TSTP Solution File: ITP081^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP081^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:40 EDT 2024
% Result : Theorem 13.15s 3.88s
% Output : Refutation 13.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 313
% Syntax : Number of formulae : 573 ( 197 unt; 55 typ; 0 def)
% Number of atoms : 1565 ( 728 equ; 8 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 6263 ( 304 ~; 34 |; 134 &;4999 @)
% ( 0 <=>; 792 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 311 ( 311 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 43 usr; 17 con; 0-7 aty)
% Number of variables : 1802 ( 26 ^1652 !; 124 ?;1802 :)
% 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_type,type,
finite_finite_node: set_node > $o ).
thf(finite_finite_val_type,type,
finite_finite_val: set_val > $o ).
thf(graph_1012773594_edgeD_type,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(graph_435229452_edgeD_type,type,
graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
thf(graph_272749361_edgeD_type,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(append_node_type,type,
append_node: list_node > list_node > list_node ).
thf(butlast_node_type,type,
butlast_node: list_node > list_node ).
thf(cons_node_type,type,
cons_node: node > list_node > list_node ).
thf(nil_node_type,type,
nil_node: list_node ).
thf(hd_node_type,type,
hd_node: list_node > node ).
thf(set_node2_type,type,
set_node2: list_node > set_node ).
thf(set_val2_type,type,
set_val2: list_val > set_val ).
thf(tl_node_type,type,
tl_node: list_node > list_node ).
thf(ord_less_eq_set_node_type,type,
ord_less_eq_set_node: set_node > set_node > $o ).
thf(ord_less_eq_set_val_type,type,
ord_less_eq_set_val: set_val > set_val > $o ).
thf(sSA_CF848637139eD_val_type,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_type,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(sSA_CF1252180629de_val_type,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(collect_node_type,type,
collect_node: ( node > $o ) > set_node ).
thf(collect_val_type,type,
collect_val: ( val > $o ) > set_val ).
thf(prefix_node_type,type,
prefix_node: list_node > list_node > $o ).
thf(suffix_node_type,type,
suffix_node: list_node > list_node > $o ).
thf(member_node_type,type,
member_node: node > set_node > $o ).
thf(member_val_type,type,
member_val: val > set_val > $o ).
thf(alpha_n_type,type,
alpha_n: g > list_node ).
thf(phi_r_type,type,
phi_r: val ).
thf(defs_type,type,
defs: g > node > set_val ).
thf(g2_type,type,
g2: g ).
thf(i_type,type,
i: node ).
thf(inEdges_type,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(invar_type,type,
invar: g > $o ).
thf(m_type,type,
m: node ).
thf(ms_type,type,
ms: list_node ).
thf(ms2_type,type,
ms2: list_node ).
thf(n_type,type,
n: node ).
thf(ns_type,type,
ns: list_node ).
thf(phis_type,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(pred_phi_r_type,type,
pred_phi_r: node ).
thf(r_type,type,
r: val ).
thf(ri_type,type,
ri: list_node ).
thf(rs_type,type,
rs: list_node ).
thf(rs2_type,type,
rs2: list_node ).
thf(s_type,type,
s: val ).
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/sandbox/benchmark/theBenchmark.p',fact_21_old_Oelem__set__implies__elem__tl__app__cons) ).
thf(1337,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(93,axiom,
! [A: node,B: list_node] :
( nil_node
!= ( cons_node @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_list_Odistinct_I1_J) ).
thf(629,plain,
! [A: node,B: list_node] :
( nil_node
!= ( cons_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
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/sandbox/benchmark/theBenchmark.p',fact_346_butlast__subset) ).
thf(365,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(143,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_append__same__eq) ).
thf(846,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(79,axiom,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_mem__Collect__eq) ).
thf(555,plain,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
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/sandbox/benchmark/theBenchmark.p',fact_33_assms_I8_J) ).
thf(1110,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(62,axiom,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_Nil__suffix) ).
thf(481,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
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/sandbox/benchmark/theBenchmark.p',fact_80_old_Opredecessor__is__node) ).
thf(977,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(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/sandbox/benchmark/theBenchmark.p',fact_212_append__eq__Cons__conv) ).
thf(1068,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(116,axiom,
! [A: list_node,B: node] :
( ( butlast_node @ ( append_node @ A @ ( cons_node @ B @ nil_node ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_butlast__snoc) ).
thf(741,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(104,axiom,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ B @ A ) )
= ( B = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_self__append__conv2) ).
thf(677,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(83,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_suffix__bot_Obot_Oextremum__unique) ).
thf(597,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
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/sandbox/benchmark/theBenchmark.p',fact_151_list__tail__coinc) ).
thf(523,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(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/sandbox/benchmark/theBenchmark.p',fact_156_append__eq__appendI) ).
thf(1158,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(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/sandbox/benchmark/theBenchmark.p',fact_65_list_Oinject) ).
thf(440,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(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/sandbox/benchmark/theBenchmark.p',fact_280_old_OCons__path) ).
thf(655,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(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/sandbox/benchmark/theBenchmark.p',fact_215_rev__induct2_H) ).
thf(1137,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(77,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_list_Oset__sel_I1_J) ).
thf(550,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(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/sandbox/benchmark/theBenchmark.p',fact_137_butlast_Osimps_I2_J) ).
thf(472,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(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/sandbox/benchmark/theBenchmark.p',fact_225_split__list__first__propE) ).
thf(1233,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(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/sandbox/benchmark/theBenchmark.p',fact_75_append__assoc) ).
thf(747,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(102,axiom,
! [A: list_node,B: list_node] :
( ( A != nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_hd__append2) ).
thf(670,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(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/sandbox/benchmark/theBenchmark.p',fact_208_list__append__eq__Cons__cases) ).
thf(1001,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(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/sandbox/benchmark/theBenchmark.p',fact_218_rev__induct) ).
thf(1127,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(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/sandbox/benchmark/theBenchmark.p',fact_188_revg_Oinduct) ).
thf(436,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(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/sandbox/benchmark/theBenchmark.p',fact_279_old_Opath__split_I1_J) ).
thf(829,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(44,axiom,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Collect__mem__eq) ).
thf(404,plain,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
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/sandbox/benchmark/theBenchmark.p',fact_240_split__list__prop) ).
thf(841,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(49,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_suffix__Nil) ).
thf(417,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
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/sandbox/benchmark/theBenchmark.p',fact_13_old_Opath2__not__Nil) ).
thf(1228,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(237,axiom,
( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_ri__is__valid) ).
thf(1254,plain,
( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(190,axiom,
( suffix_node
= ( ^ [A: list_node,B: list_node] :
? [C: list_node] :
( B
= ( append_node @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_Sublist_Osuffix__def) ).
thf(1055,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(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/sandbox/benchmark/theBenchmark.p',fact_113_old_Opath2__split__first__prop) ).
thf(1298,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(36,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( A = B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_suffix__order_Oord__eq__le__trans) ).
thf(372,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(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/sandbox/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(702,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(161,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= A )
= ( B = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_append__self__conv) ).
thf(949,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(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/sandbox/benchmark/theBenchmark.p',fact_186_list_Oinducts) ).
thf(460,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(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/sandbox/benchmark/theBenchmark.p',fact_312_suffix__same__cases) ).
thf(619,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(140,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_same__append__eq) ).
thf(838,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(156,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I7_J) ).
thf(934,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(30,axiom,
( ( butlast_node @ nil_node )
= nil_node ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_butlast_Osimps_I1_J) ).
thf(357,plain,
( ( butlast_node @ nil_node )
= nil_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
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/sandbox/benchmark/theBenchmark.p',fact_4_ri__props_I1_J) ).
thf(853,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(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/sandbox/benchmark/theBenchmark.p',fact_12_old_Opath2__split_I2_J) ).
thf(1147,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(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/sandbox/benchmark/theBenchmark.p',fact_83_old_Opath2__app_H) ).
thf(1013,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(198,axiom,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_append_Oright__neutral) ).
thf(1100,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(3,axiom,
! [A: node > $o,B: node > $o] :
( ! [C: node] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_node @ A )
= ( collect_node @ B ) ) ),
file('/export/starexec/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_142_in__set__butlast__appendI) ).
thf(924,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(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/sandbox/benchmark/theBenchmark.p',fact_16_old_Opath2__hd__in___092_060alpha_062n) ).
thf(756,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(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/sandbox/benchmark/theBenchmark.p',fact_200_Cons__eq__appendI) ).
thf(789,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(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/sandbox/benchmark/theBenchmark.p',fact_183_splice_Oinduct) ).
thf(443,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(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/sandbox/benchmark/theBenchmark.p',fact_310_suffix__appendI) ).
thf(1040,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(254,axiom,
! [A: list_node,B: list_node] :
( ( prefix_node @ ( append_node @ A @ B ) @ A )
= ( B = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_same__prefix__nil) ).
thf(1334,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(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/sandbox/benchmark/theBenchmark.p',fact_182_induct__list012) ).
thf(485,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(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/sandbox/benchmark/theBenchmark.p',fact_39_list__e__eq__lel_I2_J) ).
thf(1151,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(61,axiom,
prefix_node @ ms2 @ ms,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_ms_H__props_I2_J) ).
thf(480,plain,
prefix_node @ ms2 @ ms,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
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/sandbox/benchmark/theBenchmark.p',fact_309_suffix__appendD) ).
thf(766,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(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/sandbox/benchmark/theBenchmark.p',fact_255_old_Opath__snoc) ).
thf(1215,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(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/sandbox/benchmark/theBenchmark.p',fact_114_old_Opath2__induct) ).
thf(692,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(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/sandbox/benchmark/theBenchmark.p',fact_222_in__set__conv__decomp__first) ).
thf(956,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(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/sandbox/benchmark/theBenchmark.p',fact_180_min__list_Oinduct) ).
thf(312,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(216,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_defs__finite) ).
thf(1169,plain,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(41,axiom,
! [A: list_node] : ( prefix_node @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_prefix__order_Oorder__refl) ).
thf(397,plain,
! [A: list_node] : ( prefix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(233,axiom,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_append__Nil2) ).
thf(1242,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
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/sandbox/benchmark/theBenchmark.p',fact_230_in__set__list__format) ).
thf(849,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(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/sandbox/benchmark/theBenchmark.p',fact_301_suffix__Cons) ).
thf(307,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(67,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_suffix__order_Oantisym) ).
thf(512,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(6,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
=> ( A = nil_node ) ),
file('/export/starexec/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_254_old_Opath2__cases) ).
thf(661,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(38,axiom,
~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_ms_H__props_I3_J) ).
thf(381,plain,
~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
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/sandbox/benchmark/theBenchmark.p',fact_25_old_Opath2__split_I1_J) ).
thf(1057,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(214,axiom,
! [A: list_node] :
( ( ( tl_node @ A )
= nil_node )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_tl__Nil) ).
thf(1163,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(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/sandbox/benchmark/theBenchmark.p',fact_276_same__prefix__prefix) ).
thf(1274,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(25,axiom,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_mem__Collect__eq) ).
thf(334,plain,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
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/sandbox/benchmark/theBenchmark.p',fact_232_in__set__conv__decomp) ).
thf(1343,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(162,axiom,
member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rs_H__props_I3_J) ).
thf(952,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(16,axiom,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_List_Ofinite__set) ).
thf(302,plain,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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/sandbox/benchmark/theBenchmark.p',fact_298_suffix__ConsD2) ).
thf(297,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(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/sandbox/benchmark/theBenchmark.p',fact_270_Cons__prefix__Cons) ).
thf(407,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(113,axiom,
! [A: list_node] :
( ( nil_node
= ( tl_node @ A ) )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Nil__tl) ).
thf(729,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(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/sandbox/benchmark/theBenchmark.p',fact_291_in__hd__or__tl__conv) ).
thf(1238,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(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/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_297_ord__eq__le__eq__trans) ).
thf(349,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(32,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ B @ A )
& ( suffix_node @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_suffix__order_Odual__order_Oeq__iff) ).
thf(361,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(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/sandbox/benchmark/theBenchmark.p',fact_256_phiUses__finite) ).
thf(1210,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(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/sandbox/benchmark/theBenchmark.p',fact_339_not__suffix__induct) ).
thf(1079,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(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/sandbox/benchmark/theBenchmark.p',fact_283_old_Opath_Ocases) ).
thf(1195,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(245,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ~ ! [C: list_node] :
( B
!= ( append_node @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_suffixE) ).
thf(1281,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(21,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_suffix__order_Oantisym__conv) ).
thf(324,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(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/sandbox/benchmark/theBenchmark.p',fact_7_rs_H__props_I1_J) ).
thf(974,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(148,axiom,
( rs2
= ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rs__def) ).
thf(874,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(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/sandbox/benchmark/theBenchmark.p',fact_234_append__Cons__eq__iff) ).
thf(1270,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(205,axiom,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_append__Nil) ).
thf(1121,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
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/sandbox/benchmark/theBenchmark.p',fact_217_rev__exhaust) ).
thf(1064,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(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/sandbox/benchmark/theBenchmark.p',fact_127_old_OCons__path2) ).
thf(1111,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(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/sandbox/benchmark/theBenchmark.p',fact_30_old_Oempty__path2) ).
thf(725,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(173,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( A
= ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_list_Oexhaust__sel) ).
thf(980,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(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/sandbox/benchmark/theBenchmark.p',fact_160_strict__sorted_Oinduct) ).
thf(499,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(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/sandbox/benchmark/theBenchmark.p',fact_174_remdups__adj_Oinduct) ).
thf(420,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(204,axiom,
! [A: node,B: list_node] :
( ( tl_node @ ( cons_node @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_list_Osel_I3_J) ).
thf(1118,plain,
! [A: node,B: list_node] :
( ( tl_node @ ( cons_node @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
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/sandbox/benchmark/theBenchmark.p',fact_299_suffix__ConsI) ).
thf(328,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(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/sandbox/benchmark/theBenchmark.p',fact_23_old_Opath2__tl__in___092_060alpha_062n) ).
thf(1028,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(120,axiom,
! [A: list_node,B: list_node] :
( ( nil_node
= ( append_node @ A @ B ) )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Nil__is__append__conv) ).
thf(753,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(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/sandbox/benchmark/theBenchmark.p',fact_116_old_Opath2__prefix) ).
thf(1016,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(91,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_list_Oexhaust) ).
thf(622,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(203,axiom,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( B != nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_old_Opath__not__Nil) ).
thf(1114,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(175,axiom,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( A
= ( append_node @ nil_node @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_eq__Nil__appendI) ).
thf(997,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(68,axiom,
! [A: list_node,B: node,C: list_node] :
( ( A
= ( cons_node @ B @ C ) )
=> ( A != nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_list_OdiscI) ).
thf(515,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(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/sandbox/benchmark/theBenchmark.p',fact_293_old_Opath__in___092_060alpha_062n) ).
thf(1192,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(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/sandbox/benchmark/theBenchmark.p',fact_278_old_Oempty__path) ).
thf(779,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(85,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_neq__NilE) ).
thf(605,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(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/sandbox/benchmark/theBenchmark.p',fact_51_list__se__match_I2_J) ).
thf(1060,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(57,axiom,
! [A: list_node] :
( ( A != nil_node )
= ( ? [B: node,C: list_node] :
( A
= ( cons_node @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_neq__Nil__conv) ).
thf(457,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(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/sandbox/benchmark/theBenchmark.p',fact_227_split__list__first__prop) ).
thf(938,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(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/sandbox/benchmark/theBenchmark.p',fact_316_suffix__order_Oorder_Otrans) ).
thf(633,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(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/sandbox/benchmark/theBenchmark.p',fact_169_map__tailrec__rev_Oinduct) ).
thf(541,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(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/sandbox/benchmark/theBenchmark.p',fact_286_suffix__snoc) ).
thf(674,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(71,axiom,
! [A: node,B: list_node] : ( member_node @ A @ ( set_node2 @ ( cons_node @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_list_Oset__intros_I1_J) ).
thf(530,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(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/sandbox/benchmark/theBenchmark.p',fact_201_append__Cons) ).
thf(953,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(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/sandbox/benchmark/theBenchmark.p',fact_177_list__2pre__induct) ).
thf(558,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(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/sandbox/benchmark/theBenchmark.p',fact_211_rev__nonempty__induct) ).
thf(1071,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(132,axiom,
prefix_node @ ri @ rs2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ri__props_I4_J) ).
thf(794,plain,
prefix_node @ ri @ rs2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
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/sandbox/benchmark/theBenchmark.p',fact_167_mergesort__by__rel__merge__induct) ).
thf(586,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(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/sandbox/benchmark/theBenchmark.p',fact_253_old_Opath2__simple__loop) ).
thf(906,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(236,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= nil_node )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_append__is__Nil__conv) ).
thf(1251,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(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/sandbox/benchmark/theBenchmark.p',fact_45_list__se__match_I4_J) ).
thf(1103,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(4,axiom,
! [A: val > $o,B: val > $o] :
( ! [C: val] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_val @ A )
= ( collect_val @ B ) ) ),
file('/export/starexec/sandbox/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(9,axiom,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Collect__mem__eq) ).
thf(279,plain,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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/sandbox/benchmark/theBenchmark.p',fact_250_prefix__snoc) ).
thf(965,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(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/sandbox/benchmark/theBenchmark.p',fact_308_suffix__append) ).
thf(750,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(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/sandbox/benchmark/theBenchmark.p',fact_242_split__list__last) ).
thf(1154,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(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/sandbox/benchmark/theBenchmark.p',fact_265_old_Opath2__forget__hd) ).
thf(975,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(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/sandbox/benchmark/theBenchmark.p',fact_112_old_Opath2__prefix__ex) ).
thf(732,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(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/sandbox/benchmark/theBenchmark.p',fact_213_Cons__eq__append__conv) ).
thf(826,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(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/sandbox/benchmark/theBenchmark.p',fact_18_old_Opath2__in___092_060alpha_062n) ).
thf(1124,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(47,axiom,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_List_Ofinite__set) ).
thf(413,plain,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(238,axiom,
! [A: node] :
( ( member_node @ A @ ( set_node2 @ ( butlast_node @ ri ) ) )
=> ~ ( member_node @ A @ ( set_node2 @ ms ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_ri__props_I3_J) ).
thf(1256,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(229,axiom,
! [A: list_node] : ( suffix_node @ ( tl_node @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_suffix__tl) ).
thf(1226,plain,
! [A: list_node] : ( suffix_node @ ( tl_node @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
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/sandbox/benchmark/theBenchmark.p',fact_330_subset__code_I1_J) ).
thf(545,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(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/sandbox/benchmark/theBenchmark.p',fact_140_butlast__append) ).
thf(641,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(87,axiom,
! [A: list_node] : ( suffix_node @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_suffix__order_Oorder__refl) ).
thf(611,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
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/sandbox/benchmark/theBenchmark.p',fact_82_old_Osuccessor__in___092_060alpha_062n) ).
thf(1107,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(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/sandbox/benchmark/theBenchmark.p',fact_210_rev__nonempty__induct2_H) ).
thf(804,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(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/sandbox/benchmark/theBenchmark.p',fact_340_list_Oexpand) ).
thf(1258,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(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/sandbox/benchmark/theBenchmark.p',fact_267_old_Opath__split_I2_J) ).
thf(1224,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(123,axiom,
! [A: g] : ( invar @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_old_Oinvar) ).
thf(764,plain,
! [A: g] : ( invar @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
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/sandbox/benchmark/theBenchmark.p',fact_216_neq__Nil__revE) ).
thf(1048,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(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/sandbox/benchmark/theBenchmark.p',fact_281_old_Opath_Osimps) ).
thf(1349,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(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/sandbox/benchmark/theBenchmark.p',fact_171_list__all__zip_Oinduct) ).
thf(377,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(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/sandbox/benchmark/theBenchmark.p',fact_294_old_Opath__by__tail) ).
thf(737,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(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/sandbox/benchmark/theBenchmark.p',fact_323_suffix__order_Odual__order_Otrans) ).
thf(509,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(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/sandbox/benchmark/theBenchmark.p',fact_158_append__eq__append__conv2) ).
thf(649,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(186,axiom,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rs__props_I3_J) ).
thf(1043,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(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/sandbox/benchmark/theBenchmark.p',fact_173_list__induct__first2) ).
thf(387,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(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/sandbox/benchmark/theBenchmark.p',fact_193_list_Oset__cases) ).
thf(535,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(86,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_suffix__order_Oorder_Oeq__iff) ).
thf(609,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(63,axiom,
! [A: list_node,B: node] : ( ord_less_eq_set_node @ ( set_node2 @ A ) @ ( set_node2 @ ( cons_node @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_set__subset__Cons) ).
thf(483,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(69,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_suffix__order_Odual__order_Oantisym) ).
thf(520,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(210,axiom,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rs_H__loopfree) ).
thf(1149,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(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/sandbox/benchmark/theBenchmark.p',fact_57_list__ee__eq__leel_I2_J) ).
thf(943,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(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/sandbox/benchmark/theBenchmark.p',fact_237_split__list__first) ).
thf(1293,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(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/sandbox/benchmark/theBenchmark.p',fact_54_list__se__match_I1_J) ).
thf(1177,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(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/sandbox/benchmark/theBenchmark.p',fact_296_subset__Collect__conv) ).
thf(626,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(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/sandbox/benchmark/theBenchmark.p',fact_209_list__Cons__eq__append__cases) ).
thf(915,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(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/sandbox/benchmark/theBenchmark.p',fact_282_old_Opath_Oinducts) ).
thf(983,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(42,axiom,
! [A: list_node] : ( suffix_node @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_suffix__order_Odual__order_Orefl) ).
thf(399,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(165,axiom,
( ( append_node @ nil_node )
= ( ^ [A: list_node] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_empty__append__eq__id) ).
thf(959,plain,
( ( append_node @ nil_node )
= ( ^ [A: list_node] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
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/sandbox/benchmark/theBenchmark.p',fact_214_neq__Nil__rev__conv) ).
thf(768,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(15,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_hd__in__set) ).
thf(299,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(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/sandbox/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(100,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_hd__Cons__tl) ).
thf(658,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(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/sandbox/benchmark/theBenchmark.p',fact_266_old_Opath__hd) ).
thf(912,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(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/sandbox/benchmark/theBenchmark.p',fact_257_old_Opath2__split__last__prop) ).
thf(1171,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(95,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( B = C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_suffix__order_Oord__le__eq__trans) ).
thf(636,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(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/sandbox/benchmark/theBenchmark.p',fact_277_same__suffix__suffix) ).
thf(1245,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(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/sandbox/benchmark/theBenchmark.p',fact_145_butlast__eq__cons__conv) ).
thf(722,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(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/sandbox/benchmark/theBenchmark.p',fact_235_split__list__propE) ).
thf(1304,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(215,axiom,
! [A: g,B: list_node] :
( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B )
=> ( invar @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_old_Opath__invar) ).
thf(1166,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(76,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_suffix__order_Oeq__iff) ).
thf(548,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(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/sandbox/benchmark/theBenchmark.p',fact_264_old_Opath2__hd) ).
thf(927,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(243,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ B )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_same__suffix__nil) ).
thf(1277,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(89,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ ( butlast_node @ B ) ) )
=> ( member_node @ A @ ( set_node2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_in__set__butlastD) ).
thf(617,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(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/sandbox/benchmark/theBenchmark.p',fact_17_old_Opath2__hd__in__ns) ).
thf(1340,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(78,axiom,
! [A: node,B: list_node,C: list_node] :
( ( suffix_node @ ( cons_node @ A @ B ) @ C )
=> ( suffix_node @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_suffix__ConsD) ).
thf(553,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(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/sandbox/benchmark/theBenchmark.p',fact_32_rs_H__props_I4_J) ).
thf(795,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(105,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( ( tl_node @ A )
= nil_node )
=> ~ ! [B: node] :
( A
!= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_tl__obtain__elem) ).
thf(680,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(168,axiom,
r != phi_r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_False) ).
thf(968,plain,
r != phi_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
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/sandbox/benchmark/theBenchmark.p',fact_251_old_Opath2__split__first__last) ).
thf(1181,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(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/sandbox/benchmark/theBenchmark.p',fact_117_old_Opath2__rev__induct) ).
thf(712,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(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/sandbox/benchmark/theBenchmark.p',fact_168_mergesort__by__rel__merge_Oinduct) ).
thf(282,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(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/sandbox/benchmark/theBenchmark.p',fact_5_old_Opath2__app) ).
thf(971,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(22,axiom,
member_node @ i @ ( set_node2 @ ms ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_ri__props_I2_J) ).
thf(327,plain,
member_node @ i @ ( set_node2 @ ms ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(240,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= B )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_append__self__conv2) ).
thf(1267,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(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/sandbox/benchmark/theBenchmark.p',fact_331_set__mono__prefix) ).
thf(310,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(24,axiom,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ? [B: list_val] :
( ( set_val2 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_finite__list) ).
thf(331,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(184,axiom,
( ( tl_node @ nil_node )
= nil_node ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_list_Osel_I2_J) ).
thf(1038,plain,
( ( tl_node @ nil_node )
= nil_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
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/sandbox/benchmark/theBenchmark.p',fact_239_xy__in__set__cases) ).
thf(1317,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(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/sandbox/benchmark/theBenchmark.p',fact_295_set__mono__suffix) ).
thf(359,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(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/sandbox/benchmark/theBenchmark.p',fact_9_rs__props_I1_J) ).
thf(1220,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(59,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
& ( prefix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_prefix__order_Oeq__iff) ).
thf(470,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(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/sandbox/benchmark/theBenchmark.p',fact_184_list__induct2_H) ).
thf(576,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(246,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( A
= ( append_node @ B @ C ) )
=> ( suffix_node @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_suffixI) ).
thf(1285,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(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/sandbox/benchmark/theBenchmark.p',fact_81_old_Osuccessor__is__node) ).
thf(1218,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(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/sandbox/benchmark/theBenchmark.p',fact_224_in__set__conv__decomp__last) ).
thf(744,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(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/sandbox/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(1023,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(88,axiom,
! [A: node,B: list_node] :
( ( cons_node @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_not__Cons__self2) ).
thf(613,plain,
! [A: node,B: list_node] :
( ( cons_node @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(227,axiom,
! [A: list_node] :
( ( butlast_node @ ( tl_node @ A ) )
= ( tl_node @ ( butlast_node @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_butlast__tl) ).
thf(1221,plain,
! [A: list_node] :
( ( butlast_node @ ( tl_node @ A ) )
= ( tl_node @ ( butlast_node @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
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/sandbox/benchmark/theBenchmark.p',fact_179_shuffles_Oinduct) ).
thf(600,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(189,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_list_Ocollapse) ).
thf(1052,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(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/sandbox/benchmark/theBenchmark.p',fact_24_old_Opath2__last__in__ns) ).
thf(727,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(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/sandbox/benchmark/theBenchmark.p',fact_111_old_Opath2__split__ex_H) ).
thf(1094,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(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/sandbox/benchmark/theBenchmark.p',fact_338_not__suffix__cases) ).
thf(876,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(142,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_ms_H__props_I1_J) ).
thf(845,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
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/sandbox/benchmark/theBenchmark.p',fact_176_remdups__adj_Ocases) ).
thf(450,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(33,axiom,
! [A: list_node] : ( prefix_node @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_prefix__order_Odual__order_Orefl) ).
thf(363,plain,
! [A: list_node] : ( prefix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
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/sandbox/benchmark/theBenchmark.p',fact_220_split__list__last__prop__iff) ).
thf(931,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(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/sandbox/benchmark/theBenchmark.p',fact_226_split__list__last__propE) ).
thf(759,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(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/sandbox/benchmark/theBenchmark.p',fact_287_snoc__suffix__snoc) ).
thf(1010,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(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/sandbox/benchmark/theBenchmark.p',fact_148_butlast__eq__consE) ).
thf(1289,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(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/sandbox/benchmark/theBenchmark.p',fact_345_tl__subset) ).
thf(771,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(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/sandbox/benchmark/theBenchmark.p',fact_249_list_Oset__sel_I2_J) ).
thf(961,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(17,axiom,
! [A: set_node] :
( ( finite_finite_node @ A )
=> ? [B: list_node] :
( ( set_node2 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_finite__list) ).
thf(304,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(160,axiom,
! [A: g,B: node,C: node] :
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ nil_node @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_old_Opath2__not__Nil2) ).
thf(946,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(98,axiom,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ),
file('/export/starexec/sandbox/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(652,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(43,axiom,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_prefix__bot_Obot_Oextremum__unique) ).
thf(401,plain,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
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/sandbox/benchmark/theBenchmark.p',fact_342_not__hd__in__tl) ).
thf(786,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(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/sandbox/benchmark/theBenchmark.p',fact_228_split__list__last__prop) ).
thf(781,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(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/sandbox/benchmark/theBenchmark.p',fact_336_hd__append) ).
thf(1030,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(12,axiom,
! [A: list_node] :
( ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) )
=> ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_min__list_Ocases) ).
thf(290,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(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/sandbox/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(1308,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(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/sandbox/benchmark/theBenchmark.p',fact_60_list__ee__eq__leel_I1_J) ).
thf(1212,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(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/sandbox/benchmark/theBenchmark.p',fact_172_successively_Oinduct) ).
thf(383,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(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/sandbox/benchmark/theBenchmark.p',fact_67_append_Oassoc) ).
thf(1045,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(11,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_suffix__order_Oorder_Oantisym) ).
thf(287,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(138,axiom,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_append_Oleft__neutral) ).
thf(832,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
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/sandbox/benchmark/theBenchmark.p',fact_115_old_Opath2__split__ex) ).
thf(684,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(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/sandbox/benchmark/theBenchmark.p',fact_347_prefix__same__cases) ).
thf(447,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(244,axiom,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_assms_I10_J) ).
thf(1280,plain,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
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/sandbox/benchmark/theBenchmark.p',fact_317_suffix__order_Oorder__trans) ).
thf(410,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(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/sandbox/benchmark/theBenchmark.p',fact_219_split__list__first__prop__iff) ).
thf(835,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(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/sandbox/benchmark/theBenchmark.p',fact_202_list__match__lel__lel) ).
thf(854,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(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/sandbox/benchmark/theBenchmark.p',fact_244_split__list) ).
thf(1248,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(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/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_199_list_Oset__intros_I2_J) ).
thf(294,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(252,axiom,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ A @ B ) )
= ( B = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_self__append__conv) ).
thf(1314,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(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/sandbox/benchmark/theBenchmark.p',fact_170_list__nonempty__induct) ).
thf(341,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(72,axiom,
! [A: node,B: list_node] :
( ( hd_node @ ( cons_node @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_list_Osel_I1_J) ).
thf(532,plain,
! [A: node,B: list_node] :
( ( hd_node @ ( cons_node @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
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/sandbox/benchmark/theBenchmark.p',fact_121_append1__eq__conv) ).
thf(1346,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(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/sandbox/benchmark/theBenchmark.p',fact_337_longest__common__prefix) ).
thf(796,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(48,axiom,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_suffix__bot_Obot_Oextremum) ).
thf(415,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
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/sandbox/benchmark/theBenchmark.p',fact_48_list__se__match_I3_J) ).
thf(1019,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(8,axiom,
! [A: list_node] : ( prefix_node @ nil_node @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_prefix__code_I1_J) ).
thf(277,plain,
! [A: list_node] : ( prefix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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/sandbox/benchmark/theBenchmark.p',fact_42_list__e__eq__lel_I1_J) ).
thf(871,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(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/sandbox/benchmark/theBenchmark.p',fact_195_set__ConsD) ).
thf(369,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(26,axiom,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( suffix_node @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_suffix__order_Oeq__refl) ).
thf(337,plain,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( suffix_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(29,axiom,
! [A: list_node,B: list_node] :
( ( prefix_node @ A @ B )
=> ( ( prefix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_prefix__order_Oantisym) ).
thf(354,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(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/sandbox/benchmark/theBenchmark.p',fact_118_old_Opath2__snoc) ).
thf(935,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(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/sandbox/benchmark/theBenchmark.p',fact_36_tl__append2) ).
thf(775,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(56,axiom,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_prefix__Nil) ).
thf(454,plain,
! [A: list_node] :
( ( prefix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1361,plain,
$false,
inference(cvc4,[status(thm)],[1337,629,365,846,555,1110,481,977,1068,741,677,597,523,1158,440,655,1137,550,472,1233,747,670,1001,1127,436,829,404,841,417,1228,1254,1055,1298,372,702,949,460,619,838,934,357,853,1147,1013,1100,261,924,756,789,443,1040,1334,485,1151,480,766,1215,692,956,312,1169,397,1242,849,307,512,270,661,381,1057,1163,1274,334,1343,952,302,297,407,729,1238,260,349,361,1210,1079,1195,1281,324,974,874,1270,1121,1064,1111,725,980,499,420,1118,328,1028,753,1016,622,1114,997,515,1192,779,605,1060,457,938,633,541,674,530,953,558,1071,794,586,906,1251,1103,264,279,965,750,1154,975,732,826,1124,413,1256,1226,545,641,611,1107,804,1258,1224,764,1048,1349,377,737,509,649,1043,387,535,609,483,520,1149,943,1293,1177,626,915,983,399,959,768,299,267,658,912,1171,636,1245,722,1304,1166,548,927,1277,617,1340,553,795,680,968,1181,712,282,971,327,1267,310,331,1038,1317,359,1220,470,576,1285,1218,744,1023,613,1221,600,1052,727,1094,876,845,450,363,931,759,1010,1289,771,961,304,946,652,401,786,781,1030,290,1308,1212,383,1045,287,832,684,447,1280,410,835,854,1248,273,294,1314,341,532,1346,796,415,1019,277,871,369,337,354,935,775,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP081^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n023.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 14:50:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.99/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.18 % [INFO] Parsing done (281ms).
% 2.06/1.19 % [INFO] Running in sequential loop mode.
% 2.81/1.40 % [INFO] eprover registered as external prover.
% 2.81/1.41 % [INFO] cvc4 registered as external prover.
% 2.81/1.41 % [INFO] Scanning for conjecture ...
% 2.97/1.51 % [INFO] Found a conjecture and 350 axioms. Running axiom selection ...
% 3.45/1.61 % [INFO] Axiom selection finished. Selected 257 axioms (removed 93 axioms).
% 4.27/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 4.27/1.82 % [INFO] Type checking passed.
% 4.27/1.82 % [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 ...
% 13.15/3.87 % External prover 'cvc4' found a proof!
% 13.15/3.88 % [INFO] Killing All external provers ...
% 13.15/3.88 % Time passed: 3359ms (effective reasoning time: 2682ms)
% 13.15/3.88 % 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)>
% 13.15/3.88 % 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
% 13.15/3.88 % No. of inferences in proof: 518
% 13.15/3.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3359 ms resp. 2682 ms w/o parsing
% 13.97/4.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.97/4.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------