1.65 ((append_node @ tmp @ (cons_node @ i @ rs_rest)) = (append_node @ ri @ rs_rest))),
% 2.90/1.65 inference(definition_unfolding,[status(thm)],[f924,f907])).
% 2.90/1.65 thf(f907,plain,(
% 2.90/1.65 (rs = (append_node @ tmp @ (cons_node @ i @ rs_rest)))),
% 2.90/1.65 inference(cnf_transformation,[status(thm)],[f2])).
% 2.90/1.65 thf(f2,axiom,(
% 2.90/1.65 (rs = (append_node @ tmp @ (cons_node @ i @ rs_rest)))),
% 2.90/1.65 file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',fact_1_rs_H__rest__def)).
% 2.90/1.65 thf(f924,plain,(
% 2.90/1.65 (rs = (append_node @ ri @ rs_rest))),
% 2.90/1.65 inference(cnf_transformation,[status(thm)],[f8])).
% 2.90/1.65 thf(f8,axiom,(
% 2.90/1.65 (rs = (append_node @ ri @ rs_rest))),
% 2.90/1.65 file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',fact_7_rs_H__rest__prop)).
% 2.90/1.65 thf(f929,plain,(
% 2.90/1.65 ($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (append_node @ tmp @ (cons_node @ i @ rs_rest)) @ pred_phi_r))),
% 2.90/1.65 inference(definition_unfolding,[status(thm)],[f914,f907])).
% 2.90/1.65 thf(f914,plain,(
% 2.90/1.65 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r) = $true)),
% 2.90/1.65 inference(cnf_transformation,[status(thm)],[f449])).
% 2.90/1.65 thf(f449,plain,(
% 2.90/1.65 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r) = $true)),
% 2.90/1.65 inference(fool_elimination,[status(thm)],[f448])).
% 2.90/1.65 thf(f448,plain,(
% 2.90/1.65 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r)),
% 2.90/1.65 inference(rectify,[status(thm)],[f6])).
% 2.90/1.65 thf(f6,axiom,(
% 2.90/1.65 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r)),
% 2.90/1.65 file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',fact_5_rs_H__props_I1_J)).
% 2.90/1.65 thf(f951,plain,(
% 2.90/1.65 ( ! [X2 : node,X0 : g,X1 : node] : (($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append_node @ ri @ rs_rest) @ X2)) | ($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ i @ (cons_node @ i @ rs_rest) @ X2))) )),
% 2.90/1.65 inference(superposition,[status(thm)],[f906,f930])).
% 2.90/1.65 thf(f906,plain,(
% 2.90/1.65 ( ! [X2 : g,X3 : list_node,X0 : node,X1 : list_node,X4 : node,X5 : node] : (($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X4 @ (append_node @ X1 @ (cons_node @ X5 @ X3)) @ X0)) | ($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X5 @ (cons_node @ X5 @ X3) @ X0))) )),
% 2.90/1.65 inference(cnf_transformation,[status(thm)],[f903])).
% 2.90/1.65 thf(f903,plain,(
% 2.90/1.65 ! [X0 : node,X1 : list_node,X2 : g,X3 : list_node,X4 : node,X5 : node] : (($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X5 @ (cons_node @ X5 @ X3) @ X0)) | ($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X4 @ (append_node @ X1 @ (cons_node @ X5 @ X3)) @ X0)))),
% 2.90/1.65 inference(ennf_transformation,[status(thm)],[f749])).
% 2.90/1.65 thf(f749,plain,(
% 2.90/1.65 ! [X0 : node,X1 : list_node,X2 : g,X3 : list_node,X4 : node,X5 : node] : (($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X4 @ (append_node @ X1 @ (cons_node @ X5 @ X3)) @ X0)) => ($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X5 @ (cons_node @ X5 @ X3) @ X0)))),
% 2.90/1.65 inference(fool_elimination,[status(thm)],[f748])).
% 2.90/1.65 thf(f748,plain,(
% 2.90/1.65 ! [X0 : node,X1 : list_node,X2 : g,X3 : list_node,X4 : node,X5 : node] : ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X4 @ (append_node @ X1 @ (cons_node @ X5 @ X3)) @ X0) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2 @ X5 @ (cons_node @ X5 @ X3) @ X0))),
% 2.90/1.65 inference(rectify,[status(thm)],[f4])).
% 2.90/1.65 thf(f4,axiom,(
% 2.90/1.65 ! [X5 : node,X2 : list_node,X0 : g,X4 : list_node,X1 : node,X3 : node] : ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ (append_node @ X2 @ (cons_node @ X3 @ X4)) @ X5) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X3 @ (cons_node @ X3 @ X4) @ X5))),
% 2.90/1.65 file('/export/starexec/sandbox2/tmp/tmp.Aqufk7JJVC/DTF2THF_26027.p',fact_3_old_Opath2__split_I2_J)).
% 2.90/1.65 % SZS output end Proof for DTF2THF_26027
% 2.90/1.65 % (26266)------------------------------
% 2.90/1.65 % (26266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (26266)Termination reason: Refutation
% 2.90/1.65
% 2.90/1.65 % (26266)Memory used [KB]: 6652
% 2.90/1.65 % (26266)Time elapsed: 0.029 s
% 2.90/1.65 % (26266)Instructions burned: 81 (million)
% 2.90/1.65 % (26266)------------------------------
% 2.90/1.65 % (26266)------------------------------
% 2.90/1.65 % (26245)Success in time 0.141 s
%------------------------------------------------------------------------------