%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP080^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:41 AM UTC 2026
% Result : Theorem 27.88s 7.29s
% Output : Refutation 29.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 240
% Syntax : Number of formulae : 482 ( 168 unt; 0 typ; 0 def)
% Number of atoms : 1598 ( 648 equ; 6 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 6510 ( 293 ~; 20 |; 156 &;5241 @)
% ( 0 <=>; 800 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 210 ( 210 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 16 con; 0-9 aty)
% Number of variables : 1806 ( 18 ^;1652 !; 136 ?;1806 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_l1129649930D_node_type,type,
list_l1129649930D_node: $tType ).
thf(list_P738500740D_node_type,type,
list_P738500740D_node: $tType ).
thf(set_Pr1040144478D_node_type,type,
set_Pr1040144478D_node: $tType ).
thf(produc1453890942D_node_type,type,
produc1453890942D_node: $tType ).
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(list_node_type,type,
list_node: $tType ).
thf(list_val_type,type,
list_val: $tType ).
thf(set_node_type,type,
set_node: $tType ).
thf(set_val_type,type,
set_val: $tType ).
thf(node_type,type,
node: $tType ).
thf(val_type,type,
val: $tType ).
thf(g_type,type,
g: $tType ).
thf(finite_finite_node_decl,type,
finite_finite_node: set_node > $o ).
thf(finite_finite_val_decl,type,
finite_finite_val: set_val > $o ).
thf(graph_1994935542_edgeD_decl,type,
graph_1994935542_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > list_node > $o ).
thf(graph_1670286392_edgeD_decl,type,
graph_1670286392_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
thf(graph_436675702_edgeD_decl,type,
graph_436675702_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
thf(graph_1947481694_edgeD_decl,type,
graph_1947481694_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_P738500740D_node ).
thf(graph_1012773594_edgeD_decl,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(graph_272749361_edgeD_decl,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(append_node_decl,type,
append_node: list_node > list_node > list_node ).
thf(distinct_node_decl,type,
distinct_node: list_node > $o ).
thf(cons_list_node_decl,type,
cons_list_node: list_node > list_list_node > list_list_node ).
thf(cons_node_decl,type,
cons_node: node > list_node > list_node ).
thf(nil_list_node_decl,type,
nil_list_node: list_list_node ).
thf(nil_Pr1769730692D_node_decl,type,
nil_Pr1769730692D_node: list_P738500740D_node ).
thf(nil_node_decl,type,
nil_node: list_node ).
thf(hd_node_decl,type,
hd_node: list_node > node ).
thf(set_node2_decl,type,
set_node2: list_node > set_node ).
thf(set_val2_decl,type,
set_val2: list_val > set_val ).
thf(tl_node_decl,type,
tl_node: list_node > list_node ).
thf(graph_589078910_edgeD_decl,type,
graph_589078910_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > $o ).
thf(sSA_CF139593942de_val_decl,type,
sSA_CF139593942de_val: ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF1156973626eD_val_decl,type,
sSA_CF1156973626eD_val: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > val > $o ).
thf(sSA_CF370335846de_val_decl,type,
sSA_CF370335846de_val: ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF848637139eD_val_decl,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF551432799de_val_decl,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(sSA_CF1252180629de_val_decl,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(sSA_CF1558836456eD_val_decl,type,
sSA_CF1558836456eD_val: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > ( g > node > set_val ) > g > node > val > $o ).
thf(collect_node_decl,type,
collect_node: ( node > $o ) > set_node ).
thf(collect_val_decl,type,
collect_val: ( val > $o ) > set_val ).
thf(suffix_node_decl,type,
suffix_node: list_node > list_node > $o ).
thf(member_node_decl,type,
member_node: node > set_node > $o ).
thf(member_val_decl,type,
member_val: val > set_val > $o ).
thf(entry_decl,type,
entry: g > node ).
thf(alpha_n_decl,type,
alpha_n: g > list_node ).
thf(phi_r_decl,type,
phi_r: val ).
thf(defs_decl,type,
defs: g > node > set_val ).
thf(g2_decl,type,
g2: g ).
thf(inEdges_decl,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(invar_decl,type,
invar: g > $o ).
thf(m_decl,type,
m: node ).
thf(ms_decl,type,
ms: list_node ).
thf(n_decl,type,
n: node ).
thf(ns_decl,type,
ns: list_node ).
thf(phis_decl,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(pred_phi_r_decl,type,
pred_phi_r: node ).
thf(r_decl,type,
r: val ).
thf(rs_decl,type,
rs: list_node ).
thf(rs2_decl,type,
rs2: list_node ).
thf(s_decl,type,
s: val ).
thf(218,axiom,
! [A: g,B: node,C: val,D: list_node] :
( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ~ ! [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
=> ~ ( member_val @ C @ ( defs @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_defAss_HE) ).
thf(1237,plain,
! [A: g,B: node,C: val,D: list_node] :
( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ~ ! [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
=> ~ ( member_val @ C @ ( defs @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(136,axiom,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( B
!= ( entry @ A ) )
=> ? [C: node] :
( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
& ! [D: node] :
( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_old_Oidom__ex) ).
thf(909,plain,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( B
!= ( entry @ A ) )
=> ? [C: node] :
( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
& ! [D: node] :
( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(132,axiom,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(893,plain,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(56,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ ( append_node @ C @ B ) )
= ( suffix_node @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_same__suffix__suffix) ).
thf(518,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)],[56]) ).
thf(147,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_old_Opath2__hd__in___092_060alpha_062n) ).
thf(962,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)],[147]) ).
thf(185,axiom,
! [A: g,B: node,C: list_node,D: node,E: node > list_node > node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( invar @ A )
=> ( E @ D @ ( cons_node @ D @ nil_node ) @ D ) )
=> ( ! [F: list_node,G: node,H: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D )
=> ( ( E @ H @ F @ D )
=> ( ( member_node @ G @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ H ) ) )
=> ( E @ G @ ( cons_node @ G @ F ) @ D ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_old_Opath2__induct) ).
thf(1110,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)],[185]) ).
thf(150,axiom,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ C ) ) )
=> ( ( B != C )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_old_Odominates__unsnoc) ).
thf(977,plain,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ C ) ) )
=> ( ( B != C )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(96,axiom,
! [A: list_node,B: list_node,C: node] :
( ( A != nil_node )
=> ( ( ( append_node @ B @ A )
= ( cons_node @ C @ nil_node ) )
= ( ( B = nil_node )
& ( A
= ( cons_node @ C @ nil_node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_list__se__match_I2_J) ).
thf(762,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)],[96]) ).
thf(159,axiom,
( ( tl_node @ nil_node )
= nil_node ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_list_Osel_I2_J) ).
thf(1005,plain,
( ( tl_node @ nil_node )
= nil_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(81,axiom,
! [A: list_node,B: node,C: list_node] :
( ( A != nil_node )
=> ( ( ( cons_node @ B @ nil_node )
= ( append_node @ A @ C ) )
= ( ( A
= ( cons_node @ B @ nil_node ) )
& ( C = nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_list__se__match_I3_J) ).
thf(683,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)],[81]) ).
thf(91,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ C @ A )
=> ( suffix_node @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_suffix__order_Odual__order_Otrans) ).
thf(730,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)],[91]) ).
thf(176,axiom,
! [A: g,B: node,C: val,D: list_node] :
( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_defAssD) ).
thf(1068,plain,
! [A: g,B: node,C: val,D: list_node] :
( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(4,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ F )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ F )
=> ( A @ E @ ( cons_node @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_list__2pre__induct) ).
thf(247,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)],[4]) ).
thf(94,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_strict__sorted_Oinduct) ).
thf(741,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)],[94]) ).
thf(177,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ A @ ( cons_node @ A @ nil_node ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_old_Oempty__path2) ).
thf(1073,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)],[177]) ).
thf(127,axiom,
! [A: g,B: node] : ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( cons_node @ B @ nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_old_OEntryPath__triv) ).
thf(878,plain,
! [A: g,B: node] : ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( cons_node @ B @ nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(73,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= nil_node )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_append__is__Nil__conv) ).
thf(655,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)],[73]) ).
thf(27,axiom,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( suffix_node @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_suffix__order_Oeq__refl) ).
thf(385,plain,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( suffix_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(46,axiom,
! [A: list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: list_node] : ( A @ E @ nil_node )
=> ( ! [E: list_node] : ( A @ nil_node @ E )
=> ( ! [E: node,F: list_node,G: node,H: list_node] :
( ( B @ E @ G )
=> ( ( A @ F @ ( cons_node @ G @ H ) )
=> ( A @ ( cons_node @ E @ F ) @ ( cons_node @ G @ H ) ) ) )
=> ( ! [E: node,F: list_node,G: node,H: list_node] :
( ~ ( B @ E @ G )
=> ( ( A @ ( cons_node @ E @ F ) @ H )
=> ( A @ ( cons_node @ E @ F ) @ ( cons_node @ G @ H ) ) ) )
=> ( A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_mergesort__by__rel__merge__induct) ).
thf(472,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)],[46]) ).
thf(224,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_rs_H__props_I1_J) ).
thf(1260,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)],[224]) ).
thf(142,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_split__list__first__prop) ).
thf(945,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)],[142]) ).
thf(173,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ? [C: list_node] : ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_old_OEntry__reaches) ).
thf(1063,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ? [C: list_node] : ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(78,axiom,
! [A: ( node > node > $o ) > list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: node > node > $o,F: node,G: list_node,H: node,I: list_node] :
( ( ( E @ F @ H )
=> ( A @ E @ G @ ( cons_node @ H @ I ) ) )
=> ( ( ~ ( E @ F @ H )
=> ( A @ E @ ( cons_node @ F @ G ) @ I ) )
=> ( A @ E @ ( cons_node @ F @ G ) @ ( cons_node @ H @ I ) ) ) )
=> ( ! [E: node > node > $o,F: list_node] : ( A @ E @ F @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ nil_node @ ( cons_node @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_mergesort__by__rel__merge_Oinduct) ).
thf(670,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)],[78]) ).
thf(134,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ E ) ) )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ E @ nil_node ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_old_Opath2__snoc) ).
thf(898,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)],[134]) ).
thf(37,axiom,
! [A: node,B: list_node] :
( ( hd_node @ ( cons_node @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_list_Osel_I1_J) ).
thf(417,plain,
! [A: node,B: list_node] :
( ( hd_node @ ( cons_node @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(18,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( cons_node @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_list__tail__coinc) ).
thf(320,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)],[18]) ).
thf(39,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( ( C = D )
=> ( A @ ( cons_node @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_node @ D @ E ) ) )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_remdups__adj_Oinduct) ).
thf(436,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)],[39]) ).
thf(215,axiom,
! [A: node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ~ ( member_node @ A @ ( set_node2 @ B ) )
=> ( ~ ( member_node @ A @ ( set_node2 @ C ) )
=> ( ( ( append_node @ B @ ( cons_node @ A @ C ) )
= ( append_node @ D @ ( cons_node @ A @ E ) ) )
= ( ( B = D )
& ( C = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_append__Cons__eq__iff) ).
thf(1228,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)],[215]) ).
thf(28,axiom,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_append__Nil) ).
thf(389,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(232,axiom,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_assms_I10_J) ).
thf(1298,plain,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(90,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( append_node @ D @ ( cons_node @ C @ nil_node ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_rev__induct) ).
thf(719,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)],[90]) ).
thf(102,axiom,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ B @ A ) )
= ( B = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_self__append__conv2) ).
thf(785,plain,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ B @ A ) )
= ( B = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(226,axiom,
! [A: g,B: node,C: val] :
( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
= ( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_defAss__def) ).
thf(1264,plain,
! [A: g,B: node,C: val] :
( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
= ( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(239,axiom,
! [A: g,B: node,C: val] :
( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
= ( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( defs @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_defAss_H__def) ).
thf(1323,plain,
! [A: g,B: node,C: val] :
( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
= ( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( defs @ A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(236,axiom,
! [A: list_node,B: list_node] :
( ( A != nil_node )
=> ( ( tl_node @ ( append_node @ A @ B ) )
= ( append_node @ ( tl_node @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_tl__append2) ).
thf(1313,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)],[236]) ).
thf(61,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_neq__NilE) ).
thf(559,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)],[61]) ).
thf(119,axiom,
! [A: g] :
( ( invar @ A )
=> ( ( graph_1947481694_edgeD @ inEdges @ A @ ( entry @ A ) )
= nil_Pr1769730692D_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_old_OEntry__unreachable) ).
thf(853,plain,
! [A: g] :
( ( invar @ A )
=> ( ( graph_1947481694_edgeD @ inEdges @ A @ ( entry @ A ) )
= nil_Pr1769730692D_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(221,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( A
= ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_list_Oexhaust__sel) ).
thf(1247,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( A
= ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(149,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ~ ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_split__list__propE) ).
thf(969,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)],[149]) ).
thf(98,axiom,
! [A: list_node] :
( ~ ( distinct_node @ A )
=> ? [B: list_node,C: list_node,D: list_node,E: node] :
( A
= ( append_node @ B @ ( append_node @ ( cons_node @ E @ nil_node ) @ ( append_node @ C @ ( append_node @ ( cons_node @ E @ nil_node ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_not__distinct__decomp) ).
thf(770,plain,
! [A: list_node] :
( ~ ( distinct_node @ A )
=> ? [B: list_node,C: list_node,D: list_node,E: node] :
( A
= ( append_node @ B @ ( append_node @ ( cons_node @ E @ nil_node ) @ ( append_node @ C @ ( append_node @ ( cons_node @ E @ nil_node ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(10,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: list_node,C: node] :
( A
!= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_rev__exhaust) ).
thf(289,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)],[10]) ).
thf(216,axiom,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ E ) ) @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ ( cons_node @ D @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_old_Opath2__split_I2_J) ).
thf(1232,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)],[216]) ).
thf(140,axiom,
! [A: node,B: list_node,C: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( ( member_node @ C @ ( set_node2 @ B ) )
=> ( ( ( A = C )
=> ! [D: list_node,E: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ C @ E ) ) ) )
=> ( ( ( A != C )
=> ! [D: list_node,E: list_node,F: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ A @ ( append_node @ E @ ( cons_node @ C @ F ) ) ) ) ) )
=> ~ ( ( A != C )
=> ! [D: list_node,E: list_node,F: list_node] :
( B
!= ( append_node @ D @ ( cons_node @ C @ ( append_node @ E @ ( cons_node @ A @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_xy__in__set__cases) ).
thf(924,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)],[140]) ).
thf(167,axiom,
! [A: list_node,B: node > $o] :
( ( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) ) )
= ( ? [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_split__list__last__prop__iff) ).
thf(1040,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)],[167]) ).
thf(25,axiom,
! [A: node,B: list_node] :
( nil_node
!= ( cons_node @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_list_Odistinct_I1_J) ).
thf(376,plain,
! [A: node,B: list_node] :
( nil_node
!= ( cons_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(193,axiom,
! [A: g,B: node,C: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_dominates__antisymm_H) ).
thf(1151,plain,
! [A: g,B: node,C: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(108,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ C )
=> ( suffix_node @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_suffix__appendD) ).
thf(806,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)],[108]) ).
thf(202,axiom,
! [A: g,B: node,C: val,D: node,E: list_node] :
( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B )
=> ( ! [F: node] :
( ( member_node @ F @ ( set_node2 @ ( tl_node @ E ) ) )
=> ~ ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ A @ F ) ) )
=> ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_defAss__extend) ).
thf(1183,plain,
! [A: g,B: node,C: val,D: node,E: list_node] :
( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B )
=> ( ! [F: node] :
( ( member_node @ F @ ( set_node2 @ ( tl_node @ E ) ) )
=> ~ ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ A @ F ) ) )
=> ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(169,axiom,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ C ) ) )
=> ( ( invar @ B )
=> ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_old_Opredecessor__is__node) ).
thf(1051,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)],[169]) ).
thf(123,axiom,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_old_Odominates__trans) ).
thf(866,plain,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(40,axiom,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_append__Nil2) ).
thf(453,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(35,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( append_node @ ( append_node @ A @ B ) @ C )
= ( append_node @ A @ ( append_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_append_Oassoc) ).
thf(411,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)],[35]) ).
thf(219,axiom,
! [A: g,B: node,C: node,D: node,E: list_node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C )
=> ( ~ ( member_node @ B @ ( set_node2 @ ( tl_node @ E ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_old_Odominates__extend) ).
thf(1242,plain,
! [A: g,B: node,C: node,D: node,E: list_node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C )
=> ( ~ ( member_node @ B @ ( set_node2 @ ( tl_node @ E ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(53,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( B = C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_suffix__order_Oord__le__eq__trans) ).
thf(507,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)],[53]) ).
thf(151,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_assms_I7_J) ).
thf(981,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)],[151]) ).
thf(97,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ! [B: node] :
( A
!= ( cons_node @ B @ nil_node ) )
=> ~ ! [B: node,C: node,D: list_node] :
( A
!= ( cons_node @ B @ ( cons_node @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_remdups__adj_Ocases) ).
thf(766,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)],[97]) ).
thf(31,axiom,
! [A: list_node,B: list_node,C: node] :
( ( suffix_node @ A @ ( append_node @ B @ ( cons_node @ C @ nil_node ) ) )
= ( ( A = nil_node )
| ? [D: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
& ( suffix_node @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_suffix__snoc) ).
thf(397,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)],[31]) ).
thf(82,axiom,
! [A: node,B: list_node,C: list_node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( append_node @ C @ D ) )
=> ( ( ( C = nil_node )
=> ( D
!= ( cons_node @ A @ B ) ) )
=> ~ ! [E: list_node] :
( ( C
= ( cons_node @ A @ E ) )
=> ( ( append_node @ E @ D )
!= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_list__Cons__eq__append__cases) ).
thf(687,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)],[82]) ).
thf(11,axiom,
! [A: list_node] : ( suffix_node @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_suffix__order_Odual__order_Orefl) ).
thf(293,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(144,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_assms_I8_J) ).
thf(956,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)],[144]) ).
thf(26,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ F @ E )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_splice_Oinduct) ).
thf(380,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)],[26]) ).
thf(75,axiom,
! [A: list_node,B: node,C: list_node] :
( ( A != nil_node )
=> ( ( ( cons_node @ B @ nil_node )
= ( append_node @ C @ A ) )
= ( ( C = nil_node )
& ( A
= ( cons_node @ B @ nil_node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_list__se__match_I4_J) ).
thf(661,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)],[75]) ).
thf(104,axiom,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_append_Oleft__neutral) ).
thf(793,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(234,axiom,
! [A: set_node] :
( ( finite_finite_node @ A )
=> ? [B: list_node] :
( ( set_node2 @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_finite__list) ).
thf(1306,plain,
! [A: set_node] :
( ( finite_finite_node @ A )
=> ? [B: list_node] :
( ( set_node2 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(175,axiom,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_rs_H__props_I2_J) ).
thf(1067,plain,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(54,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( cons_node @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_list_Oinject) ).
thf(512,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)],[54]) ).
thf(141,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ B ) ) )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons_node @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_old_OCons__path2) ).
thf(942,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)],[141]) ).
thf(145,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_list_Ocollapse) ).
thf(957,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(182,axiom,
! [A: g,B: node,C: list_node,D: node,E: node > list_node > node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( E @ B @ ( cons_node @ B @ nil_node ) @ B ) )
=> ( ! [F: list_node,G: node,H: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G )
=> ( ( E @ B @ F @ G )
=> ( ( member_node @ G @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ H ) ) )
=> ( E @ B @ ( append_node @ F @ ( cons_node @ H @ nil_node ) ) @ H ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_old_Opath2__rev__induct) ).
thf(1091,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)],[182]) ).
thf(100,axiom,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ A @ B ) )
= ( B = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_self__append__conv) ).
thf(778,plain,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ A @ B ) )
= ( B = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(15,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ nil_node @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ G )
=> ( A @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_rev__induct2_H) ).
thf(302,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)],[15]) ).
thf(199,axiom,
! [A: g,B: node,C: list_node,D: node,E: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member_node @ E @ ( set_node2 @ C ) )
=> ( member_node @ E @ ( set_node2 @ ( alpha_n @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_old_Opath2__in___092_060alpha_062n) ).
thf(1174,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)],[199]) ).
thf(29,axiom,
! [A: list_node] :
( ( A != nil_node )
= ( ? [B: list_node,C: node] :
( A
= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_neq__Nil__rev__conv) ).
thf(392,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)],[29]) ).
thf(103,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( A = B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_suffix__order_Oord__eq__le__trans) ).
thf(788,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)],[103]) ).
thf(187,axiom,
! [A: g,B: node,C: node,D: node,E: list_node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ D )
=> ( ( invar @ A )
=> ( member_node @ C @ ( set_node2 @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_old_Odominates__mid) ).
thf(1123,plain,
! [A: g,B: node,C: node,D: node,E: list_node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ D )
=> ( ( invar @ A )
=> ( member_node @ C @ ( set_node2 @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(122,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ~ ! [C: list_node,D: list_node] :
( B
!= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_in__set__list__format) ).
thf(862,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)],[122]) ).
thf(137,axiom,
! [A: node,B: list_node] :
( ( tl_node @ ( cons_node @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_list_Osel_I3_J) ).
thf(916,plain,
! [A: node,B: list_node] :
( ( tl_node @ ( cons_node @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(76,axiom,
! [A: list_node,B: list_node,C: list_node,D: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ C @ D ) )
= ( ? [E: list_node] :
( ( ( A
= ( append_node @ C @ E ) )
& ( ( append_node @ E @ B )
= D ) )
| ( ( ( append_node @ A @ E )
= C )
& ( B
= ( append_node @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_append__eq__append__conv2) ).
thf(665,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)],[76]) ).
thf(179,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( C != nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_old_Opath2__not__Nil) ).
thf(1079,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)],[179]) ).
thf(206,axiom,
r != phi_r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_False) ).
thf(1195,plain,
r != phi_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(162,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( C
= ( cons_node @ B @ nil_node ) )
=> ( D != B ) )
=> ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd_node @ ( tl_node @ C ) ) @ ( tl_node @ C ) @ D )
=> ~ ( member_node @ B @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( hd_node @ ( tl_node @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_old_Opath2__cases) ).
thf(1012,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)],[162]) ).
thf(8,axiom,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_List_Ofinite__set) ).
thf(285,plain,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(117,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_same__append__eq) ).
thf(847,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)],[117]) ).
thf(47,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_suffix__order_Oantisym) ).
thf(484,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)],[47]) ).
thf(41,axiom,
! [A: list_node,B: node,C: list_node,D: node] :
( ( ( append_node @ A @ ( cons_node @ B @ nil_node ) )
= ( append_node @ C @ ( cons_node @ D @ nil_node ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_append1__eq__conv) ).
thf(456,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)],[41]) ).
thf(115,axiom,
! [A: node,B: list_node,C: list_node] :
( ( append_node @ ( cons_node @ A @ B ) @ C )
= ( cons_node @ A @ ( append_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_append__Cons) ).
thf(842,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)],[115]) ).
thf(191,axiom,
! [A: node,B: list_node] : ( member_node @ A @ ( set_node2 @ ( cons_node @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_list_Oset__intros_I1_J) ).
thf(1143,plain,
! [A: node,B: list_node] : ( member_node @ A @ ( set_node2 @ ( cons_node @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(17,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_suffix__order_Oorder__trans) ).
thf(317,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)],[17]) ).
thf(71,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_suffix__order_Oorder_Oantisym) ).
thf(650,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)],[71]) ).
thf(186,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_old_Opath2__tl__in___092_060alpha_062n) ).
thf(1121,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)],[186]) ).
thf(33,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( append_node @ ( append_node @ A @ B ) @ C )
= ( append_node @ A @ ( append_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_append__assoc) ).
thf(403,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)],[33]) ).
thf(124,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_defs__finite) ).
thf(869,plain,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(38,axiom,
! [A: list_node,B: list_node,C: list_node > list_node > $o] :
( ~ ( suffix_node @ A @ B )
=> ( ! [D: node,E: list_node] : ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ nil_node )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( D != F )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( D = F )
=> ( ~ ( suffix_node @ E @ G )
=> ( ( C @ E @ G )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_not__suffix__induct) ).
thf(420,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)],[38]) ).
thf(51,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( suffix_node @ A @ ( append_node @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_suffix__appendI) ).
thf(499,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)],[51]) ).
thf(154,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_phiDefs__finite) ).
thf(989,plain,
! [A: g,B: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(83,axiom,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_mem__Collect__eq) ).
thf(697,plain,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(217,axiom,
! [A: node,B: list_node,C: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( member_node @ A @ ( set_node2 @ ( cons_node @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_list_Oset__intros_I2_J) ).
thf(1234,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)],[217]) ).
thf(210,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_split__list__last__propE) ).
thf(1207,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)],[210]) ).
thf(195,axiom,
~ ! [A: list_node,B: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ A @ B )
=> ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ A )
=> ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ B ) )
=> ~ ( member_node @ B @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(1155,plain,
~ ! [A: list_node,B: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ A @ B )
=> ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ A )
=> ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ B ) )
=> ~ ( member_node @ B @ ( 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)],[195]) ).
thf(86,axiom,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_Nil__suffix) ).
thf(706,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(129,axiom,
! [A: g,B: node,C: node] :
( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
= ( ( C != B )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
& ! [D: node] :
( ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( ( D != B )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_old_OisIdom__def) ).
thf(884,plain,
! [A: g,B: node,C: node] :
( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
= ( ( C != B )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
& ! [D: node] :
( ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( ( D != B )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(241,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd_node @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_old_Opath2__forget__hd) ).
thf(1329,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)],[241]) ).
thf(135,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_split__list__prop) ).
thf(901,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)],[135]) ).
thf(178,axiom,
! [A: node,B: g,C: node,D: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_allDefs__disjoint_H) ).
thf(1075,plain,
! [A: node,B: g,C: node,D: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(55,axiom,
! [A: node,B: list_node,C: list_node,D: list_node] :
( ( ( cons_node @ A @ B )
= ( append_node @ C @ D ) )
= ( ( ( C = nil_node )
& ( ( cons_node @ A @ B )
= D ) )
| ? [E: list_node] :
( ( ( cons_node @ A @ E )
= C )
& ( B
= ( append_node @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Cons__eq__append__conv) ).
thf(515,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)],[55]) ).
thf(189,axiom,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( tl_node @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_old_Opath2__app) ).
thf(1131,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)],[189]) ).
thf(205,axiom,
! [A: node,B: list_node,C: list_node,D: node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( member_node @ A @ ( set_node2 @ ( tl_node @ ( append_node @ C @ ( cons_node @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_old_Oelem__set__implies__elem__tl__app__cons) ).
thf(1192,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)],[205]) ).
thf(172,axiom,
! [A: g,B: node] :
( ( ( graph_272749361_edgeD @ inEdges @ A @ B )
!= nil_node )
=> ( ( invar @ A )
=> ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_old_Osuccessor__in___092_060alpha_062n) ).
thf(1060,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)],[172]) ).
thf(63,axiom,
! [A: list_node,B: list_node] :
( ~ ( suffix_node @ A @ B )
=> ( ( ( A != nil_node )
=> ( B != nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
=> ! [E: node,F: list_node] :
( ( B
= ( append_node @ F @ ( cons_node @ E @ nil_node ) ) )
=> ( ( E = C )
=> ( suffix_node @ D @ F ) ) ) )
=> ~ ! [C: node] :
( ? [D: list_node] :
( A
= ( append_node @ D @ ( cons_node @ C @ nil_node ) ) )
=> ! [D: node] :
( ? [E: list_node] :
( B
= ( append_node @ E @ ( cons_node @ D @ nil_node ) ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_not__suffix__cases) ).
thf(569,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)],[63]) ).
thf(68,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( A @ E )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_list__induct__first2) ).
thf(622,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)],[68]) ).
thf(113,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_suffix__bot_Obot_Oextremum__unique) ).
thf(837,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(3,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_suffix__Nil) ).
thf(244,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(208,axiom,
( rs2
= ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_rs__def) ).
thf(1202,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)],[208]) ).
thf(5,axiom,
! [A: list_node > $o,B: list_node] :
( ! [C: node,D: list_node] :
( ! [E: node,F: list_node] :
( ( D
= ( cons_node @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( ( A @ nil_node )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_min__list_Oinduct) ).
thf(266,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)],[5]) ).
thf(69,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ B @ A )
& ( suffix_node @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_suffix__order_Odual__order_Oeq__iff) ).
thf(633,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)],[69]) ).
thf(59,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ C @ B )
=> ( ( suffix_node @ A @ C )
| ( suffix_node @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_suffix__same__cases) ).
thf(541,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)],[59]) ).
thf(170,axiom,
! [A: g,B: node,C: val] :
( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( defs @ A @ E ) ) ) )
=> ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_defAss_HI) ).
thf(1054,plain,
! [A: g,B: node,C: val] :
( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( defs @ A @ E ) ) ) )
=> ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
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 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_in__set__conv__decomp__last) ).
thf(1026,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)],[164]) ).
thf(99,axiom,
! [A: ( node > node > $o ) > list_node > list_node > $o,B: node > node > $o,C: list_node,D: list_node] :
( ! [E: node > node > $o] : ( A @ E @ nil_node @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node,H: node,I: list_node] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons_node @ F @ G ) @ ( cons_node @ H @ I ) ) )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ ( cons_node @ F @ G ) @ nil_node )
=> ( ! [E: node > node > $o,F: node,G: list_node] : ( A @ E @ nil_node @ ( cons_node @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_list__all__zip_Oinduct) ).
thf(773,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)],[99]) ).
thf(13,axiom,
distinct_node @ nil_node,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_distinct_Osimps_I1_J) ).
thf(298,plain,
distinct_node @ nil_node,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(148,axiom,
! [A: g,B: node,C: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ~ ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ~ ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ C )
=> ( member_node @ B @ ( set_node2 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_old_OdominatesE) ).
thf(965,plain,
! [A: g,B: node,C: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ~ ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ~ ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ C )
=> ( member_node @ B @ ( set_node2 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(228,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ~ ! [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_split__list__first__propE) ).
thf(1273,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)],[228]) ).
thf(120,axiom,
! [A: list_node] :
( ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) )
=> ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_min__list_Ocases) ).
thf(856,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)],[120]) ).
thf(6,axiom,
! [A: list_node,B: list_node] :
( ( nil_node
= ( append_node @ A @ B ) )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Nil__is__append__conv) ).
thf(279,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)],[6]) ).
thf(92,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_suffix__order_Odual__order_Oantisym) ).
thf(733,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)],[92]) ).
thf(194,axiom,
member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_rs_H__props_I3_J) ).
thf(1154,plain,
member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(160,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( defs @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_defs__in__allDefs) ).
thf(1007,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( defs @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(126,axiom,
! [A: g,B: node,C: node] :
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ nil_node @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_old_Opath2__not__Nil2) ).
thf(875,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)],[126]) ).
thf(88,axiom,
! [A: ( node > node > $o ) > list_node > $o,B: node > node > $o,C: list_node] :
( ! [D: node > node > $o] : ( A @ D @ nil_node )
=> ( ! [D: node > node > $o,E: node] : ( A @ D @ ( cons_node @ E @ nil_node ) )
=> ( ! [D: node > node > $o,E: node,F: node,G: list_node] :
( ( A @ D @ ( cons_node @ F @ G ) )
=> ( A @ D @ ( cons_node @ E @ ( cons_node @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_successively_Oinduct) ).
thf(711,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)],[88]) ).
thf(16,axiom,
! [A: node,B: list_node] :
( ( cons_node @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_not__Cons__self2) ).
thf(313,plain,
! [A: node,B: list_node] :
( ( cons_node @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(67,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ( A @ nil_node @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ ( cons_node @ D @ E ) @ nil_node )
=> ( ! [D: node,E: list_node] : ( A @ nil_node @ ( cons_node @ D @ E ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ G )
=> ( A @ ( cons_node @ D @ E ) @ ( cons_node @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_list__induct2_H) ).
thf(611,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)],[67]) ).
thf(171,axiom,
! [A: list_node] :
( ( distinct_node @ A )
=> ~ ( member_node @ ( hd_node @ A ) @ ( set_node2 @ ( tl_node @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_FormalSSA__Misc_Odistinct__hd__tl) ).
thf(1058,plain,
! [A: list_node] :
( ( distinct_node @ A )
=> ~ ( member_node @ ( hd_node @ A ) @ ( set_node2 @ ( tl_node @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(44,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
=> ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_suffix__bot_Obot_Oextremum__uniqueI) ).
thf(466,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
=> ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(138,axiom,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_old_Odominates__refl) ).
thf(919,plain,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(34,axiom,
! [A: list_node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ( ( append_node @ A @ B )
= C )
=> ( ( D
= ( append_node @ B @ E ) )
=> ( ( append_node @ A @ D )
= ( append_node @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_append__eq__appendI) ).
thf(406,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)],[34]) ).
thf(229,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ D @ ( set_node2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_old_Opath2__last__in__ns) ).
thf(1282,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)],[229]) ).
thf(93,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: node,E: list_node,F: list_node] :
( ( A @ E @ ( cons_node @ D @ F ) )
=> ( A @ ( cons_node @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_revg_Oinduct) ).
thf(736,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)],[93]) ).
thf(157,axiom,
! [A: g,B: node,C: val] :
( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ A @ E ) ) ) )
=> ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_defAssI) ).
thf(996,plain,
! [A: g,B: node,C: val] :
( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member_node @ E @ ( set_node2 @ D ) )
& ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ A @ E ) ) ) )
=> ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(128,axiom,
! [A: list_node,B: node] :
( ( A != nil_node )
=> ( ( ( B
= ( hd_node @ A ) )
| ( member_node @ B @ ( set_node2 @ ( tl_node @ A ) ) ) )
= ( member_node @ B @ ( set_node2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_in__hd__or__tl__conv) ).
thf(880,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)],[128]) ).
thf(168,axiom,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( ( B != C )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C ) )
=> ( ( ( C != D )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D ) )
=> ( ( B != D )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_old_Ostrict__dom__trans) ).
thf(1043,plain,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( ( B != C )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C ) )
=> ( ( ( C != D )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D ) )
=> ( ( B != D )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(131,axiom,
! [A: list_node] :
( ( nil_node
= ( tl_node @ A ) )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Nil__tl) ).
thf(890,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)],[131]) ).
thf(50,axiom,
! [A: ( node > node ) > list_node > list_node > $o,B: node > node,C: list_node,D: list_node] :
( ! [E: node > node,F: list_node] : ( A @ E @ nil_node @ F )
=> ( ! [E: node > node,F: node,G: list_node,H: list_node] :
( ( A @ E @ G @ ( cons_node @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_node @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_map__tailrec__rev_Oinduct) ).
thf(494,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)],[50]) ).
thf(22,axiom,
! [A: node] : ( distinct_node @ ( cons_node @ A @ nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_distinct__singleton) ).
thf(367,plain,
! [A: node] : ( distinct_node @ ( cons_node @ A @ nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(66,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_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)],[66]) ).
thf(84,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_suffix__order_Oorder_Otrans) ).
thf(700,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)],[84]) ).
thf(165,axiom,
! [A: node,B: node,C: g,D: node] :
( ( ( A != B )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ B ) )
=> ( ( ( B != D )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ B @ D ) )
=> ( ( A != D )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_strict__dom__trans_H) ).
thf(1029,plain,
! [A: node,B: node,C: g,D: node] :
( ( ( A != B )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ B ) )
=> ( ( ( B != D )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ B @ D ) )
=> ( ( A != D )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(163,axiom,
! [A: g,B: list_node] :
( ( invar @ A )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ B @ ( entry @ A ) )
=> ( B
= ( cons_node @ ( entry @ A ) @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_old_OEntry__loop) ).
thf(1022,plain,
! [A: g,B: list_node] :
( ( invar @ A )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ B @ ( entry @ A ) )
=> ( B
= ( cons_node @ ( entry @ A ) @ nil_node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(77,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_suffix__order_Oeq__iff) ).
thf(668,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)],[77]) ).
thf(200,axiom,
! [A: g,B: node,C: node,D: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_dominates__trans_H) ).
thf(1177,plain,
! [A: g,B: node,C: node,D: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(19,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node,D: list_node] :
( ( A @ D )
=> ( A @ ( cons_node @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_list_Oinducts) ).
thf(330,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)],[19]) ).
thf(106,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_list_Oexhaust) ).
thf(799,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)],[106]) ).
thf(196,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( B
= ( hd_node @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_old_Opath2__hd) ).
thf(1162,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)],[196]) ).
thf(207,axiom,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ B @ A @ C )
= ( ? [D: node] :
( ( member_node @ D @ ( set_node2 @ ( alpha_n @ B ) ) )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ D @ A )
& ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_defAss__dominating) ).
thf(1198,plain,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ B @ A @ C )
= ( ? [D: node] :
( ( member_node @ D @ ( set_node2 @ ( alpha_n @ B ) ) )
& ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ D @ A )
& ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(220,axiom,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_List_Ofinite__set) ).
thf(1245,plain,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(153,axiom,
! [A: list_node,B: node > $o] :
( ( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) ) )
= ( ? [C: list_node,D: node] :
( ? [E: list_node] :
( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ~ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_split__list__first__prop__iff) ).
thf(986,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)],[153]) ).
thf(62,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: node,E: list_node,F: node,G: list_node] :
( ( ( D = F )
=> ( A @ E @ G ) )
=> ( A @ ( cons_node @ D @ E ) @ ( cons_node @ F @ G ) ) )
=> ( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: list_node] : ( A @ D @ nil_node )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_longest__common__prefix_Oinduct) ).
thf(563,plain,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: node,E: list_node,F: node,G: list_node] :
( ( ( D = F )
=> ( A @ E @ G ) )
=> ( A @ ( cons_node @ D @ E ) @ ( cons_node @ F @ G ) ) )
=> ( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: list_node] : ( A @ D @ nil_node )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(158,axiom,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ D @ A )
=> ( member_node @ C @ ( set_node2 @ D ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_old_OdominatesI) ).
thf(1000,plain,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ D @ A )
=> ( member_node @ C @ ( set_node2 @ D ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(14,axiom,
! [A: g] :
( ( graph_272749361_edgeD @ inEdges @ A @ ( entry @ A ) )
= nil_node ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_old_OEntry__no__predecessor) ).
thf(299,plain,
! [A: g] :
( ( graph_272749361_edgeD @ inEdges @ A @ ( entry @ A ) )
= nil_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(222,axiom,
! [A: list_node] :
( ~ ( distinct_node @ A )
=> ~ ! [B: node,C: list_node] :
( ( distinct_node @ C )
=> ( ( member_node @ B @ ( set_node2 @ C ) )
=> ! [D: list_node] :
( A
!= ( append_node @ C @ ( append_node @ ( cons_node @ B @ nil_node ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_not__distinct__split__distinct) ).
thf(1250,plain,
! [A: list_node] :
( ~ ( distinct_node @ A )
=> ~ ! [B: node,C: list_node] :
( ( distinct_node @ C )
=> ( ( member_node @ B @ ( set_node2 @ C ) )
=> ! [D: list_node] :
( A
!= ( append_node @ C @ ( append_node @ ( cons_node @ B @ nil_node ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(183,axiom,
! [A: g,B: node,C: node,D: node,E: list_node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C )
=> ( ! [F: node] :
( ( member_node @ F @ ( set_node2 @ ( tl_node @ E ) ) )
=> ( F != B ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_old_Odominates__unsnoc_H) ).
thf(1102,plain,
! [A: g,B: node,C: node,D: node,E: list_node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C )
=> ( ! [F: node] :
( ( member_node @ F @ ( set_node2 @ ( tl_node @ E ) ) )
=> ( F != B ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(72,axiom,
! [A: g] : ( invar @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_old_Oinvar) ).
thf(653,plain,
! [A: g] : ( invar @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(139,axiom,
! [A: g] : ( member_node @ ( entry @ A ) @ ( set_node2 @ ( alpha_n @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_old_OEntry__in__graph) ).
thf(922,plain,
! [A: g] : ( member_node @ ( entry @ A ) @ ( set_node2 @ ( alpha_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(74,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_append__same__eq) ).
thf(658,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)],[74]) ).
thf(57,axiom,
! [A: list_node,B: node,C: list_node,D: list_node,E: node,F: list_node] :
( ( ( append_node @ A @ ( cons_node @ B @ C ) )
= ( append_node @ D @ ( cons_node @ E @ F ) ) )
=> ( ! [G: list_node] :
( ( A
= ( append_node @ D @ ( cons_node @ E @ G ) ) )
=> ( F
!= ( append_node @ G @ ( cons_node @ B @ C ) ) ) )
=> ( ( ( D = A )
=> ( ( E = B )
=> ( F != C ) ) )
=> ~ ! [G: list_node] :
( ( D
= ( append_node @ A @ ( cons_node @ B @ G ) ) )
=> ( C
!= ( append_node @ G @ ( cons_node @ E @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_list__match__lel__lel) ).
thf(521,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)],[57]) ).
thf(198,axiom,
! [A: list_node] :
( ( ( tl_node @ A )
= nil_node )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_tl__Nil) ).
thf(1171,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)],[198]) ).
thf(49,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: list_node,C: node] :
( A
!= ( append_node @ B @ ( cons_node @ C @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_neq__Nil__revE) ).
thf(490,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)],[49]) ).
thf(197,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_split__list__last) ).
thf(1166,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)],[197]) ).
thf(80,axiom,
! [A: list_node,B: list_node,C: node] :
( ( suffix_node @ A @ B )
=> ( suffix_node @ A @ ( cons_node @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_suffix__ConsI) ).
thf(680,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)],[80]) ).
thf(192,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( A
!= ( entry @ B ) )
=> ~ ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ A ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_non__dominated__predecessor) ).
thf(1145,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( A
!= ( entry @ B ) )
=> ~ ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ A ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(110,axiom,
! [A: ( node > node > $o ) > list_node > $o,B: node > node > $o,C: list_node] :
( ! [D: node > node > $o] : ( A @ D @ nil_node )
=> ( ! [D: node > node > $o,E: node,F: list_node] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_node @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_sorted__wrt_Oinduct) ).
thf(823,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)],[110]) ).
thf(190,axiom,
! [A: list_node,B: node > $o] :
( ? [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
& ( B @ C ) )
=> ? [C: list_node,D: node,E: list_node] :
( ( A
= ( append_node @ C @ ( cons_node @ D @ E ) ) )
& ( B @ D )
& ! [F: node] :
( ( member_node @ F @ ( set_node2 @ E ) )
=> ~ ( B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_split__list__last__prop) ).
thf(1134,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)],[190]) ).
thf(48,axiom,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ? [B: list_val] :
( ( set_val2 @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_finite__list) ).
thf(487,plain,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ? [B: list_val] :
( ( set_val2 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(12,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= A )
= ( B = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_append__self__conv) ).
thf(295,plain,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= A )
= ( B = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_append_Oright__neutral) ).
thf(282,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(214,axiom,
! [A: g,B: node,C: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
= ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
& ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ C )
=> ( member_node @ B @ ( set_node2 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_old_Odominates__def) ).
thf(1225,plain,
! [A: g,B: node,C: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
= ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
& ! [D: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ C )
=> ( member_node @ B @ ( set_node2 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(130,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
= ( ? [C: list_node,D: list_node] :
( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_in__set__conv__decomp) ).
thf(887,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)],[130]) ).
thf(36,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_suffix__order_Oantisym__conv) ).
thf(414,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)],[36]) ).
thf(143,axiom,
! [A: g] :
( ( invar @ A )
=> ( distinct_node @ ( alpha_n @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_old_O_092_060alpha_062n__distinct) ).
thf(954,plain,
! [A: g] :
( ( invar @ A )
=> ( distinct_node @ ( alpha_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(227,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_split__list__first) ).
thf(1267,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)],[227]) ).
thf(156,axiom,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( entry @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_old_OEntry__dominates) ).
thf(993,plain,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( entry @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(203,axiom,
member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_rs_H__props_I4_J) ).
thf(1188,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)],[203]) ).
thf(52,axiom,
! [A: node,B: list_node,C: list_node,D: list_node,E: list_node] :
( ( ( cons_node @ A @ B )
= C )
=> ( ( D
= ( append_node @ B @ E ) )
=> ( ( cons_node @ A @ D )
= ( append_node @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Cons__eq__appendI) ).
thf(502,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)],[52]) ).
thf(114,axiom,
! [A: node,B: list_node,C: list_node] :
( ( suffix_node @ ( cons_node @ A @ B ) @ C )
=> ( suffix_node @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_suffix__ConsD) ).
thf(840,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)],[114]) ).
thf(43,axiom,
! [A: node,B: node,C: list_node] :
( ( distinct_node @ ( cons_node @ A @ ( cons_node @ B @ C ) ) )
= ( ( A != B )
& ( distinct_node @ ( cons_node @ A @ C ) )
& ( distinct_node @ ( cons_node @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_distinct__length__2__or__more) ).
thf(463,plain,
! [A: node,B: node,C: list_node] :
( ( distinct_node @ ( cons_node @ A @ ( cons_node @ B @ C ) ) )
= ( ( A != B )
& ( distinct_node @ ( cons_node @ A @ C ) )
& ( distinct_node @ ( cons_node @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(237,axiom,
! [A: list_node] :
( ( ~ ( distinct_node @ A ) )
= ( ? [B: list_node,C: node,D: list_node] :
( ( member_node @ C @ ( set_node2 @ B ) )
& ( distinct_node @ B )
& ( A
= ( append_node @ B @ ( cons_node @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_not__distinct__conv__prefix) ).
thf(1317,plain,
! [A: list_node] :
( ( ~ ( distinct_node @ A ) )
= ( ? [B: list_node,C: node,D: list_node] :
( ( member_node @ C @ ( set_node2 @ B ) )
& ( distinct_node @ B )
& ( A
= ( append_node @ B @ ( cons_node @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(109,axiom,
! [A: list_node,B: list_node > $o] :
( ( A != nil_node )
=> ( ! [C: node] : ( B @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( D != nil_node )
=> ( ( B @ D )
=> ( B @ ( append_node @ D @ ( cons_node @ C @ nil_node ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_rev__nonempty__induct) ).
thf(808,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)],[109]) ).
thf(212,axiom,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C )
=> ( ~ ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_old_Odominates__antitrans) ).
thf(1218,plain,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C )
=> ( ~ ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(60,axiom,
! [A: list_node > $o,B: list_node] :
( ( A @ nil_node )
=> ( ! [C: node] : ( A @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: node,E: list_node] :
( ( A @ E )
=> ( ( A @ ( cons_node @ D @ E ) )
=> ( A @ ( cons_node @ C @ ( cons_node @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_induct__list012) ).
thf(544,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)],[60]) ).
thf(223,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ? [C: list_node,D: list_node] :
( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_split__list) ).
thf(1257,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)],[223]) ).
thf(85,axiom,
! [A: list_node,B: node,C: list_node,D: node] :
( ( suffix_node @ ( append_node @ A @ ( cons_node @ B @ nil_node ) ) @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) )
= ( ( B = D )
& ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_snoc__suffix__snoc) ).
thf(703,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)],[85]) ).
thf(64,axiom,
! [A: list_node,B: node,C: list_node,D: node] :
( ( ( append_node @ A @ ( cons_node @ B @ C ) )
= ( cons_node @ D @ nil_node ) )
= ( ( A = nil_node )
& ( B = D )
& ( C = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_list__e__eq__lel_I2_J) ).
thf(600,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)],[64]) ).
thf(155,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_allDefs__finite) ).
thf(991,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(213,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ~ ! [C: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ C @ A )
=> ~ ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_old_OEntry__reachesE) ).
thf(1221,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ~ ! [C: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ C @ A )
=> ~ ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(230,axiom,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( ( graph_272749361_edgeD @ inEdges @ A @ B )
= nil_node )
= ( B
= ( entry @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_old_OEntry__iff__unreachable) ).
thf(1284,plain,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( ( graph_272749361_edgeD @ inEdges @ A @ B )
= nil_node )
= ( B
= ( entry @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(116,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( suffix_node @ ( cons_node @ A @ B ) @ ( cons_node @ C @ D ) )
=> ( suffix_node @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_suffix__ConsD2) ).
thf(845,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)],[116]) ).
thf(180,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( ( tl_node @ A )
= nil_node )
=> ~ ! [B: node] :
( A
!= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_tl__obtain__elem) ).
thf(1084,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)],[180]) ).
thf(201,axiom,
! [A: g] :
( ( graph_589078910_edgeD @ alpha_n @ invar @ inEdges @ entry @ A )
= ( ! [B: node,C: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B )
=> ? [D: node] :
( ( member_node @ D @ ( set_node2 @ C ) )
& ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_old_Oreducible__def) ).
thf(1180,plain,
! [A: g] :
( ( graph_589078910_edgeD @ alpha_n @ invar @ inEdges @ entry @ A )
= ( ! [B: node,C: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B )
=> ? [D: node] :
( ( member_node @ D @ ( set_node2 @ C ) )
& ! [E: node] :
( ( member_node @ E @ ( set_node2 @ C ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(58,axiom,
! [A: list_node] : ( suffix_node @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_suffix__order_Oorder__refl) ).
thf(539,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(211,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_phiUses__finite) ).
thf(1216,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)],[211]) ).
thf(188,axiom,
! [A: g,B: node,C: val,D: node,E: list_node] :
( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B )
=> ( ! [F: node] :
( ( member_node @ F @ ( set_node2 @ ( tl_node @ E ) ) )
=> ~ ( member_val @ C @ ( defs @ A @ F ) ) )
=> ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_defAss_H__extend) ).
thf(1126,plain,
! [A: g,B: node,C: val,D: node,E: list_node] :
( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B )
=> ( ! [F: node] :
( ( member_node @ F @ ( set_node2 @ ( tl_node @ E ) ) )
=> ~ ( member_val @ C @ ( defs @ A @ F ) ) )
=> ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(204,axiom,
! [A: g,B: node,C: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( invar @ A )
=> ~ ! [D: list_node] :
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_old_Odominates__path) ).
thf(1189,plain,
! [A: g,B: node,C: node] :
( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( invar @ A )
=> ~ ! [D: list_node] :
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(184,axiom,
! [A: g,B: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( distinct_node @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_old_OEntryPath__distinct) ).
thf(1108,plain,
! [A: g,B: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( distinct_node @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(240,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
= ( ? [C: list_node,D: list_node] :
( ( B
= ( append_node @ C @ ( cons_node @ A @ D ) ) )
& ~ ( member_node @ A @ ( set_node2 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_in__set__conv__decomp__first) ).
thf(1326,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)],[240]) ).
thf(133,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_dominates__refl_H) ).
thf(896,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(101,axiom,
! [A: list_node,B: node,C: list_node,D: list_node,E: list_node] :
( ( distinct_node @ ( append_node @ A @ ( cons_node @ B @ C ) ) )
=> ( ( ( append_node @ A @ ( cons_node @ B @ C ) )
= ( append_node @ D @ ( cons_node @ B @ E ) ) )
= ( ( A = D )
& ( C = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_distinct__match) ).
thf(781,plain,
! [A: list_node,B: node,C: list_node,D: list_node,E: list_node] :
( ( distinct_node @ ( append_node @ A @ ( cons_node @ B @ C ) ) )
=> ( ( ( append_node @ A @ ( cons_node @ B @ C ) )
= ( append_node @ D @ ( cons_node @ B @ E ) ) )
= ( ( A = D )
& ( C = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(112,axiom,
! [A: list_node,B: node,C: list_node] :
( ( A
= ( cons_node @ B @ C ) )
=> ( A != nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_list_OdiscI) ).
thf(832,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)],[112]) ).
thf(235,axiom,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_defNode__eq) ).
thf(1309,plain,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(89,axiom,
! [A: list_node,B: list_node,C: node,D: list_node] :
( ( ( append_node @ A @ B )
= ( cons_node @ C @ D ) )
= ( ( ( A = nil_node )
& ( B
= ( cons_node @ C @ D ) ) )
| ? [E: list_node] :
( ( A
= ( cons_node @ C @ E ) )
& ( ( append_node @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_append__eq__Cons__conv) ).
thf(716,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)],[89]) ).
thf(9,axiom,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_suffix__bot_Obot_Oextremum) ).
thf(287,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(95,axiom,
! [A: list_node,B: list_node,C: node,D: list_node] :
( ( ( append_node @ A @ B )
= ( cons_node @ C @ D ) )
=> ( ( ( A = nil_node )
=> ( B
!= ( cons_node @ C @ D ) ) )
=> ~ ! [E: list_node] :
( ( A
= ( cons_node @ C @ E ) )
=> ( ( append_node @ E @ B )
!= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_list__append__eq__Cons__cases) ).
thf(752,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)],[95]) ).
thf(24,axiom,
! [A: list_node] :
( ( A != nil_node )
= ( ? [B: node,C: list_node] :
( A
= ( cons_node @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_neq__Nil__conv) ).
thf(373,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)],[24]) ).
thf(65,axiom,
! [A: list_node > list_node > $o,B: list_node,C: list_node] :
( ! [D: list_node] : ( A @ nil_node @ D )
=> ( ! [D: list_node] : ( A @ D @ nil_node )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( A @ E @ ( cons_node @ F @ G ) )
=> ( ( A @ ( cons_node @ D @ E ) @ G )
=> ( A @ ( cons_node @ D @ E ) @ ( cons_node @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_shuffles_Oinduct) ).
thf(603,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)],[65]) ).
thf(1,conjecture,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(242,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)],[2]) ).
thf(20,axiom,
! [A: list_node,B: list_node,C: list_node > list_node > $o] :
( ( A != nil_node )
=> ( ( B != nil_node )
=> ( ! [D: node,E: node] : ( C @ ( cons_node @ D @ nil_node ) @ ( cons_node @ E @ nil_node ) )
=> ( ! [D: node,E: list_node,F: node] :
( ( E != nil_node )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( cons_node @ F @ nil_node ) ) )
=> ( ! [D: node,E: node,F: list_node] :
( ( F != nil_node )
=> ( C @ ( cons_node @ D @ nil_node ) @ ( append_node @ F @ ( cons_node @ E @ nil_node ) ) ) )
=> ( ! [D: node,E: list_node,F: node,G: list_node] :
( ( C @ E @ G )
=> ( ( E != nil_node )
=> ( ( G != nil_node )
=> ( C @ ( append_node @ E @ ( cons_node @ D @ nil_node ) ) @ ( append_node @ G @ ( cons_node @ F @ nil_node ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_rev__nonempty__induct2_H) ).
thf(341,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)],[20]) ).
thf(111,axiom,
! [A: list_node,B: list_node,C: node] :
( ( A != nil_node )
=> ( ( ( append_node @ A @ B )
= ( cons_node @ C @ nil_node ) )
= ( ( A
= ( cons_node @ C @ nil_node ) )
& ( B = nil_node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_list__se__match_I1_J) ).
thf(828,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)],[111]) ).
thf(174,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF370335846de_val @ phis @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_phiDefs__in__allDefs) ).
thf(1065,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF370335846de_val @ phis @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(105,axiom,
! [A: list_node,B: node,C: list_node] :
( ( suffix_node @ A @ ( cons_node @ B @ C ) )
= ( ( A
= ( cons_node @ B @ C ) )
| ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_suffix__Cons) ).
thf(796,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)],[105]) ).
thf(231,axiom,
! [A: g,B: node,C: list_node,D: node,E: node > $o] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ? [F: node] :
( ( member_node @ F @ ( set_node2 @ C ) )
& ( E @ F ) )
=> ~ ! [F: node,G: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D )
=> ( ( E @ F )
=> ( ! [H: node] :
( ( member_node @ H @ ( set_node2 @ ( tl_node @ G ) ) )
=> ~ ( E @ H ) )
=> ~ ( suffix_node @ G @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_old_Opath2__split__last__prop) ).
thf(1288,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)],[231]) ).
thf(32,axiom,
! [A: node,B: node,C: list_node,D: node,E: node,F: list_node] :
( ( ( cons_node @ A @ ( cons_node @ B @ nil_node ) )
= ( append_node @ C @ ( cons_node @ D @ ( cons_node @ E @ F ) ) ) )
= ( ( C = nil_node )
& ( A = D )
& ( B = E )
& ( F = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_list__ee__eq__leel_I1_J) ).
thf(400,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)],[32]) ).
thf(146,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ ( tl_node @ B ) ) )
=> ( member_node @ A @ ( set_node2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_FormalSSA__Misc_Oin__set__tlD) ).
thf(960,plain,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ ( tl_node @ B ) ) )
=> ( member_node @ A @ ( set_node2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(70,axiom,
! [A: list_node,B: list_node > $o] :
( ( A != nil_node )
=> ( ! [C: node] : ( B @ ( cons_node @ C @ nil_node ) )
=> ( ! [C: node,D: list_node] :
( ( D != nil_node )
=> ( ( B @ D )
=> ( B @ ( cons_node @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_list__nonempty__induct) ).
thf(635,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)],[70]) ).
thf(30,axiom,
( ( append_node @ nil_node )
= ( ^ [A: list_node] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_empty__append__eq__id) ).
thf(395,plain,
( ( append_node @ nil_node )
= ( ^ [A: list_node] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(225,axiom,
! [A: node,B: node,C: list_node] :
( ( member_node @ A @ ( set_node2 @ ( cons_node @ B @ C ) ) )
=> ( ( A = B )
| ( member_node @ A @ ( set_node2 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_set__ConsD) ).
thf(1261,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)],[225]) ).
thf(121,axiom,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ C ) ) )
=> ( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_old_Osuccessor__is__node) ).
thf(860,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)],[121]) ).
thf(42,axiom,
! [A: list_node,B: list_node] :
( ( A != nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_hd__append2) ).
thf(459,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)],[42]) ).
thf(118,axiom,
! [A: node,B: list_node,C: node,D: list_node] :
( ( ( cons_node @ A @ nil_node )
= ( append_node @ B @ ( cons_node @ C @ D ) ) )
= ( ( B = nil_node )
& ( C = A )
& ( D = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_list__e__eq__lel_I1_J) ).
thf(850,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)],[118]) ).
thf(152,axiom,
! [A: g,B: node,C: node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_old_Odominates__antisymm) ).
thf(982,plain,
! [A: g,B: node,C: node] :
( ( invar @ A )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(233,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ B ) )
=> ( ! [C: list_node] :
( B
!= ( cons_node @ A @ C ) )
=> ~ ! [C: node,D: list_node] :
( ( B
= ( cons_node @ C @ D ) )
=> ~ ( member_node @ A @ ( set_node2 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_list_Oset__cases) ).
thf(1299,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)],[233]) ).
thf(125,axiom,
! [A: g,B: list_node,C: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( ( suffix_node @ C @ B )
=> ( ( C != nil_node )
=> ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_old_OEntryPath__suffix) ).
thf(871,plain,
! [A: g,B: list_node,C: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( ( suffix_node @ C @ B )
=> ( ( C != nil_node )
=> ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(23,axiom,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( A
= ( append_node @ nil_node @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_eq__Nil__appendI) ).
thf(369,plain,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( A
= ( append_node @ nil_node @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(107,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= B )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_append__self__conv2) ).
thf(803,plain,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= B )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(238,axiom,
! [A: g,B: node,C: list_node,D: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member_node @ B @ ( set_node2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_old_Opath2__hd__in__ns) ).
thf(1320,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)],[238]) ).
thf(45,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ B )
= ( A = nil_node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_same__suffix__nil) ).
thf(469,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)],[45]) ).
thf(161,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_hd__Cons__tl) ).
thf(1009,plain,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(166,axiom,
! [A: g,B: node,C: list_node,D: node,E: list_node,F: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ E ) ) @ F )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append_node @ C @ ( cons_node @ D @ nil_node ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_old_Opath2__split_I1_J) ).
thf(1037,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)],[166]) ).
thf(79,axiom,
! [A: list_list_node] :
( ( A != nil_list_node )
=> ( ! [B: list_list_node] :
( A
!= ( cons_list_node @ nil_node @ B ) )
=> ~ ! [B: node,C: list_node,D: list_list_node] :
( A
!= ( cons_list_node @ ( cons_node @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_transpose_Ocases) ).
thf(676,plain,
! [A: list_list_node] :
( ( A != nil_list_node )
=> ( ! [B: list_list_node] :
( A
!= ( cons_list_node @ nil_node @ B ) )
=> ~ ! [B: node,C: list_node,D: list_list_node] :
( A
!= ( cons_list_node @ ( cons_node @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(181,axiom,
! [A: node,B: list_node] :
( ( distinct_node @ ( cons_node @ A @ B ) )
= ( ~ ( member_node @ A @ ( set_node2 @ B ) )
& ( distinct_node @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_distinct_Osimps_I2_J) ).
thf(1088,plain,
! [A: node,B: list_node] :
( ( distinct_node @ ( cons_node @ A @ B ) )
= ( ~ ( member_node @ A @ ( set_node2 @ B ) )
& ( distinct_node @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(209,axiom,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_mem__Collect__eq) ).
thf(1204,plain,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(21,axiom,
! [A: list_node,B: node,C: node,D: list_node,E: node,F: node] :
( ( ( append_node @ A @ ( cons_node @ B @ ( cons_node @ C @ D ) ) )
= ( cons_node @ E @ ( cons_node @ F @ nil_node ) ) )
= ( ( A = nil_node )
& ( E = B )
& ( F = C )
& ( D = nil_node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_list__ee__eq__leel_I2_J) ).
thf(364,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)],[21]) ).
thf(87,axiom,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Collect__mem__eq) ).
thf(708,plain,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(2047,plain,
$false,
inference(e,[status(thm)],[1237,909,893,518,962,1110,977,762,1005,683,730,1068,247,741,1073,878,655,385,472,1260,945,1063,670,898,417,320,436,1228,389,1298,719,785,1264,1323,1313,559,853,1247,969,770,289,1232,924,1040,376,1151,806,1183,1051,866,453,411,1242,507,981,766,397,687,293,956,380,661,793,1306,1067,512,942,957,1091,778,302,1174,392,788,1123,862,916,665,1079,1195,1012,285,847,484,456,842,1143,317,650,1121,403,869,420,499,989,697,1234,1207,1155,706,884,1329,901,1075,515,1131,1192,1060,569,622,837,244,1202,266,633,541,1054,1026,773,298,965,1273,856,279,733,1154,1007,875,711,313,611,1058,466,919,406,1282,736,996,880,1043,890,494,367,609,700,1029,1022,668,1177,330,799,1162,1198,1245,986,563,1000,299,1250,1102,653,922,658,521,1171,490,1166,680,1145,823,1134,487,295,282,1225,887,414,954,1267,993,1188,502,840,463,1317,808,1218,544,1257,703,600,991,1221,1284,845,1084,1180,539,1216,1126,1189,1108,1326,896,781,832,1309,716,287,752,373,603,242,341,828,1065,796,1288,400,960,635,395,1261,860,459,850,982,1299,871,369,803,1320,469,1009,1037,676,1088,1204,364,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP080^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n004.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:48:37 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.23/1.21 % [INFO] Parsing done (419ms).
% 2.23/1.23 % [INFO] Running in sequential loop mode.
% 3.42/1.62 % [INFO] eprover registered as external prover.
% 3.42/1.63 % [INFO] Scanning for conjecture ...
% 3.59/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 351 axioms. Running axiom selection ...
% 4.16/1.95 % [INFO] Axiom selection finished. Selected 239 axioms (removed 112 axioms).
% 5.24/2.23 % [INFO] Problem is higher-order (TPTP THF).
% 5.24/2.26 % [INFO] Type checking passed.
% 5.24/2.26 % [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 ...
% 27.88/7.29 % External prover 'e' found a proof!
% 27.88/7.29 % [INFO] Killing All external provers ...
% 27.88/7.29 % Time passed: 6938ms (effective reasoning time: 6052ms)
% 27.88/7.29 % 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)>
% 27.88/7.29 % Axioms used in derivation (239): fact_162_neq__NilE, fact_241_list__Cons__eq__append__cases, fact_70_old_OEntryPath__suffix, fact_205_list__match__lel__lel, fact_253_neq__Nil__rev__conv, fact_184_min__list_Oinduct, fact_288_split__list__last__prop__iff, fact_67_old_Odominates__unsnoc, fact_282_split__list__last__propE, fact_178_splice_Oinduct, fact_227_list__tail__coinc, fact_289_split__list__first__prop__iff, fact_42_old_Osuccessor__in___092_060alpha_062n, fact_52_old_Opath2__app, fact_101_old_Opath2__split_I2_J, fact_217_mergesort__by__rel__merge_Oinduct, fact_164_list_OdiscI, fact_195_suffix__ConsD2, fact_102_List_Ofinite__set, fact_223_longest__common__prefix_Oinduct, fact_329_suffix__same__cases, fact_87_hd__append2, fact_45_allDefs__finite, fact_44_old_Opath2__split__last__prop, fact_224_strict__sorted_Oinduct, fact_68_non__dominated__predecessor, fact_27_old_OEntry__reaches, fact_341_suffix__bot_Obot_Oextremum__uniqueI, fact_277_in__set__conv__decomp, fact_1_False, fact_332_append_Oleft__neutral, fact_330_finite__list, fact_23_old_Opredecessor__is__node, fact_133_list__ee__eq__leel_I1_J, fact_213_list__nonempty__induct, fact_350_old_OEntry__unreachable, fact_170_list_Oinducts, fact_24_old_Opath2__forget__hd, fact_135_list__ee__eq__leel_I2_J, fact_73_old_OEntry__no__predecessor, fact_18_old_Opath2__in___092_060alpha_062n, fact_6_old_O_092_060alpha_062n__distinct, fact_116_self__append__conv, fact_9_allDefs__disjoint_H, fact_160_list_Odistinct_I1_J, fact_229_distinct__length__2__or__more, fact_304_not__distinct__conv__prefix, fact_323_suffix__order_Oantisym__conv, fact_345_Nil__suffix, fact_31_defAss_H__extend, fact_106_empty__append__eq__id, fact_33_defAss_HI, fact_28_old_Oidom__ex, fact_10_assms_I7_J, fact_283_split__list__first__propE, fact_62_dominates__refl_H, fact_317_suffix__order_Odual__order_Oeq__iff, fact_231_list_Oset__cases, fact_120_append__Nil2, fact_233_set__ConsD, fact_41_defAss__dominating, fact_96_append__same__eq, fact_268_split__list__prop, fact_55_strict__dom__trans_H, fact_300_tl__obtain__elem, fact_32_defAss_H__def, fact_30_FormalSSA__Misc_Odistinct__hd__tl, fact_112_self__append__conv2, fact_334_append__Nil, fact_97_append__assoc, fact_16_old_Opath2__hd__in___092_060alpha_062n, fact_321_suffix__order_Oorder_Oantisym, fact_182_suffix__Cons, fact_99_suffix__order_Odual__order_Orefl, fact_319_suffix__order_Oord__le__eq__trans, fact_63_old_Odominates__path, fact_331_finite__list, fact_64_old_Odominates__mid, fact_259_neq__Nil__revE, fact_34_defAss_HE, fact_118_append__self__conv, fact_158_old_OCons__path2, fact_249_append__eq__Cons__conv, fact_75_old_OEntry__dominates, fact_53_defs__finite, fact_35_defAss__extend, fact_147_list__e__eq__lel_I2_J, fact_114_append__self__conv2, fact_5_old_OEntryPath__distinct, fact_316_suffix__order_Odual__order_Oantisym, fact_157_old_Oempty__path2, fact_83_old_Opath2__snoc, fact_310_list_Oexhaust__sel, fact_69_old_OisIdom__def, fact_293_distinct_Osimps_I2_J, fact_94_list_Oinject, fact_215_map__tailrec__rev_Oinduct, fact_72_old_Odominates__extend, fact_4_rs_H__props_I1_J, fact_336_eq__Nil__appendI, fact_2_old_OEntry__in__graph, fact_59_old_Odominates__antisymm, fact_40_phiDefs__in__allDefs, fact_60_dominates__trans_H, fact_90_same__suffix__nil, fact_149_snoc__suffix__snoc, fact_137_list__se__match_I1_J, fact_327_suffix__order_Oantisym, fact_318_suffix__order_Odual__order_Otrans, fact_348_suffix__appendI, fact_98_append_Oassoc, fact_189_suffix__ConsD, fact_294_distinct__match, fact_125_suffix__Nil, fact_110_Nil__is__append__conv, fact_25_old_OEntry__reachesE, fact_320_suffix__order_Oord__eq__le__trans, fact_11_defNode__eq, fact_324_suffix__order_Oorder__trans, fact_251_Cons__eq__append__conv, fact_19_old_Oinvar, fact_71_old_Odominates__unsnoc_H, fact_273_split__list__propE, fact_139_list__se__match_I2_J, fact_57_old_Odominates__trans, fact_322_suffix__order_Oorder_Oeq__iff, fact_314_append__eq__append__conv2, fact_13_defs__in__allDefs, fact_186_shuffles_Oinduct, fact_204_list__induct__first2, fact_270_xy__in__set__cases, fact_108_append__is__Nil__conv, fact_281_split__list__first__prop, fact_151_suffix__snoc, fact_302_not__distinct__decomp, fact_197_remdups__adj_Ocases, fact_272_split__list__first, fact_315_append__eq__appendI, fact_126_same__suffix__suffix, fact_7_rs_H__props_I3_J, fact_285_in__set__conv__decomp__last, fact_12_rs_H__props_I4_J, fact_61_dominates__antisymm_H, fact_81_in__hd__or__tl__conv, fact_38_defAssI, fact_76_old_OdominatesI, fact_56_old_Ostrict__dom__trans, fact_226_list_Osel_I3_J, fact_8_assms_I10_J, fact_237_list_Oset__intros_I2_J, fact_211_list__all__zip_Oinduct, fact_21_old_Opath2__last__in__ns, fact_228_not__Cons__self2, fact_15_FormalSSA__Misc_Oin__set__tlD, fact_46_old_Opath2__not__Nil, fact_58_old_Odominates__antitrans, fact_326_suffix__order_Oeq__refl, fact_298_tl__Nil, fact_202_remdups__adj_Oinduct, fact_279_in__set__list__format, fact_296_Nil__tl, fact_180_induct__list012, fact_48_mem__Collect__eq, fact_168_list_Oexhaust, fact_50_Collect__mem__eq, fact_129_old_OEntryPath__triv, fact_247_rev__nonempty__induct, fact_145_list__e__eq__lel_I1_J, fact_54_phiDefs__finite, fact_103_List_Ofinite__set, fact_207_successively_Oinduct, fact_104_append_Oright__neutral, fact_306_not__suffix__induct, fact_49_Collect__mem__eq, fact_153_list_Ocollapse, fact_39_defAssD, fact_235_list_Oset__intros_I1_J, fact_225_list_Osel_I1_J, fact_0_old_Opath2__hd, fact_95_same__append__eq, fact_100_suffix__order_Oorder__refl, fact_190_suffix__ConsI, fact_194_list__2pre__induct, fact_183_Cons__eq__appendI, fact_78_old_Oreducible__def, fact_51_old_Opath2__not__Nil2, fact_84_old_Opath2__rev__induct, fact_22_old_Osuccessor__is__node, fact_176_list__induct2_H, fact_131_append1__eq__conv, fact_328_suffix__order_Oeq__iff, fact_93_old_Oelem__set__implies__elem__tl__app__cons, fact_166_revg_Oinduct, fact_91_old_Opath2__induct, fact_291_distinct__singleton, fact_349_suffix__appendD, fact_143_list__se__match_I4_J, fact_43_phiUses__finite, fact_280_split__list__last__prop, fact_77_old_OEntry__iff__unreachable, fact_128_old_OEntry__loop, fact_47_mem__Collect__eq, fact_156_rs__def, fact_325_suffix__order_Oorder_Otrans, fact_261_rev__exhaust, fact_257_rev__induct2_H, fact_245_rev__nonempty__induct2_H, fact_338_distinct_Osimps_I1_J, fact_181_min__list_Ocases, fact_287_in__set__conv__decomp__first, fact_36_assms_I8_J, fact_313_not__distinct__split__distinct, fact_221_mergesort__by__rel__merge__induct, fact_74_old_Odominates__refl, fact_200_append__Cons, fact_346_list_Osel_I2_J, fact_127_old_Opath2__split_I1_J, fact_85_tl__append2, fact_155_hd__Cons__tl, fact_188_transpose_Ocases, fact_239_list__append__eq__Cons__cases, fact_20_old_Opath2__tl__in___092_060alpha_062n, fact_263_rev__induct, fact_265_split__list, fact_275_append__Cons__eq__iff, fact_343_suffix__bot_Obot_Oextremum, fact_172_neq__Nil__conv, fact_123_suffix__bot_Obot_Oextremum__unique, fact_26__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_3_rs_H__props_I2_J, fact_267_split__list__last, fact_82_old_Opath2__cases, fact_65_old_Odominates__def, fact_17_old_Opath2__hd__in__ns, fact_37_defAss__def, fact_308_not__suffix__cases, fact_141_list__se__match_I3_J, fact_199_sorted__wrt_Oinduct, fact_66_old_OdominatesE
% 27.88/7.29 % No. of inferences in proof: 482
% 27.88/7.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6938 ms resp. 6052 ms w/o parsing
% 29.18/7.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.18/7.58 % [INFO] Killing All external provers ...
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