TSTP Solution File: ITP080^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP080^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:22:42 EDT 2024
% Result : Theorem 14.72s 4.34s
% Output : Refutation 15.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 304
% Syntax : Number of formulae : 546 ( 168 unt; 64 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 : 385 ( 385 >; 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_type,type,
finite_finite_node: set_node > $o ).
thf(finite_finite_val_type,type,
finite_finite_val: set_val > $o ).
thf(graph_1994935542_edgeD_type,type,
graph_1994935542_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > list_node > $o ).
thf(graph_1670286392_edgeD_type,type,
graph_1670286392_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
thf(graph_436675702_edgeD_type,type,
graph_436675702_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
thf(graph_1947481694_edgeD_type,type,
graph_1947481694_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_P738500740D_node ).
thf(graph_1012773594_edgeD_type,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(graph_272749361_edgeD_type,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(append_node_type,type,
append_node: list_node > list_node > list_node ).
thf(distinct_node_type,type,
distinct_node: list_node > $o ).
thf(cons_list_node_type,type,
cons_list_node: list_node > list_list_node > list_list_node ).
thf(cons_node_type,type,
cons_node: node > list_node > list_node ).
thf(nil_list_node_type,type,
nil_list_node: list_list_node ).
thf(nil_Pr1769730692D_node_type,type,
nil_Pr1769730692D_node: list_P738500740D_node ).
thf(nil_node_type,type,
nil_node: list_node ).
thf(hd_node_type,type,
hd_node: list_node > node ).
thf(set_node2_type,type,
set_node2: list_node > set_node ).
thf(set_val2_type,type,
set_val2: list_val > set_val ).
thf(tl_node_type,type,
tl_node: list_node > list_node ).
thf(graph_589078910_edgeD_type,type,
graph_589078910_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > $o ).
thf(sSA_CF139593942de_val_type,type,
sSA_CF139593942de_val: ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF1156973626eD_val_type,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_type,type,
sSA_CF370335846de_val: ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF848637139eD_val_type,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF551432799de_val_type,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(sSA_CF1252180629de_val_type,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(sSA_CF1558836456eD_val_type,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_type,type,
collect_node: ( node > $o ) > set_node ).
thf(collect_val_type,type,
collect_val: ( val > $o ) > set_val ).
thf(suffix_node_type,type,
suffix_node: list_node > list_node > $o ).
thf(member_node_type,type,
member_node: node > set_node > $o ).
thf(member_val_type,type,
member_val: val > set_val > $o ).
thf(entry_type,type,
entry: g > node ).
thf(alpha_n_type,type,
alpha_n: g > list_node ).
thf(phi_r_type,type,
phi_r: val ).
thf(defs_type,type,
defs: g > node > set_val ).
thf(g2_type,type,
g2: g ).
thf(inEdges_type,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(invar_type,type,
invar: g > $o ).
thf(m_type,type,
m: node ).
thf(ms_type,type,
ms: list_node ).
thf(n_type,type,
n: node ).
thf(ns_type,type,
ns: list_node ).
thf(phis_type,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(pred_phi_r_type,type,
pred_phi_r: node ).
thf(r_type,type,
r: val ).
thf(rs_type,type,
rs: list_node ).
thf(rs2_type,type,
rs2: list_node ).
thf(s_type,type,
s: val ).
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/sandbox/benchmark/theBenchmark.p',fact_71_old_Odominates__unsnoc_H) ).
thf(1036,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(24,axiom,
! [A: list_node] :
( ( A != nil_node )
= ( ? [B: node,C: list_node] :
( A
= ( cons_node @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_neq__Nil__conv) ).
thf(365,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(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/sandbox/benchmark/theBenchmark.p',fact_158_old_OCons__path2) ).
thf(893,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(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/sandbox/benchmark/theBenchmark.p',fact_76_old_OdominatesI) ).
thf(941,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(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/sandbox/benchmark/theBenchmark.p',fact_16_old_Opath2__hd__in___092_060alpha_062n) ).
thf(909,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(73,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= nil_node )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_append__is__Nil__conv) ).
thf(628,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(37,axiom,
! [A: node,B: list_node] :
( ( hd_node @ ( cons_node @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_list_Osel_I1_J) ).
thf(408,plain,
! [A: node,B: list_node] :
( ( hd_node @ ( cons_node @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(171,axiom,
! [A: list_node] :
( ( distinct_node @ A )
=> ~ ( member_node @ ( hd_node @ A ) @ ( set_node2 @ ( tl_node @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_FormalSSA__Misc_Odistinct__hd__tl) ).
thf(994,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(232,axiom,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_assms_I10_J) ).
thf(1205,plain,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
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/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_141_list__se__match_I3_J) ).
thf(655,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(86,axiom,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_Nil__suffix) ).
thf(677,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(184,axiom,
! [A: g,B: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( distinct_node @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_old_OEntryPath__distinct) ).
thf(1041,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(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/sandbox/benchmark/theBenchmark.p',fact_265_split__list) ).
thf(1173,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(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/sandbox/benchmark/theBenchmark.p',fact_58_old_Odominates__antitrans) ).
thf(1137,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(47,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_suffix__order_Oantisym) ).
thf(472,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(159,axiom,
( ( tl_node @ nil_node )
= nil_node ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_list_Osel_I2_J) ).
thf(945,plain,
( ( tl_node @ nil_node )
= nil_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(221,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( A
= ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_list_Oexhaust__sel) ).
thf(1164,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(114,axiom,
! [A: node,B: list_node,C: list_node] :
( ( suffix_node @ ( cons_node @ A @ B ) @ C )
=> ( suffix_node @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_suffix__ConsD) ).
thf(797,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(198,axiom,
! [A: list_node] :
( ( ( tl_node @ A )
= nil_node )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_tl__Nil) ).
thf(1095,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(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/sandbox/benchmark/theBenchmark.p',fact_40_phiDefs__in__allDefs) ).
thf(1001,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(209,axiom,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_mem__Collect__eq) ).
thf(1127,plain,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
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/sandbox/benchmark/theBenchmark.p',fact_224_strict__sorted_Oinduct) ).
thf(709,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(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/sandbox/benchmark/theBenchmark.p',fact_69_old_OisIdom__def) ).
thf(841,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(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/sandbox/benchmark/theBenchmark.p',fact_64_old_Odominates__mid) ).
thf(1055,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(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/sandbox/benchmark/theBenchmark.p',fact_239_list__append__eq__Cons__cases) ).
thf(719,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(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/sandbox/benchmark/theBenchmark.p',fact_137_list__se__match_I1_J) ).
thf(785,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(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/sandbox/benchmark/theBenchmark.p',fact_178_splice_Oinduct) ).
thf(372,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(92,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_suffix__order_Odual__order_Oantisym) ).
thf(702,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(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/sandbox/benchmark/theBenchmark.p',fact_195_suffix__ConsD2) ).
thf(802,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(161,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_hd__Cons__tl) ).
thf(949,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(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/sandbox/benchmark/theBenchmark.p',fact_22_old_Osuccessor__is__node) ).
thf(817,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(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/sandbox/benchmark/theBenchmark.p',fact_0_old_Opath2__hd) ).
thf(1087,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(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/sandbox/benchmark/theBenchmark.p',fact_93_old_Oelem__set__implies__elem__tl__app__cons) ).
thf(1115,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(42,axiom,
! [A: list_node,B: list_node] :
( ( A != nil_node )
=> ( ( hd_node @ ( append_node @ A @ B ) )
= ( hd_node @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_hd__append2) ).
thf(448,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(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/sandbox/benchmark/theBenchmark.p',fact_287_in__set__conv__decomp__first) ).
thf(1232,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(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/sandbox/benchmark/theBenchmark.p',fact_314_append__eq__append__conv2) ).
thf(638,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(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/sandbox/benchmark/theBenchmark.p',fact_62_dominates__refl_H) ).
thf(853,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(112,axiom,
! [A: list_node,B: node,C: list_node] :
( ( A
= ( cons_node @ B @ C ) )
=> ( A != nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_list_OdiscI) ).
thf(789,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(66,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_suffix__order_Oorder_Oeq__iff) ).
thf(591,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(27,axiom,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( suffix_node @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_suffix__order_Oeq__refl) ).
thf(376,plain,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( suffix_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(71,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_suffix__order_Oorder_Oantisym) ).
thf(623,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(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/sandbox/benchmark/theBenchmark.p',fact_272_split__list__first) ).
thf(1183,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(48,axiom,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ? [B: list_val] :
( ( set_val2 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_finite__list) ).
thf(475,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(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/sandbox/benchmark/theBenchmark.p',fact_59_old_Odominates__antisymm) ).
thf(924,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(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/sandbox/benchmark/theBenchmark.p',fact_56_old_Ostrict__dom__trans) ).
thf(981,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(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/sandbox/benchmark/theBenchmark.p',fact_315_append__eq__appendI) ).
thf(397,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(7,axiom,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_append_Oright__neutral) ).
thf(280,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= A )
= ( B = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_append__self__conv) ).
thf(293,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(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/sandbox/benchmark/theBenchmark.p',fact_68_non__dominated__predecessor) ).
thf(1072,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(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/sandbox/benchmark/theBenchmark.p',fact_329_suffix__same__cases) ).
thf(527,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(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/sandbox/benchmark/theBenchmark.p',fact_11_defNode__eq) ).
thf(1215,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(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/sandbox/benchmark/theBenchmark.p',fact_143_list__se__match_I4_J) ).
thf(634,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(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/sandbox/benchmark/theBenchmark.p',fact_306_not__suffix__induct) ).
thf(411,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(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/sandbox/benchmark/theBenchmark.p',fact_23_old_Opredecessor__is__node) ).
thf(988,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(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/sandbox/benchmark/theBenchmark.p',fact_78_old_Oreducible__def) ).
thf(1104,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(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/sandbox/benchmark/theBenchmark.p',fact_184_min__list_Oinduct) ).
thf(265,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(28,axiom,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_append__Nil) ).
thf(380,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
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/sandbox/benchmark/theBenchmark.p',fact_44_old_Opath2__split__last__prop) ).
thf(1199,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(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/sandbox/benchmark/theBenchmark.p',fact_182_suffix__Cons) ).
thf(761,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(119,axiom,
! [A: g] :
( ( invar @ A )
=> ( ( graph_1947481694_edgeD @ inEdges @ A @ ( entry @ A ) )
= nil_Pr1769730692D_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_old_OEntry__unreachable) ).
thf(810,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(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/sandbox/benchmark/theBenchmark.p',fact_231_list_Oset__cases) ).
thf(1206,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(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/sandbox/benchmark/theBenchmark.p',fact_229_distinct__length__2__or__more) ).
thf(452,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(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/sandbox/benchmark/theBenchmark.p',fact_245_rev__nonempty__induct2_H) ).
thf(334,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(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/sandbox/benchmark/theBenchmark.p',fact_304_not__distinct__conv__prefix) ).
thf(1223,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(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/sandbox/benchmark/theBenchmark.p',fact_82_old_Opath2__cases) ).
thf(952,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(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/sandbox/benchmark/theBenchmark.p',fact_28_old_Oidom__ex) ).
thf(862,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(14,axiom,
! [A: g] :
( ( graph_272749361_edgeD @ inEdges @ A @ ( entry @ A ) )
= nil_node ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_old_OEntry__no__predecessor) ).
thf(297,plain,
! [A: g] :
( ( graph_272749361_edgeD @ inEdges @ A @ ( entry @ A ) )
= nil_node ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
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/sandbox/benchmark/theBenchmark.p',fact_294_distinct__match) ).
thf(746,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(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/sandbox/benchmark/theBenchmark.p',fact_267_split__list__last) ).
thf(1091,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(131,axiom,
! [A: list_node] :
( ( nil_node
= ( tl_node @ A ) )
= ( ( A = nil_node )
| ? [B: node] :
( A
= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_Nil__tl) ).
thf(847,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(23,axiom,
! [A: list_node,B: list_node] :
( ( A = B )
=> ( A
= ( append_node @ nil_node @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_eq__Nil__appendI) ).
thf(361,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(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/sandbox/benchmark/theBenchmark.p',fact_147_list__e__eq__lel_I2_J) ).
thf(583,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(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/sandbox/benchmark/theBenchmark.p',fact_170_list_Oinducts) ).
thf(324,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(9,axiom,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_suffix__bot_Obot_Oextremum) ).
thf(285,plain,
! [A: list_node] : ( suffix_node @ nil_node @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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/sandbox/benchmark/theBenchmark.p',fact_72_old_Odominates__extend) ).
thf(1159,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(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/sandbox/benchmark/theBenchmark.p',fact_221_mergesort__by__rel__merge__induct) ).
thf(461,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(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/sandbox/benchmark/theBenchmark.p',fact_207_successively_Oinduct) ).
thf(682,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(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/sandbox/benchmark/theBenchmark.p',fact_77_old_OEntry__iff__unreachable) ).
thf(1195,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(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/sandbox/benchmark/theBenchmark.p',fact_227_list__tail__coinc) ).
thf(317,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(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/sandbox/benchmark/theBenchmark.p',fact_213_list__nonempty__induct) ).
thf(615,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(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/sandbox/benchmark/theBenchmark.p',fact_41_defAss__dominating) ).
thf(1121,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(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/sandbox/benchmark/theBenchmark.p',fact_12_rs_H__props_I4_J) ).
thf(1111,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(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/sandbox/benchmark/theBenchmark.p',fact_151_suffix__snoc) ).
thf(388,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(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/sandbox/benchmark/theBenchmark.p',fact_135_list__ee__eq__leel_I2_J) ).
thf(356,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(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/sandbox/benchmark/theBenchmark.p',fact_176_list__induct2_H) ).
thf(593,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(206,axiom,
r != phi_r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_False) ).
thf(1118,plain,
r != phi_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
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/sandbox/benchmark/theBenchmark.p',fact_94_list_Oinject) ).
thf(499,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(139,axiom,
! [A: g] : ( member_node @ ( entry @ A ) @ ( set_node2 @ ( alpha_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_old_OEntry__in__graph) ).
thf(874,plain,
! [A: g] : ( member_node @ ( entry @ A ) @ ( set_node2 @ ( alpha_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
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/sandbox/benchmark/theBenchmark.p',fact_65_old_Odominates__def) ).
thf(1143,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(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/sandbox/benchmark/theBenchmark.p',fact_45_allDefs__finite) ).
thf(933,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(103,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( A = B )
=> ( ( suffix_node @ B @ C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_suffix__order_Oord__eq__le__trans) ).
thf(753,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(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/sandbox/benchmark/theBenchmark.p',fact_183_Cons__eq__appendI) ).
thf(489,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(87,axiom,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Collect__mem__eq) ).
thf(679,plain,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
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/sandbox/benchmark/theBenchmark.p',fact_34_defAss_HE) ).
thf(1155,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(143,axiom,
! [A: g] :
( ( invar @ A )
=> ( distinct_node @ ( alpha_n @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_old_O_092_060alpha_062n__distinct) ).
thf(901,plain,
! [A: g] :
( ( invar @ A )
=> ( distinct_node @ ( alpha_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
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/sandbox/benchmark/theBenchmark.p',fact_249_append__eq__Cons__conv) ).
thf(686,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(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/sandbox/benchmark/theBenchmark.p',fact_81_in__hd__or__tl__conv) ).
thf(837,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(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/sandbox/benchmark/theBenchmark.p',fact_101_old_Opath2__split_I2_J) ).
thf(1150,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(3,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_38_defAssI) ).
thf(938,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(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/sandbox/benchmark/theBenchmark.p',fact_205_list__match__lel__lel) ).
thf(508,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(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/sandbox/benchmark/theBenchmark.p',fact_149_snoc__suffix__snoc) ).
thf(674,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(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/sandbox/benchmark/theBenchmark.p',fact_180_induct__list012) ).
thf(530,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(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/sandbox/benchmark/theBenchmark.p',fact_84_old_Opath2__rev__induct) ).
thf(1026,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(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/sandbox/benchmark/theBenchmark.p',fact_313_not__distinct__split__distinct) ).
thf(1167,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(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/sandbox/benchmark/theBenchmark.p',fact_247_rev__nonempty__induct) ).
thf(773,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(113,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_suffix__bot_Obot_Oextremum__unique) ).
thf(794,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
= ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
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/sandbox/benchmark/theBenchmark.p',fact_186_shuffles_Oinduct) ).
thf(586,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(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/sandbox/benchmark/theBenchmark.p',fact_43_phiUses__finite) ).
thf(1135,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(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/sandbox/benchmark/theBenchmark.p',fact_275_append__Cons__eq__iff) ).
thf(1146,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(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/sandbox/benchmark/theBenchmark.p',fact_85_tl__append2) ).
thf(1219,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(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/sandbox/benchmark/theBenchmark.p',fact_285_in__set__conv__decomp__last) ).
thf(965,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(102,axiom,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ B @ A ) )
= ( B = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_self__append__conv2) ).
thf(750,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(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/sandbox/benchmark/theBenchmark.p',fact_263_rev__induct) ).
thf(689,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(13,axiom,
distinct_node @ nil_node,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_distinct_Osimps_I1_J) ).
thf(296,plain,
distinct_node @ nil_node,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
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/sandbox/benchmark/theBenchmark.p',fact_279_in__set__list__format) ).
thf(819,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(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/sandbox/benchmark/theBenchmark.p',fact_98_append_Oassoc) ).
thf(402,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(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/sandbox/benchmark/theBenchmark.p',fact_197_remdups__adj_Ocases) ).
thf(732,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(208,axiom,
( rs2
= ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_rs__def) ).
thf(1125,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(100,axiom,
! [A: list_node,B: list_node] :
( ( A
= ( append_node @ A @ B ) )
= ( B = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_self__append__conv) ).
thf(743,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(124,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_defs__finite) ).
thf(826,plain,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(11,axiom,
! [A: list_node] : ( suffix_node @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_suffix__order_Odual__order_Orefl) ).
thf(291,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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/sandbox/benchmark/theBenchmark.p',fact_17_old_Opath2__hd__in__ns) ).
thf(1226,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(145,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( cons_node @ ( hd_node @ A ) @ ( tl_node @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_list_Ocollapse) ).
thf(904,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(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/sandbox/benchmark/theBenchmark.p',fact_127_old_Opath2__split_I1_J) ).
thf(975,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(77,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
& ( suffix_node @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_suffix__order_Oeq__iff) ).
thf(641,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(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/sandbox/benchmark/theBenchmark.p',fact_133_list__ee__eq__leel_I1_J) ).
thf(391,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(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/sandbox/benchmark/theBenchmark.p',fact_131_append1__eq__conv) ).
thf(445,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(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/sandbox/benchmark/theBenchmark.p',fact_13_defs__in__allDefs) ).
thf(947,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(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/sandbox/benchmark/theBenchmark.p',fact_31_defAss_H__extend) ).
thf(1058,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(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/sandbox/benchmark/theBenchmark.p',fact_35_defAss__extend) ).
thf(1107,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(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/sandbox/benchmark/theBenchmark.p',fact_67_old_Odominates__unsnoc) ).
thf(919,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(117,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_same__append__eq) ).
thf(804,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(106,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_list_Oexhaust) ).
thf(764,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(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/sandbox/benchmark/theBenchmark.p',fact_302_not__distinct__decomp) ).
thf(736,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(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/sandbox/benchmark/theBenchmark.p',fact_42_old_Osuccessor__in___092_060alpha_062n) ).
thf(996,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(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/sandbox/benchmark/theBenchmark.p',fact_91_old_Opath2__induct) ).
thf(1043,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(74,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( ( append_node @ A @ B )
= ( append_node @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_append__same__eq) ).
thf(631,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(104,axiom,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_append_Oleft__neutral) ).
thf(758,plain,
! [A: list_node] :
( ( append_node @ nil_node @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
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/sandbox/benchmark/theBenchmark.p',fact_268_split__list__prop) ).
thf(858,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(83,axiom,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_mem__Collect__eq) ).
thf(668,plain,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
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/sandbox/benchmark/theBenchmark.p',fact_233_set__ConsD) ).
thf(1177,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(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/sandbox/benchmark/theBenchmark.p',fact_63_old_Odominates__path) ).
thf(1112,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(53,axiom,
! [A: list_node,B: list_node,C: list_node] :
( ( suffix_node @ A @ B )
=> ( ( B = C )
=> ( suffix_node @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_suffix__order_Oord__le__eq__trans) ).
thf(494,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(194,axiom,
member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rs_H__props_I3_J) ).
thf(1080,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(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/sandbox/benchmark/theBenchmark.p',fact_200_append__Cons) ).
thf(799,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(220,axiom,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_List_Ofinite__set) ).
thf(1162,plain,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(72,axiom,
! [A: g] : ( invar @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_old_Oinvar) ).
thf(626,plain,
! [A: g] : ( invar @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
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/sandbox/benchmark/theBenchmark.p',fact_273_split__list__propE) ).
thf(915,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(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/sandbox/benchmark/theBenchmark.p',fact_66_old_OdominatesE) ).
thf(912,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(107,axiom,
! [A: list_node,B: list_node] :
( ( ( append_node @ A @ B )
= B )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_append__self__conv2) ).
thf(768,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(137,axiom,
! [A: node,B: list_node] :
( ( tl_node @ ( cons_node @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_list_Osel_I3_J) ).
thf(868,plain,
! [A: node,B: list_node] :
( ( tl_node @ ( cons_node @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(44,axiom,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
=> ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_suffix__bot_Obot_Oextremum__uniqueI) ).
thf(455,plain,
! [A: list_node] :
( ( suffix_node @ A @ nil_node )
=> ( A = nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
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/sandbox/benchmark/theBenchmark.p',fact_4_rs_H__props_I1_J) ).
thf(1176,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(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/sandbox/benchmark/theBenchmark.p',fact_97_append__assoc) ).
thf(394,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(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/sandbox/benchmark/theBenchmark.p',fact_126_same__suffix__suffix) ).
thf(505,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(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/sandbox/benchmark/theBenchmark.p',fact_202_remdups__adj_Oinduct) ).
thf(426,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(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/sandbox/benchmark/theBenchmark.p',fact_223_longest__common__prefix_Oinduct) ).
thf(548,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(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/sandbox/benchmark/theBenchmark.p',fact_188_transpose_Ocases) ).
thf(648,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(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/sandbox/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(1081,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(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/sandbox/benchmark/theBenchmark.p',fact_308_not__suffix__cases) ).
thf(553,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(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/sandbox/benchmark/theBenchmark.p',fact_55_strict__dom__trans_H) ).
thf(968,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(45,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ ( append_node @ A @ B ) @ B )
= ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_same__suffix__nil) ).
thf(458,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(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/sandbox/benchmark/theBenchmark.p',fact_57_old_Odominates__trans) ).
thf(823,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(58,axiom,
! [A: list_node] : ( suffix_node @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_suffix__order_Oorder__refl) ).
thf(525,plain,
! [A: list_node] : ( suffix_node @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(175,axiom,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_rs_H__props_I2_J) ).
thf(1003,plain,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
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/sandbox/benchmark/theBenchmark.p',fact_83_old_Opath2__snoc) ).
thf(855,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(191,axiom,
! [A: node,B: list_node] : ( member_node @ A @ ( set_node2 @ ( cons_node @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_list_Oset__intros_I1_J) ).
thf(1070,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(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/sandbox/benchmark/theBenchmark.p',fact_166_revg_Oinduct) ).
thf(705,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(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/sandbox/benchmark/theBenchmark.p',fact_211_list__all__zip_Oinduct) ).
thf(739,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(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/sandbox/benchmark/theBenchmark.p',fact_18_old_Opath2__in___092_060alpha_062n) ).
thf(1098,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(16,axiom,
! [A: node,B: list_node] :
( ( cons_node @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_not__Cons__self2) ).
thf(310,plain,
! [A: node,B: list_node] :
( ( cons_node @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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/sandbox/benchmark/theBenchmark.p',fact_20_old_Opath2__tl__in___092_060alpha_062n) ).
thf(1053,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(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/sandbox/benchmark/theBenchmark.p',fact_283_split__list__first__propE) ).
thf(1188,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(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/sandbox/benchmark/theBenchmark.p',fact_251_Cons__eq__append__conv) ).
thf(502,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(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/sandbox/benchmark/theBenchmark.p',fact_24_old_Opath2__forget__hd) ).
thf(1235,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(22,axiom,
! [A: node] : ( distinct_node @ ( cons_node @ A @ nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_distinct__singleton) ).
thf(359,plain,
! [A: node] : ( distinct_node @ ( cons_node @ A @ nil_node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
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/sandbox/benchmark/theBenchmark.p',fact_282_split__list__last__propE) ).
thf(1130,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(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/sandbox/benchmark/theBenchmark.p',fact_217_mergesort__by__rel__merge_Oinduct) ).
thf(643,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(61,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ~ ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_neq__NilE) ).
thf(544,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(146,axiom,
! [A: node,B: list_node] :
( ( member_node @ A @ ( set_node2 @ ( tl_node @ B ) ) )
=> ( member_node @ A @ ( set_node2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_FormalSSA__Misc_Oin__set__tlD) ).
thf(907,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(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/sandbox/benchmark/theBenchmark.p',fact_293_distinct_Osimps_I2_J) ).
thf(1023,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(69,axiom,
( ( (=) @ list_node )
= ( ^ [A: list_node,B: list_node] :
( ( suffix_node @ B @ A )
& ( suffix_node @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_suffix__order_Odual__order_Oeq__iff) ).
thf(613,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(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/sandbox/benchmark/theBenchmark.p',fact_157_old_Oempty__path2) ).
thf(1008,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(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/sandbox/benchmark/theBenchmark.p',fact_324_suffix__order_Oorder__trans) ).
thf(314,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(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/sandbox/benchmark/theBenchmark.p',fact_270_xy__in__set__cases) ).
thf(876,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(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/sandbox/benchmark/theBenchmark.p',fact_33_defAss_HI) ).
thf(991,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(30,axiom,
( ( append_node @ nil_node )
= ( ^ [A: list_node] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_empty__append__eq__id) ).
thf(386,plain,
( ( append_node @ nil_node )
= ( ^ [A: list_node] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
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/sandbox/benchmark/theBenchmark.p',fact_288_split__list__last__prop__iff) ).
thf(978,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(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/sandbox/benchmark/theBenchmark.p',fact_25_old_OEntry__reachesE) ).
thf(1140,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(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/sandbox/benchmark/theBenchmark.p',fact_37_defAss__def) ).
thf(1180,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(154,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_phiDefs__finite) ).
thf(931,plain,
! [A: g,B: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
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/sandbox/benchmark/theBenchmark.p',fact_215_map__tailrec__rev_Oinduct) ).
thf(482,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(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/sandbox/benchmark/theBenchmark.p',fact_325_suffix__order_Oorder_Otrans) ).
thf(671,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(144,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_assms_I8_J) ).
thf(903,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(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/sandbox/benchmark/theBenchmark.p',fact_9_allDefs__disjoint_H) ).
thf(1010,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(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/sandbox/benchmark/theBenchmark.p',fact_349_suffix__appendD) ).
thf(771,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(25,axiom,
! [A: node,B: list_node] :
( nil_node
!= ( cons_node @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_list_Odistinct_I1_J) ).
thf(368,plain,
! [A: node,B: list_node] :
( nil_node
!= ( cons_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
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/sandbox/benchmark/theBenchmark.p',fact_277_in__set__conv__decomp) ).
thf(844,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(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/sandbox/benchmark/theBenchmark.p',fact_318_suffix__order_Odual__order_Otrans) ).
thf(699,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(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/sandbox/benchmark/theBenchmark.p',fact_281_split__list__first__prop) ).
thf(896,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(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/sandbox/benchmark/theBenchmark.p',fact_52_old_Opath2__app) ).
thf(1062,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(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/sandbox/benchmark/theBenchmark.p',fact_60_dominates__trans_H) ).
thf(1101,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(80,axiom,
! [A: list_node,B: list_node,C: node] :
( ( suffix_node @ A @ B )
=> ( suffix_node @ A @ ( cons_node @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_suffix__ConsI) ).
thf(652,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(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/sandbox/benchmark/theBenchmark.p',fact_199_sorted__wrt_Oinduct) ).
thf(781,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(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/sandbox/benchmark/theBenchmark.p',fact_128_old_OEntry__loop) ).
thf(961,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(120,axiom,
! [A: list_node] :
( ! [B: node,C: list_node] :
( A
!= ( cons_node @ B @ C ) )
=> ( A = nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_min__list_Ocases) ).
thf(813,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(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/sandbox/benchmark/theBenchmark.p',fact_21_old_Opath2__last__in__ns) ).
thf(1193,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(234,axiom,
! [A: set_node] :
( ( finite_finite_node @ A )
=> ? [B: list_node] :
( ( set_node2 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_finite__list) ).
thf(1212,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(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/sandbox/benchmark/theBenchmark.p',fact_253_neq__Nil__rev__conv) ).
thf(383,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(126,axiom,
! [A: g,B: node,C: node] :
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ nil_node @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_old_Opath2__not__Nil2) ).
thf(832,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(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/sandbox/benchmark/theBenchmark.p',fact_261_rev__exhaust) ).
thf(287,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(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/sandbox/benchmark/theBenchmark.p',fact_61_dominates__antisymm_H) ).
thf(1077,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(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/sandbox/benchmark/theBenchmark.p',fact_259_neq__Nil__revE) ).
thf(478,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(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/sandbox/benchmark/theBenchmark.p',fact_257_rev__induct2_H) ).
thf(300,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(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/sandbox/benchmark/theBenchmark.p',fact_27_old_OEntry__reaches) ).
thf(999,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(127,axiom,
! [A: g,B: node] : ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( cons_node @ B @ nil_node ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_old_OEntryPath__triv) ).
thf(835,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(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/sandbox/benchmark/theBenchmark.p',fact_32_defAss_H__def) ).
thf(1229,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(36,axiom,
! [A: list_node,B: list_node] :
( ( suffix_node @ A @ B )
=> ( ( suffix_node @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_suffix__order_Oantisym__conv) ).
thf(405,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(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/sandbox/benchmark/theBenchmark.p',fact_204_list__induct__first2) ).
thf(603,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(1,conjecture,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
file('/export/starexec/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_145_list__e__eq__lel_I1_J) ).
thf(807,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(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/sandbox/benchmark/theBenchmark.p',fact_70_old_OEntryPath__suffix) ).
thf(828,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(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/sandbox/benchmark/theBenchmark.p',fact_280_split__list__last__prop) ).
thf(1065,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(8,axiom,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_List_Ofinite__set) ).
thf(283,plain,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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/sandbox/benchmark/theBenchmark.p',fact_289_split__list__first__prop__iff) ).
thf(928,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(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/sandbox/benchmark/theBenchmark.p',fact_139_list__se__match_I2_J) ).
thf(728,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(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/sandbox/benchmark/theBenchmark.p',fact_237_list_Oset__intros_I2_J) ).
thf(1152,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(180,axiom,
! [A: list_node] :
( ( A != nil_node )
=> ( ( ( tl_node @ A )
= nil_node )
=> ~ ! [B: node] :
( A
!= ( cons_node @ B @ nil_node ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_tl__obtain__elem) ).
thf(1019,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(132,axiom,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(850,plain,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
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/sandbox/benchmark/theBenchmark.p',fact_39_defAssD) ).
thf(1004,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(6,axiom,
! [A: list_node,B: list_node] :
( ( nil_node
= ( append_node @ A @ B ) )
= ( ( A = nil_node )
& ( B = nil_node ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Nil__is__append__conv) ).
thf(277,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(40,axiom,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_append__Nil2) ).
thf(442,plain,
! [A: list_node] :
( ( append_node @ A @ nil_node )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
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/sandbox/benchmark/theBenchmark.p',fact_74_old_Odominates__refl) ).
thf(871,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(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/sandbox/benchmark/theBenchmark.p',fact_348_suffix__appendI) ).
thf(486,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(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/sandbox/benchmark/theBenchmark.p',fact_75_old_OEntry__dominates) ).
thf(935,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(151,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_assms_I7_J) ).
thf(923,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(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/sandbox/benchmark/theBenchmark.p',fact_241_list__Cons__eq__append__cases) ).
thf(659,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(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/sandbox/benchmark/theBenchmark.p',fact_46_old_Opath2__not__Nil) ).
thf(1014,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(1256,plain,
$false,
inference(cvc4,[status(thm)],[1036,365,893,941,909,628,408,994,1205,247,655,677,1041,1173,1137,472,945,1164,797,1095,1001,1127,709,841,1055,719,785,372,702,802,949,817,1087,1115,448,1232,638,853,789,591,376,623,1183,475,924,981,397,280,293,1072,527,1215,634,411,988,1104,265,380,1199,761,810,1206,452,334,1223,952,862,297,746,1091,847,361,583,324,285,1159,461,682,1195,317,615,1121,1111,388,356,593,1118,499,874,1143,933,753,489,679,1155,901,686,837,1150,244,938,508,674,530,1026,1167,773,794,586,1135,1146,1219,965,750,689,296,819,402,732,1125,743,826,291,1226,904,975,641,391,445,947,1058,1107,919,804,764,736,996,1043,631,758,858,668,1177,1112,494,1080,799,1162,626,915,912,768,868,455,1176,394,505,426,548,648,1081,553,968,458,823,525,1003,855,1070,705,739,1098,310,1053,1188,502,1235,359,1130,643,544,907,1023,613,1008,314,876,991,386,978,1140,1180,931,482,671,903,1010,771,368,844,699,896,1062,1101,652,781,961,813,1193,1212,383,832,287,1077,478,300,999,835,1229,405,603,242,807,828,1065,283,928,728,1152,1019,850,1004,277,442,871,486,935,923,659,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ITP080^1 : TPTP v8.2.0. Released v7.5.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n016.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sat May 18 18:12:09 EDT 2024
% 0.17/0.38 % CPUTime :
% 1.05/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.93/1.24 % [INFO] Parsing done (301ms).
% 2.12/1.25 % [INFO] Running in sequential loop mode.
% 2.77/1.49 % [INFO] eprover registered as external prover.
% 2.77/1.49 % [INFO] cvc4 registered as external prover.
% 2.77/1.50 % [INFO] Scanning for conjecture ...
% 3.01/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 351 axioms. Running axiom selection ...
% 3.54/1.71 % [INFO] Axiom selection finished. Selected 239 axioms (removed 112 axioms).
% 4.40/1.93 % [INFO] Problem is higher-order (TPTP THF).
% 4.40/1.95 % [INFO] Type checking passed.
% 4.40/1.95 % [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 ...
% 14.72/4.33 % External prover 'cvc4' found a proof!
% 14.72/4.34 % [INFO] Killing All external provers ...
% 14.72/4.34 % Time passed: 3791ms (effective reasoning time: 3078ms)
% 14.72/4.34 % 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)>
% 14.72/4.34 % 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
% 14.72/4.34 % No. of inferences in proof: 482
% 14.72/4.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3791 ms resp. 3078 ms w/o parsing
% 15.44/4.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.44/4.54 % [INFO] Killing All external provers ...
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