%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP081^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:41 AM UTC 2026
% Result : Theorem 250.29s 74.28s
% Output : Refutation 243.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 292
% Syntax : Number of formulae : 883 ( 338 unt; 0 typ; 34 def)
% Number of atoms : 2467 (1212 equ; 35 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 9415 ( 739 ~; 369 |; 153 &;7274 @)
% ( 0 <=>; 880 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 411 ( 411 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 77 usr; 21 con; 0-7 aty)
% Number of variables : 2372 ( 124 ^;2077 !; 137 ?;2372 :)
% ( 0 !>; 0 ?*; 0 @-; 34 @+)
% Comments :
%------------------------------------------------------------------------------
thf(list_P561207620_edgeD_type,type,
list_P561207620_edgeD: $tType ).
thf(option_list_val_type,type,
option_list_val: $tType ).
thf(produc1432036078de_val_type,type,
produc1432036078de_val: $tType ).
thf(list_list_node_type,type,
list_list_node: $tType ).
thf(set_list_node_type,type,
set_list_node: $tType ).
thf(list_node_type,type,
list_node: $tType ).
thf(list_val_type,type,
list_val: $tType ).
thf(set_node_type,type,
set_node: $tType ).
thf(set_val_type,type,
set_val: $tType ).
thf(node_type,type,
node: $tType ).
thf(val_type,type,
val: $tType ).
thf(g_type,type,
g: $tType ).
thf(finite_finite_node_decl,type,
finite_finite_node: set_node > $o ).
thf(finite_finite_val_decl,type,
finite_finite_val: set_val > $o ).
thf(graph_1012773594_edgeD_decl,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(graph_435229452_edgeD_decl,type,
graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
thf(graph_272749361_edgeD_decl,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(append_node_decl,type,
append_node: list_node > list_node > list_node ).
thf(butlast_node_decl,type,
butlast_node: list_node > list_node ).
thf(cons_node_decl,type,
cons_node: node > list_node > list_node ).
thf(nil_node_decl,type,
nil_node: list_node ).
thf(hd_node_decl,type,
hd_node: list_node > node ).
thf(set_node2_decl,type,
set_node2: list_node > set_node ).
thf(set_val2_decl,type,
set_val2: list_val > set_val ).
thf(tl_node_decl,type,
tl_node: list_node > list_node ).
thf(ord_less_eq_set_node_decl,type,
ord_less_eq_set_node: set_node > set_node > $o ).
thf(ord_less_eq_set_val_decl,type,
ord_less_eq_set_val: set_val > set_val > $o ).
thf(sSA_CF848637139eD_val_decl,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF551432799de_val_decl,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(sSA_CF1252180629de_val_decl,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(collect_node_decl,type,
collect_node: ( node > $o ) > set_node ).
thf(collect_val_decl,type,
collect_val: ( val > $o ) > set_val ).
thf(prefix_node_decl,type,
prefix_node: list_node > list_node > $o ).
thf(suffix_node_decl,type,
suffix_node: list_node > list_node > $o ).
thf(member_node_decl,type,
member_node: node > set_node > $o ).
thf(member_val_decl,type,
member_val: val > set_val > $o ).
thf(alpha_n_decl,type,
alpha_n: g > list_node ).
thf(phi_r_decl,type,
phi_r: val ).
thf(defs_decl,type,
defs: g > node > set_val ).
thf(g2_decl,type,
g2: g ).
thf(i_decl,type,
i: node ).
thf(inEdges_decl,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(invar_decl,type,
invar: g > $o ).
thf(m_decl,type,
m: node ).
thf(ms_decl,type,
ms: list_node ).
thf(ms2_decl,type,
ms2: list_node ).
thf(n_decl,type,
n: node ).
thf(ns_decl,type,
ns: list_node ).
thf(phis_decl,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(pred_phi_r_decl,type,
pred_phi_r: node ).
thf(r_decl,type,
r: val ).
thf(ri_decl,type,
ri: list_node ).
thf(rs_decl,type,
rs: list_node ).
thf(rs2_decl,type,
rs2: list_node ).
thf(s_decl,type,
s: val ).
thf(sk1_decl,type,
sk1: ( node > $o ) > ( node > $o ) > node ).
thf(sk2_decl,type,
sk2: ( val > $o ) > ( val > $o ) > val ).
thf(sk3_decl,type,
sk3: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(sk4_decl,type,
sk4: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(sk5_decl,type,
sk5: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(sk6_decl,type,
sk6: ( ( node > node > $o ) > list_node > $o ) > list_node ).
thf(sk7_decl,type,
sk7: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(sk8_decl,type,
sk8: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(sk9_decl,type,
sk9: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(sk10_decl,type,
sk10: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(sk11_decl,type,
sk11: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(sk12_decl,type,
sk12: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(sk13_decl,type,
sk13: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(sk14_decl,type,
sk14: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(sk15_decl,type,
sk15: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(sk16_decl,type,
sk16: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(sk17_decl,type,
sk17: list_node > node ).
thf(sk18_decl,type,
sk18: list_node > list_node ).
thf(sk19_decl,type,
sk19: set_node > list_node ).
thf(sk20_decl,type,
sk20: ( list_node > $o ) > node ).
thf(sk21_decl,type,
sk21: ( list_node > $o ) > list_node ).
thf(sk22_decl,type,
sk22: set_val > list_val ).
thf(sk23_decl,type,
sk23: ( list_node > $o ) > list_node > node ).
thf(sk24_decl,type,
sk24: ( list_node > $o ) > list_node > node ).
thf(sk25_decl,type,
sk25: ( list_node > $o ) > list_node > list_node ).
thf(sk65_decl,type,
sk65: ( list_node > $o ) > node ).
thf(sk66_decl,type,
sk66: ( list_node > $o ) > list_node ).
thf(sk71_decl,type,
sk71: ( list_node > $o ) > node ).
thf(sk72_decl,type,
sk72: ( list_node > $o ) > list_node ).
thf(sk176_decl,type,
sk176: list_node ).
thf(sk196_decl,type,
sk196: ( list_node > $o ) > node ).
thf(sk197_decl,type,
sk197: ( list_node > $o ) > list_node ).
thf(sk230_decl,type,
sk230: node ).
thf(sk231_decl,type,
sk231: list_node ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: node > $o,B: node > $o] :
@+[C: node] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: val > $o,B: val > $o] :
@+[C: val] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( node > node > $o ) > list_node > $o] :
@+[B: node > node > $o] :
~ ( A @ B @ nil_node ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: ( node > node > $o ) > list_node > $o] :
@+[B: node > node > $o] :
~ ! [C: node,D: list_node] :
( ( A @ B @ D )
=> ( A @ B @ ( cons_node @ C @ D ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: ( node > node > $o ) > list_node > $o] :
@+[B: node] :
~ ! [C: list_node] :
( ( A @ ( sk4 @ A ) @ C )
=> ( A @ ( sk4 @ A ) @ ( cons_node @ B @ C ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: ( node > node > $o ) > list_node > $o] :
@+[B: list_node] :
~ ( ( A @ ( sk4 @ A ) @ B )
=> ( A @ ( sk4 @ A ) @ ( cons_node @ ( sk5 @ A ) @ B ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: node > node > $o] :
~ ! [C: node,D: list_node,E: node,F: list_node] :
( ( ( B @ C @ E )
=> ( A @ B @ D @ ( cons_node @ E @ F ) ) )
=> ( ( ~ ( B @ C @ E )
=> ( A @ B @ ( cons_node @ C @ D ) @ F ) )
=> ( A @ B @ ( cons_node @ C @ D ) @ ( cons_node @ E @ F ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: node] :
~ ! [C: list_node,D: node,E: list_node] :
( ( ( sk7 @ A @ B @ D )
=> ( A @ ( sk7 @ A ) @ C @ ( cons_node @ D @ E ) ) )
=> ( ( ~ ( sk7 @ A @ B @ D )
=> ( A @ ( sk7 @ A ) @ ( cons_node @ B @ C ) @ E ) )
=> ( A @ ( sk7 @ A ) @ ( cons_node @ B @ C ) @ ( cons_node @ D @ E ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: list_node] :
~ ! [C: node,D: list_node] :
( ( ( sk7 @ A @ ( sk8 @ A ) @ C )
=> ( A @ ( sk7 @ A ) @ B @ ( cons_node @ C @ D ) ) )
=> ( ( ~ ( sk7 @ A @ ( sk8 @ A ) @ C )
=> ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ B ) @ D ) )
=> ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ B ) @ ( cons_node @ C @ D ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: node] :
~ ! [C: list_node] :
( ( ( sk7 @ A @ ( sk8 @ A ) @ B )
=> ( A @ ( sk7 @ A ) @ ( sk9 @ A ) @ ( cons_node @ B @ C ) ) )
=> ( ( ~ ( sk7 @ A @ ( sk8 @ A ) @ B )
=> ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ C ) )
=> ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( cons_node @ B @ C ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: list_node] :
~ ( ( ( sk7 @ A @ ( sk8 @ A ) @ ( sk10 @ A ) )
=> ( A @ ( sk7 @ A ) @ ( sk9 @ A ) @ ( cons_node @ ( sk10 @ A ) @ B ) ) )
=> ( ( ~ ( sk7 @ A @ ( sk8 @ A ) @ ( sk10 @ A ) )
=> ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ B ) )
=> ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( cons_node @ ( sk10 @ A ) @ B ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: node > node > $o] :
~ ! [C: list_node] : ( A @ B @ C @ nil_node ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: list_node] :
~ ( A @ ( sk12 @ A ) @ B @ nil_node ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: node > node > $o] :
~ ! [C: node,D: list_node] : ( A @ B @ nil_node @ ( cons_node @ C @ D ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: node] :
~ ! [C: list_node] : ( A @ ( sk14 @ A ) @ nil_node @ ( cons_node @ B @ C ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: ( node > node > $o ) > list_node > list_node > $o] :
@+[B: list_node] :
~ ( A @ ( sk14 @ A ) @ nil_node @ ( cons_node @ ( sk15 @ A ) @ B ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: list_node] :
@+[B: node] :
? [C: list_node] :
( A
= ( cons_node @ B @ C ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: list_node] :
@+[B: list_node] :
( A
= ( cons_node @ ( sk17 @ A ) @ B ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: set_node] :
@+[B: list_node] :
( ( set_node2 @ B )
= A ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: list_node > $o] :
@+[B: node] :
~ ! [C: list_node] :
( ( ? [D: node,E: list_node] :
( C
= ( cons_node @ D @ E ) )
=> ( A @ C ) )
=> ( A @ ( cons_node @ B @ C ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: list_node > $o] :
@+[B: list_node] :
~ ( ( ? [C: node,D: list_node] :
( B
= ( cons_node @ C @ D ) )
=> ( A @ B ) )
=> ( A @ ( cons_node @ ( sk20 @ A ) @ B ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: set_val] :
@+[B: list_val] :
( ( set_val2 @ B )
= A ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [A: list_node > $o,B: list_node] :
@+[C: node] :
~ ( A @ ( cons_node @ C @ nil_node ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: list_node > $o,B: list_node] :
@+[C: node] :
~ ! [D: list_node] :
( ( D != nil_node )
=> ( ( A @ D )
=> ( A @ ( cons_node @ C @ D ) ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: list_node > $o,B: list_node] :
@+[C: list_node] :
~ ( ( C != nil_node )
=> ( ( A @ C )
=> ( A @ ( cons_node @ ( sk24 @ A @ B ) @ C ) ) ) ) ) ) ).
thf(sk65_def,definition,
( sk65
= ( ^ [A: list_node > $o] :
@+[B: node] :
~ ! [C: list_node] :
( ( A @ C )
=> ( A @ ( cons_node @ B @ C ) ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( ^ [A: list_node > $o] :
@+[B: list_node] :
~ ( ( A @ B )
=> ( A @ ( cons_node @ ( sk65 @ A ) @ B ) ) ) ) ) ).
thf(sk71_def,definition,
( sk71
= ( ^ [A: list_node > $o] :
@+[B: node] :
~ ! [C: list_node] :
( ( A @ C )
=> ( A @ ( cons_node @ B @ C ) ) ) ) ) ).
thf(sk72_def,definition,
( sk72
= ( ^ [A: list_node > $o] :
@+[B: list_node] :
~ ( ( A @ B )
=> ( A @ ( cons_node @ ( sk71 @ A ) @ B ) ) ) ) ) ).
thf(sk176_def,definition,
( sk176
= ( @+[A: list_node] :
~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ A @ i )
=> ( ( prefix_node @ A @ ms )
=> ( member_node @ i @ ( set_node2 @ ( butlast_node @ A ) ) ) ) ) ) ) ).
thf(sk196_def,definition,
( sk196
= ( ^ [A: list_node > $o] :
@+[B: node] :
~ ! [C: list_node] :
( ( A @ C )
=> ( A @ ( append_node @ C @ ( cons_node @ B @ nil_node ) ) ) ) ) ) ).
thf(sk197_def,definition,
( sk197
= ( ^ [A: list_node > $o] :
@+[B: list_node] :
~ ( ( A @ B )
=> ( A @ ( append_node @ B @ ( cons_node @ ( sk196 @ A ) @ nil_node ) ) ) ) ) ) ).
thf(sk230_def,definition,
( sk230
= ( @+[A: node] :
~ ! [B: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ B @ A )
=> ( ( member_node @ A @ ( set_node2 @ ms ) )
=> ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( butlast_node @ B ) ) )
=> ~ ( member_node @ C @ ( set_node2 @ ms ) ) )
=> ~ ( prefix_node @ B @ rs2 ) ) ) ) ) ) ).
thf(sk231_def,definition,
( sk231
= ( @+[A: list_node] :
~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ A @ sk230 )
=> ( ( member_node @ sk230 @ ( set_node2 @ ms ) )
=> ( ! [B: node] :
( ( member_node @ B @ ( set_node2 @ ( butlast_node @ A ) ) )
=> ~ ( member_node @ B @ ( set_node2 @ ms ) ) )
=> ~ ( prefix_node @ A @ rs2 ) ) ) ) ) ) ).
thf(230,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( C != nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_old_Opath2__not__Nil) ).
thf(1322,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( C != nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(125,axiom,
! [A: list_node] :
( ( A != nil_node )
= ( ? [B: list_node,C: node] :
( A
= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_neq__Nil__rev__conv) ).
thf(809,plain,
! [A: list_node] :
( ( A != nil_node )
= ( ? [B: list_node,C: node] :
( A
= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(241,axiom,
! [A: node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ~ ( member_node @ A @ ( set_node2 @ B ) )
=> ( ~ ( member_node @ A @ ( set_node2 @ C ) )
=> ( ( ( append_node @ B @ ( cons_node @ A @ C ) )
= ( append_node @ D @ ( cons_node @ A @ E ) ) )
= ( ( B = D )
& ( C = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_append__Cons__eq__iff) ).
thf(1369,plain,
! [A: node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ~ ( member_node @ A @ ( set_node2 @ B ) )
=> ( ~ ( member_node @ A @ ( set_node2 @ C ) )
=> ( ( ( append_node @ B @ ( cons_node @ A @ C ) )
= ( append_node @ D @ ( cons_node @ A @ E ) ) )
= ( ( B = D )
& ( C = E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(181,axiom,
~ ! [A: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ A @ i )
=> ( ( prefix_node @ A @ ms )
=> ( member_node @ i @ ( set_node2 @ ( butlast_node @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125__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) ).
thf(1097,plain,
~ ! [A: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ A @ i )
=> ( ( prefix_node @ A @ ms )
=> ( member_node @ i @ ( set_node2 @ ( butlast_node @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1098,plain,
~ ! [A: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ A @ i )
=> ( ( prefix_node @ A @ ms )
=> ( member_node @ i @ ( set_node2 @ ( butlast_node @ A ) ) ) ) ),
inference(polarity_switch,[status(thm)],[1097]) ).
thf(1099,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ sk176 @ i )
& ( prefix_node @ sk176 @ ms )
& ~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ sk176 ) ) ) ),
inference(cnf,[status(esa)],[1098]) ).
thf(1100,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ sk176 @ i,
inference(cnfConj,[status(thm)],[1099]) ).
thf(123,axiom,
! [A: g] : ( invar @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_old_Oinvar) ).
thf(805,plain,
! [A: g] : ( invar @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(806,plain,
! [A: g] : ( invar @ A ),
inference(cnf,[status(esa)],[805]) ).
thf(2018,plain,
( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ m
@ sk176
@ i ),
inference(rewrite,[status(thm)],[1100,806]) ).
thf(1,conjecture,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(260,plain,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1467,plain,
~ ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ n
@ ( append_node @ ns @ ( tl_node @ ri ) )
@ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(rewrite,[status(thm)],[260,806]) ).
thf(237,axiom,
( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_ri__is__valid) ).
thf(1352,plain,
( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1353,plain,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
= i ),
inference(lifteq,[status(thm)],[1352]) ).
thf(1648,plain,
~ ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ n
@ ( append_node @ ns @ ( tl_node @ ri ) )
@ i ),
inference(rewrite,[status(thm)],[1467,1353]) ).
thf(2023,plain,
( ~ $true
| ( ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ n
@ ( append_node @ ns @ ( tl_node @ ri ) )
@ i )
!= ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ m
@ sk176
@ i ) ) ),
inference(paramod_ordered,[status(thm)],[2018,1648]) ).
thf(2024,plain,
( ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ n
@ ( append_node @ ns @ ( tl_node @ ri ) )
@ i )
!= ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ m
@ sk176
@ i ) ),
inference(simp,[status(thm)],[2023]) ).
thf(2027,plain,
( ( alpha_n != alpha_n )
| ( ( ^ [A: g] : $true )
!= ( ^ [A: g] : $true ) )
| ( inEdges != inEdges )
| ( g2 != g2 )
| ( n != m )
| ( ( append_node @ ns @ ( tl_node @ ri ) )
!= sk176 )
| ( i != i ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2031,plain,
( ( n != m )
| ( ( append_node @ ns @ ( tl_node @ ri ) )
!= sk176 ) ),
inference(simp,[status(thm)],[2027]) ).
thf(183,axiom,
! [A: list_node,B: list_node] :
( ( ( A = nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ B ) ) )
& ( ( A != nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_hd__append) ).
thf(1105,plain,
! [A: list_node,B: list_node] :
( ( ( A = nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ B ) ) )
& ( ( A != nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(61,axiom,
prefix_node @ ms2 @ ms,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_ms_H__props_I2_J) ).
thf(498,plain,
prefix_node @ ms2 @ ms,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(19,axiom,
! [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
=> ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_set__mono__prefix) ).
thf(312,plain,
! [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
=> ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(313,plain,
! [B: list_node,A: list_node] :
( ~ ( prefix_node @ A @ B )
| ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) ) ),
inference(cnf,[status(esa)],[312]) ).
thf(10211,plain,
! [B: list_node,A: list_node] :
( ~ $true
| ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) )
| ( ( prefix_node @ ms2 @ ms )
!= ( prefix_node @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[498,313]) ).
thf(10212,plain,
! [B: list_node,A: list_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) )
| ( ( prefix_node @ ms2 @ ms )
!= ( prefix_node @ A @ B ) ) ),
inference(simp,[status(thm)],[10211]) ).
thf(10213,plain,
ord_less_eq_set_node @ ( set_node2 @ ms2 ) @ ( set_node2 @ ms ),
inference(pattern_uni,[status(thm)],[10212:[bind(A,$thf( ms2 )),bind(B,$thf( ms ))]]) ).
thf(210,axiom,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rs_H__loopfree) ).
thf(1236,plain,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1237,plain,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
inference(polarity_switch,[status(thm)],[1236]) ).
thf(72,axiom,
! [A: node,B: list_node] :
( ( hd_node @ ( cons_node @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_list_Osel_I1_J) ).
thf(555,plain,
! [A: node,B: list_node] :
( ( hd_node @ ( cons_node @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(22,axiom,
member_node @ i @ ( set_node2 @ ms ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_ri__props_I2_J) ).
thf(330,plain,
member_node @ i @ ( set_node2 @ ms ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(13,axiom,
! [A: node,B: list_node,C: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_list_Oset__intros_I2_J) ).
thf(296,plain,
! [A: node,B: list_node,C: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(297,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ! [C: node] : ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) ) ),
inference(miniscope,[status(thm)],[296]) ).
thf(298,plain,
! [C: node,B: list_node,A: node] :
( ~ ( member_node @ A @ ( set_node2 @ B ) )
| ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[297]) ).
thf(7035,plain,
! [C: node,B: list_node,A: node] :
( ~ $true
| ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) )
| ( ( member_node @ i @ ( set_node2 @ ms ) )
!= ( member_node @ A @ ( set_node2 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[330,298]) ).
thf(7036,plain,
! [C: node,B: list_node,A: node] :
( ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) )
| ( ( member_node @ i @ ( set_node2 @ ms ) )
!= ( member_node @ A @ ( set_node2 @ B ) ) ) ),
inference(simp,[status(thm)],[7035]) ).
thf(7037,plain,
! [A: node] : ( member_node @ i @ ( set_node2 @ ( cons_node @ A @ ms ) ) ),
inference(pattern_uni,[status(thm)],[7036:[bind(A,$thf( i )),bind(B,$thf( ms ))]]) ).
thf(7135,plain,
! [A: node] : ( member_node @ i @ ( set_node2 @ ( cons_node @ A @ ms ) ) ),
inference(simp,[status(thm)],[7037]) ).
thf(38,axiom,
~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_ms_H__props_I3_J) ).
thf(392,plain,
~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(393,plain,
~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ),
inference(polarity_switch,[status(thm)],[392]) ).
thf(7224,plain,
! [A: node] :
( ~ $true
| ( ( member_node @ i @ ( set_node2 @ ( cons_node @ A @ ms ) ) )
!= ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7135,393]) ).
thf(7225,plain,
! [A: node] :
( ( member_node @ i @ ( set_node2 @ ( cons_node @ A @ ms ) ) )
!= ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ) ),
inference(simp,[status(thm)],[7224]) ).
thf(7270,plain,
! [A: node] :
( ( i != i )
| ( ( set_node2 @ ( cons_node @ A @ ms ) )
!= ( set_node2 @ ( butlast_node @ ms2 ) ) ) ),
inference(simp,[status(thm)],[7225]) ).
thf(7285,plain,
! [A: node] :
( ( set_node2 @ ( cons_node @ A @ ms ) )
!= ( set_node2 @ ( butlast_node @ ms2 ) ) ),
inference(simp,[status(thm)],[7270]) ).
thf(111,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ A @ ( cons_node @ A @ nil_node ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_old_Oempty__path2) ).
thf(760,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ A @ ( cons_node @ A @ nil_node ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(138,axiom,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_append_Oleft__neutral) ).
thf(879,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(880,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(cnf,[status(esa)],[879]) ).
thf(881,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(lifteq,[status(thm)],[880]) ).
thf(184,axiom,
( ( tl_node @ nil_node )
= nil_node ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_list_Osel_I2_J) ).
thf(1114,plain,
( ( tl_node @ nil_node )
= nil_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1115,plain,
( ( tl_node @ nil_node )
= nil_node ),
inference(lifteq,[status(thm)],[1114]) ).
thf(2216,plain,
( ( n != m )
| ( ( append_node @ ns @ nil_node )
!= sk176 )
| ( ( tl_node @ ri )
!= ( tl_node @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[1115,2031]) ).
thf(2230,plain,
( ( n != m )
| ( ( append_node @ ns @ nil_node )
!= sk176 )
| ( ri != nil_node ) ),
inference(simp,[status(thm)],[2216]) ).
thf(4460,plain,
! [A: list_node] :
( ( n != m )
| ( A != sk176 )
| ( ri != nil_node )
| ( ( append_node @ nil_node @ A )
!= ( append_node @ ns @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[881,2230]) ).
thf(4464,plain,
( ( n != m )
| ( ri != nil_node )
| ( ns != nil_node )
| ( sk176 != nil_node ) ),
inference(simp,[status(thm)],[4460]) ).
thf(15,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_hd__in__set) ).
thf(301,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(302,plain,
! [A: list_node] :
( ( A = nil_node )
| ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ),
inference(cnf,[status(esa)],[301]) ).
thf(303,plain,
! [A: list_node] :
( ( A = nil_node )
| ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ),
inference(lifteq,[status(thm)],[302]) ).
thf(198,axiom,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_append_Oright__neutral) ).
thf(1185,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1186,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(cnf,[status(esa)],[1185]) ).
thf(1187,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(lifteq,[status(thm)],[1186]) ).
thf(5229,plain,
( ( n != m )
| ( sk176 != ns )
| ( ri != nil_node ) ),
inference(rewrite,[status(thm)],[2230,1187]) ).
thf(8336,plain,
! [A: list_node] :
( ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) )
| ( n != m )
| ( sk176 != ns )
| ( nil_node != nil_node )
| ( A != ri ) ),
inference(paramod_ordered,[status(thm)],[303,5229]) ).
thf(8337,plain,
! [A: list_node] :
( ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) )
| ( n != m )
| ( sk176 != ns )
| ( A != ri ) ),
inference(simp,[status(thm)],[8336]) ).
thf(8338,plain,
( ( member_node @ ( hd_node @ ri ) @ ( set_node2 @ ri ) )
| ( n != m )
| ( sk176 != ns ) ),
inference(pattern_uni,[status(thm)],[8337:[bind(A,$thf( ri ))]]) ).
thf(84,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: list_node] : ( A @ D @ nil_node )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ ( cons_node @ F @ G ) )
=> ( ( A @ ( cons_node @ D @ E ) @ G )
=> ( A @ ( cons_node @ D @ E ) @ ( cons_node @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_shuffles_Oinduct) ).
thf(628,plain,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: list_node] : ( A @ D @ nil_node )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ ( cons_node @ F @ G ) )
=> ( ( A @ ( cons_node @ D @ E ) @ G )
=> ( A @ ( cons_node @ D @ E ) @ ( cons_node @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(169,axiom,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( tl_node @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_old_Opath2__app) ).
thf(1031,plain,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( tl_node @ E ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(227,axiom,
! [A: list_node] :
( ( butlast_node @ ( tl_node @ A ) )
= ( tl_node @ ( butlast_node @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_butlast__tl) ).
thf(1315,plain,
! [A: list_node] :
( ( butlast_node @ ( tl_node @ A ) )
= ( tl_node @ ( butlast_node @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(65,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_strict__sorted_Oinduct) ).
thf(518,plain,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(112,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ D @ ( set_node2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_old_Opath2__last__in__ns) ).
thf(762,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ D @ ( set_node2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(7,axiom,
! [A: ( node > node > $o ) > list_node > $o,B: node > node > $o,C: list_node] :
( ! [D: node > node > $o] : ( A @ D @ nil_node )
=> ( ! [D: node > node > $o,E: node,F: list_node] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_node @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_sorted__wrt_Oinduct) ).
thf(273,plain,
! [A: ( node > node > $o ) > list_node > $o,B: node > node > $o,C: list_node] :
( ! [D: node > node > $o] : ( A @ D @ nil_node )
=> ( ! [D: node > node > $o,E: node,F: list_node] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_node @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(274,plain,
! [A: ( node > node > $o ) > list_node > $o] :
( ! [B: node > node > $o] : ( A @ B @ nil_node )
=> ( ! [B: node > node > $o,C: node,D: list_node] :
( ( A @ B @ D )
=> ( A @ B @ ( cons_node @ C @ D ) ) )
=> ! [B: node > node > $o,C: list_node] : ( A @ B @ C ) ) ),
inference(miniscope,[status(thm)],[273]) ).
thf(275,plain,
! [C: list_node,B: node > node > $o,A: ( node > node > $o ) > list_node > $o] :
( ( ~ ( A @ ( sk3 @ A ) @ nil_node )
| ( A @ ( sk4 @ A ) @ ( sk6 @ A ) )
| ( A @ B @ C ) )
& ( ~ ( A @ ( sk3 @ A ) @ nil_node )
| ~ ( A @ ( sk4 @ A ) @ ( cons_node @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
| ( A @ B @ C ) ) ),
inference(cnf,[status(esa)],[274]) ).
thf(276,plain,
! [C: list_node,B: node > node > $o,A: ( node > node > $o ) > list_node > $o] :
( ~ ( A @ ( sk3 @ A ) @ nil_node )
| ( A @ ( sk4 @ A ) @ ( sk6 @ A ) )
| ( A @ B @ C ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(158,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_split__list__first__prop) ).
thf(994,plain,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(16,axiom,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_List_Ofinite__set) ).
thf(304,plain,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(305,plain,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
inference(cnf,[status(esa)],[304]) ).
thf(17,axiom,
! [A: set_node] :
( ( finite_finite_node @ A )
=> ? [B: list_node] :
( ( set_node2 @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_finite__list) ).
thf(306,plain,
! [A: set_node] :
( ( finite_finite_node @ A )
=> ? [B: list_node] :
( ( set_node2 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(307,plain,
! [A: set_node] :
( ~ ( finite_finite_node @ A )
| ( ( set_node2 @ ( sk19 @ A ) )
= A ) ),
inference(cnf,[status(esa)],[306]) ).
thf(308,plain,
! [A: set_node] :
( ( ( set_node2 @ ( sk19 @ A ) )
= A )
| ~ ( finite_finite_node @ A ) ),
inference(lifteq,[status(thm)],[307]) ).
thf(9088,plain,
! [B: set_node,A: list_node] :
( ( ( set_node2 @ ( sk19 @ B ) )
= B )
| ~ $true
| ( ( finite_finite_node @ ( set_node2 @ A ) )
!= ( finite_finite_node @ B ) ) ),
inference(paramod_ordered,[status(thm)],[305,308]) ).
thf(9089,plain,
! [B: set_node,A: list_node] :
( ( ( set_node2 @ ( sk19 @ B ) )
= B )
| ( ( finite_finite_node @ ( set_node2 @ A ) )
!= ( finite_finite_node @ B ) ) ),
inference(simp,[status(thm)],[9088]) ).
thf(9090,plain,
! [A: list_node] :
( ( set_node2 @ ( sk19 @ ( set_node2 @ A ) ) )
= ( set_node2 @ A ) ),
inference(pattern_uni,[status(thm)],[9089:[bind(A,$thf( C )),bind(B,$thf( set_node2 @ C ))]]) ).
thf(9133,plain,
! [A: list_node] :
( ( set_node2 @ ( sk19 @ ( set_node2 @ A ) ) )
= ( set_node2 @ A ) ),
inference(simp,[status(thm)],[9090]) ).
thf(1471,plain,
( ~ $true
| ( ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) )
!= ( member_node @ i @ ( set_node2 @ ms ) ) ) ),
inference(paramod_ordered,[status(thm)],[330,393]) ).
thf(1472,plain,
( ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) )
!= ( member_node @ i @ ( set_node2 @ ms ) ) ),
inference(simp,[status(thm)],[1471]) ).
thf(1475,plain,
( ( i != i )
| ( ( set_node2 @ ( butlast_node @ ms2 ) )
!= ( set_node2 @ ms ) ) ),
inference(simp,[status(thm)],[1472]) ).
thf(1477,plain,
( ( set_node2 @ ( butlast_node @ ms2 ) )
!= ( set_node2 @ ms ) ),
inference(simp,[status(thm)],[1475]) ).
thf(13627,plain,
! [A: list_node] :
( ( ( set_node2 @ A )
!= ( set_node2 @ ms ) )
| ( ( set_node2 @ ( sk19 @ ( set_node2 @ A ) ) )
!= ( set_node2 @ ( butlast_node @ ms2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9133,1477]) ).
thf(13677,plain,
! [A: list_node] :
( ( A != ms )
| ( ( sk19 @ ( set_node2 @ A ) )
!= ( butlast_node @ ms2 ) ) ),
inference(simp,[status(thm)],[13627]) ).
thf(13707,plain,
( ( sk19 @ ( set_node2 @ ms ) )
!= ( butlast_node @ ms2 ) ),
inference(simp,[status(thm)],[13677]) ).
thf(136,axiom,
! [A: node,B: list_node,C: list_node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( append_node @ C @ D ) )
= ( ( ( C = nil_node )
& ( ( cons_node @ A @ B )
= D ) )
| ? [E: list_node] :
( ( ( cons_node @ A @ E )
= C )
& ( B
= ( append_node @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_Cons__eq__append__conv) ).
thf(873,plain,
! [A: node,B: list_node,C: list_node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( append_node @ C @ D ) )
= ( ( ( C = nil_node )
& ( ( cons_node @ A @ B )
= D ) )
| ? [E: list_node] :
( ( ( cons_node @ A @ E )
= C )
& ( B
= ( append_node @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(92,axiom,
! [A: set_node,B: node > $o] :
( ( ord_less_eq_set_node @ A @ ( collect_node @ B ) )
= ( ! [C: node] :
( ( member_node @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_subset__Collect__conv) ).
thf(655,plain,
! [A: set_node,B: node > $o] :
( ( ord_less_eq_set_node @ A @ ( collect_node @ B ) )
= ( ! [C: node] :
( ( member_node @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(5,axiom,
! [A: list_val,B: set_val] :
( ( ord_less_eq_set_val @ ( set_val2 @ A ) @ B )
= ( ! [C: val] :
( ( member_val @ C @ ( set_val2 @ A ) )
=> ( member_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_subset__code_I1_J) ).
thf(267,plain,
! [A: list_val,B: set_val] :
( ( ord_less_eq_set_val @ ( set_val2 @ A ) @ B )
= ( ! [C: val] :
( ( member_val @ C @ ( set_val2 @ A ) )
=> ( member_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(268,plain,
! [B: set_val,A: list_val] :
( ( ord_less_eq_set_val @ ( set_val2 @ A ) @ B )
= ( ! [C: val] :
( ( member_val @ C @ ( set_val2 @ A ) )
=> ( member_val @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[267]) ).
thf(269,plain,
! [B: set_val,A: list_val] :
( ( ord_less_eq_set_val @ ( set_val2 @ A ) @ B )
= ( ! [C: val] :
( ( member_val @ C @ ( set_val2 @ A ) )
=> ( member_val @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[268]) ).
thf(251,axiom,
~ ! [A: node,B: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ B @ A )
=> ( ( member_node @ A @ ( set_node2 @ ms ) )
=> ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( butlast_node @ B ) ) )
=> ~ ( member_node @ C @ ( set_node2 @ ms ) ) )
=> ~ ( prefix_node @ B @ rs2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126__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) ).
thf(1416,plain,
~ ! [A: node,B: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ B @ A )
=> ( ( member_node @ A @ ( set_node2 @ ms ) )
=> ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( butlast_node @ B ) ) )
=> ~ ( member_node @ C @ ( set_node2 @ ms ) ) )
=> ~ ( prefix_node @ B @ rs2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1417,plain,
~ ! [A: node,B: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ B @ A )
=> ( ( member_node @ A @ ( set_node2 @ ms ) )
=> ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( butlast_node @ B ) ) )
=> ~ ( member_node @ C @ ( set_node2 @ ms ) ) )
=> ~ ( prefix_node @ B @ rs2 ) ) ) ),
inference(polarity_switch,[status(thm)],[1416]) ).
thf(1418,plain,
! [A: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ sk231 @ sk230 )
& ( member_node @ sk230 @ ( set_node2 @ ms ) )
& ( ~ ( member_node @ A @ ( set_node2 @ ( butlast_node @ sk231 ) ) )
| ~ ( member_node @ A @ ( set_node2 @ ms ) ) )
& ( prefix_node @ sk231 @ rs2 ) ),
inference(cnf,[status(esa)],[1417]) ).
thf(1422,plain,
prefix_node @ sk231 @ rs2,
inference(cnfConj,[status(thm)],[1418]) ).
thf(35,axiom,
! [A: node,B: node,C: list_node] :
( ( member_node @ A @ ( set_node2 @ ( cons_node @ B @ C ) ) )
=> ( ( A = B )
| ( member_node @ A @ ( set_node2 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_set__ConsD) ).
thf(379,plain,
! [A: node,B: node,C: list_node] :
( ( member_node @ A @ ( set_node2 @ ( cons_node @ B @ C ) ) )
=> ( ( A = B )
| ( member_node @ A @ ( set_node2 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(218,axiom,
! [A: list_node,B: list_node,C: node] :
( ( A != nil_node )
=> ( ( ( append_node @ A @ B )
= ( cons_node @ C @ nil_node ) )
= ( ( A
= ( cons_node @ C @ nil_node ) )
& ( B = nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_list__se__match_I1_J) ).
thf(1269,plain,
! [A: list_node,B: list_node,C: node] :
( ( A != nil_node )
=> ( ( ( append_node @ A @ B )
= ( cons_node @ C @ nil_node ) )
= ( ( A
= ( cons_node @ C @ nil_node ) )
& ( B = nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(253,axiom,
! [A: node,B: list_node,C: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( ( member_node @ C @ ( set_node2 @ B ) )
=> ( ( ( A = C )
=> ! [D: list_node,E: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ C @ E ) ) ) )
=> ( ( ( A != C )
=> ! [D: list_node,E: list_node,F: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ A @ ( append_node @ E @ ( cons_node @ C @ F ) ) ) ) ) )
=> ~ ( ( A != C )
=> ! [D: list_node,E: list_node,F: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ C @ ( append_node @ E @ ( cons_node @ A @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_xy__in__set__cases) ).
thf(1426,plain,
! [A: node,B: list_node,C: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( ( member_node @ C @ ( set_node2 @ B ) )
=> ( ( ( A = C )
=> ! [D: list_node,E: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ C @ E ) ) ) )
=> ( ( ( A != C )
=> ! [D: list_node,E: list_node,F: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ A @ ( append_node @ E @ ( cons_node @ C @ F ) ) ) ) ) )
=> ~ ( ( A != C )
=> ! [D: list_node,E: list_node,F: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ C @ ( append_node @ E @ ( cons_node @ A @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(8031,plain,
! [A: list_node] :
( ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) )
| ( prefix_node @ sk231 @ nil_node )
| ( A != rs2 ) ),
inference(paramod_ordered,[status(thm)],[303,1422]) ).
thf(8032,plain,
( ( member_node @ ( hd_node @ rs2 ) @ ( set_node2 @ rs2 ) )
| ( prefix_node @ sk231 @ nil_node ) ),
inference(pattern_uni,[status(thm)],[8031:[bind(A,$thf( rs2 ))]]) ).
thf(43,axiom,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_prefix__bot_Obot_Oextremum__unique) ).
thf(414,plain,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(415,plain,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(cnf,[status(esa)],[414]) ).
thf(416,plain,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(lifteq,[status(thm)],[415]) ).
thf(10102,plain,
( ( member_node @ ( hd_node @ rs2 ) @ ( set_node2 @ rs2 ) )
| ( sk231 = nil_node ) ),
inference(rewrite,[status(thm)],[8032,416]) ).
thf(10103,plain,
( ( sk231 = nil_node )
| ( member_node @ ( hd_node @ rs2 ) @ ( set_node2 @ rs2 ) ) ),
inference(lifteq,[status(thm)],[10102]) ).
thf(106,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ! [F: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
=> ! [G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D )
=> ( ( C
= ( append_node @ F @ ( tl_node @ G ) ) )
=> ( C
!= ( append_node @ ( butlast_node @ F ) @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_old_Opath2__split__ex) ).
thf(715,plain,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ! [F: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
=> ! [G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D )
=> ( ( C
= ( append_node @ F @ ( tl_node @ G ) ) )
=> ( C
!= ( append_node @ ( butlast_node @ F ) @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(9,axiom,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Collect__mem__eq) ).
thf(280,plain,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(281,plain,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[280]) ).
thf(282,plain,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[281]) ).
thf(47,axiom,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_List_Ofinite__set) ).
thf(426,plain,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(427,plain,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
inference(cnf,[status(esa)],[426]) ).
thf(2675,plain,
! [B: list_val,A: set_val] :
( ( finite_finite_val
@ ( collect_val
@ ^ [C: val] : ( member_val @ C @ A ) ) )
| ( A
!= ( set_val2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[282,427]) ).
thf(2676,plain,
! [A: list_val] :
( finite_finite_val
@ ( collect_val
@ ^ [B: val] : ( member_val @ B @ ( set_val2 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2675:[bind(A,$thf( set_val2 @ C )),bind(B,$thf( C ))]]) ).
thf(2680,plain,
! [A: list_val] :
( finite_finite_val
@ ( collect_val
@ ^ [B: val] : ( member_val @ B @ ( set_val2 @ A ) ) ) ),
inference(simp,[status(thm)],[2676]) ).
thf(2693,plain,
! [B: list_val,A: set_val] :
( ( finite_finite_val
@ ( collect_val
@ ^ [C: val] :
( member_val @ C
@ ( collect_val
@ ^ [D: val] : ( member_val @ D @ A ) ) ) ) )
| ( A
!= ( set_val2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[282,2680]) ).
thf(2694,plain,
! [A: list_val] :
( finite_finite_val
@ ( collect_val
@ ^ [B: val] :
( member_val @ B
@ ( collect_val
@ ^ [C: val] : ( member_val @ C @ ( set_val2 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2693:[bind(A,$thf( set_val2 @ C )),bind(B,$thf( C ))]]) ).
thf(2712,plain,
! [A: list_val] :
( finite_finite_val
@ ( collect_val
@ ^ [B: val] :
( member_val @ B
@ ( collect_val
@ ^ [C: val] : ( member_val @ C @ ( set_val2 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[2694]) ).
thf(231,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_split__list__first__propE) ).
thf(1327,plain,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(26,axiom,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( suffix_node @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_suffix__order_Oeq__refl) ).
thf(340,plain,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( suffix_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(238,axiom,
! [A: node] :
( ( member_node @ A @ ( set_node2 @ ( butlast_node @ ri ) ) )
=> ~ ( member_node @ A @ ( set_node2 @ ms ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_ri__props_I3_J) ).
thf(1354,plain,
! [A: node] :
( ( member_node @ A @ ( set_node2 @ ( butlast_node @ ri ) ) )
=> ~ ( member_node @ A @ ( set_node2 @ ms ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(96,axiom,
! [A: list_node,B: list_node] :
( ( ( A = nil_node )
=> ( ( butlast_node @ ( append_node @ B @ A ) )
= ( butlast_node @ B ) ) )
& ( ( A != nil_node )
=> ( ( butlast_node @ ( append_node @ B @ A ) )
= ( append_node @ B @ ( butlast_node @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_butlast__append) ).
thf(670,plain,
! [A: list_node,B: list_node] :
( ( ( A = nil_node )
=> ( ( butlast_node @ ( append_node @ B @ A ) )
= ( butlast_node @ B ) ) )
& ( ( A != nil_node )
=> ( ( butlast_node @ ( append_node @ B @ A ) )
= ( append_node @ B @ ( butlast_node @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(30,axiom,
( ( butlast_node @ nil_node )
= nil_node ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_butlast_Osimps_I1_J) ).
thf(367,plain,
( ( butlast_node @ nil_node )
= nil_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(368,plain,
( ( butlast_node @ nil_node )
= nil_node ),
inference(lifteq,[status(thm)],[367]) ).
thf(1316,plain,
! [A: list_node] :
( ( butlast_node @ ( tl_node @ A ) )
= ( tl_node @ ( butlast_node @ A ) ) ),
inference(cnf,[status(esa)],[1315]) ).
thf(1317,plain,
! [A: list_node] :
( ( tl_node @ ( butlast_node @ A ) )
= ( butlast_node @ ( tl_node @ A ) ) ),
inference(lifteq,[status(thm)],[1316]) ).
thf(229,axiom,
! [A: list_node] : ( suffix_node @ ( tl_node @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_suffix__tl) ).
thf(1320,plain,
! [A: list_node] : ( suffix_node @ ( tl_node @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1321,plain,
! [A: list_node] : ( suffix_node @ ( tl_node @ A ) @ A ),
inference(cnf,[status(esa)],[1320]) ).
thf(12852,plain,
! [B: list_node,A: list_node] :
( ( suffix_node @ ( butlast_node @ ( tl_node @ A ) ) @ B )
| ( ( tl_node @ ( butlast_node @ A ) )
!= ( tl_node @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1317,1321]) ).
thf(12853,plain,
! [A: list_node] : ( suffix_node @ ( butlast_node @ ( tl_node @ A ) ) @ ( butlast_node @ A ) ),
inference(pattern_uni,[status(thm)],[12852:[bind(A,$thf( C )),bind(B,$thf( butlast_node @ C ))]]) ).
thf(12876,plain,
! [A: list_node] : ( suffix_node @ ( butlast_node @ ( tl_node @ A ) ) @ ( butlast_node @ A ) ),
inference(simp,[status(thm)],[12853]) ).
thf(14315,plain,
! [A: list_node] :
( ( suffix_node @ ( butlast_node @ ( tl_node @ A ) ) @ nil_node )
| ( ( butlast_node @ nil_node )
!= ( butlast_node @ A ) ) ),
inference(paramod_ordered,[status(thm)],[368,12876]) ).
thf(14316,plain,
suffix_node @ ( butlast_node @ ( tl_node @ nil_node ) ) @ nil_node,
inference(pattern_uni,[status(thm)],[14315:[bind(A,$thf( nil_node ))]]) ).
thf(49,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_suffix__Nil) ).
thf(430,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(431,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(cnf,[status(esa)],[430]) ).
thf(432,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(lifteq,[status(thm)],[431]) ).
thf(14412,plain,
( ( butlast_node @ ( tl_node @ nil_node ) )
= nil_node ),
inference(rewrite,[status(thm)],[14316,432]) ).
thf(14413,plain,
( ( butlast_node @ ( tl_node @ nil_node ) )
= nil_node ),
inference(lifteq,[status(thm)],[14412]) ).
thf(14474,plain,
! [A: list_node] :
( ( suffix_node @ ( butlast_node @ ( tl_node @ A ) ) @ nil_node )
| ( ( butlast_node @ ( tl_node @ nil_node ) )
!= ( butlast_node @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14413,12876]) ).
thf(14475,plain,
suffix_node @ ( butlast_node @ ( tl_node @ ( tl_node @ nil_node ) ) ) @ nil_node,
inference(pattern_uni,[status(thm)],[14474:[bind(A,$thf( tl_node @ nil_node ))]]) ).
thf(14501,plain,
( ( butlast_node @ ( tl_node @ ( tl_node @ nil_node ) ) )
= nil_node ),
inference(rewrite,[status(thm)],[14475,432]) ).
thf(14502,plain,
( ( butlast_node @ ( tl_node @ ( tl_node @ nil_node ) ) )
= nil_node ),
inference(lifteq,[status(thm)],[14501]) ).
thf(14576,plain,
! [A: list_node] :
( ( suffix_node @ ( butlast_node @ ( tl_node @ A ) ) @ nil_node )
| ( ( butlast_node @ ( tl_node @ ( tl_node @ nil_node ) ) )
!= ( butlast_node @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14502,12876]) ).
thf(14577,plain,
suffix_node @ ( butlast_node @ ( tl_node @ ( tl_node @ ( tl_node @ nil_node ) ) ) ) @ nil_node,
inference(pattern_uni,[status(thm)],[14576:[bind(A,$thf( tl_node @ ( tl_node @ nil_node ) ))]]) ).
thf(14601,plain,
( ( butlast_node @ ( tl_node @ ( tl_node @ ( tl_node @ nil_node ) ) ) )
= nil_node ),
inference(rewrite,[status(thm)],[14577,432]) ).
thf(14602,plain,
( ( butlast_node @ ( tl_node @ ( tl_node @ ( tl_node @ nil_node ) ) ) )
= nil_node ),
inference(lifteq,[status(thm)],[14601]) ).
thf(44,axiom,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Collect__mem__eq) ).
thf(417,plain,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(418,plain,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[417]) ).
thf(419,plain,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[418]) ).
thf(3426,plain,
! [B: list_node,A: set_node] :
( ( finite_finite_node
@ ( collect_node
@ ^ [C: node] : ( member_node @ C @ A ) ) )
| ( A
!= ( set_node2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[419,305]) ).
thf(3427,plain,
! [A: list_node] :
( finite_finite_node
@ ( collect_node
@ ^ [B: node] : ( member_node @ B @ ( set_node2 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[3426:[bind(A,$thf( set_node2 @ C )),bind(B,$thf( C ))]]) ).
thf(3429,plain,
! [A: list_node] :
( finite_finite_node
@ ( collect_node
@ ^ [B: node] : ( member_node @ B @ ( set_node2 @ A ) ) ) ),
inference(simp,[status(thm)],[3427]) ).
thf(202,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ B ) ) )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons_node @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_old_OCons__path2) ).
thf(1196,plain,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ B ) ) )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons_node @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(8,axiom,
! [A: list_node] : ( prefix_node @ nil_node @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_prefix__code_I1_J) ).
thf(278,plain,
! [A: list_node] : ( prefix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(279,plain,
! [A: list_node] : ( prefix_node @ nil_node @ A ),
inference(cnf,[status(esa)],[278]) ).
thf(10204,plain,
! [C: list_node,B: list_node,A: list_node] :
( ~ $true
| ( ord_less_eq_set_node @ ( set_node2 @ B ) @ ( set_node2 @ C ) )
| ( ( prefix_node @ nil_node @ A )
!= ( prefix_node @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[279,313]) ).
thf(10205,plain,
! [C: list_node,B: list_node,A: list_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ B ) @ ( set_node2 @ C ) )
| ( ( prefix_node @ nil_node @ A )
!= ( prefix_node @ B @ C ) ) ),
inference(simp,[status(thm)],[10204]) ).
thf(10206,plain,
! [A: list_node] : ( ord_less_eq_set_node @ ( set_node2 @ nil_node ) @ ( set_node2 @ A ) ),
inference(pattern_uni,[status(thm)],[10205:[bind(A,$thf( A )),bind(B,$thf( nil_node )),bind(C,$thf( A ))]]) ).
thf(11495,plain,
! [B: list_node,A: set_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ nil_node )
@ ( collect_node
@ ^ [C: node] : ( member_node @ C @ A ) ) )
| ( A
!= ( set_node2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[419,10206]) ).
thf(11496,plain,
! [A: list_node] :
( ord_less_eq_set_node @ ( set_node2 @ nil_node )
@ ( collect_node
@ ^ [B: node] : ( member_node @ B @ ( set_node2 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11495:[bind(A,$thf( set_node2 @ C )),bind(B,$thf( C ))]]) ).
thf(11542,plain,
! [A: list_node] :
( ord_less_eq_set_node @ ( set_node2 @ nil_node )
@ ( collect_node
@ ^ [B: node] : ( member_node @ B @ ( set_node2 @ A ) ) ) ),
inference(simp,[status(thm)],[11496]) ).
thf(140,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_same__append__eq) ).
thf(885,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(10,axiom,
! [A: ( node > node > $o ) > list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: node > node > $o,F: node,G: list_node,H: node,I: list_node] :
( ( ( E @ F @ H )
=> ( A @ E @ G @ ( cons_node @ H @ I ) ) )
=> ( ( ~ ( E @ F @ H )
=> ( A @ E @ ( cons_node @ F @ G ) @ I ) )
=> ( A @ E @ ( cons_node @ F @ G ) @ ( cons_node @ H @ I ) ) ) )
=> ( ! [E: node > node > $o,F: list_node] : ( A @ E @ F @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ nil_node @ ( cons_node @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_mergesort__by__rel__merge_Oinduct) ).
thf(283,plain,
! [A: ( node > node > $o ) > list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: node > node > $o,F: node,G: list_node,H: node,I: list_node] :
( ( ( E @ F @ H )
=> ( A @ E @ G @ ( cons_node @ H @ I ) ) )
=> ( ( ~ ( E @ F @ H )
=> ( A @ E @ ( cons_node @ F @ G ) @ I ) )
=> ( A @ E @ ( cons_node @ F @ G ) @ ( cons_node @ H @ I ) ) ) )
=> ( ! [E: node > node > $o,F: list_node] : ( A @ E @ F @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ nil_node @ ( cons_node @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(284,plain,
! [A: ( node > node > $o ) > list_node > list_node > $o] :
( ! [B: node > node > $o,C: node,D: list_node,E: node,F: list_node] :
( ( ( B @ C @ E )
=> ( A @ B @ D @ ( cons_node @ E @ F ) ) )
=> ( ( ~ ( B @ C @ E )
=> ( A @ B @ ( cons_node @ C @ D ) @ F ) )
=> ( A @ B @ ( cons_node @ C @ D ) @ ( cons_node @ E @ F ) ) ) )
=> ( ! [B: node > node > $o,C: list_node] : ( A @ B @ C @ nil_node )
=> ( ! [B: node > node > $o,C: node,D: list_node] : ( A @ B @ nil_node @ ( cons_node @ C @ D ) )
=> ! [B: node > node > $o,C: list_node,D: list_node] : ( A @ B @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[283]) ).
thf(285,plain,
! [D: list_node,C: list_node,B: node > node > $o,A: ( node > node > $o ) > list_node > list_node > $o] :
( ( ~ ( sk7 @ A @ ( sk8 @ A ) @ ( sk10 @ A ) )
| ( A @ ( sk7 @ A ) @ ( sk9 @ A ) @ ( cons_node @ ( sk10 @ A ) @ ( sk11 @ A ) ) )
| ~ ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ nil_node )
| ~ ( A @ ( sk14 @ A ) @ nil_node @ ( cons_node @ ( sk15 @ A ) @ ( sk16 @ A ) ) )
| ( A @ B @ C @ D ) )
& ( ( sk7 @ A @ ( sk8 @ A ) @ ( sk10 @ A ) )
| ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk11 @ A ) )
| ~ ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ nil_node )
| ~ ( A @ ( sk14 @ A ) @ nil_node @ ( cons_node @ ( sk15 @ A ) @ ( sk16 @ A ) ) )
| ( A @ B @ C @ D ) )
& ( ~ ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( cons_node @ ( sk10 @ A ) @ ( sk11 @ A ) ) )
| ~ ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ nil_node )
| ~ ( A @ ( sk14 @ A ) @ nil_node @ ( cons_node @ ( sk15 @ A ) @ ( sk16 @ A ) ) )
| ( A @ B @ C @ D ) ) ),
inference(cnf,[status(esa)],[284]) ).
thf(288,plain,
! [D: list_node,C: list_node,B: node > node > $o,A: ( node > node > $o ) > list_node > list_node > $o] :
( ~ ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( cons_node @ ( sk10 @ A ) @ ( sk11 @ A ) ) )
| ~ ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ nil_node )
| ~ ( A @ ( sk14 @ A ) @ nil_node @ ( cons_node @ ( sk15 @ A ) @ ( sk16 @ A ) ) )
| ( A @ B @ C @ D ) ),
inference(cnfConj,[status(thm)],[285]) ).
thf(1102,plain,
~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ sk176 ) ) ),
inference(cnfConj,[status(thm)],[1099]) ).
thf(1473,plain,
( ~ $true
| ( ( member_node @ i @ ( set_node2 @ ( butlast_node @ sk176 ) ) )
!= ( member_node @ i @ ( set_node2 @ ms ) ) ) ),
inference(paramod_ordered,[status(thm)],[330,1102]) ).
thf(1474,plain,
( ( member_node @ i @ ( set_node2 @ ( butlast_node @ sk176 ) ) )
!= ( member_node @ i @ ( set_node2 @ ms ) ) ),
inference(simp,[status(thm)],[1473]) ).
thf(1476,plain,
( ( i != i )
| ( ( set_node2 @ ( butlast_node @ sk176 ) )
!= ( set_node2 @ ms ) ) ),
inference(simp,[status(thm)],[1474]) ).
thf(1478,plain,
( ( set_node2 @ ( butlast_node @ sk176 ) )
!= ( set_node2 @ ms ) ),
inference(simp,[status(thm)],[1476]) ).
thf(1526,plain,
( ( ( set_node2 @ ms )
!= ( set_node2 @ nil_node ) )
| ( ( butlast_node @ sk176 )
!= ( butlast_node @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[368,1478]) ).
thf(1529,plain,
( ( ms != nil_node )
| ( sk176 != nil_node ) ),
inference(simp,[status(thm)],[1526]) ).
thf(142,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ms_H__props_I1_J) ).
thf(896,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1714,plain,
( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ m
@ ms2
@ i ),
inference(rewrite,[status(thm)],[896,806]) ).
thf(1718,plain,
( ~ $true
| ( ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ n
@ ( append_node @ ns @ ( tl_node @ ri ) )
@ i )
!= ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ m
@ ms2
@ i ) ) ),
inference(paramod_ordered,[status(thm)],[1714,1648]) ).
thf(1719,plain,
( ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ n
@ ( append_node @ ns @ ( tl_node @ ri ) )
@ i )
!= ( graph_1012773594_edgeD @ alpha_n
@ ^ [A: g] : $true
@ inEdges
@ g2
@ m
@ ms2
@ i ) ),
inference(simp,[status(thm)],[1718]) ).
thf(1728,plain,
( ( alpha_n != alpha_n )
| ( ( ^ [A: g] : $true )
!= ( ^ [A: g] : $true ) )
| ( inEdges != inEdges )
| ( g2 != g2 )
| ( n != m )
| ( ( append_node @ ns @ ( tl_node @ ri ) )
!= ms2 )
| ( i != i ) ),
inference(simp,[status(thm)],[1719]) ).
thf(1730,plain,
( ( n != m )
| ( ( append_node @ ns @ ( tl_node @ ri ) )
!= ms2 ) ),
inference(simp,[status(thm)],[1728]) ).
thf(1731,plain,
( ( n != m )
| ( ( append_node @ ns @ nil_node )
!= ms2 )
| ( ( tl_node @ ri )
!= ( tl_node @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[1115,1730]) ).
thf(1740,plain,
( ( n != m )
| ( ( append_node @ ns @ nil_node )
!= ms2 )
| ( ri != nil_node ) ),
inference(simp,[status(thm)],[1731]) ).
thf(4452,plain,
! [A: list_node] :
( ( n != m )
| ( A != ms2 )
| ( ri != nil_node )
| ( ( append_node @ nil_node @ A )
!= ( append_node @ ns @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[881,1740]) ).
thf(4467,plain,
( ( n != m )
| ( ri != nil_node )
| ( ns != nil_node )
| ( ms2 != nil_node ) ),
inference(simp,[status(thm)],[4452]) ).
thf(134,axiom,
! [A: list_node,B: list_node] :
? [C: list_node,D: list_node,E: list_node] :
( ( A
= ( append_node @ C @ D ) )
& ( B
= ( append_node @ C @ E ) )
& ( ( D = nil_node )
| ( E = nil_node )
| ( ( hd_node @ D )
!= ( hd_node @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_longest__common__prefix) ).
thf(841,plain,
! [A: list_node,B: list_node] :
? [C: list_node,D: list_node,E: list_node] :
( ( A
= ( append_node @ C @ D ) )
& ( B
= ( append_node @ C @ E ) )
& ( ( D = nil_node )
| ( E = nil_node )
| ( ( hd_node @ D )
!= ( hd_node @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(74,axiom,
! [A: ( node > node ) > list_node > list_node > $o,B: node > node,C: list_node,D: list_node] :
( ! [E: node > node,F: list_node] : ( A @ E @ nil_node @ F )
=> ( ! [E: node > node,F: node,G: list_node,H: list_node] :
( ( A @ E @ G @ ( cons_node @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_node @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_map__tailrec__rev_Oinduct) ).
thf(565,plain,
! [A: ( node > node ) > list_node > list_node > $o,B: node > node,C: list_node,D: list_node] :
( ! [E: node > node,F: list_node] : ( A @ E @ nil_node @ F )
=> ( ! [E: node > node,F: node,G: list_node,H: list_node] :
( ( A @ E @ G @ ( cons_node @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_node @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(240,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= B )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_append__self__conv2) ).
thf(1366,plain,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= B )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1480,plain,
( ( ( set_node2 @ ms )
!= ( set_node2 @ nil_node ) )
| ( ( butlast_node @ ms2 )
!= ( butlast_node @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[368,1477]) ).
thf(1482,plain,
( ( ( set_node2 @ ms )
!= ( set_node2 @ nil_node ) )
| ( ms2 != nil_node ) ),
inference(simp,[status(thm)],[1480]) ).
thf(215,axiom,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( invar @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_old_Opath__invar) ).
thf(1254,plain,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( invar @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(91,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_list_Oexhaust) ).
thf(651,plain,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(60,axiom,
! [A: list_node,B: node] :
( ( ( A = nil_node )
=> ( ( butlast_node @ ( cons_node @ B @ A ) )
= nil_node ) )
& ( ( A != nil_node )
=> ( ( butlast_node @ ( cons_node @ B @ A ) )
= ( cons_node @ B @ ( butlast_node @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_butlast_Osimps_I2_J) ).
thf(489,plain,
! [A: list_node,B: node] :
( ( ( A = nil_node )
=> ( ( butlast_node @ ( cons_node @ B @ A ) )
= nil_node ) )
& ( ( A != nil_node )
=> ( ( butlast_node @ ( cons_node @ B @ A ) )
= ( cons_node @ B @ ( butlast_node @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(490,plain,
( ! [A: list_node] :
( ( A = nil_node )
=> ! [B: node] :
( ( butlast_node @ ( cons_node @ B @ A ) )
= nil_node ) )
& ! [A: list_node] :
( ( A != nil_node )
=> ! [B: node] :
( ( butlast_node @ ( cons_node @ B @ A ) )
= ( cons_node @ B @ ( butlast_node @ A ) ) ) ) ),
inference(miniscope,[status(thm)],[489]) ).
thf(491,plain,
! [D: node,C: list_node,B: node,A: list_node] :
( ( ( A != nil_node )
| ( ( butlast_node @ ( cons_node @ B @ A ) )
= nil_node ) )
& ( ( C = nil_node )
| ( ( butlast_node @ ( cons_node @ D @ C ) )
= ( cons_node @ D @ ( butlast_node @ C ) ) ) ) ),
inference(cnf,[status(esa)],[490]) ).
thf(492,plain,
! [B: node,A: list_node] :
( ( A != nil_node )
| ( ( butlast_node @ ( cons_node @ B @ A ) )
= nil_node ) ),
inference(cnfConj,[status(thm)],[491]) ).
thf(494,plain,
! [B: node,A: list_node] :
( ( A != nil_node )
| ( ( butlast_node @ ( cons_node @ B @ A ) )
= nil_node ) ),
inference(lifteq,[status(thm)],[492]) ).
thf(495,plain,
! [A: node] :
( ( butlast_node @ ( cons_node @ A @ nil_node ) )
= nil_node ),
inference(simp,[status(thm)],[494]) ).
thf(12854,plain,
! [B: list_node,A: node] :
( ( ( tl_node @ nil_node )
= ( butlast_node @ ( tl_node @ B ) ) )
| ( ( butlast_node @ ( cons_node @ A @ nil_node ) )
!= ( butlast_node @ B ) ) ),
inference(paramod_ordered,[status(thm)],[495,1317]) ).
thf(12855,plain,
! [A: node] :
( ( tl_node @ nil_node )
= ( butlast_node @ ( tl_node @ ( cons_node @ A @ nil_node ) ) ) ),
inference(pattern_uni,[status(thm)],[12854:[bind(A,$thf( C )),bind(B,$thf( cons_node @ C @ nil_node ))]]) ).
thf(12877,plain,
! [A: node] :
( ( tl_node @ nil_node )
= ( butlast_node @ ( tl_node @ ( cons_node @ A @ nil_node ) ) ) ),
inference(simp,[status(thm)],[12855]) ).
thf(12879,plain,
! [A: node] :
( ( butlast_node @ ( tl_node @ ( cons_node @ A @ nil_node ) ) )
= nil_node ),
inference(rewrite,[status(thm)],[12877,1115]) ).
thf(107,axiom,
! [A: g,B: node,C: list_node,D: node,E: node > list_node > node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( invar @ A )
=> ( E @ D @ ( cons_node @ D @ nil_node ) @ D ) )
=> ( ! [F: list_node,G: node,H: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D )
=> ( ( E @ H @ F @ D )
=> ( ( member_node @ G @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ H ) ) )
=> ( E @ G @ ( cons_node @ G @ F ) @ D ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_old_Opath2__induct) ).
thf(724,plain,
! [A: g,B: node,C: list_node,D: node,E: node > list_node > node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( invar @ A )
=> ( E @ D @ ( cons_node @ D @ nil_node ) @ D ) )
=> ( ! [F: list_node,G: node,H: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D )
=> ( ( E @ H @ F @ D )
=> ( ( member_node @ G @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ H ) ) )
=> ( E @ G @ ( cons_node @ G @ F ) @ D ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(75,axiom,
! [A: list_node,B: set_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ B )
= ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
=> ( member_node @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_subset__code_I1_J) ).
thf(570,plain,
! [A: list_node,B: set_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ B )
= ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
=> ( member_node @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(32,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ B @ A )
& ( suffix_node @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_suffix__order_Odual__order_Oeq__iff) ).
thf(371,plain,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ B @ A )
& ( suffix_node @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(372,plain,
( ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ B @ A )
& ( suffix_node @ A @ B ) ) )
= ( (=) @ list_node ) ),
inference(lifteq,[status(thm)],[371]) ).
thf(7245,plain,
! [B: node,A: set_node] :
( ( member_node @ i
@ ( collect_node
@ ^ [C: node] : ( member_node @ C @ A ) ) )
| ( A
!= ( set_node2 @ ( cons_node @ B @ ms ) ) ) ),
inference(paramod_ordered,[status(thm)],[419,7135]) ).
thf(7246,plain,
! [A: node] :
( member_node @ i
@ ( collect_node
@ ^ [B: node] : ( member_node @ B @ ( set_node2 @ ( cons_node @ A @ ms ) ) ) ) ),
inference(pattern_uni,[status(thm)],[7245:[bind(A,$thf( set_node2 @ ( cons_node @ D @ ms ) )),bind(B,$thf( D ))]]) ).
thf(7294,plain,
! [A: node] :
( member_node @ i
@ ( collect_node
@ ^ [B: node] : ( member_node @ B @ ( set_node2 @ ( cons_node @ A @ ms ) ) ) ) ),
inference(simp,[status(thm)],[7246]) ).
thf(190,axiom,
( suffix_node
= ( ^ [A: list_node,B: list_node] :
? [C: list_node] :
( B
= ( append_node @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_Sublist_Osuffix__def) ).
thf(1131,plain,
( suffix_node
= ( ^ [A: list_node,B: list_node] :
? [C: list_node] :
( B
= ( append_node @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1132,plain,
( suffix_node
= ( ^ [A: list_node,B: list_node] :
? [C: list_node] :
( B
= ( append_node @ C @ A ) ) ) ),
inference(lifteq,[status(thm)],[1131]) ).
thf(1511,plain,
! [A: list_node] :
( ( suffix_node @ A )
= ( ^ [B: list_node] :
? [C: list_node] :
( B
= ( append_node @ C @ A ) ) ) ),
inference(func_ext,[status(esa)],[1132]) ).
thf(27,axiom,
! [A: list_node,B: list_node > $o] :
( ( A != nil_node )
=> ( ! [C: node] : ( B @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( D != nil_node )
=> ( ( B @ D )
=> ( B @ ( cons_node @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_list__nonempty__induct) ).
thf(344,plain,
! [A: list_node,B: list_node > $o] :
( ( A != nil_node )
=> ( ! [C: node] : ( B @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( D != nil_node )
=> ( ( B @ D )
=> ( B @ ( cons_node @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(86,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_suffix__order_Oorder_Oeq__iff) ).
thf(638,plain,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(244,axiom,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_assms_I10_J) ).
thf(1379,plain,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(178,axiom,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ ( butlast_node @ C ) @ E ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_old_Opath2__app_H) ).
thf(1087,plain,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ ( butlast_node @ C ) @ E ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(195,axiom,
! [A: list_node,B: list_node > $o] :
( ( A != nil_node )
=> ( ! [C: node] : ( B @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( D != nil_node )
=> ( ( B @ D )
=> ( B @ ( append_node @ D @ ( cons_node @ C @ nil_node ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_rev__nonempty__induct) ).
thf(1147,plain,
! [A: list_node,B: list_node > $o] :
( ( A != nil_node )
=> ( ! [C: node] : ( B @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( D != nil_node )
=> ( ( B @ D )
=> ( B @ ( append_node @ D @ ( cons_node @ C @ nil_node ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1479,plain,
( ( butlast_node @ ms2 )
!= ms ),
inference(simp,[status(thm)],[1477]) ).
thf(152,axiom,
! [A: node,B: list_node,C: list_node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( append_node @ C @ D ) )
=> ( ( ( C = nil_node )
=> ( D
!= ( cons_node @ A @ B ) ) )
=> ~ ! [E: list_node] :
( ( C
= ( cons_node @ A @ E ) )
=> ( ( append_node @ E @ D )
!= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_list__Cons__eq__append__cases) ).
thf(969,plain,
! [A: node,B: list_node,C: list_node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( append_node @ C @ D ) )
=> ( ( ( C = nil_node )
=> ( D
!= ( cons_node @ A @ B ) ) )
=> ~ ! [E: list_node] :
( ( C
= ( cons_node @ A @ E ) )
=> ( ( append_node @ E @ D )
!= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(163,axiom,
! [A: node,B: list_node,C: list_node] :
( ( append_node @ ( cons_node @ A @ B ) @ C )
= ( cons_node @ A @ ( append_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_append__Cons) ).
thf(1013,plain,
! [A: node,B: list_node,C: list_node] :
( ( append_node @ ( cons_node @ A @ B ) @ C )
= ( cons_node @ A @ ( append_node @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1420,plain,
member_node @ sk230 @ ( set_node2 @ ms ),
inference(cnfConj,[status(thm)],[1418]) ).
thf(7040,plain,
! [C: node,B: list_node,A: node] :
( ~ $true
| ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) )
| ( ( member_node @ sk230 @ ( set_node2 @ ms ) )
!= ( member_node @ A @ ( set_node2 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1420,298]) ).
thf(7041,plain,
! [C: node,B: list_node,A: node] :
( ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) )
| ( ( member_node @ sk230 @ ( set_node2 @ ms ) )
!= ( member_node @ A @ ( set_node2 @ B ) ) ) ),
inference(simp,[status(thm)],[7040]) ).
thf(7042,plain,
! [A: node] : ( member_node @ sk230 @ ( set_node2 @ ( cons_node @ A @ ms ) ) ),
inference(pattern_uni,[status(thm)],[7041:[bind(A,$thf( sk230 )),bind(B,$thf( ms ))]]) ).
thf(7094,plain,
! [A: node] : ( member_node @ sk230 @ ( set_node2 @ ( cons_node @ A @ ms ) ) ),
inference(simp,[status(thm)],[7042]) ).
thf(7165,plain,
! [B: node,A: set_node] :
( ( member_node @ sk230
@ ( collect_node
@ ^ [C: node] : ( member_node @ C @ A ) ) )
| ( A
!= ( set_node2 @ ( cons_node @ B @ ms ) ) ) ),
inference(paramod_ordered,[status(thm)],[419,7094]) ).
thf(7166,plain,
! [A: node] :
( member_node @ sk230
@ ( collect_node
@ ^ [B: node] : ( member_node @ B @ ( set_node2 @ ( cons_node @ A @ ms ) ) ) ) ),
inference(pattern_uni,[status(thm)],[7165:[bind(A,$thf( set_node2 @ ( cons_node @ D @ ms ) )),bind(B,$thf( D ))]]) ).
thf(7215,plain,
! [A: node] :
( member_node @ sk230
@ ( collect_node
@ ^ [B: node] : ( member_node @ B @ ( set_node2 @ ( cons_node @ A @ ms ) ) ) ) ),
inference(simp,[status(thm)],[7166]) ).
thf(11,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_suffix__order_Oorder_Oantisym) ).
thf(289,plain,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: node > $o,B: node > $o] :
( ! [C: node] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_node @ A )
= ( collect_node @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Collect__cong) ).
thf(261,plain,
! [A: node > $o,B: node > $o] :
( ! [C: node] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_node @ A )
= ( collect_node @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(249,axiom,
! [A: g,B: node,C: list_node,D: node,E: node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ? [F: node] :
( ( member_node @ F @ ( set_node2 @ C ) )
& ( E @ F ) )
=> ~ ! [F: node,G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ G @ F )
=> ( ( E @ F )
=> ( ! [H: node] :
( ( member_node @ H @ ( set_node2 @ ( butlast_node @ G ) ) )
=> ~ ( E @ H ) )
=> ~ ( prefix_node @ G @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_old_Opath2__split__first__prop) ).
thf(1398,plain,
! [A: g,B: node,C: list_node,D: node,E: node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ? [F: node] :
( ( member_node @ F @ ( set_node2 @ C ) )
& ( E @ F ) )
=> ~ ! [F: node,G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ G @ F )
=> ( ( E @ F )
=> ( ! [H: node] :
( ( member_node @ H @ ( set_node2 @ ( butlast_node @ G ) ) )
=> ~ ( E @ H ) )
=> ~ ( prefix_node @ G @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(256,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ B @ ( set_node2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_old_Opath2__hd__in__ns) ).
thf(1450,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ B @ ( set_node2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(89,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ ( butlast_node @ B ) ) )
=> ( member_node @ A @ ( set_node2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_in__set__butlastD) ).
thf(646,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ ( butlast_node @ B ) ) )
=> ( member_node @ A @ ( set_node2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(76,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_suffix__order_Oeq__iff) ).
thf(573,plain,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(574,plain,
( ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) )
= ( (=) @ list_node ) ),
inference(lifteq,[status(thm)],[573]) ).
thf(146,axiom,
! [A: list_node,B: node,C: list_node,D: list_node,E: node,F: list_node] :
( ( ( append_node @ A @ ( cons_node @ B @ C ) )
= ( append_node @ D @ ( cons_node @ E @ F ) ) )
=> ( ! [G: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ E @ G ) ) )
=> ( F
!= ( append_node @ G @ ( cons_node @ B @ C ) ) ) )
=> ( ( ( D = A )
=> ( ( E = B )
=> ( F != C ) ) )
=> ~ ! [G: list_node] :
( ( D
= ( append_node @ A @ ( cons_node @ B @ G ) ) )
=> ( C
!= ( append_node @ G @ ( cons_node @ E @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_list__match__lel__lel) ).
thf(905,plain,
! [A: list_node,B: node,C: list_node,D: list_node,E: node,F: list_node] :
( ( ( append_node @ A @ ( cons_node @ B @ C ) )
= ( append_node @ D @ ( cons_node @ E @ F ) ) )
=> ( ! [G: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ E @ G ) ) )
=> ( F
!= ( append_node @ G @ ( cons_node @ B @ C ) ) ) )
=> ( ( ( D = A )
=> ( ( E = B )
=> ( F != C ) ) )
=> ~ ! [G: list_node] :
( ( D
= ( append_node @ A @ ( cons_node @ B @ G ) ) )
=> ( C
!= ( append_node @ G @ ( cons_node @ E @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(7300,plain,
! [A: node] :
( ( cons_node @ A @ ms )
!= ( butlast_node @ ms2 ) ),
inference(simp,[status(thm)],[7285]) ).
thf(242,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( prefix_node @ ( append_node @ A @ B ) @ ( append_node @ A @ C ) )
= ( prefix_node @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_same__prefix__prefix) ).
thf(1373,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( prefix_node @ ( append_node @ A @ B ) @ ( append_node @ A @ C ) )
= ( prefix_node @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(173,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( A
= ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_list_Oexhaust__sel) ).
thf(1040,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( A
= ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(20,axiom,
! [A: list_node > $o,B: list_node] :
( ! [C: node,D: list_node] :
( ! [E: node,F: list_node] :
( ( D
= ( cons_node @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( ( A @ nil_node )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_min__list_Oinduct) ).
thf(314,plain,
! [A: list_node > $o,B: list_node] :
( ! [C: node,D: list_node] :
( ! [E: node,F: list_node] :
( ( D
= ( cons_node @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( ( A @ nil_node )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(315,plain,
! [A: list_node > $o] :
( ! [B: node,C: list_node] :
( ( ? [D: node,E: list_node] :
( C
= ( cons_node @ D @ E ) )
=> ( A @ C ) )
=> ( A @ ( cons_node @ B @ C ) ) )
=> ( ( A @ nil_node )
=> ! [B: list_node] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[314]) ).
thf(316,plain,
! [D: list_node,C: list_node,B: node,A: list_node > $o] :
( ( ( ( sk21 @ A )
!= ( cons_node @ B @ C ) )
| ( A @ ( sk21 @ A ) )
| ~ ( A @ nil_node )
| ( A @ D ) )
& ( ~ ( A @ ( cons_node @ ( sk20 @ A ) @ ( sk21 @ A ) ) )
| ~ ( A @ nil_node )
| ( A @ D ) ) ),
inference(cnf,[status(esa)],[315]) ).
thf(317,plain,
! [D: list_node,C: list_node,B: node,A: list_node > $o] :
( ( ( sk21 @ A )
!= ( cons_node @ B @ C ) )
| ( A @ ( sk21 @ A ) )
| ~ ( A @ nil_node )
| ( A @ D ) ),
inference(cnfConj,[status(thm)],[316]) ).
thf(321,plain,
! [D: list_node,C: list_node,B: node,A: list_node > $o] :
( ( ( sk21 @ A )
!= ( cons_node @ B @ C ) )
| ( A @ ( sk21 @ A ) )
| ~ ( A @ nil_node )
| ( A @ D ) ),
inference(lifteq,[status(thm)],[317]) ).
thf(192,axiom,
! [A: list_node,B: list_node,C: node] :
( ( A != nil_node )
=> ( ( ( append_node @ B @ A )
= ( cons_node @ C @ nil_node ) )
= ( ( B = nil_node )
& ( A
= ( cons_node @ C @ nil_node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_list__se__match_I2_J) ).
thf(1136,plain,
! [A: list_node,B: list_node,C: node] :
( ( A != nil_node )
=> ( ( ( append_node @ B @ A )
= ( cons_node @ C @ nil_node ) )
= ( ( B = nil_node )
& ( A
= ( cons_node @ C @ nil_node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(131,axiom,
! [A: node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ( ( cons_node @ A @ B )
= C )
=> ( ( D
= ( append_node @ B @ E ) )
=> ( ( cons_node @ A @ D )
= ( append_node @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Cons__eq__appendI) ).
thf(834,plain,
! [A: node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ( ( cons_node @ A @ B )
= C )
=> ( ( D
= ( append_node @ B @ E ) )
=> ( ( cons_node @ A @ D )
= ( append_node @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(345,plain,
! [A: list_node] :
( ( A != nil_node )
=> ! [B: list_node > $o] :
( ! [C: node] : ( B @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( D != nil_node )
=> ( ( B @ D )
=> ( B @ ( cons_node @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(miniscope,[status(thm)],[344]) ).
thf(346,plain,
! [B: list_node > $o,A: list_node] :
( ( ( A = nil_node )
| ~ ( B @ ( cons_node @ ( sk23 @ B @ A ) @ nil_node ) )
| ( ( sk25 @ B @ A )
!= nil_node )
| ( B @ A ) )
& ( ( A = nil_node )
| ~ ( B @ ( cons_node @ ( sk23 @ B @ A ) @ nil_node ) )
| ( B @ ( sk25 @ B @ A ) )
| ( B @ A ) )
& ( ( A = nil_node )
| ~ ( B @ ( cons_node @ ( sk23 @ B @ A ) @ nil_node ) )
| ~ ( B @ ( cons_node @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) )
| ( B @ A ) ) ),
inference(cnf,[status(esa)],[345]) ).
thf(348,plain,
! [B: list_node > $o,A: list_node] :
( ( A = nil_node )
| ~ ( B @ ( cons_node @ ( sk23 @ B @ A ) @ nil_node ) )
| ( B @ ( sk25 @ B @ A ) )
| ( B @ A ) ),
inference(cnfConj,[status(thm)],[346]) ).
thf(353,plain,
! [B: list_node > $o,A: list_node] :
( ( A = nil_node )
| ~ ( B @ ( cons_node @ ( sk23 @ B @ A ) @ nil_node ) )
| ( B @ ( sk25 @ B @ A ) )
| ( B @ A ) ),
inference(lifteq,[status(thm)],[348]) ).
thf(151,axiom,
! [A: g,B: node,C: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ B @ C ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ B @ nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_old_Opath__hd) ).
thf(966,plain,
! [A: g,B: node,C: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ B @ C ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ B @ nil_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(81,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ ( cons_node @ D @ E ) @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ nil_node @ ( cons_node @ D @ E ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ G )
=> ( A @ ( cons_node @ D @ E ) @ ( cons_node @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_list__induct2_H) ).
thf(602,plain,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ ( cons_node @ D @ E ) @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ nil_node @ ( cons_node @ D @ E ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ G )
=> ( A @ ( cons_node @ D @ E ) @ ( cons_node @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(85,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_neq__NilE) ).
thf(634,plain,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(255,axiom,
! [A: node,B: list_node,C: list_node,D: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( member_node @ A @ ( set_node2 @ ( tl_node @ ( append_node @ C @ ( cons_node @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_old_Oelem__set__implies__elem__tl__app__cons) ).
thf(1447,plain,
! [A: node,B: list_node,C: list_node,D: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( member_node @ A @ ( set_node2 @ ( tl_node @ ( append_node @ C @ ( cons_node @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(186,axiom,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rs__props_I3_J) ).
thf(1119,plain,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(5230,plain,
! [A: list_node] :
( ( n != m )
| ( A != sk176 )
| ( ( append_node @ A @ nil_node )
!= ( append_node @ ns @ ( tl_node @ ri ) ) ) ),
inference(paramod_ordered,[status(thm)],[1187,2031]) ).
thf(5246,plain,
( ( n != m )
| ( sk176 != ns )
| ( ( tl_node @ ri )
!= nil_node ) ),
inference(simp,[status(thm)],[5230]) ).
thf(48,axiom,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_suffix__bot_Obot_Oextremum) ).
thf(428,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1527,plain,
( ( ms != nil_node )
| ( ( butlast_node @ sk176 )
!= ( butlast_node @ nil_node ) ) ),
inference(simp,[status(thm)],[1526]) ).
thf(4475,plain,
( ( ms != nil_node )
| ( ( butlast_node @ sk176 )
!= nil_node ) ),
inference(rewrite,[status(thm)],[1527,368]) ).
thf(33,axiom,
! [A: list_node] : ( prefix_node @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_prefix__order_Odual__order_Orefl) ).
thf(373,plain,
! [A: list_node] : ( prefix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(374,plain,
! [A: list_node] : ( prefix_node @ A @ A ),
inference(cnf,[status(esa)],[373]) ).
thf(10214,plain,
! [C: list_node,B: list_node,A: list_node] :
( ~ $true
| ( ord_less_eq_set_node @ ( set_node2 @ B ) @ ( set_node2 @ C ) )
| ( ( prefix_node @ A @ A )
!= ( prefix_node @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[374,313]) ).
thf(10215,plain,
! [C: list_node,B: list_node,A: list_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ B ) @ ( set_node2 @ C ) )
| ( ( prefix_node @ A @ A )
!= ( prefix_node @ B @ C ) ) ),
inference(simp,[status(thm)],[10214]) ).
thf(10216,plain,
! [A: list_node] : ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ A ) ),
inference(pattern_uni,[status(thm)],[10215:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(176,axiom,
! [A: list_node,B: list_node,C: node,D: list_node] :
( ( ( append_node @ A @ B )
= ( cons_node @ C @ D ) )
=> ( ( ( A = nil_node )
=> ( B
!= ( cons_node @ C @ D ) ) )
=> ~ ! [E: list_node] :
( ( A
= ( cons_node @ C @ E ) )
=> ( ( append_node @ E @ B )
!= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_list__append__eq__Cons__cases) ).
thf(1074,plain,
! [A: list_node,B: list_node,C: node,D: list_node] :
( ( ( append_node @ A @ B )
= ( cons_node @ C @ D ) )
=> ( ( ( A = nil_node )
=> ( B
!= ( cons_node @ C @ D ) ) )
=> ~ ! [E: list_node] :
( ( A
= ( cons_node @ C @ E ) )
=> ( ( append_node @ E @ B )
!= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(12,axiom,
! [A: list_node] :
( ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) )
=> ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_min__list_Ocases) ).
thf(292,plain,
! [A: list_node] :
( ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) )
=> ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(205,axiom,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_append__Nil) ).
thf(1206,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(121,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_old_Opath2__hd__in___092_060alpha_062n) ).
thf(793,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(223,axiom,
! [A: node,B: node,C: list_node,D: node,E: node,F: list_node] :
( ( ( cons_node @ A @ ( cons_node @ B @ nil_node ) )
= ( append_node @ C @ ( cons_node @ D @ ( cons_node @ E @ F ) ) ) )
= ( ( C = nil_node )
& ( A = D )
& ( B = E )
& ( F = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_list__ee__eq__leel_I1_J) ).
thf(1306,plain,
! [A: node,B: node,C: list_node,D: node,E: node,F: list_node] :
( ( ( cons_node @ A @ ( cons_node @ B @ nil_node ) )
= ( append_node @ C @ ( cons_node @ D @ ( cons_node @ E @ F ) ) ) )
= ( ( C = nil_node )
& ( A = D )
& ( B = E )
& ( F = nil_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(203,axiom,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( B != nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_old_Opath__not__Nil) ).
thf(1199,plain,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( B != nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(6,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
=> ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_suffix__bot_Obot_Oextremum__uniqueI) ).
thf(270,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
=> ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(66,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ C @ A )
=> ( suffix_node @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_suffix__order_Odual__order_Otrans) ).
thf(529,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ C @ A )
=> ( suffix_node @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(24,axiom,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ? [B: list_val] :
( ( set_val2 @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_finite__list) ).
thf(334,plain,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ? [B: list_val] :
( ( set_val2 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(208,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ nil_node @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ G )
=> ( A @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_rev__induct2_H) ).
thf(1223,plain,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ nil_node @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ G )
=> ( A @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(109,axiom,
! [A: g,B: node,C: list_node,D: node,E: node > list_node > node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( E @ B @ ( cons_node @ B @ nil_node ) @ B ) )
=> ( ! [F: list_node,G: node,H: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G )
=> ( ( E @ B @ F @ G )
=> ( ( member_node @ G @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ H ) ) )
=> ( E @ B @ ( append_node @ F @ ( cons_node @ H @ nil_node ) ) @ H ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_old_Opath2__rev__induct) ).
thf(746,plain,
! [A: g,B: node,C: list_node,D: node,E: node > list_node > node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( E @ B @ ( cons_node @ B @ nil_node ) @ B ) )
=> ( ! [F: list_node,G: node,H: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G )
=> ( ( E @ B @ F @ G )
=> ( ( member_node @ G @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ H ) ) )
=> ( E @ B @ ( append_node @ F @ ( cons_node @ H @ nil_node ) ) @ H ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(234,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ ( append_node @ C @ B ) )
= ( suffix_node @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_same__suffix__suffix) ).
thf(1343,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ ( append_node @ C @ B ) )
= ( suffix_node @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(128,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ B @ ( cons_node @ A @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_old_Oempty__path) ).
thf(820,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ B @ ( cons_node @ A @ nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(429,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(cnf,[status(esa)],[428]) ).
thf(211,axiom,
! [A: list_node,B: node,C: list_node,D: node] :
( ( ( append_node @ A @ ( cons_node @ B @ C ) )
= ( cons_node @ D @ nil_node ) )
= ( ( A = nil_node )
& ( B = D )
& ( C = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_list__e__eq__lel_I2_J) ).
thf(1238,plain,
! [A: list_node,B: node,C: list_node,D: node] :
( ( ( append_node @ A @ ( cons_node @ B @ C ) )
= ( cons_node @ D @ nil_node ) )
= ( ( A = nil_node )
& ( B = D )
& ( C = nil_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(3436,plain,
! [B: list_node,A: set_node] :
( ( finite_finite_node
@ ( collect_node
@ ^ [C: node] :
( member_node @ C
@ ( collect_node
@ ^ [D: node] : ( member_node @ D @ A ) ) ) ) )
| ( A
!= ( set_node2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[419,3429]) ).
thf(3437,plain,
! [A: list_node] :
( finite_finite_node
@ ( collect_node
@ ^ [B: node] :
( member_node @ B
@ ( collect_node
@ ^ [C: node] : ( member_node @ C @ ( set_node2 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3436:[bind(A,$thf( set_node2 @ C )),bind(B,$thf( C ))]]) ).
thf(3471,plain,
! [A: list_node] :
( finite_finite_node
@ ( collect_node
@ ^ [B: node] :
( member_node @ B
@ ( collect_node
@ ^ [C: node] : ( member_node @ C @ ( set_node2 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[3437]) ).
thf(166,axiom,
! [A: list_node,B: node] :
( ( A != nil_node )
=> ( ( member_node @ B @ ( set_node2 @ ( tl_node @ A ) ) )
=> ( member_node @ B @ ( set_node2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_list_Oset__sel_I2_J) ).
thf(1021,plain,
! [A: list_node,B: node] :
( ( A != nil_node )
=> ( ( member_node @ B @ ( set_node2 @ ( tl_node @ A ) ) )
=> ( member_node @ B @ ( set_node2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(116,axiom,
! [A: list_node,B: node] :
( ( butlast_node @ ( append_node @ A @ ( cons_node @ B @ nil_node ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_butlast__snoc) ).
thf(778,plain,
! [A: list_node,B: node] :
( ( butlast_node @ ( append_node @ A @ ( cons_node @ B @ nil_node ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(252,axiom,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ A @ B ) )
= ( B = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_self__append__conv) ).
thf(1423,plain,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ A @ B ) )
= ( B = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(83,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_suffix__bot_Obot_Oextremum__unique) ).
thf(625,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(95,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( B = C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_suffix__order_Oord__le__eq__trans) ).
thf(665,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( B = C )
=> ( suffix_node @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(80,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ F )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ F )
=> ( A @ E @ ( cons_node @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_list__2pre__induct) ).
thf(583,plain,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ F )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ F )
=> ( A @ E @ ( cons_node @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(341,plain,
! [B: list_node,A: list_node] :
( ( A != B )
| ( suffix_node @ A @ B ) ),
inference(cnf,[status(esa)],[340]) ).
thf(342,plain,
! [B: list_node,A: list_node] :
( ( A != B )
| ( suffix_node @ A @ B ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(343,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(simp,[status(thm)],[342]) ).
thf(271,plain,
! [A: list_node] :
( ~ ( suffix_node @ A @ nil_node )
| ( A = nil_node ) ),
inference(cnf,[status(esa)],[270]) ).
thf(272,plain,
! [A: list_node] :
( ( A = nil_node )
| ~ ( suffix_node @ A @ nil_node ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(1533,plain,
! [A: list_node] :
( ~ ( suffix_node @ A @ nil_node )
| ( nil_node != nil_node )
| ( sk176 != nil_node )
| ( A != ms ) ),
inference(paramod_ordered,[status(thm)],[272,1529]) ).
thf(1534,plain,
! [A: list_node] :
( ~ ( suffix_node @ A @ nil_node )
| ( sk176 != nil_node )
| ( A != ms ) ),
inference(simp,[status(thm)],[1533]) ).
thf(1535,plain,
( ~ ( suffix_node @ ms @ nil_node )
| ( sk176 != nil_node ) ),
inference(pattern_uni,[status(thm)],[1534:[bind(A,$thf( ms ))]]) ).
thf(1688,plain,
! [A: list_node] :
( ~ ( suffix_node @ A @ nil_node )
| ~ ( suffix_node @ ms @ nil_node )
| ( nil_node != nil_node )
| ( A != sk176 ) ),
inference(paramod_ordered,[status(thm)],[272,1535]) ).
thf(1689,plain,
! [A: list_node] :
( ~ ( suffix_node @ A @ nil_node )
| ~ ( suffix_node @ ms @ nil_node )
| ( A != sk176 ) ),
inference(simp,[status(thm)],[1688]) ).
thf(1690,plain,
( ~ ( suffix_node @ sk176 @ nil_node )
| ~ ( suffix_node @ ms @ nil_node ) ),
inference(pattern_uni,[status(thm)],[1689:[bind(A,$thf( sk176 ))]]) ).
thf(7775,plain,
( ~ ( suffix_node @ ms @ nil_node )
| ( ( suffix_node @ sk176 @ nil_node )
!= ( suffix_node @ ms @ nil_node ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1690]) ).
thf(7779,plain,
( ~ ( suffix_node @ ms @ nil_node )
| ( sk176 != ms )
| ( nil_node != nil_node ) ),
inference(simp,[status(thm)],[7775]) ).
thf(7842,plain,
( ~ ( suffix_node @ ms @ nil_node )
| ( sk176 != ms ) ),
inference(simp,[status(thm)],[7779]) ).
thf(7865,plain,
! [A: list_node] :
( ~ $true
| ( sk176 != ms )
| ( ( suffix_node @ A @ A )
!= ( suffix_node @ ms @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[343,7842]) ).
thf(7866,plain,
! [A: list_node] :
( ( sk176 != ms )
| ( ( suffix_node @ A @ A )
!= ( suffix_node @ ms @ nil_node ) ) ),
inference(simp,[status(thm)],[7865]) ).
thf(7913,plain,
! [A: list_node] :
( ( sk176 != ms )
| ( A != ms )
| ( A != nil_node ) ),
inference(simp,[status(thm)],[7866]) ).
thf(7934,plain,
( ( sk176 != ms )
| ( ms != nil_node ) ),
inference(simp,[status(thm)],[7913]) ).
thf(110,axiom,
! [A: list_node,B: node,C: list_node] :
( ( ( butlast_node @ A )
= ( cons_node @ B @ C ) )
= ( ? [D: node] :
( A
= ( cons_node @ B @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_butlast__eq__cons__conv) ).
thf(757,plain,
! [A: list_node,B: node,C: list_node] :
( ( ( butlast_node @ A )
= ( cons_node @ B @ C ) )
= ( ? [D: node] :
( A
= ( cons_node @ B @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(189,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_list_Ocollapse) ).
thf(1128,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(248,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_split__list__first) ).
thf(1392,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(319,plain,
! [C: list_node,B: list_node,A: node] :
( ( ( sk21 @ ( (=) @ list_node @ nil_node ) )
!= ( cons_node @ A @ B ) )
| ( nil_node
= ( sk21 @ ( (=) @ list_node @ nil_node ) ) )
| ( nil_node != nil_node )
| ( nil_node = C ) ),
inference(replace_leibeq,[status(thm)],[317:[bind(A,$thf( (=) @ list_node @ nil_node ))]]) ).
thf(323,plain,
! [C: list_node,B: list_node,A: node] :
( ( ( cons_node @ A @ B )
!= ( sk21 @ ( (=) @ list_node @ nil_node ) ) )
| ( ( sk21 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node != nil_node )
| ( nil_node = C ) ),
inference(lifteq,[status(thm)],[319]) ).
thf(324,plain,
! [C: list_node,B: list_node,A: node] :
( ( ( cons_node @ A @ B )
!= ( sk21 @ ( (=) @ list_node @ nil_node ) ) )
| ( ( sk21 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node = C ) ),
inference(simp,[status(thm)],[323]) ).
thf(162,axiom,
member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rs_H__props_I3_J) ).
thf(1012,plain,
member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(21,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_suffix__order_Oantisym__conv) ).
thf(327,plain,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(328,plain,
! [B: list_node,A: list_node] :
( ~ ( suffix_node @ A @ B )
| ( ( suffix_node @ B @ A )
= ( B = A ) ) ),
inference(cnf,[status(esa)],[327]) ).
thf(329,plain,
! [B: list_node,A: list_node] :
( ( ( suffix_node @ B @ A )
= ( B = A ) )
| ~ ( suffix_node @ A @ B ) ),
inference(lifteq,[status(thm)],[328]) ).
thf(197,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ! [F: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
=> ! [G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D )
=> ( C
!= ( append_node @ ( butlast_node @ F ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_old_Opath2__split__ex_H) ).
thf(1178,plain,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ! [F: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
=> ! [G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D )
=> ( C
!= ( append_node @ ( butlast_node @ F ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(98,axiom,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062) ).
thf(682,plain,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(201,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_assms_I8_J) ).
thf(1195,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(78,axiom,
! [A: node,B: list_node,C: list_node] :
( ( suffix_node @ ( cons_node @ A @ B ) @ C )
=> ( suffix_node @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_suffix__ConsD) ).
thf(578,plain,
! [A: node,B: list_node,C: list_node] :
( ( suffix_node @ ( cons_node @ A @ B ) @ C )
=> ( suffix_node @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(209,axiom,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ E ) ) @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ ( cons_node @ D @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_old_Opath2__split_I2_J) ).
thf(1234,plain,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ E ) ) @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ ( cons_node @ D @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(217,axiom,
! [A: g,B: node,C: list_node,D: node,E: node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ? [F: node] :
( ( member_node @ F @ ( set_node2 @ C ) )
& ( E @ F ) )
=> ~ ! [F: node,G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D )
=> ( ( E @ F )
=> ( ! [H: node] :
( ( member_node @ H @ ( set_node2 @ ( tl_node @ G ) ) )
=> ~ ( E @ H ) )
=> ~ ( suffix_node @ G @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_old_Opath2__split__last__prop) ).
thf(1259,plain,
! [A: g,B: node,C: list_node,D: node,E: node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ? [F: node] :
( ( member_node @ F @ ( set_node2 @ C ) )
& ( E @ F ) )
=> ~ ! [F: node,G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D )
=> ( ( E @ F )
=> ( ! [H: node] :
( ( member_node @ H @ ( set_node2 @ ( tl_node @ G ) ) )
=> ~ ( E @ H ) )
=> ~ ( suffix_node @ G @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(187,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( append_node @ ( append_node @ A @ B ) @ C )
= ( append_node @ A @ ( append_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_append_Oassoc) ).
thf(1121,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( append_node @ ( append_node @ A @ B ) @ C )
= ( append_node @ A @ ( append_node @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(160,axiom,
! [A: g,B: node,C: node] :
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ nil_node @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_old_Opath2__not__Nil2) ).
thf(1006,plain,
! [A: g,B: node,C: node] :
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ nil_node @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(45,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( prefix_node @ ( cons_node @ A @ B ) @ ( cons_node @ C @ D ) )
= ( ( A = C )
& ( prefix_node @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_Cons__prefix__Cons) ).
thf(420,plain,
! [A: node,B: list_node,C: node,D: list_node] :
( ( prefix_node @ ( cons_node @ A @ B ) @ ( cons_node @ C @ D ) )
= ( ( A = C )
& ( prefix_node @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(62,axiom,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_Nil__suffix) ).
thf(499,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(168,axiom,
r != phi_r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False) ).
thf(1028,plain,
r != phi_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(59,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
& ( prefix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_prefix__order_Oeq__iff) ).
thf(487,plain,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
& ( prefix_node @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(488,plain,
( ( ^ [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
& ( prefix_node @ B @ A ) ) )
= ( (=) @ list_node ) ),
inference(lifteq,[status(thm)],[487]) ).
thf(25,axiom,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mem__Collect__eq) ).
thf(337,plain,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(338,plain,
! [B: node > $o,A: node] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
inference(cnf,[status(esa)],[337]) ).
thf(339,plain,
! [B: node > $o,A: node] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
inference(lifteq,[status(thm)],[338]) ).
thf(58,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_list_Oinducts) ).
thf(476,plain,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(88,axiom,
! [A: node,B: list_node] :
( ( cons_node @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_not__Cons__self2) ).
thf(642,plain,
! [A: node,B: list_node] :
( ( cons_node @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(164,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
= ( ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_in__set__conv__decomp__first) ).
thf(1016,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
= ( ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(97,axiom,
! [A: list_node,B: list_node,C: list_node,D: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ C @ D ) )
= ( ? [E: list_node] :
( ( ( A
= ( append_node @ C @ E ) )
& ( ( append_node @ E @ B )
= D ) )
| ( ( ( append_node @ A @ E )
= C )
& ( B
= ( append_node @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_append__eq__append__conv2) ).
thf(679,plain,
! [A: list_node,B: list_node,C: list_node,D: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ C @ D ) )
= ( ? [E: list_node] :
( ( ( A
= ( append_node @ C @ E ) )
& ( ( append_node @ E @ B )
= D ) )
| ( ( ( append_node @ A @ E )
= C )
& ( B
= ( append_node @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(102,axiom,
! [A: list_node,B: list_node] :
( ( A != nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_hd__append2) ).
thf(701,plain,
! [A: list_node,B: list_node] :
( ( A != nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(258,axiom,
! [A: list_node,B: node,C: list_node,D: node] :
( ( ( append_node @ A @ ( cons_node @ B @ nil_node ) )
= ( append_node @ C @ ( cons_node @ D @ nil_node ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_append1__eq__conv) ).
thf(1456,plain,
! [A: list_node,B: node,C: list_node,D: node] :
( ( ( append_node @ A @ ( cons_node @ B @ nil_node ) )
= ( append_node @ C @ ( cons_node @ D @ nil_node ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(200,axiom,
! [A: g,B: node] :
( ( ( graph_272749361_edgeD @ inEdges @ A @ B )
!= nil_node )
=> ( ( invar @ A )
=> ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_old_Osuccessor__in___092_060alpha_062n) ).
thf(1192,plain,
! [A: g,B: node] :
( ( ( graph_272749361_edgeD @ inEdges @ A @ B )
!= nil_node )
=> ( ( invar @ A )
=> ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(213,axiom,
! [A: list_node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ( ( append_node @ A @ B )
= C )
=> ( ( D
= ( append_node @ B @ E ) )
=> ( ( append_node @ A @ D )
= ( append_node @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_append__eq__appendI) ).
thf(1246,plain,
! [A: list_node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ( ( append_node @ A @ B )
= C )
=> ( ( D
= ( append_node @ B @ E ) )
=> ( ( append_node @ A @ D )
= ( append_node @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1525,plain,
( ( butlast_node @ sk176 )
!= ms ),
inference(simp,[status(thm)],[1478]) ).
thf(1528,plain,
( ( ( set_node2 @ ms )
!= ( set_node2 @ nil_node ) )
| ( sk176 != nil_node ) ),
inference(simp,[status(thm)],[1526]) ).
thf(13626,plain,
! [A: list_node] :
( ( ( set_node2 @ A )
!= ( set_node2 @ nil_node ) )
| ( sk176 != nil_node )
| ( ( set_node2 @ ( sk19 @ ( set_node2 @ A ) ) )
!= ( set_node2 @ ms ) ) ),
inference(paramod_ordered,[status(thm)],[9133,1528]) ).
thf(13655,plain,
! [A: list_node] :
( ( A != nil_node )
| ( sk176 != nil_node )
| ( ( sk19 @ ( set_node2 @ A ) )
!= ms ) ),
inference(simp,[status(thm)],[13626]) ).
thf(13699,plain,
( ( sk176 != nil_node )
| ( ( sk19 @ ( set_node2 @ nil_node ) )
!= ms ) ),
inference(simp,[status(thm)],[13655]) ).
thf(64,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( A @ E )
=> ( ( A @ ( cons_node @ D @ E ) )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_induct__list012) ).
thf(503,plain,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( A @ E )
=> ( ( A @ ( cons_node @ D @ E ) )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(18,axiom,
! [A: list_node,B: node,C: list_node] :
( ( suffix_node @ A @ ( cons_node @ B @ C ) )
= ( ( A
= ( cons_node @ B @ C ) )
| ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_suffix__Cons) ).
thf(309,plain,
! [A: list_node,B: node,C: list_node] :
( ( suffix_node @ A @ ( cons_node @ B @ C ) )
= ( ( A
= ( cons_node @ B @ C ) )
| ( suffix_node @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(310,plain,
! [C: list_node,B: node,A: list_node] :
( ( suffix_node @ A @ ( cons_node @ B @ C ) )
= ( ( A
= ( cons_node @ B @ C ) )
| ( suffix_node @ A @ C ) ) ),
inference(cnf,[status(esa)],[309]) ).
thf(311,plain,
! [C: list_node,B: node,A: list_node] :
( ( suffix_node @ A @ ( cons_node @ B @ C ) )
= ( ( A
= ( cons_node @ B @ C ) )
| ( suffix_node @ A @ C ) ) ),
inference(lifteq,[status(thm)],[310]) ).
thf(171,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd_node @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_old_Opath2__forget__hd) ).
thf(1035,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd_node @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(115,axiom,
! [A: g,B: node,C: node,D: list_node,E: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ B @ ( cons_node @ C @ D ) ) )
=> ( ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ C @ D ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ C @ E ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ B @ ( cons_node @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_old_Opath__by__tail) ).
thf(773,plain,
! [A: g,B: node,C: node,D: list_node,E: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ B @ ( cons_node @ C @ D ) ) )
=> ( ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ C @ D ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ C @ E ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ B @ ( cons_node @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(148,axiom,
( rs2
= ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_rs__def) ).
thf(926,plain,
( rs2
= ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(228,axiom,
! [A: g,B: list_node,C: node,D: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ D ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_old_Opath__split_I2_J) ).
thf(1318,plain,
! [A: g,B: list_node,C: node,D: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ D ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(212,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_split__list__last) ).
thf(1241,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(4,axiom,
! [A: val > $o,B: val > $o] :
( ! [C: val] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_val @ A )
= ( collect_val @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Collect__cong) ).
thf(264,plain,
! [A: val > $o,B: val > $o] :
( ! [C: val] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_val @ A )
= ( collect_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(265,plain,
! [B: val > $o,A: val > $o] :
( ( ( A @ ( sk2 @ B @ A ) )
!= ( B @ ( sk2 @ B @ A ) ) )
| ( ( collect_val @ A )
= ( collect_val @ B ) ) ),
inference(cnf,[status(esa)],[264]) ).
thf(266,plain,
! [B: val > $o,A: val > $o] :
( ( ( A @ ( sk2 @ B @ A ) )
!= ( B @ ( sk2 @ B @ A ) ) )
| ( ( collect_val @ A )
= ( collect_val @ B ) ) ),
inference(lifteq,[status(thm)],[265]) ).
thf(1465,plain,
( ~ ( member_node @ i @ ( set_node2 @ nil_node ) )
| ( ( butlast_node @ sk176 )
!= ( butlast_node @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[368,1102]) ).
thf(1466,plain,
( ~ ( member_node @ i @ ( set_node2 @ nil_node ) )
| ( sk176 != nil_node ) ),
inference(simp,[status(thm)],[1465]) ).
thf(73,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( ! [C: list_node] :
( B
!= ( cons_node @ A @ C ) )
=> ~ ! [C: node,D: list_node] :
( ( B
= ( cons_node @ C @ D ) )
=> ~ ( member_node @ A @ ( set_node2 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_list_Oset__cases) ).
thf(558,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( ! [C: list_node] :
( B
!= ( cons_node @ A @ C ) )
=> ~ ! [C: node,D: list_node] :
( ( B
= ( cons_node @ C @ D ) )
=> ~ ( member_node @ A @ ( set_node2 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(94,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_suffix__order_Oorder_Otrans) ).
thf(662,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(141,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_split__list__prop) ).
thf(888,plain,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(214,axiom,
! [A: list_node] :
( ( ( tl_node @ A )
= nil_node )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_tl__Nil) ).
thf(1251,plain,
! [A: list_node] :
( ( ( tl_node @ A )
= nil_node )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(182,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_old_Opath2__tl__in___092_060alpha_062n) ).
thf(1103,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1483,plain,
( ( ms != nil_node )
| ( ms2 != nil_node ) ),
inference(simp,[status(thm)],[1480]) ).
thf(219,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ! [F: list_node,G: list_node,H: list_node] :
( ( C
= ( append_node @ F @ ( append_node @ G @ H ) ) )
=> ( ( prefix_node @ ( append_node @ F @ ( cons_node @ E @ nil_node ) ) @ C )
=> ( ( suffix_node @ ( cons_node @ E @ H ) @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ F @ ( cons_node @ E @ nil_node ) ) @ E )
=> ( ~ ( member_node @ E @ ( set_node2 @ F ) )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ E )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons_node @ E @ H ) @ D )
=> ( member_node @ E @ ( set_node2 @ H ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_old_Opath2__split__first__last) ).
thf(1273,plain,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ! [F: list_node,G: list_node,H: list_node] :
( ( C
= ( append_node @ F @ ( append_node @ G @ H ) ) )
=> ( ( prefix_node @ ( append_node @ F @ ( cons_node @ E @ nil_node ) ) @ C )
=> ( ( suffix_node @ ( cons_node @ E @ H ) @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ F @ ( cons_node @ E @ nil_node ) ) @ E )
=> ( ~ ( member_node @ E @ ( set_node2 @ F ) )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ E )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons_node @ E @ H ) @ D )
=> ( member_node @ E @ ( set_node2 @ H ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(34,axiom,
! [A: list_node,B: set_node] :
( ( A != nil_node )
=> ( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ B )
=> ( ord_less_eq_set_node @ ( set_node2 @ ( butlast_node @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_butlast__subset) ).
thf(375,plain,
! [A: list_node,B: set_node] :
( ( A != nil_node )
=> ( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ B )
=> ( ord_less_eq_set_node @ ( set_node2 @ ( butlast_node @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7247,plain,
! [A: node] :
( ~ $true
| ( ( member_node @ i @ ( set_node2 @ ( cons_node @ A @ ms ) ) )
!= ( member_node @ i @ ( set_node2 @ ( butlast_node @ sk176 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7135,1102]) ).
thf(7248,plain,
! [A: node] :
( ( member_node @ i @ ( set_node2 @ ( cons_node @ A @ ms ) ) )
!= ( member_node @ i @ ( set_node2 @ ( butlast_node @ sk176 ) ) ) ),
inference(simp,[status(thm)],[7247]) ).
thf(7274,plain,
! [A: node] :
( ( i != i )
| ( ( set_node2 @ ( cons_node @ A @ ms ) )
!= ( set_node2 @ ( butlast_node @ sk176 ) ) ) ),
inference(simp,[status(thm)],[7248]) ).
thf(7291,plain,
! [A: node] :
( ( set_node2 @ ( cons_node @ A @ ms ) )
!= ( set_node2 @ ( butlast_node @ sk176 ) ) ),
inference(simp,[status(thm)],[7274]) ).
thf(13639,plain,
! [B: node,A: list_node] :
( ( ( set_node2 @ A )
!= ( set_node2 @ ( butlast_node @ sk176 ) ) )
| ( ( set_node2 @ ( sk19 @ ( set_node2 @ A ) ) )
!= ( set_node2 @ ( cons_node @ B @ ms ) ) ) ),
inference(paramod_ordered,[status(thm)],[9133,7291]) ).
thf(13664,plain,
! [B: node,A: list_node] :
( ( A
!= ( butlast_node @ sk176 ) )
| ( ( sk19 @ ( set_node2 @ A ) )
!= ( cons_node @ B @ ms ) ) ),
inference(simp,[status(thm)],[13639]) ).
thf(13703,plain,
! [A: node] :
( ( cons_node @ A @ ms )
!= ( sk19 @ ( set_node2 @ ( butlast_node @ sk176 ) ) ) ),
inference(simp,[status(thm)],[13664]) ).
thf(42,axiom,
! [A: list_node] : ( suffix_node @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_suffix__order_Odual__order_Orefl) ).
thf(412,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(145,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_ri__props_I1_J) ).
thf(904,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(46,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_suffix__order_Oorder__trans) ).
thf(423,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(286,plain,
! [D: list_node,C: list_node,B: node > node > $o,A: ( node > node > $o ) > list_node > list_node > $o] :
( ~ ( sk7 @ A @ ( sk8 @ A ) @ ( sk10 @ A ) )
| ( A @ ( sk7 @ A ) @ ( sk9 @ A ) @ ( cons_node @ ( sk10 @ A ) @ ( sk11 @ A ) ) )
| ~ ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ nil_node )
| ~ ( A @ ( sk14 @ A ) @ nil_node @ ( cons_node @ ( sk15 @ A ) @ ( sk16 @ A ) ) )
| ( A @ B @ C @ D ) ),
inference(cnfConj,[status(thm)],[285]) ).
thf(12880,plain,
! [B: list_node,A: node] :
( ( ( tl_node @ nil_node )
= ( butlast_node @ ( tl_node @ B ) ) )
| ( ( butlast_node @ ( tl_node @ ( cons_node @ A @ nil_node ) ) )
!= ( butlast_node @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12879,1317]) ).
thf(12881,plain,
! [A: node] :
( ( tl_node @ nil_node )
= ( butlast_node @ ( tl_node @ ( tl_node @ ( cons_node @ A @ nil_node ) ) ) ) ),
inference(pattern_uni,[status(thm)],[12880:[bind(A,$thf( D )),bind(B,$thf( tl_node @ ( cons_node @ D @ nil_node ) ))]]) ).
thf(12946,plain,
! [A: node] :
( ( tl_node @ nil_node )
= ( butlast_node @ ( tl_node @ ( tl_node @ ( cons_node @ A @ nil_node ) ) ) ) ),
inference(simp,[status(thm)],[12881]) ).
thf(12958,plain,
! [A: node] :
( ( butlast_node @ ( tl_node @ ( tl_node @ ( cons_node @ A @ nil_node ) ) ) )
= nil_node ),
inference(rewrite,[status(thm)],[12946,1115]) ).
thf(247,axiom,
! [A: list_node,B: node,C: list_node] :
( ( ( butlast_node @ A )
= ( cons_node @ B @ C ) )
=> ~ ! [D: node] :
( A
!= ( cons_node @ B @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_butlast__eq__consE) ).
thf(1388,plain,
! [A: list_node,B: node,C: list_node] :
( ( ( butlast_node @ A )
= ( cons_node @ B @ C ) )
=> ~ ! [D: node] :
( A
!= ( cons_node @ B @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(105,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( ( tl_node @ A )
= nil_node )
=> ~ ! [B: node] :
( A
!= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_tl__obtain__elem) ).
thf(711,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( ( ( tl_node @ A )
= nil_node )
=> ~ ! [B: node] :
( A
!= ( cons_node @ B @ nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(290,plain,
! [B: list_node,A: list_node] :
( ~ ( suffix_node @ A @ B )
| ~ ( suffix_node @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[289]) ).
thf(291,plain,
! [B: list_node,A: list_node] :
( ( A = B )
| ~ ( suffix_node @ A @ B )
| ~ ( suffix_node @ B @ A ) ),
inference(lifteq,[status(thm)],[290]) ).
thf(188,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: list_node,C: node] :
( A
!= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_neq__Nil__revE) ).
thf(1124,plain,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: list_node,C: node] :
( A
!= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(36,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( A = B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_suffix__order_Oord__eq__le__trans) ).
thf(382,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( A = B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(225,axiom,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ C ) ) )
=> ( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_old_Osuccessor__is__node) ).
thf(1312,plain,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ C ) ) )
=> ( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(119,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ ( append_node @ B @ C ) )
= ( ( suffix_node @ A @ C )
| ? [D: list_node] :
( ( A
= ( append_node @ D @ C ) )
& ( suffix_node @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_suffix__append) ).
thf(787,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ ( append_node @ B @ C ) )
= ( ( suffix_node @ A @ C )
| ? [D: list_node] :
( ( A
= ( append_node @ D @ C ) )
& ( suffix_node @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(55,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ! [B: node] :
( A
!= ( cons_node @ B @ nil_node ) )
=> ~ ! [B: node,C: node,D: list_node] :
( A
!= ( cons_node @ B @ ( cons_node @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_remdups__adj_Ocases) ).
thf(466,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( ! [B: node] :
( A
!= ( cons_node @ B @ nil_node ) )
=> ~ ! [B: node,C: node,D: list_node] :
( A
!= ( cons_node @ B @ ( cons_node @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(179,axiom,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( prefix_node @ ( append_node @ E @ ( cons_node @ F @ nil_node ) ) @ C )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ E @ ( cons_node @ F @ nil_node ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_old_Opath2__prefix) ).
thf(1090,plain,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( prefix_node @ ( append_node @ E @ ( cons_node @ F @ nil_node ) ) @ C )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ E @ ( cons_node @ F @ nil_node ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(216,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_defs__finite) ).
thf(1257,plain,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1258,plain,
! [B: node,A: g] : ( finite_finite_val @ ( defs @ A @ B ) ),
inference(cnf,[status(esa)],[1257]) ).
thf(1463,plain,
( ~ ( member_node @ i @ ( set_node2 @ nil_node ) )
| ( ( butlast_node @ ms2 )
!= ( butlast_node @ nil_node ) ) ),
inference(paramod_ordered,[status(thm)],[368,393]) ).
thf(1464,plain,
( ~ ( member_node @ i @ ( set_node2 @ nil_node ) )
| ( ms2 != nil_node ) ),
inference(simp,[status(thm)],[1463]) ).
thf(239,axiom,
! [A: list_node,B: list_node] :
( ( ( A = nil_node )
= ( B = nil_node ) )
=> ( ( ( A != nil_node )
=> ( ( B != nil_node )
=> ( ( ( hd_node @ A )
= ( hd_node @ B ) )
& ( ( tl_node @ A )
= ( tl_node @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_list_Oexpand) ).
thf(1356,plain,
! [A: list_node,B: list_node] :
( ( ( A = nil_node )
= ( B = nil_node ) )
=> ( ( ( A != nil_node )
=> ( ( B != nil_node )
=> ( ( ( hd_node @ A )
= ( hd_node @ B ) )
& ( ( tl_node @ A )
= ( tl_node @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(69,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_suffix__order_Odual__order_Oantisym) ).
thf(540,plain,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(206,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ( member_node @ E @ ( set_node2 @ ( alpha_n @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_old_Opath2__in___092_060alpha_062n) ).
thf(1209,plain,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ( member_node @ E @ ( set_node2 @ ( alpha_n @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(144,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ~ ! [C: list_node,D: list_node] :
( B
!= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_in__set__list__format) ).
thf(900,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ~ ! [C: list_node,D: list_node] :
( B
!= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(130,axiom,
! [A: node,B: list_node] :
( ( A
!= ( hd_node @ B ) )
=> ( ( member_node @ A @ ( set_node2 @ B ) )
=> ( member_node @ A @ ( set_node2 @ ( tl_node @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_not__hd__in__tl) ).
thf(831,plain,
! [A: node,B: list_node] :
( ( A
!= ( hd_node @ B ) )
=> ( ( member_node @ A @ ( set_node2 @ B ) )
=> ( member_node @ A @ ( set_node2 @ ( tl_node @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(250,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ~ ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_split__list__propE) ).
thf(1408,plain,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ~ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(5231,plain,
! [A: list_node] :
( ( n != m )
| ( A != ms2 )
| ( ( append_node @ A @ nil_node )
!= ( append_node @ ns @ ( tl_node @ ri ) ) ) ),
inference(paramod_ordered,[status(thm)],[1187,1730]) ).
thf(5244,plain,
( ( n != m )
| ( ns != ms2 )
| ( ( tl_node @ ri )
!= nil_node ) ),
inference(simp,[status(thm)],[5231]) ).
thf(118,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( append_node @ ( append_node @ A @ B ) @ C )
= ( append_node @ A @ ( append_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_append__assoc) ).
thf(784,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( append_node @ ( append_node @ A @ B ) @ C )
= ( append_node @ A @ ( append_node @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(236,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= nil_node )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_append__is__Nil__conv) ).
thf(1349,plain,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= nil_node )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(156,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I7_J) ).
thf(990,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(174,axiom,
! [A: g,B: list_node,C: list_node > $o] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( ! [D: node] :
( ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( invar @ A )
=> ( C @ ( cons_node @ D @ nil_node ) ) ) )
=> ( ! [D: list_node,E: node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ D )
=> ( ( C @ D )
=> ( ( member_node @ E @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ D ) ) ) )
=> ( C @ ( cons_node @ E @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_old_Opath_Oinducts) ).
thf(1043,plain,
! [A: g,B: list_node,C: list_node > $o] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( ! [D: node] :
( ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( invar @ A )
=> ( C @ ( cons_node @ D @ nil_node ) ) ) )
=> ( ! [D: list_node,E: node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ D )
=> ( ( C @ D )
=> ( ( member_node @ E @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ D ) ) ) )
=> ( C @ ( cons_node @ E @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(243,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ B )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_same__suffix__nil) ).
thf(1376,plain,
! [A: list_node,B: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ B )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(113,axiom,
! [A: list_node] :
( ( nil_node
= ( tl_node @ A ) )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Nil__tl) ).
thf(764,plain,
! [A: list_node] :
( ( nil_node
= ( tl_node @ A ) )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(153,axiom,
! [A: node,B: list_node,C: list_node] :
( ( ( member_node @ A @ ( set_node2 @ ( butlast_node @ B ) ) )
| ( member_node @ A @ ( set_node2 @ ( butlast_node @ C ) ) ) )
=> ( member_node @ A @ ( set_node2 @ ( butlast_node @ ( append_node @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_in__set__butlast__appendI) ).
thf(979,plain,
! [A: node,B: list_node,C: list_node] :
( ( ( member_node @ A @ ( set_node2 @ ( butlast_node @ B ) ) )
| ( member_node @ A @ ( set_node2 @ ( butlast_node @ C ) ) ) )
=> ( member_node @ A @ ( set_node2 @ ( butlast_node @ ( append_node @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(194,axiom,
! [A: list_node,B: list_node,C: node,D: list_node] :
( ( ( append_node @ A @ B )
= ( cons_node @ C @ D ) )
= ( ( ( A = nil_node )
& ( B
= ( cons_node @ C @ D ) ) )
| ? [E: list_node] :
( ( A
= ( cons_node @ C @ E ) )
& ( ( append_node @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_append__eq__Cons__conv) ).
thf(1144,plain,
! [A: list_node,B: list_node,C: node,D: list_node] :
( ( ( append_node @ A @ B )
= ( cons_node @ C @ D ) )
= ( ( ( A = nil_node )
& ( B
= ( cons_node @ C @ D ) ) )
| ? [E: list_node] :
( ( A
= ( cons_node @ C @ E ) )
& ( ( append_node @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(13576,plain,
! [B: node,A: list_node] :
( ( ( set_node2 @ A )
!= ( set_node2 @ ( butlast_node @ ms2 ) ) )
| ( ( set_node2 @ ( sk19 @ ( set_node2 @ A ) ) )
!= ( set_node2 @ ( cons_node @ B @ ms ) ) ) ),
inference(paramod_ordered,[status(thm)],[9133,7285]) ).
thf(13667,plain,
! [B: node,A: list_node] :
( ( A
!= ( butlast_node @ ms2 ) )
| ( ( sk19 @ ( set_node2 @ A ) )
!= ( cons_node @ B @ ms ) ) ),
inference(simp,[status(thm)],[13576]) ).
thf(13705,plain,
! [A: node] :
( ( cons_node @ A @ ms )
!= ( sk19 @ ( set_node2 @ ( butlast_node @ ms2 ) ) ) ),
inference(simp,[status(thm)],[13667]) ).
thf(37,axiom,
! [A: ( node > node > $o ) > list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: node > node > $o] : ( A @ E @ nil_node @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node,H: node,I: list_node] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons_node @ F @ G ) @ ( cons_node @ H @ I ) ) )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ ( cons_node @ F @ G ) @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ nil_node @ ( cons_node @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_list__all__zip_Oinduct) ).
thf(387,plain,
! [A: ( node > node > $o ) > list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: node > node > $o] : ( A @ E @ nil_node @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node,H: node,I: list_node] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons_node @ F @ G ) @ ( cons_node @ H @ I ) ) )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ ( cons_node @ F @ G ) @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ nil_node @ ( cons_node @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(68,axiom,
! [A: list_node,B: node,C: list_node] :
( ( A
= ( cons_node @ B @ C ) )
=> ( A != nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_list_OdiscI) ).
thf(535,plain,
! [A: list_node,B: node,C: list_node] :
( ( A
= ( cons_node @ B @ C ) )
=> ( A != nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(127,axiom,
! [A: list_node,B: list_node] :
( ( A != nil_node )
=> ( ( tl_node @ ( append_node @ A @ B ) )
= ( append_node @ ( tl_node @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_tl__append2) ).
thf(816,plain,
! [A: list_node,B: list_node] :
( ( A != nil_node )
=> ( ( tl_node @ ( append_node @ A @ B ) )
= ( append_node @ ( tl_node @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(4450,plain,
! [A: list_node] :
( ( n != m )
| ( A != sk176 )
| ( ( append_node @ nil_node @ A )
!= ( append_node @ ns @ ( tl_node @ ri ) ) ) ),
inference(paramod_ordered,[status(thm)],[881,2031]) ).
thf(4462,plain,
( ( n != m )
| ( ns != nil_node )
| ( ( tl_node @ ri )
!= sk176 ) ),
inference(simp,[status(thm)],[4450]) ).
thf(196,axiom,
! [A: list_node,B: list_node,C: list_node > list_node > $o] :
( ~ ( suffix_node @ A @ B )
=> ( ! [D: node,E: list_node] : ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ nil_node )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( D != F )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( D = F )
=> ( ~ ( suffix_node @ E @ G )
=> ( ( C @ E @ G )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_not__suffix__induct) ).
thf(1162,plain,
! [A: list_node,B: list_node,C: list_node > list_node > $o] :
( ~ ( suffix_node @ A @ B )
=> ( ! [D: node,E: list_node] : ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ nil_node )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( D != F )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( D = F )
=> ( ~ ( suffix_node @ E @ G )
=> ( ( C @ E @ G )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1101,plain,
prefix_node @ sk176 @ ms,
inference(cnfConj,[status(thm)],[1099]) ).
thf(10217,plain,
! [B: list_node,A: list_node] :
( ~ $true
| ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) )
| ( ( prefix_node @ sk176 @ ms )
!= ( prefix_node @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1101,313]) ).
thf(10218,plain,
! [B: list_node,A: list_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) )
| ( ( prefix_node @ sk176 @ ms )
!= ( prefix_node @ A @ B ) ) ),
inference(simp,[status(thm)],[10217]) ).
thf(10219,plain,
ord_less_eq_set_node @ ( set_node2 @ sk176 ) @ ( set_node2 @ ms ),
inference(pattern_uni,[status(thm)],[10218:[bind(A,$thf( sk176 )),bind(B,$thf( ms ))]]) ).
thf(99,axiom,
! [A: g,B: list_node,C: node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( ( member_node @ C @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ B ) ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_old_OCons__path) ).
thf(685,plain,
! [A: g,B: list_node,C: node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( ( member_node @ C @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ B ) ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons_node @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(154,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( B
= ( hd_node @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_old_Opath2__hd) ).
thf(983,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( B
= ( hd_node @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(40,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( A @ E )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_list__induct__first2) ).
thf(399,plain,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( A @ E )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(8390,plain,
! [A: list_node] :
( ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) )
| ( prefix_node @ sk176 @ nil_node )
| ( A != ms ) ),
inference(paramod_ordered,[status(thm)],[303,1101]) ).
thf(8391,plain,
( ( member_node @ ( hd_node @ ms ) @ ( set_node2 @ ms ) )
| ( prefix_node @ sk176 @ nil_node ) ),
inference(pattern_uni,[status(thm)],[8390:[bind(A,$thf( ms ))]]) ).
thf(15897,plain,
( ( member_node @ ( hd_node @ ms ) @ ( set_node2 @ ms ) )
| ( sk176 = nil_node ) ),
inference(rewrite,[status(thm)],[8391,416]) ).
thf(15898,plain,
( ( sk176 = nil_node )
| ( member_node @ ( hd_node @ ms ) @ ( set_node2 @ ms ) ) ),
inference(lifteq,[status(thm)],[15897]) ).
thf(52,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( cons_node @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_list_Oinject) ).
thf(455,plain,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( cons_node @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(477,plain,
! [A: list_node > $o] :
( ( A @ nil_node )
=> ( ! [B: node,C: list_node] :
( ( A @ C )
=> ( A @ ( cons_node @ B @ C ) ) )
=> ! [B: list_node] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[476]) ).
thf(478,plain,
! [B: list_node,A: list_node > $o] :
( ( ~ ( A @ nil_node )
| ( A @ ( sk66 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ nil_node )
| ~ ( A @ ( cons_node @ ( sk65 @ A ) @ ( sk66 @ A ) ) )
| ( A @ B ) ) ),
inference(cnf,[status(esa)],[477]) ).
thf(479,plain,
! [B: list_node,A: list_node > $o] :
( ~ ( A @ nil_node )
| ( A @ ( sk66 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[478]) ).
thf(481,plain,
! [A: list_node] :
( ( nil_node != nil_node )
| ( nil_node
= ( sk66 @ ( (=) @ list_node @ nil_node ) ) )
| ( nil_node = A ) ),
inference(replace_leibeq,[status(thm)],[479:[bind(A,$thf( (=) @ list_node @ nil_node ))]]) ).
thf(483,plain,
! [A: list_node] :
( ( nil_node != nil_node )
| ( ( sk66 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node = A ) ),
inference(lifteq,[status(thm)],[481]) ).
thf(484,plain,
! [A: list_node] :
( ( ( sk66 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node = A ) ),
inference(simp,[status(thm)],[483]) ).
thf(2211,plain,
! [A: list_node] :
( ( ( sk66 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node != nil_node )
| ( A
!= ( sk66 @ ( (=) @ list_node @ nil_node ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[484]) ).
thf(2212,plain,
( ( sk66 @ ( (=) @ list_node @ nil_node ) )
= nil_node ),
inference(pattern_uni,[status(thm)],[2211:[bind(A,$thf( sk66 @ ( (=) @ list_node @ nil_node ) ))]]) ).
thf(150,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B )
=> ( ( member_node @ D @ ( set_node2 @ C ) )
=> ~ ! [E: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ B )
=> ( ( member_node @ D @ ( set_node2 @ E ) )
=> ( ~ ( member_node @ B @ ( set_node2 @ ( tl_node @ ( butlast_node @ E ) ) ) )
=> ~ ( ord_less_eq_set_node @ ( set_node2 @ E ) @ ( set_node2 @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_old_Opath2__simple__loop) ).
thf(959,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B )
=> ( ( member_node @ D @ ( set_node2 @ C ) )
=> ~ ! [E: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ B )
=> ( ( member_node @ D @ ( set_node2 @ E ) )
=> ( ~ ( member_node @ B @ ( set_node2 @ ( tl_node @ ( butlast_node @ E ) ) ) )
=> ~ ( ord_less_eq_set_node @ ( set_node2 @ E ) @ ( set_node2 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(207,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( append_node @ D @ ( cons_node @ C @ nil_node ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_rev__induct) ).
thf(1212,plain,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( append_node @ D @ ( cons_node @ C @ nil_node ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1213,plain,
! [A: list_node > $o] :
( ( A @ nil_node )
=> ( ! [B: node,C: list_node] :
( ( A @ C )
=> ( A @ ( append_node @ C @ ( cons_node @ B @ nil_node ) ) ) )
=> ! [B: list_node] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[1212]) ).
thf(1214,plain,
! [B: list_node,A: list_node > $o] :
( ( ~ ( A @ nil_node )
| ( A @ ( sk197 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ nil_node )
| ~ ( A @ ( append_node @ ( sk197 @ A ) @ ( cons_node @ ( sk196 @ A ) @ nil_node ) ) )
| ( A @ B ) ) ),
inference(cnf,[status(esa)],[1213]) ).
thf(1215,plain,
! [B: list_node,A: list_node > $o] :
( ~ ( A @ nil_node )
| ( A @ ( sk197 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[1214]) ).
thf(1217,plain,
! [A: list_node] :
( ( nil_node != nil_node )
| ( nil_node
= ( sk197 @ ( (=) @ list_node @ nil_node ) ) )
| ( nil_node = A ) ),
inference(replace_leibeq,[status(thm)],[1215:[bind(A,$thf( (=) @ list_node @ nil_node ))]]) ).
thf(1219,plain,
! [A: list_node] :
( ( nil_node != nil_node )
| ( ( sk197 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node = A ) ),
inference(lifteq,[status(thm)],[1217]) ).
thf(1220,plain,
! [A: list_node] :
( ( ( sk197 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node = A ) ),
inference(simp,[status(thm)],[1219]) ).
thf(536,plain,
! [A: list_node] :
( ? [B: node,C: list_node] :
( A
= ( cons_node @ B @ C ) )
=> ( A != nil_node ) ),
inference(miniscope,[status(thm)],[535]) ).
thf(537,plain,
! [C: list_node,B: node,A: list_node] :
( ( A
!= ( cons_node @ B @ C ) )
| ( A != nil_node ) ),
inference(cnf,[status(esa)],[536]) ).
thf(538,plain,
! [C: list_node,B: node,A: list_node] :
( ( A
!= ( cons_node @ B @ C ) )
| ( A != nil_node ) ),
inference(lifteq,[status(thm)],[537]) ).
thf(539,plain,
! [B: list_node,A: node] :
( ( cons_node @ A @ B )
!= nil_node ),
inference(simp,[status(thm)],[538]) ).
thf(6447,plain,
! [C: list_node,B: node,A: list_node] :
( ( ( sk197 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node != nil_node )
| ( A
!= ( cons_node @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1220,539]) ).
thf(6448,plain,
! [C: list_node,B: node,A: list_node] :
( ( ( sk197 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( A
!= ( cons_node @ B @ C ) ) ),
inference(simp,[status(thm)],[6447]) ).
thf(6449,plain,
( ( sk197 @ ( (=) @ list_node @ nil_node ) )
= nil_node ),
inference(pattern_uni,[status(thm)],[6448:[bind(A,$thf( cons_node @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(39,axiom,
! [A: ( node > node > $o ) > list_node > $o,B: node > node > $o,C: list_node] :
( ! [D: node > node > $o] : ( A @ D @ nil_node )
=> ( ! [D: node > node > $o,E: node] : ( A @ D @ ( cons_node @ E @ nil_node ) )
=> ( ! [D: node > node > $o,E: node,F: node,G: list_node] :
( ( A @ D @ ( cons_node @ F @ G ) )
=> ( A @ D @ ( cons_node @ E @ ( cons_node @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_successively_Oinduct) ).
thf(394,plain,
! [A: ( node > node > $o ) > list_node > $o,B: node > node > $o,C: list_node] :
( ! [D: node > node > $o] : ( A @ D @ nil_node )
=> ( ! [D: node > node > $o,E: node] : ( A @ D @ ( cons_node @ E @ nil_node ) )
=> ( ! [D: node > node > $o,E: node,F: node,G: list_node] :
( ( A @ D @ ( cons_node @ F @ G ) )
=> ( A @ D @ ( cons_node @ E @ ( cons_node @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1200,plain,
! [B: list_node,A: g] :
( ~ ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
| ( B != nil_node ) ),
inference(cnf,[status(esa)],[1199]) ).
thf(1201,plain,
! [B: list_node,A: g] :
( ( B != nil_node )
| ~ ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B ) ),
inference(lifteq,[status(thm)],[1200]) ).
thf(1202,plain,
! [A: g] :
~ ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ nil_node ),
inference(simp,[status(thm)],[1201]) ).
thf(2633,plain,
! [A: g] :
~ ( graph_435229452_edgeD @ alpha_n
@ ^ [B: g] : $true
@ inEdges
@ A
@ nil_node ),
inference(rewrite,[status(thm)],[1202,806]) ).
thf(14,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( suffix_node @ ( cons_node @ A @ B ) @ ( cons_node @ C @ D ) )
=> ( suffix_node @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_suffix__ConsD2) ).
thf(299,plain,
! [A: node,B: list_node,C: node,D: list_node] :
( ( suffix_node @ ( cons_node @ A @ B ) @ ( cons_node @ C @ D ) )
=> ( suffix_node @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(132,axiom,
prefix_node @ ri @ rs2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_ri__props_I4_J) ).
thf(839,plain,
prefix_node @ ri @ rs2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(10224,plain,
! [B: list_node,A: list_node] :
( ~ $true
| ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) )
| ( ( prefix_node @ ri @ rs2 )
!= ( prefix_node @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[839,313]) ).
thf(10225,plain,
! [B: list_node,A: list_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) )
| ( ( prefix_node @ ri @ rs2 )
!= ( prefix_node @ A @ B ) ) ),
inference(simp,[status(thm)],[10224]) ).
thf(10226,plain,
ord_less_eq_set_node @ ( set_node2 @ ri ) @ ( set_node2 @ rs2 ),
inference(pattern_uni,[status(thm)],[10225:[bind(A,$thf( ri )),bind(B,$thf( rs2 ))]]) ).
thf(93,axiom,
! [A: node,B: list_node] :
( nil_node
!= ( cons_node @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_list_Odistinct_I1_J) ).
thf(658,plain,
! [A: node,B: list_node] :
( nil_node
!= ( cons_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(57,axiom,
! [A: list_node] :
( ( A != nil_node )
= ( ? [B: node,C: list_node] :
( A
= ( cons_node @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_neq__Nil__conv) ).
thf(473,plain,
! [A: list_node] :
( ( A != nil_node )
= ( ? [B: node,C: list_node] :
( A
= ( cons_node @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(170,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/benchmark/theBenchmark.p',fact_7_rs_H__props_I1_J) ).
thf(1034,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(222,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_phiUses__finite) ).
thf(1304,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(204,axiom,
! [A: node,B: list_node] :
( ( tl_node @ ( cons_node @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_list_Osel_I3_J) ).
thf(1203,plain,
! [A: node,B: list_node] :
( ( tl_node @ ( cons_node @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(126,axiom,
! [A: list_node,B: set_node] :
( ( A != nil_node )
=> ( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ B )
=> ( ord_less_eq_set_node @ ( set_node2 @ ( tl_node @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_tl__subset) ).
thf(812,plain,
! [A: list_node,B: set_node] :
( ( A != nil_node )
=> ( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ B )
=> ( ord_less_eq_set_node @ ( set_node2 @ ( tl_node @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(233,axiom,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_append__Nil2) ).
thf(1340,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(71,axiom,
! [A: node,B: list_node] : ( member_node @ A @ ( set_node2 @ ( cons_node @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_list_Oset__intros_I1_J) ).
thf(553,plain,
! [A: node,B: list_node] : ( member_node @ A @ ( set_node2 @ ( cons_node @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(53,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ F @ E )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_splice_Oinduct) ).
thf(458,plain,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ F @ E )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(90,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ C @ B )
=> ( ( suffix_node @ A @ C )
| ( suffix_node @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_suffix__same__cases) ).
thf(648,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ C @ B )
=> ( ( suffix_node @ A @ C )
| ( suffix_node @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(159,axiom,
! [A: list_node,B: node,C: node,D: list_node,E: node,F: node] :
( ( ( append_node @ A @ ( cons_node @ B @ ( cons_node @ C @ D ) ) )
= ( cons_node @ E @ ( cons_node @ F @ nil_node ) ) )
= ( ( A = nil_node )
& ( E = B )
& ( F = C )
& ( D = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_list__ee__eq__leel_I2_J) ).
thf(1003,plain,
! [A: list_node,B: node,C: node,D: list_node,E: node,F: node] :
( ( ( append_node @ A @ ( cons_node @ B @ ( cons_node @ C @ D ) ) )
= ( cons_node @ E @ ( cons_node @ F @ nil_node ) ) )
= ( ( A = nil_node )
& ( E = B )
& ( F = C )
& ( D = nil_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(79,axiom,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mem__Collect__eq) ).
thf(580,plain,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(87,axiom,
! [A: list_node] : ( suffix_node @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_suffix__order_Oorder__refl) ).
thf(640,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(175,axiom,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( A
= ( append_node @ nil_node @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_eq__Nil__appendI) ).
thf(1070,plain,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( A
= ( append_node @ nil_node @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(4451,plain,
! [A: list_node] :
( ( n != m )
| ( A != ms2 )
| ( ( append_node @ nil_node @ A )
!= ( append_node @ ns @ ( tl_node @ ri ) ) ) ),
inference(paramod_ordered,[status(thm)],[881,1730]) ).
thf(4469,plain,
( ( n != m )
| ( ns != nil_node )
| ( ( tl_node @ ri )
!= ms2 ) ),
inference(simp,[status(thm)],[4451]) ).
thf(262,plain,
! [B: node > $o,A: node > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_node @ A )
= ( collect_node @ B ) ) ),
inference(cnf,[status(esa)],[261]) ).
thf(263,plain,
! [B: node > $o,A: node > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_node @ A )
= ( collect_node @ B ) ) ),
inference(lifteq,[status(thm)],[262]) ).
thf(167,axiom,
! [A: list_node,B: list_node,C: node] :
( ( prefix_node @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
= ( ( A
= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
| ( prefix_node @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_prefix__snoc) ).
thf(1025,plain,
! [A: list_node,B: list_node,C: node] :
( ( prefix_node @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
= ( ( A
= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
| ( prefix_node @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(293,plain,
! [A: list_node] :
( ~ ? [B: node,C: list_node] :
( A
= ( cons_node @ B @ C ) )
=> ( A = nil_node ) ),
inference(miniscope,[status(thm)],[292]) ).
thf(294,plain,
! [A: list_node] :
( ( A
= ( cons_node @ ( sk17 @ A ) @ ( sk18 @ A ) ) )
| ( A = nil_node ) ),
inference(cnf,[status(esa)],[293]) ).
thf(295,plain,
! [A: list_node] :
( ( ( cons_node @ ( sk17 @ A ) @ ( sk18 @ A ) )
= A )
| ( A = nil_node ) ),
inference(lifteq,[status(thm)],[294]) ).
thf(103,axiom,
! [A: list_node,B: list_node,C: node] :
( ( suffix_node @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
= ( ( A = nil_node )
| ? [D: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
& ( suffix_node @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_suffix__snoc) ).
thf(705,plain,
! [A: list_node,B: list_node,C: node] :
( ( suffix_node @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
= ( ( A = nil_node )
| ? [D: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
& ( suffix_node @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(5228,plain,
( ( n != m )
| ( ns != ms2 )
| ( ri != nil_node ) ),
inference(rewrite,[status(thm)],[1740,1187]) ).
thf(8394,plain,
! [A: list_node] :
( ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) )
| ( n != m )
| ( ns != ms2 )
| ( nil_node != nil_node )
| ( A != ri ) ),
inference(paramod_ordered,[status(thm)],[303,5228]) ).
thf(8395,plain,
! [A: list_node] :
( ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) )
| ( n != m )
| ( ns != ms2 )
| ( A != ri ) ),
inference(simp,[status(thm)],[8394]) ).
thf(8396,plain,
( ( member_node @ ( hd_node @ ri ) @ ( set_node2 @ ri ) )
| ( n != m )
| ( ns != ms2 ) ),
inference(pattern_uni,[status(thm)],[8395:[bind(A,$thf( ri ))]]) ).
thf(133,axiom,
member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rs_H__props_I4_J) ).
thf(840,plain,
member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(54,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( prefix_node @ A @ B )
=> ( ( prefix_node @ C @ B )
=> ( ( prefix_node @ A @ C )
| ( prefix_node @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_prefix__same__cases) ).
thf(463,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( prefix_node @ A @ B )
=> ( ( prefix_node @ C @ B )
=> ( ( prefix_node @ A @ C )
| ( prefix_node @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(56,axiom,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_prefix__Nil) ).
thf(470,plain,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(28,axiom,
! [A: set_node,B: set_node,C: set_node,D: set_node] :
( ( A = B )
=> ( ( ord_less_eq_set_node @ B @ C )
=> ( ( C = D )
=> ( ord_less_eq_set_node @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_ord__eq__le__eq__trans) ).
thf(359,plain,
! [A: set_node,B: set_node,C: set_node,D: set_node] :
( ( A = B )
=> ( ( ord_less_eq_set_node @ B @ C )
=> ( ( C = D )
=> ( ord_less_eq_set_node @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(220,axiom,
! [A: g,B: list_node,C: node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( ( member_node @ C @ ( set_node2 @ B ) )
=> ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_old_Opath__in___092_060alpha_062n) ).
thf(1285,plain,
! [A: g,B: list_node,C: node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( ( member_node @ C @ ( set_node2 @ B ) )
=> ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(232,axiom,
! [A: list_node,B: node] :
( ( A != nil_node )
=> ( ( ( B
= ( hd_node @ A ) )
| ( member_node @ B @ ( set_node2 @ ( tl_node @ A ) ) ) )
= ( member_node @ B @ ( set_node2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_in__hd__or__tl__conv) ).
thf(1336,plain,
! [A: list_node,B: node] :
( ( A != nil_node )
=> ( ( ( B
= ( hd_node @ A ) )
| ( member_node @ B @ ( set_node2 @ ( tl_node @ A ) ) ) )
= ( member_node @ B @ ( set_node2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(23,axiom,
! [A: list_node,B: list_node,C: node] :
( ( suffix_node @ A @ B )
=> ( suffix_node @ A @ ( cons_node @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_suffix__ConsI) ).
thf(331,plain,
! [A: list_node,B: list_node,C: node] :
( ( suffix_node @ A @ B )
=> ( suffix_node @ A @ ( cons_node @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(199,axiom,
! [A: list_node,B: node,C: list_node] :
( ( A != nil_node )
=> ( ( ( cons_node @ B @ nil_node )
= ( append_node @ C @ A ) )
= ( ( C = nil_node )
& ( A
= ( cons_node @ B @ nil_node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_list__se__match_I4_J) ).
thf(1188,plain,
! [A: list_node,B: node,C: list_node] :
( ( A != nil_node )
=> ( ( ( cons_node @ B @ nil_node )
= ( append_node @ C @ A ) )
= ( ( C = nil_node )
& ( A
= ( cons_node @ B @ nil_node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(335,plain,
! [A: set_val] :
( ~ ( finite_finite_val @ A )
| ( ( set_val2 @ ( sk22 @ A ) )
= A ) ),
inference(cnf,[status(esa)],[334]) ).
thf(336,plain,
! [A: set_val] :
( ( ( set_val2 @ ( sk22 @ A ) )
= A )
| ~ ( finite_finite_val @ A ) ),
inference(lifteq,[status(thm)],[335]) ).
thf(82,axiom,
! [A: list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: list_node] : ( A @ E @ nil_node )
=> ( ! [E: list_node] : ( A @ nil_node @ E )
=> ( ! [E: node,F: list_node,G: node,H: list_node] :
( ( B @ E @ G )
=> ( ( A @ F @ ( cons_node @ G @ H ) )
=> ( A @ ( cons_node @ E @ F ) @ ( cons_node @ G @ H ) ) ) )
=> ( ! [E: node,F: list_node,G: node,H: list_node] :
( ~ ( B @ E @ G )
=> ( ( A @ ( cons_node @ E @ F ) @ H )
=> ( A @ ( cons_node @ E @ F ) @ ( cons_node @ G @ H ) ) ) )
=> ( A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_mergesort__by__rel__merge__induct) ).
thf(613,plain,
! [A: list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: list_node] : ( A @ E @ nil_node )
=> ( ! [E: list_node] : ( A @ nil_node @ E )
=> ( ! [E: node,F: list_node,G: node,H: list_node] :
( ( B @ E @ G )
=> ( ( A @ F @ ( cons_node @ G @ H ) )
=> ( A @ ( cons_node @ E @ F ) @ ( cons_node @ G @ H ) ) ) )
=> ( ! [E: node,F: list_node,G: node,H: list_node] :
( ~ ( B @ E @ G )
=> ( ( A @ ( cons_node @ E @ F ) @ H )
=> ( A @ ( cons_node @ E @ F ) @ ( cons_node @ G @ H ) ) ) )
=> ( A @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(193,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: list_node,C: node] :
( A
!= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_rev__exhaust) ).
thf(1140,plain,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: list_node,C: node] :
( A
!= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(137,axiom,
! [A: g,B: list_node,C: node,D: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ D ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_old_Opath__split_I1_J) ).
thf(876,plain,
! [A: g,B: list_node,C: node,D: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ D ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(157,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ E ) ) )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ E @ nil_node ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_old_Opath2__snoc) ).
thf(991,plain,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ E ) ) )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ E @ nil_node ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(8245,plain,
! [A: list_node] :
( ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) )
| ( prefix_node @ ms2 @ nil_node )
| ( A != ms ) ),
inference(paramod_ordered,[status(thm)],[303,498]) ).
thf(8246,plain,
( ( member_node @ ( hd_node @ ms ) @ ( set_node2 @ ms ) )
| ( prefix_node @ ms2 @ nil_node ) ),
inference(pattern_uni,[status(thm)],[8245:[bind(A,$thf( ms ))]]) ).
thf(13755,plain,
( ( member_node @ ( hd_node @ ms ) @ ( set_node2 @ ms ) )
| ( ms2 = nil_node ) ),
inference(rewrite,[status(thm)],[8246,416]) ).
thf(13756,plain,
( ( ms2 = nil_node )
| ( member_node @ ( hd_node @ ms ) @ ( set_node2 @ ms ) ) ),
inference(lifteq,[status(thm)],[13755]) ).
thf(259,axiom,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
= ( ? [C: node] :
( ( B
= ( cons_node @ C @ nil_node ) )
& ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
& ( invar @ A ) )
| ? [C: list_node,D: node] :
( ( B
= ( cons_node @ D @ C ) )
& ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ C )
& ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_old_Opath_Osimps) ).
thf(1459,plain,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
= ( ? [C: node] :
( ( B
= ( cons_node @ C @ nil_node ) )
& ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
& ( invar @ A ) )
| ? [C: list_node,D: node] :
( ( B
= ( cons_node @ D @ C ) )
& ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ C )
& ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(100,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_hd__Cons__tl) ).
thf(688,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(10197,plain,
! [B: list_node,A: list_node] :
( ~ $true
| ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) )
| ( ( prefix_node @ sk231 @ rs2 )
!= ( prefix_node @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1422,313]) ).
thf(10198,plain,
! [B: list_node,A: list_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) )
| ( ( prefix_node @ sk231 @ rs2 )
!= ( prefix_node @ A @ B ) ) ),
inference(simp,[status(thm)],[10197]) ).
thf(10199,plain,
ord_less_eq_set_node @ ( set_node2 @ sk231 ) @ ( set_node2 @ rs2 ),
inference(pattern_uni,[status(thm)],[10198:[bind(A,$thf( sk231 )),bind(B,$thf( rs2 ))]]) ).
thf(15093,plain,
! [B: node > $o,A: node] :
( ( member_node @ A @ ( collect_node @ B ) )
| ( ( member_node @ i @ ( set_node2 @ ms ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[330,339]) ).
thf(15294,plain,
( member_node @ i
@ ( collect_node
@ ^ [A: node] : ( member_node @ A @ ( set_node2 @ ms ) ) ) ),
inference(pre_uni,[status(thm)],[15093:[bind(A,$thf( i )),bind(B,$thf( ^ [C: node] : ( member_node @ C @ ( set_node2 @ ms ) ) ))]]) ).
thf(1481,plain,
( ( ms != nil_node )
| ( ( butlast_node @ ms2 )
!= ( butlast_node @ nil_node ) ) ),
inference(simp,[status(thm)],[1480]) ).
thf(3478,plain,
( ( ms != nil_node )
| ( ( butlast_node @ ms2 )
!= nil_node ) ),
inference(rewrite,[status(thm)],[1481,368]) ).
thf(51,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ ( cons_node @ D @ F ) )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_revg_Oinduct) ).
thf(450,plain,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ ( cons_node @ D @ F ) )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(177,axiom,
! [A: list_node,B: node,C: list_node,D: node] :
( ( suffix_node @ ( append_node @ A @ ( cons_node @ B @ nil_node ) ) @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) )
= ( ( B = D )
& ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_snoc__suffix__snoc) ).
thf(1084,plain,
! [A: list_node,B: node,C: list_node,D: node] :
( ( suffix_node @ ( append_node @ A @ ( cons_node @ B @ nil_node ) ) @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) )
= ( ( B = D )
& ( suffix_node @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(257,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
= ( ? [C: list_node,D: list_node] :
( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_in__set__conv__decomp) ).
thf(1453,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
= ( ? [C: list_node,D: list_node] :
( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(117,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
= ( ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_in__set__conv__decomp__last) ).
thf(781,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
= ( ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1029,plain,
r != phi_r,
inference(polarity_switch,[status(thm)],[1028]) ).
thf(1030,plain,
r != phi_r,
inference(lifteq,[status(thm)],[1029]) ).
thf(50,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( ( C = D )
=> ( A @ ( cons_node @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_node @ D @ E ) ) )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_remdups__adj_Oinduct) ).
thf(433,plain,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( ( C = D )
=> ( A @ ( cons_node @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_node @ D @ E ) ) )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(254,axiom,
! [A: list_node,B: list_node] :
( ( prefix_node @ ( append_node @ A @ B ) @ A )
= ( B = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_same__prefix__nil) ).
thf(1444,plain,
! [A: list_node,B: list_node] :
( ( prefix_node @ ( append_node @ A @ B ) @ A )
= ( B = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(224,axiom,
! [A: g,B: list_node,C: node,D: node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
=> ( ( member_node @ C @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ D ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ ( cons_node @ D @ nil_node ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_old_Opath__snoc) ).
thf(1309,plain,
! [A: g,B: list_node,C: node,D: node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
=> ( ( member_node @ C @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ D ) ) )
=> ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ ( append_node @ B @ ( cons_node @ C @ ( cons_node @ D @ nil_node ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(519,plain,
! [A: list_node > $o] :
( ( A @ nil_node )
=> ( ! [B: node,C: list_node] :
( ( A @ C )
=> ( A @ ( cons_node @ B @ C ) ) )
=> ! [B: list_node] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[518]) ).
thf(520,plain,
! [B: list_node,A: list_node > $o] :
( ( ~ ( A @ nil_node )
| ( A @ ( sk72 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ nil_node )
| ~ ( A @ ( cons_node @ ( sk71 @ A ) @ ( sk72 @ A ) ) )
| ( A @ B ) ) ),
inference(cnf,[status(esa)],[519]) ).
thf(521,plain,
! [B: list_node,A: list_node > $o] :
( ~ ( A @ nil_node )
| ( A @ ( sk72 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[520]) ).
thf(523,plain,
! [A: list_node] :
( ( nil_node != nil_node )
| ( nil_node
= ( sk72 @ ( (=) @ list_node @ nil_node ) ) )
| ( nil_node = A ) ),
inference(replace_leibeq,[status(thm)],[521:[bind(A,$thf( (=) @ list_node @ nil_node ))]]) ).
thf(525,plain,
! [A: list_node] :
( ( nil_node != nil_node )
| ( ( sk72 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node = A ) ),
inference(lifteq,[status(thm)],[523]) ).
thf(526,plain,
! [A: list_node] :
( ( ( sk72 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node = A ) ),
inference(simp,[status(thm)],[525]) ).
thf(3643,plain,
! [C: list_node,B: node,A: list_node] :
( ( ( sk72 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( nil_node != nil_node )
| ( A
!= ( cons_node @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[526,539]) ).
thf(3644,plain,
! [C: list_node,B: node,A: list_node] :
( ( ( sk72 @ ( (=) @ list_node @ nil_node ) )
= nil_node )
| ( A
!= ( cons_node @ B @ C ) ) ),
inference(simp,[status(thm)],[3643]) ).
thf(3645,plain,
( ( sk72 @ ( (=) @ list_node @ nil_node ) )
= nil_node ),
inference(pattern_uni,[status(thm)],[3644:[bind(A,$thf( cons_node @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(5265,plain,
! [C: node,B: g,A: set_val] :
( ( finite_finite_val
@ ( collect_val
@ ^ [D: val] : ( member_val @ D @ A ) ) )
| ( A
!= ( defs @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[282,1258]) ).
thf(5266,plain,
! [B: node,A: g] :
( finite_finite_val
@ ( collect_val
@ ^ [C: val] : ( member_val @ C @ ( defs @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[5265:[bind(A,$thf( defs @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(5287,plain,
! [B: node,A: g] :
( finite_finite_val
@ ( collect_val
@ ^ [C: val] : ( member_val @ C @ ( defs @ A @ B ) ) ) ),
inference(simp,[status(thm)],[5266]) ).
thf(287,plain,
! [D: list_node,C: list_node,B: node > node > $o,A: ( node > node > $o ) > list_node > list_node > $o] :
( ( sk7 @ A @ ( sk8 @ A ) @ ( sk10 @ A ) )
| ( A @ ( sk7 @ A ) @ ( cons_node @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk11 @ A ) )
| ~ ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ nil_node )
| ~ ( A @ ( sk14 @ A ) @ nil_node @ ( cons_node @ ( sk15 @ A ) @ ( sk16 @ A ) ) )
| ( A @ B @ C @ D ) ),
inference(cnfConj,[status(thm)],[285]) ).
thf(185,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( suffix_node @ A @ ( append_node @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_suffix__appendI) ).
thf(1116,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( suffix_node @ A @ ( append_node @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(191,axiom,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ E ) ) @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_old_Opath2__split_I1_J) ).
thf(1133,plain,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ E ) ) @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(41,axiom,
! [A: list_node] : ( prefix_node @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_prefix__order_Oorder__refl) ).
thf(410,plain,
! [A: list_node] : ( prefix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(245,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ~ ! [C: list_node] :
( B
!= ( append_node @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_suffixE) ).
thf(1380,plain,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ~ ! [C: list_node] :
( B
!= ( append_node @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(120,axiom,
! [A: list_node,B: list_node] :
( ( nil_node
= ( append_node @ A @ B ) )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_Nil__is__append__conv) ).
thf(790,plain,
! [A: list_node,B: list_node] :
( ( nil_node
= ( append_node @ A @ B ) )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(108,axiom,
( ( i
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
=> ( ( ( i
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
=> ( m != i ) )
=> ~ ( ( i
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
=> ( m = i ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(735,plain,
( ( i
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
=> ( ( ( i
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
=> ( m != i ) )
=> ~ ( ( i
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
=> ( m = i ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(14689,plain,
! [A: list_node] :
( ( suffix_node @ ( butlast_node @ ( tl_node @ A ) ) @ nil_node )
| ( ( butlast_node @ ( tl_node @ ( tl_node @ ( tl_node @ nil_node ) ) ) )
!= ( butlast_node @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14602,12876]) ).
thf(14690,plain,
suffix_node @ ( butlast_node @ ( tl_node @ ( tl_node @ ( tl_node @ ( tl_node @ nil_node ) ) ) ) ) @ nil_node,
inference(pattern_uni,[status(thm)],[14689:[bind(A,$thf( tl_node @ ( tl_node @ ( tl_node @ nil_node ) ) ))]]) ).
thf(14813,plain,
( ( butlast_node @ ( tl_node @ ( tl_node @ ( tl_node @ ( tl_node @ nil_node ) ) ) ) )
= nil_node ),
inference(rewrite,[status(thm)],[14690,432]) ).
thf(14814,plain,
( ( butlast_node @ ( tl_node @ ( tl_node @ ( tl_node @ ( tl_node @ nil_node ) ) ) ) )
= nil_node ),
inference(lifteq,[status(thm)],[14813]) ).
thf(13604,plain,
! [A: list_node] :
( ( ( set_node2 @ A )
!= ( set_node2 @ ms ) )
| ( ( set_node2 @ ( sk19 @ ( set_node2 @ A ) ) )
!= ( set_node2 @ ( butlast_node @ sk176 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9133,1478]) ).
thf(13661,plain,
! [A: list_node] :
( ( A != ms )
| ( ( sk19 @ ( set_node2 @ A ) )
!= ( butlast_node @ sk176 ) ) ),
inference(simp,[status(thm)],[13604]) ).
thf(13701,plain,
( ( sk19 @ ( set_node2 @ ms ) )
!= ( butlast_node @ sk176 ) ),
inference(simp,[status(thm)],[13661]) ).
thf(7557,plain,
! [A: node] :
( ( cons_node @ A @ ms )
!= ( butlast_node @ sk176 ) ),
inference(simp,[status(thm)],[7291]) ).
thf(124,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ C )
=> ( suffix_node @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_suffix__appendD) ).
thf(807,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ C )
=> ( suffix_node @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(221,axiom,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( ! [C: node] :
( ( B
= ( cons_node @ C @ nil_node ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ~ ( invar @ A ) ) )
=> ~ ! [C: list_node,D: node] :
( ( B
= ( cons_node @ D @ C ) )
=> ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ C )
=> ~ ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_old_Opath_Ocases) ).
thf(1288,plain,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( ! [C: node] :
( ( B
= ( cons_node @ C @ nil_node ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ~ ( invar @ A ) ) )
=> ~ ! [C: list_node,D: node] :
( ( B
= ( cons_node @ D @ C ) )
=> ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ C )
=> ~ ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(67,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_suffix__order_Oantisym) ).
thf(532,plain,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(235,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_split__list) ).
thf(1346,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(149,axiom,
! [A: list_node,B: list_node] :
( ~ ( suffix_node @ A @ B )
=> ( ( ( A != nil_node )
=> ( B != nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
=> ! [E: node,F: list_node] :
( ( B
= ( append_node @ F @ ( cons_node @ E @ nil_node ) ) )
=> ( ( E = C )
=> ( suffix_node @ D @ F ) ) ) )
=> ~ ! [C: node] :
( ? [D: list_node] :
( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
=> ! [D: node] :
( ? [E: list_node] :
( B
= ( append_node @ E @ ( cons_node @ D @ nil_node ) ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_not__suffix__cases) ).
thf(928,plain,
! [A: list_node,B: list_node] :
( ~ ( suffix_node @ A @ B )
=> ( ( ( A != nil_node )
=> ( B != nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
=> ! [E: node,F: list_node] :
( ( B
= ( append_node @ F @ ( cons_node @ E @ nil_node ) ) )
=> ( ( E = C )
=> ( suffix_node @ D @ F ) ) ) )
=> ~ ! [C: node] :
( ? [D: list_node] :
( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
=> ! [D: node] :
( ? [E: list_node] :
( B
= ( append_node @ E @ ( cons_node @ D @ nil_node ) ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(15103,plain,
! [B: node > $o,A: node] :
( ( member_node @ A @ ( collect_node @ B ) )
| ( ( member_node @ sk230 @ ( set_node2 @ ms ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1420,339]) ).
thf(15292,plain,
( member_node @ sk230
@ ( collect_node
@ ^ [A: node] : ( member_node @ A @ ( set_node2 @ ms ) ) ) ),
inference(pre_uni,[status(thm)],[15103:[bind(A,$thf( sk230 )),bind(B,$thf( ^ [C: node] : ( member_node @ C @ ( set_node2 @ ms ) ) ))]]) ).
thf(226,axiom,
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 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_rs__props_I1_J) ).
thf(1314,plain,
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 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(143,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_append__same__eq) ).
thf(897,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(114,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ! [F: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
=> ( ( prefix_node @ F @ C )
=> ( member_node @ E @ ( set_node2 @ ( butlast_node @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_old_Opath2__prefix__ex) ).
thf(767,plain,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ! [F: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
=> ( ( prefix_node @ F @ C )
=> ( member_node @ E @ ( set_node2 @ ( butlast_node @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(122,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_split__list__last__propE) ).
thf(796,plain,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(77,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_list_Oset__sel_I1_J) ).
thf(575,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(246,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( A
= ( append_node @ B @ C ) )
=> ( suffix_node @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_suffixI) ).
thf(1384,plain,
! [A: list_node,B: list_node,C: list_node] :
( ( A
= ( append_node @ B @ C ) )
=> ( suffix_node @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(165,axiom,
( ( append_node @ nil_node )
= ( ^ [A: list_node] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_empty__append__eq__id) ).
thf(1019,plain,
( ( append_node @ nil_node )
= ( ^ [A: list_node] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(129,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_split__list__last__prop) ).
thf(822,plain,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(135,axiom,
! [A: list_node,B: list_node,C: list_node > list_node > $o] :
( ( A != nil_node )
=> ( ( B != nil_node )
=> ( ! [D: node,E: node] : ( C @ ( cons_node @ D @ nil_node ) @ ( cons_node @ E @ nil_node ) )
=> ( ! [D: node,E: list_node,F: node] :
( ( E != nil_node )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( cons_node @ F @ nil_node ) ) )
=> ( ! [D: node,E: node,F: list_node] :
( ( F != nil_node )
=> ( C @ ( cons_node @ D @ nil_node ) @ ( append_node @ F @ ( cons_node @ E @ nil_node ) ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( C @ E @ G )
=> ( ( E != nil_node )
=> ( ( G != nil_node )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_rev__nonempty__induct2_H) ).
thf(850,plain,
! [A: list_node,B: list_node,C: list_node > list_node > $o] :
( ( A != nil_node )
=> ( ( B != nil_node )
=> ( ! [D: node,E: node] : ( C @ ( cons_node @ D @ nil_node ) @ ( cons_node @ E @ nil_node ) )
=> ( ! [D: node,E: list_node,F: node] :
( ( E != nil_node )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( cons_node @ F @ nil_node ) ) )
=> ( ! [D: node,E: node,F: list_node] :
( ( F != nil_node )
=> ( C @ ( cons_node @ D @ nil_node ) @ ( append_node @ F @ ( cons_node @ E @ nil_node ) ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( C @ E @ G )
=> ( ( E != nil_node )
=> ( ( G != nil_node )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1120,plain,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ),
inference(polarity_switch,[status(thm)],[1119]) ).
thf(63,axiom,
! [A: list_node,B: node] : ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ ( cons_node @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_set__subset__Cons) ).
thf(501,plain,
! [A: list_node,B: node] : ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ ( cons_node @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(31,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_set__mono__suffix) ).
thf(369,plain,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(180,axiom,
! [A: list_node,B: node,C: list_node] :
( ( A != nil_node )
=> ( ( ( cons_node @ B @ nil_node )
= ( append_node @ A @ C ) )
= ( ( A
= ( cons_node @ B @ nil_node ) )
& ( C = nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_list__se__match_I3_J) ).
thf(1093,plain,
! [A: list_node,B: node,C: list_node] :
( ( A != nil_node )
=> ( ( ( cons_node @ B @ nil_node )
= ( append_node @ A @ C ) )
= ( ( A
= ( cons_node @ B @ nil_node ) )
& ( C = nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(155,axiom,
! [A: list_node,B: node > $o] :
( ( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) ) )
= ( ? [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_split__list__last__prop__iff) ).
thf(987,plain,
! [A: list_node,B: node > $o] :
( ( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) ) )
= ( ? [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(277,plain,
! [C: list_node,B: node > node > $o,A: ( node > node > $o ) > list_node > $o] :
( ~ ( A @ ( sk3 @ A ) @ nil_node )
| ~ ( A @ ( sk4 @ A ) @ ( cons_node @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
| ( A @ B @ C ) ),
inference(cnfConj,[status(thm)],[275]) ).
thf(101,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( C
= ( cons_node @ B @ nil_node ) )
=> ( D != B ) )
=> ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd_node @ ( tl_node @ C ) ) @ ( tl_node @ C ) @ D )
=> ~ ( member_node @ B @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ ( tl_node @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_old_Opath2__cases) ).
thf(691,plain,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( C
= ( cons_node @ B @ nil_node ) )
=> ( D != B ) )
=> ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd_node @ ( tl_node @ C ) ) @ ( tl_node @ C ) @ D )
=> ~ ( member_node @ B @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ ( tl_node @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(318,plain,
! [B: list_node,A: list_node > $o] :
( ~ ( A @ ( cons_node @ ( sk20 @ A ) @ ( sk21 @ A ) ) )
| ~ ( A @ nil_node )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[316]) ).
thf(322,plain,
! [B: list_node,A: list_node > $o] :
( ~ ( A @ ( cons_node @ ( sk20 @ A ) @ ( sk21 @ A ) ) )
| ~ ( A @ nil_node )
| ( A @ B ) ),
inference(simp,[status(thm)],[318]) ).
thf(161,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= A )
= ( B = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_append__self__conv) ).
thf(1009,plain,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= A )
= ( B = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(147,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ nil_node )
= ( append_node @ B @ ( cons_node @ C @ D ) ) )
= ( ( B = nil_node )
& ( C = A )
& ( D = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_list__e__eq__lel_I1_J) ).
thf(923,plain,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ nil_node )
= ( append_node @ B @ ( cons_node @ C @ D ) ) )
= ( ( B = nil_node )
& ( C = A )
& ( D = nil_node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(172,axiom,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ C ) ) )
=> ( ( invar @ B )
=> ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_old_Opredecessor__is__node) ).
thf(1037,plain,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ C ) ) )
=> ( ( invar @ B )
=> ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(29,axiom,
! [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
=> ( ( prefix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_prefix__order_Oantisym) ).
thf(364,plain,
! [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
=> ( ( prefix_node @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(104,axiom,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ B @ A ) )
= ( B = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_self__append__conv2) ).
thf(708,plain,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ B @ A ) )
= ( B = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(139,axiom,
! [A: list_node,B: node > $o] :
( ( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) ) )
= ( ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_split__list__first__prop__iff) ).
thf(882,plain,
! [A: list_node,B: node > $o] :
( ( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) ) )
= ( ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(70,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( cons_node @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_list__tail__coinc) ).
thf(543,plain,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( cons_node @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(22723,plain,
$false,
inference(e,[status(thm)],[1322,809,1369,2031,1105,10213,1237,555,7285,760,4464,8338,628,1031,1315,518,762,276,994,13707,873,655,269,1422,308,379,1269,1426,10103,715,2712,1327,340,1354,670,14602,3429,1196,11542,885,288,301,1529,4467,841,417,565,1366,1482,1254,651,12879,724,570,372,7294,1511,344,1132,638,1379,1087,1147,1479,969,1013,1115,7215,289,261,1398,881,416,10206,1714,1450,646,574,806,905,7300,1373,1040,321,1136,834,353,966,602,280,634,1447,1119,5246,428,312,4475,10216,1074,292,1206,793,1306,1199,1730,270,529,334,1223,746,1343,260,820,392,429,1238,3471,1021,778,1423,625,879,665,583,7934,757,1128,1392,324,1012,329,1178,682,1195,578,1234,1259,1121,1006,14413,420,499,1028,488,339,476,642,489,1016,679,701,1478,1456,1131,1192,1246,371,1525,393,1114,13699,503,805,311,1035,1187,1185,773,926,343,1318,1241,266,1466,558,662,888,298,1251,430,1103,1483,1273,264,279,573,296,375,13703,1648,412,904,423,286,12958,1388,711,291,1124,382,313,1312,787,498,7094,466,1090,1258,1464,1356,540,14502,1209,900,831,1408,5244,784,419,1349,990,1043,303,1376,764,979,1144,13705,387,367,535,816,4462,1162,10219,330,685,983,399,15898,455,1477,9133,2212,959,6449,278,1528,394,306,2633,299,267,1102,10226,658,473,1034,1304,426,1203,1420,374,812,1340,553,458,648,487,5229,1003,580,640,1070,414,327,4469,263,1025,295,705,282,8396,840,463,1317,470,359,1285,1336,331,1188,336,1257,613,1353,1140,314,876,991,13756,1459,539,1321,688,10199,495,15294,3478,450,1084,368,1453,896,304,1101,5228,781,1030,433,1444,7135,2680,1212,1309,3645,5287,287,1116,1133,432,410,1097,12876,1380,790,735,273,14814,373,13701,305,7557,807,1288,532,7291,1346,928,15292,1314,897,767,796,283,1352,575,427,1384,1019,822,850,1120,501,369,1093,839,1236,987,277,691,322,1320,337,1009,923,309,1037,1416,364,708,882,543,2018]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP081^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.07/0.25 % Computer : n002.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8046.5625MB
% 0.07/0.25 % OS : Linux 6.8.0-71-generic
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Sep 29 19:51:37 UTC 2026
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.16/1.03 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.07/1.58 % [INFO] Parsing done (547ms).
% 3.07/1.60 % [INFO] Running in sequential loop mode.
% 4.99/2.13 % [INFO] eprover registered as external prover.
% 4.99/2.13 % [INFO] Scanning for conjecture ...
% 5.66/2.32 % [INFO] Found a conjecture (or negated_conjecture) and 350 axioms. Running axiom selection ...
% 6.41/2.51 % [INFO] Axiom selection finished. Selected 257 axioms (removed 93 axioms).
% 7.88/2.90 % [INFO] Problem is higher-order (TPTP THF).
% 7.88/2.94 % [INFO] Type checking passed.
% 7.88/2.94 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 250.29/74.27 % External prover 'e' found a proof!
% 250.29/74.27 % [INFO] Killing All external provers ...
% 250.29/74.27 % Time passed: 73804ms (effective reasoning time: 72664ms)
% 250.29/74.27 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 250.29/74.28 % Axioms used in derivation (257): fact_200_Cons__eq__appendI, fact_287_snoc__suffix__snoc, fact_3_assms_I7_J, fact_12_old_Opath2__split_I2_J, fact_224_in__set__conv__decomp__last, fact_67_append_Oassoc, fact_189_list_OdiscI, fact_295_set__mono__suffix, fact_176_remdups__adj_Ocases, fact_191_list_Odistinct_I1_J, fact_177_list__2pre__induct, fact_239_xy__in__set__cases, fact_270_Cons__prefix__Cons, fact_115_old_Opath2__split__ex, fact_71_Collect__mem__eq, fact_160_strict__sorted_Oinduct, fact_256_phiUses__finite, fact_114_old_Opath2__induct, fact_130_butlast_Osimps_I1_J, fact_118_old_Opath2__snoc, fact_312_suffix__same__cases, fact_23_old_Opath2__tl__in___092_060alpha_062n, fact_261_suffix__order_Oorder__refl, fact_32_rs_H__props_I4_J, fact_266_old_Opath__hd, fact_245_tl__obtain__elem, fact_227_split__list__first__prop, fact_327_finite__list, fact_291_in__hd__or__tl__conv, fact_274_suffix__bot_Obot_Oextremum__unique, fact_113_old_Opath2__split__first__prop, fact_259_prefix__order_Oorder__refl, fact_39_list__e__eq__lel_I2_J, fact_95_append__self__conv2, fact_217_rev__exhaust, fact_7_rs_H__props_I1_J, fact_42_list__e__eq__lel_I1_J, fact_75_append__assoc, fact_168_mergesort__by__rel__merge_Oinduct, fact_107_empty__append__eq__id, fact_226_split__list__last__propE, fact_204_append__Nil, fact_148_butlast__eq__consE, fact_29_ri__props_I4_J, fact_137_butlast_Osimps_I2_J, fact_254_old_Opath2__cases, fact_127_old_OCons__path2, fact_45_list__se__match_I4_J, fact_195_set__ConsD, fact_215_rev__induct2_H, fact_277_same__suffix__suffix, fact_331_set__mono__prefix, fact_307_Sublist_Osuffix__def, fact_15_rs_H__props_I3_J, fact_27_rs_H__loopfree, fact_213_Cons__eq__append__conv, fact_343_set__subset__Cons, fact_180_min__list_Oinduct, fact_267_old_Opath__split_I2_J, fact_321_suffix__order_Oord__eq__le__trans, fact_170_list__nonempty__induct, fact_347_prefix__same__cases, fact_263_old_Opath__not__Nil, fact_61_ms_H__props_I2_J, fact_126__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, fact_299_suffix__ConsI, fact_201_append__Cons, fact_302_suffix__bot_Obot_Oextremum__uniqueI, fact_18_old_Opath2__in___092_060alpha_062n, fact_172_successively_Oinduct, fact_280_old_OCons__path, fact_21_old_Oelem__set__implies__elem__tl__app__cons, fact_30_old_Oempty__path2, fact_190_neq__NilE, fact_5_old_Opath2__app, fact_293_old_Opath__in___092_060alpha_062n, fact_228_split__list__last__prop, fact_209_list__Cons__eq__append__cases, fact_335_hd__in__set, fact_77_append__same__eq, fact_25_old_Opath2__split_I1_J, fact_286_suffix__snoc, fact_142_in__set__butlast__appendI, fact_54_list__se__match_I1_J, fact_179_shuffles_Oinduct, fact_325_suffix__order_Odual__order_Oantisym, fact_16_old_Opath2__hd__in___092_060alpha_062n, fact_230_in__set__list__format, fact_310_suffix__appendI, fact_298_suffix__ConsD2, fact_319_suffix__order_Oorder_Oeq__iff, fact_333_list_Oset__sel_I1_J, fact_70_Collect__mem__eq, fact_306_suffixI, fact_346_butlast__subset, fact_242_split__list__last, fact_260_prefix__order_Odual__order_Orefl, fact_24_old_Opath2__last__in__ns, fact_276_same__prefix__prefix, fact_73_Collect__cong, fact_82_old_Osuccessor__in___092_060alpha_062n, fact_275_suffix__Nil, fact_249_list_Oset__sel_I2_J, fact_134_butlast__tl, fact_154_not__Cons__self2, fact_314_suffix__order_Oantisym, fact_303_suffix__bot_Obot_Oextremum, fact_246_tl__Nil, fact_62_ri__props_I3_J, fact_79_same__append__eq, fact_284_same__suffix__nil, fact_247_Nil__tl, fact_193_list_Oset__cases, fact_60_list__ee__eq__leel_I1_J, fact_203_eq__Nil__appendI, fact_28_rs__def, fact_9_rs__props_I1_J, fact_288_hd__Cons__tl, fact_219_split__list__first__prop__iff, fact_292_old_Opath__invar, fact_197_list_Oset__intros_I1_J, fact_278_old_Oempty__path, fact_326_list_Osel_I1_J, fact_320_suffix__order_Oorder_Oantisym, fact_340_list_Oexpand, fact_264_old_Opath2__hd, fact_175_sorted__wrt_Oinduct, fact_2_old_Oinvar, fact_10_ms_H__props_I1_J, fact_80_old_Opredecessor__is__node, fact_289_list_Ocollapse, fact_89_append__self__conv, fact_296_subset__Collect__conv, fact_339_not__suffix__induct, fact_208_list__append__eq__Cons__cases, fact_104_append__is__Nil__conv, fact_205_append_Oleft__neutral, fact_262_suffix__order_Odual__order_Orefl, fact_188_revg_Oinduct, fact_183_splice_Oinduct, fact_300_suffix__ConsD, fact_140_butlast__append, fact_317_suffix__order_Oorder__trans, fact_313_suffix__order_Oeq__iff, fact_211_rev__nonempty__induct, fact_116_old_Opath2__prefix, fact_111_old_Opath2__split__ex_H, fact_68_mem__Collect__eq, fact_309_suffix__appendD, fact_330_subset__code_I1_J, fact_272_prefix__Nil, fact_225_split__list__first__propE, fact_285_hd__append2, fact_98_self__append__conv2, fact_257_old_Opath2__split__last__prop, fact_318_suffix__order_Oantisym__conv, fact_218_rev__induct, fact_348_prefix__order_Oeq__iff, fact_65_list_Oinject, fact_151_list__tail__coinc, fact_1_ri__is__valid, fact_216_neq__Nil__revE, fact_234_append__Cons__eq__iff, fact_69_mem__Collect__eq, fact_48_list__se__match_I3_J, fact_283_old_Opath_Ocases, fact_237_split__list__first, fact_185_neq__Nil__conv, fact_8_assms_I10_J, fact_145_butlast__eq__cons__conv, fact_57_list__ee__eq__leel_I2_J, fact_345_tl__subset, fact_220_split__list__last__prop__iff, fact_207_list_Osel_I2_J, fact_297_ord__eq__le__eq__trans, fact_344_list_Oexhaust__sel, fact_279_old_Opath__split_I1_J, fact_315_suffix__order_Oeq__refl, fact_338_not__suffix__cases, fact_26_rs__props_I3_J, fact_51_list__se__match_I2_J, fact_281_old_Opath_Osimps, fact_273_prefix__bot_Obot_Oextremum__unique, fact_222_in__set__conv__decomp__first, fact_4_ri__props_I1_J, fact_336_hd__append, fact_214_neq__Nil__rev__conv, fact_210_rev__nonempty__induct2_H, fact_329_subset__code_I1_J, fact_187_list_Oexhaust, fact_182_induct__list012, fact_110_append_Oright__neutral, fact_269_List_Ofinite__set, fact_132_in__set__butlastD, fact_244_split__list, fact_171_list__all__zip_Oinduct, fact_206_list_Osel_I3_J, fact_282_old_Opath_Oinducts, fact_308_suffix__append, fact_173_list__induct__first2, fact_235_split__list__propE, fact_101_Nil__is__append__conv, fact_117_old_Opath2__rev__induct, fact_121_append1__eq__conv, fact_14_old_Opath2__not__Nil2, fact_0_False, fact_36_tl__append2, fact_294_old_Opath__by__tail, fact_212_append__eq__Cons__conv, fact_324_suffix__order_Odual__order_Oeq__iff, fact_86_append__Nil2, fact_316_suffix__order_Oorder_Otrans, fact_255_old_Opath__snoc, fact_92_self__append__conv, fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062, fact_174_remdups__adj_Oinduct, fact_112_old_Opath2__prefix__ex, fact_33_assms_I8_J, fact_11__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_305_suffixE, fact_301_suffix__Cons, fact_268_List_Ofinite__set, fact_83_old_Opath2__app_H, fact_251_old_Opath2__split__first__last, fact_31_ms_H__props_I3_J, fact_169_map__tailrec__rev_Oinduct, fact_125__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, fact_349_prefix__order_Oantisym, fact_250_prefix__snoc, fact_199_list_Oset__intros_I2_J, fact_311_suffix__tl, fact_265_old_Opath2__forget__hd, fact_181_min__list_Ocases, fact_252_same__prefix__nil, fact_240_split__list__prop, fact_253_old_Opath2__simple__loop, fact_158_append__eq__append__conv2, fact_22_ri__props_I2_J, fact_337_longest__common__prefix, fact_342_not__hd__in__tl, fact_202_list__match__lel__lel, fact_328_finite__list, fact_323_suffix__order_Odual__order_Otrans, fact_124_butlast__snoc, fact_81_old_Osuccessor__is__node, fact_72_Collect__cong, fact_13_old_Opath2__not__Nil, fact_184_list__induct2_H, fact_186_list_Oinducts, fact_271_prefix__code_I1_J, fact_258_defs__finite, fact_167_mergesort__by__rel__merge__induct, fact_304_Nil__suffix, fact_322_suffix__order_Oord__le__eq__trans, fact_17_old_Opath2__hd__in__ns, fact_156_append__eq__appendI, fact_232_in__set__conv__decomp
% 250.29/74.28 % No. of inferences in proof: 849
% 250.29/74.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 73804 ms resp. 72664 ms w/o parsing
% 243.15/74.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 243.15/74.64 % [INFO] Killing All external provers ...
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