%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP080^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:41 AM UTC 2026
% Result : Theorem 148.06s 66.47s
% Output : Refutation 149.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 262
% Syntax : Number of formulae : 528 ( 180 unt; 0 typ; 0 def)
% Number of atoms : 1736 ( 706 equ; 6 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 10912 ( 317 ~; 26 |; 168 &;9529 @)
% ( 0 <=>; 872 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 258 ( 258 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 17 con; 0-13 aty)
% Number of variables : 2292 ( 20 ^;2126 !; 146 ?;2292 :)
% Comments :
%------------------------------------------------------------------------------
thf(edgeD_type,type,
edgeD: $tType ).
thf(node_type,type,
node: $tType ).
thf(val_type,type,
val: $tType ).
thf(g_type,type,
g: $tType ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(graph_2081878492ryPath_decl,type,
graph_2081878492ryPath:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > $o ) > ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > ( TC > TB ) > TC > ( list @ TB ) > $o ) ).
thf(graph_graph_isIdom_decl,type,
graph_graph_isIdom:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > $o ) > ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > ( TC > TB ) > TC > TB > TB > $o ) ).
thf(graph_709200220inates_decl,type,
graph_709200220inates:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > $o ) > ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > ( TC > TB ) > TC > TB > TB > $o ) ).
thf(graph_1822314308nEdges_decl,type,
graph_1822314308nEdges:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > TC > TB > ( list @ ( product_prod @ TB @ ( product_prod @ TA @ TB ) ) ) ) ).
thf(graph_1661282752_path2_decl,type,
graph_1661282752_path2:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > $o ) > ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > TC > TB > ( list @ TB ) > TB > $o ) ).
thf(graph_1201503639essors_decl,type,
graph_1201503639essors:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > TC > TB > ( list @ TB ) ) ).
thf(append_decl,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(distinct_decl,type,
distinct:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(hd_decl,type,
hd:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(set2_decl,type,
set2:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(tl_decl,type,
tl:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(graph_reducible_decl,type,
graph_reducible:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > $o ) > ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > ( TC > TB ) > TC > $o ) ).
thf(sSA_CFG_SSA_allDefs_decl,type,
sSA_CFG_SSA_allDefs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( set @ TA ) ) > ( TC > ( product_prod @ TB @ TA ) > ( option @ ( list @ TA ) ) ) > TC > TB > ( set @ TA ) ) ).
thf(sSA_CFG_SSA_defAss_decl,type,
sSA_CFG_SSA_defAss:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > ( list @ TC ) ) > ( TD > $o ) > ( TD > TC > ( list @ ( product_prod @ TC @ TB ) ) ) > ( TD > TC ) > ( TD > TC > ( set @ TA ) ) > ( TD > ( product_prod @ TC @ TA ) > ( option @ ( list @ TA ) ) ) > TD > TC > TA > $o ) ).
thf(sSA_CFG_SSA_phiDefs_decl,type,
sSA_CFG_SSA_phiDefs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( product_prod @ TB @ TA ) > ( option @ ( list @ TA ) ) ) > TC > TB > ( set @ TA ) ) ).
thf(sSA_CFG_SSA_phiUses_decl,type,
sSA_CFG_SSA_phiUses:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > ( list @ TC ) ) > ( TD > TC > ( list @ ( product_prod @ TC @ TB ) ) ) > ( TD > ( product_prod @ TC @ TA ) > ( option @ ( list @ TA ) ) ) > TD > TC > ( set @ TA ) ) ).
thf(sSA_CF1081484811efNode_decl,type,
sSA_CF1081484811efNode:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > TB > ( set @ TA ) ) > ( TC > ( product_prod @ TB @ TA ) > ( option @ ( list @ TA ) ) ) > TC > TA > TB ) ).
thf(sSA_CF1165125185phiArg_decl,type,
sSA_CF1165125185phiArg:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > TB > ( set @ TA ) ) > ( TC > ( product_prod @ TB @ TA ) > ( option @ ( list @ TA ) ) ) > TC > TA > TA > $o ) ).
thf(sSA_CFG_defAss_decl,type,
sSA_CFG_defAss:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > ( list @ TC ) ) > ( TD > $o ) > ( TD > TC > ( list @ ( product_prod @ TC @ TB ) ) ) > ( TD > TC ) > ( TD > TC > ( set @ TA ) ) > TD > TC > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(suffix_decl,type,
suffix:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(entry_decl,type,
entry: g > node ).
thf(alpha_n_decl,type,
alpha_n: g > ( list @ node ) ).
thf(phi_r_decl,type,
phi_r: val ).
thf(defs_decl,type,
defs: g > node > ( set @ val ) ).
thf(g2_decl,type,
g2: g ).
thf(inEdges_decl,type,
inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).
thf(invar_decl,type,
invar: g > $o ).
thf(m_decl,type,
m: node ).
thf(ms_decl,type,
ms: list @ node ).
thf(n_decl,type,
n: node ).
thf(ns_decl,type,
ns: list @ node ).
thf(phis_decl,type,
phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).
thf(pred_phi_r_decl,type,
pred_phi_r: node ).
thf(r_decl,type,
r: val ).
thf(rs_decl,type,
rs: list @ node ).
thf(rs2_decl,type,
rs2: list @ node ).
thf(s_decl,type,
s: val ).
thf(258,axiom,
! [A: node,B: g,C: node,D: val] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( member @ val @ D @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ A ) )
=> ( ( member @ val @ D @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ C ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_allDefs__disjoint_H) ).
thf(1322,plain,
! [A: node,B: g,C: node,D: val] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( member @ val @ D @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ A ) )
=> ( ( member @ val @ D @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ C ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(186,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( member @ TA @ C @ ( set2 @ TA @ B ) )
=> ( ( ( A = C )
=> ! [D: list @ TA,E: list @ TA] :
( B
!= ( append @ TA @ D @ ( cons @ TA @ C @ E ) ) ) )
=> ( ( ( A != C )
=> ! [D: list @ TA,E: list @ TA,F: list @ TA] :
( B
!= ( append @ TA @ D @ ( cons @ TA @ A @ ( append @ TA @ E @ ( cons @ TA @ C @ F ) ) ) ) ) )
=> ~ ( ( A != C )
=> ! [D: list @ TA,E: list @ TA,F: list @ TA] :
( B
!= ( append @ TA @ D @ ( cons @ TA @ C @ ( append @ TA @ E @ ( cons @ TA @ A @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_xy__in__set__cases) ).
thf(1036,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( member @ TA @ C @ ( set2 @ TA @ B ) )
=> ( ( ( A = C )
=> ! [D: list @ TA,E: list @ TA] :
( B
!= ( append @ TA @ D @ ( cons @ TA @ C @ E ) ) ) )
=> ( ( ( A != C )
=> ! [D: list @ TA,E: list @ TA,F: list @ TA] :
( B
!= ( append @ TA @ D @ ( cons @ TA @ A @ ( append @ TA @ E @ ( cons @ TA @ C @ F ) ) ) ) ) )
=> ~ ( ( A != C )
=> ! [D: list @ TA,E: list @ TA,F: list @ TA] :
( B
!= ( append @ TA @ D @ ( cons @ TA @ C @ ( append @ TA @ E @ ( cons @ TA @ A @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(125,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ ( append @ TA @ B @ C ) )
= ( ( suffix @ TA @ A @ C )
| ? [D: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( suffix @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_suffix__append) ).
thf(809,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ ( append @ TA @ B @ C ) )
= ( ( suffix @ TA @ A @ C )
| ? [D: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( suffix @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(262,axiom,
! [A: g,B: node,C: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
= ( ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) )
& ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ C )
=> ( member @ node @ B @ ( set2 @ node @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_old_Odominates__def) ).
thf(1337,plain,
! [A: g,B: node,C: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
= ( ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) )
& ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ C )
=> ( member @ node @ B @ ( set2 @ node @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(84,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_append_Oassoc) ).
thf(628,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(255,axiom,
( rs2
= ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_rs__def) ).
thf(1315,plain,
( rs2
= ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(21,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_splice_Oinduct) ).
thf(352,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(192,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) )
=> ( member @ TA @ B @ ( set2 @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_list_Oset__sel_I2_J) ).
thf(1068,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) )
=> ( member @ TA @ B @ ( set2 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(29,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_append_Oleft__neutral) ).
thf(379,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Nil__is__append__conv) ).
thf(269,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(253,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_split__list__last__propE) ).
thf(1305,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(250,axiom,
! [A: g,B: list @ node] :
( ( invar @ A )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ B @ ( entry @ A ) )
=> ( B
= ( cons @ node @ ( entry @ A ) @ ( nil @ node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_old_OEntry__loop) ).
thf(1290,plain,
! [A: g,B: list @ node] :
( ( invar @ A )
=> ( ( graph_1661282752_path2 @ g @ node @ 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)],[250]) ).
thf(7,axiom,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_distinct_Osimps_I1_J) ).
thf(276,plain,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(40,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( append @ TA @ B @ A )
= ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( ( B
= ( nil @ TA ) )
& ( A
= ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_list__se__match_I2_J) ).
thf(440,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( append @ TA @ B @ A )
= ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( ( B
= ( nil @ TA ) )
& ( A
= ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(91,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( cons @ TA @ B @ ( nil @ TA ) )
= ( append @ TA @ C @ A ) )
= ( ( C
= ( nil @ TA ) )
& ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_list__se__match_I4_J) ).
thf(655,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( cons @ TA @ B @ ( nil @ TA ) )
= ( append @ TA @ C @ A ) )
= ( ( C
= ( nil @ TA ) )
& ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(194,axiom,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd @ node @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_old_Opath2__forget__hd) ).
thf(1078,plain,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd @ node @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(215,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_split__list__first__propE) ).
thf(1137,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( B @ D )
=> ~ ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(61,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_hd__append2) ).
thf(533,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(109,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_rev__nonempty__induct) ).
thf(715,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(236,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( tl @ TA @ A )
= ( nil @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_tl__obtain__elem) ).
thf(1233,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( tl @ TA @ A )
= ( nil @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_append__Cons) ).
thf(340,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(202,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_hd__Cons__tl) ).
thf(1095,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(107,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA,D: TA,E: TA,F: list @ TA] :
( ( ( cons @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( cons @ TA @ E @ F ) ) ) )
= ( ( C
= ( nil @ TA ) )
& ( A = D )
& ( B = E )
& ( F
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_list__ee__eq__leel_I1_J) ).
thf(709,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA,D: TA,E: TA,F: list @ TA] :
( ( ( cons @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( cons @ TA @ E @ F ) ) ) )
= ( ( C
= ( nil @ TA ) )
& ( A = D )
& ( B = E )
& ( F
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(39,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( A = B )
=> ( ( suffix @ TA @ B @ C )
=> ( suffix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_suffix__order_Oord__eq__le__trans) ).
thf(436,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( A = B )
=> ( ( suffix @ TA @ B @ C )
=> ( suffix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(244,axiom,
! [A: g,B: list @ node] :
( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( distinct @ node @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_old_OEntryPath__distinct) ).
thf(1265,plain,
! [A: g,B: list @ node] :
( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( distinct @ node @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(241,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_in__set__conv__decomp) ).
thf(1254,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(90,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_list_OdiscI) ).
thf(651,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( suffix @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
=> ( suffix @ TA @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_suffix__ConsD2) ).
thf(504,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( suffix @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
=> ( suffix @ TA @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(78,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ~ ( suffix @ TA @ A @ B )
=> ( ! [D: TA,E: list @ TA] : ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( D != F )
=> ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( D = F )
=> ( ~ ( suffix @ TA @ E @ G )
=> ( ( C @ E @ G )
=> ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_not__suffix__induct) ).
thf(587,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ~ ( suffix @ TA @ A @ B )
=> ( ! [D: TA,E: list @ TA] : ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( D != F )
=> ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( D = F )
=> ( ~ ( suffix @ TA @ E @ G )
=> ( ( C @ E @ G )
=> ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(189,axiom,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( C
!= ( nil @ node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_old_Opath2__not__Nil) ).
thf(1059,plain,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( C
!= ( nil @ node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct @ TA @ ( cons @ TA @ A @ C ) )
& ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_distinct__length__2__or__more) ).
thf(542,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct @ TA @ ( cons @ TA @ A @ C ) )
& ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
=> ( ( A = B )
| ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_set__ConsD) ).
thf(917,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
=> ( ( A = B )
| ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ ( cons @ TA @ A @ B ) @ C )
=> ( suffix @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_suffix__ConsD) ).
thf(702,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ ( cons @ TA @ A @ B ) @ C )
=> ( suffix @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(115,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( B = C )
=> ( suffix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_suffix__order_Oord__le__eq__trans) ).
thf(751,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( B = C )
=> ( suffix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(70,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_append__self__conv) ).
thf(559,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(180,axiom,
! [A: g,B: node,C: node] :
~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( nil @ node ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_old_Opath2__not__Nil2) ).
thf(1013,plain,
! [A: g,B: node,C: node] :
~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( nil @ node ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(152,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_list_Oset__sel_I1_J) ).
thf(924,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(252,axiom,
! [TA: $tType,A: list @ TA] :
( ( ~ ( distinct @ TA @ A ) )
= ( ? [B: list @ TA,C: TA,D: list @ TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B )
& ( A
= ( append @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_not__distinct__conv__prefix) ).
thf(1302,plain,
! [TA: $tType,A: list @ TA] :
( ( ~ ( distinct @ TA @ A ) )
= ( ? [B: list @ TA,C: TA,D: list @ TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B )
& ( A
= ( append @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(41,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA,E: TA,F: list @ TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TA @ D @ ( cons @ TA @ E @ F ) ) )
=> ( ! [G: list @ TA] :
( ( A
= ( append @ TA @ D @ ( cons @ TA @ E @ G ) ) )
=> ( F
!= ( append @ TA @ G @ ( cons @ TA @ B @ C ) ) ) )
=> ( ( ( D = A )
=> ( ( E = B )
=> ( F != C ) ) )
=> ~ ! [G: list @ TA] :
( ( D
= ( append @ TA @ A @ ( cons @ TA @ B @ G ) ) )
=> ( C
!= ( append @ TA @ G @ ( cons @ TA @ E @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_list__match__lel__lel) ).
thf(443,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA,E: TA,F: list @ TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TA @ D @ ( cons @ TA @ E @ F ) ) )
=> ( ! [G: list @ TA] :
( ( A
= ( append @ TA @ D @ ( cons @ TA @ E @ G ) ) )
=> ( F
!= ( append @ TA @ G @ ( cons @ TA @ B @ C ) ) ) )
=> ( ( ( D = A )
=> ( ( E = B )
=> ( F != C ) ) )
=> ~ ! [G: list @ TA] :
( ( D
= ( append @ TA @ A @ ( cons @ TA @ B @ G ) ) )
=> ( C
!= ( append @ TA @ G @ ( cons @ TA @ E @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(261,axiom,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( entry @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_old_OEntry__dominates) ).
thf(1334,plain,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( entry @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(46,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_append__self__conv2) ).
thf(485,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(74,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( cons @ TA @ D @ ( nil @ TA ) ) )
= ( ( A
= ( nil @ TA ) )
& ( B = D )
& ( C
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_list__e__eq__lel_I2_J) ).
thf(574,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( cons @ TA @ D @ ( nil @ TA ) ) )
= ( ( A
= ( nil @ TA ) )
& ( B = D )
& ( C
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(167,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) )
=> ( ( ( A
!= ( nil @ TA ) )
=> ( ( B
!= ( nil @ TA ) )
=> ( ( ( hd @ TA @ A )
= ( hd @ TA @ B ) )
& ( ( tl @ TA @ A )
= ( tl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_list_Oexpand) ).
thf(966,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) )
=> ( ( ( A
!= ( nil @ TA ) )
=> ( ( B
!= ( nil @ TA ) )
=> ( ( ( hd @ TA @ A )
= ( hd @ TA @ B ) )
& ( ( tl @ TA @ A )
= ( tl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(227,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_split__list__first__prop) ).
thf(1183,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(248,axiom,
! [TA: $tType,A: list @ TA] :
( ~ ( distinct @ TA @ A )
=> ~ ! [B: TA,C: list @ TA] :
( ( distinct @ TA @ C )
=> ( ( member @ TA @ B @ ( set2 @ TA @ C ) )
=> ! [D: list @ TA] :
( A
!= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ B @ ( nil @ TA ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_not__distinct__split__distinct) ).
thf(1283,plain,
! [TA: $tType,A: list @ TA] :
( ~ ( distinct @ TA @ A )
=> ~ ! [B: TA,C: list @ TA] :
( ( distinct @ TA @ C )
=> ( ( member @ TA @ B @ ( set2 @ TA @ C ) )
=> ! [D: list @ TA] :
( A
!= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ B @ ( nil @ TA ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(147,axiom,
! [A: g,B: node,C: node,D: node,E: list @ node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ D )
=> ( ( invar @ A )
=> ( member @ node @ C @ ( set2 @ node @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_old_Odominates__mid) ).
thf(905,plain,
! [A: g,B: node,C: node,D: node,E: list @ node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ D )
=> ( ( invar @ A )
=> ( member @ node @ C @ ( set2 @ node @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(44,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___HOL_Otype) ).
thf(480,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(79,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_shuffles_Oinduct) ).
thf(602,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_in__set__conv__decomp__last) ).
thf(1215,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(172,axiom,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( B
= ( hd @ node @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_old_Opath2__hd) ).
thf(988,plain,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( B
= ( hd @ node @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(15,axiom,
! [TA: $tType,A: list @ TA] :
( ( suffix @ TA @ A @ ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_suffix__Nil) ).
thf(312,plain,
! [TA: $tType,A: list @ TA] :
( ( suffix @ TA @ A @ ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(222,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_distinct_Osimps_I2_J) ).
thf(1169,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(99,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: list @ TA,C: TA] :
( A
= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_neq__Nil__rev__conv) ).
thf(687,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: list @ TA,C: TA] :
( A
= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(139,axiom,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_list_Osel_I2_J) ).
thf(877,plain,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(101,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_list_Oexhaust) ).
thf(692,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(210,axiom,
graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_assms_I8_J) ).
thf(1119,plain,
graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(122,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct @ TA @ A )
=> ( ( suffix @ TA @ B @ A )
=> ( distinct @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_distinct__suffix) ).
thf(774,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct @ TA @ A )
=> ( ( suffix @ TA @ B @ A )
=> ( distinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(13,axiom,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_distinct__singleton) ).
thf(307,plain,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(151,axiom,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ C ) ) )
=> ( ( B != C )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_old_Odominates__unsnoc) ).
thf(920,plain,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ C ) ) )
=> ( ( B != C )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(159,axiom,
! [A: g,B: list @ node,C: list @ node] :
( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( ( suffix @ node @ C @ B )
=> ( ( C
!= ( nil @ node ) )
=> ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_old_OEntryPath__suffix) ).
thf(942,plain,
! [A: g,B: list @ node,C: list @ node] :
( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B )
=> ( ( suffix @ node @ C @ B )
=> ( ( C
!= ( nil @ node ) )
=> ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_map__tailrec__rev_Oinduct) ).
thf(529,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(93,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(661,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(25,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA,D: list @ TA] :
( ! [E: TA > TA > $o,F: TA,G: list @ TA,H: TA,I: list @ TA] :
( ( ( E @ F @ H )
=> ( A @ E @ G @ ( cons @ TA @ H @ I ) ) )
=> ( ( ~ ( E @ F @ H )
=> ( A @ E @ ( cons @ TA @ F @ G ) @ I ) )
=> ( A @ E @ ( cons @ TA @ F @ G ) @ ( cons @ TA @ H @ I ) ) ) )
=> ( ! [E: TA > TA > $o,F: list @ TA] : ( A @ E @ F @ ( nil @ TA ) )
=> ( ! [E: TA > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TA ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_mergesort__by__rel__merge_Oinduct) ).
thf(366,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA,D: list @ TA] :
( ! [E: TA > TA > $o,F: TA,G: list @ TA,H: TA,I: list @ TA] :
( ( ( E @ F @ H )
=> ( A @ E @ G @ ( cons @ TA @ H @ I ) ) )
=> ( ( ~ ( E @ F @ H )
=> ( A @ E @ ( cons @ TA @ F @ G ) @ I ) )
=> ( A @ E @ ( cons @ TA @ F @ G ) @ ( cons @ TA @ H @ I ) ) ) )
=> ( ! [E: TA > TA > $o,F: list @ TA] : ( A @ E @ F @ ( nil @ TA ) )
=> ( ! [E: TA > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TA ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(163,axiom,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C )
=> ( ~ ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_old_Odominates__antitrans) ).
thf(957,plain,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C )
=> ( ~ ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(200,axiom,
! [A: g,B: node,C: list @ node,D: node,E: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member @ node @ E @ ( set2 @ node @ C ) )
=> ( member @ node @ E @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_old_Opath2__in___092_060alpha_062n) ).
thf(1091,plain,
! [A: g,B: node,C: list @ node,D: node,E: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member @ node @ E @ ( set2 @ node @ C ) )
=> ( member @ node @ E @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(128,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_append__eq__Cons__conv) ).
thf(825,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(124,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ~ ( suffix @ TA @ A @ B )
=> ( ( ( A
!= ( nil @ TA ) )
=> ( B
!= ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A
= ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ! [E: TA,F: list @ TA] :
( ( B
= ( append @ TA @ F @ ( cons @ TA @ E @ ( nil @ TA ) ) ) )
=> ( ( E = C )
=> ( suffix @ TA @ D @ F ) ) ) )
=> ~ ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_not__suffix__cases) ).
thf(778,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ~ ( suffix @ TA @ A @ B )
=> ( ( ( A
!= ( nil @ TA ) )
=> ( B
!= ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A
= ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ! [E: TA,F: list @ TA] :
( ( B
= ( append @ TA @ F @ ( cons @ TA @ E @ ( nil @ TA ) ) ) )
=> ( ( E = C )
=> ( suffix @ TA @ D @ F ) ) ) )
=> ~ ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(162,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_split__list__first) ).
thf(952,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(212,axiom,
! [A: g,B: node,C: node,D: node,E: list @ node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C )
=> ( ! [F: node] :
( ( member @ node @ F @ ( set2 @ node @ ( tl @ node @ E ) ) )
=> ( F != B ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_old_Odominates__unsnoc_H) ).
thf(1123,plain,
! [A: g,B: node,C: node,D: node,E: list @ node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C )
=> ( ! [F: node] :
( ( member @ node @ F @ ( set2 @ node @ ( tl @ node @ E ) ) )
=> ( F != B ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(127,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_min__list_Oinduct) ).
thf(815,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(110,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_min__list_Ocases) ).
thf(729,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(83,axiom,
! [TA: $tType,A: list @ TA] :
( ( suffix @ TA @ A @ ( nil @ TA ) )
=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_suffix__bot_Obot_Oextremum__uniqueI) ).
thf(625,plain,
! [TA: $tType,A: list @ TA] :
( ( suffix @ TA @ A @ ( nil @ TA ) )
=> ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(225,axiom,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_dominates__refl_H) ).
thf(1178,plain,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(95,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_induct__list012) ).
thf(665,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_rev__induct2_H) ).
thf(522,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(42,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_suffix__order_Oantisym) ).
thf(461,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(231,axiom,
! [A: g,B: node] : ( finite_finite @ val @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_phiDefs__finite) ).
thf(1210,plain,
! [A: g,B: node] : ( finite_finite @ val @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(131,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(842,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(138,axiom,
! [A: g] :
( ( invar @ A )
=> ( ( graph_1822314308nEdges @ g @ node @ edgeD @ inEdges @ A @ ( entry @ A ) )
= ( nil @ ( product_prod @ node @ ( product_prod @ edgeD @ node ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_old_OEntry__unreachable) ).
thf(874,plain,
! [A: g] :
( ( invar @ A )
=> ( ( graph_1822314308nEdges @ g @ node @ edgeD @ inEdges @ A @ ( entry @ A ) )
= ( nil @ ( product_prod @ node @ ( product_prod @ edgeD @ node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(161,axiom,
! [A: g,B: node,C: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ~ ( ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ~ ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ C )
=> ( member @ node @ B @ ( set2 @ node @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_old_OdominatesE) ).
thf(948,plain,
! [A: g,B: node,C: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ~ ( ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ~ ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ C )
=> ( member @ node @ B @ ( set2 @ node @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(190,axiom,
! [TA: $tType,A: list @ TA] :
( ( distinct @ TA @ A )
=> ( distinct @ TA @ ( tl @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_distinct__tl) ).
thf(1064,plain,
! [TA: $tType,A: list @ TA] :
( ( distinct @ TA @ A )
=> ( distinct @ TA @ ( tl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(207,axiom,
! [A: g] :
( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( entry @ A ) )
= ( nil @ node ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_old_OEntry__no__predecessor) ).
thf(1111,plain,
! [A: g] :
( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( entry @ A ) )
= ( nil @ node ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(22,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( suffix @ TA @ A @ ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
= ( ( A
= ( nil @ TA ) )
| ? [D: list @ TA] :
( ( A
= ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
& ( suffix @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_suffix__snoc) ).
thf(356,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( suffix @ TA @ A @ ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
= ( ( A
= ( nil @ TA ) )
| ? [D: list @ TA] :
( ( A
= ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
& ( suffix @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(136,axiom,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ A @ ( cons @ node @ A @ ( nil @ node ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_old_Oempty__path2) ).
thf(869,plain,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ A @ ( cons @ node @ A @ ( nil @ node ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(34,axiom,
! [TA: $tType,A: list @ TA] :
( ~ ( distinct @ TA @ A )
=> ? [B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( A
= ( append @ TA @ B @ ( append @ TA @ ( cons @ TA @ E @ ( nil @ TA ) ) @ ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ E @ ( nil @ TA ) ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_not__distinct__decomp) ).
thf(420,plain,
! [TA: $tType,A: list @ TA] :
( ~ ( distinct @ TA @ A )
=> ? [B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( A
= ( append @ TA @ B @ ( append @ TA @ ( cons @ TA @ E @ ( nil @ TA ) ) @ ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ E @ ( nil @ TA ) ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(857,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(57,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_Cons__eq__append__conv) ).
thf(519,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(112,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
& ( suffix @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_suffix__order_Oeq__iff) ).
thf(742,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
& ( suffix @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(196,axiom,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( tl @ TA @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_suffix__tl) ).
thf(1082,plain,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( tl @ TA @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(47,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( ( A
= ( cons @ TA @ C @ ( nil @ TA ) ) )
& ( B
= ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_list__se__match_I1_J) ).
thf(488,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( ( A
= ( cons @ TA @ C @ ( nil @ TA ) ) )
& ( B
= ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(156,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( A
= ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_list_Oexhaust__sel) ).
thf(933,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( A
= ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(145,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ ( append @ TA @ C @ ( cons @ TA @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_old_Oelem__set__implies__elem__tl__app__cons) ).
thf(901,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ ( append @ TA @ C @ ( cons @ TA @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA] :
( ( suffix @ TA @ A @ ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_suffix__bot_Obot_Oextremum__unique) ).
thf(526,plain,
! [TA: $tType,A: list @ TA] :
( ( suffix @ TA @ A @ ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(96,axiom,
! [A: g] : ( invar @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_old_Oinvar) ).
thf(679,plain,
! [A: g] : ( invar @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ C @ B )
=> ( ( suffix @ TA @ A @ C )
| ( suffix @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_suffix__same__cases) ).
thf(547,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ C @ B )
=> ( ( suffix @ TA @ A @ C )
| ( suffix @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(106,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_append1__eq__conv) ).
thf(706,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(141,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_list_Oset__intros_I2_J) ).
thf(884,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(260,axiom,
! [A: g,B: node,C: val,D: node,E: list @ node] :
( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B )
=> ( ! [F: node] :
( ( member @ node @ F @ ( set2 @ node @ ( tl @ node @ E ) ) )
=> ~ ( member @ val @ C @ ( defs @ A @ F ) ) )
=> ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_defAss_H__extend) ).
thf(1329,plain,
! [A: g,B: node,C: val,D: node,E: list @ node] :
( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B )
=> ( ! [F: node] :
( ( member @ node @ F @ ( set2 @ node @ ( tl @ node @ E ) ) )
=> ~ ( member @ val @ C @ ( defs @ A @ F ) ) )
=> ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(181,axiom,
! [A: g,B: node,C: node,D: node,E: list @ node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C )
=> ( ~ ( member @ node @ B @ ( set2 @ node @ ( tl @ node @ E ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_old_Odominates__extend) ).
thf(1016,plain,
! [A: g,B: node,C: node,D: node,E: list @ node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C )
=> ( ~ ( member @ node @ B @ ( set2 @ node @ ( tl @ node @ E ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(230,axiom,
r != phi_r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_False) ).
thf(1207,plain,
r != phi_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(208,axiom,
! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ E ) ) @ F )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ ( nil @ node ) ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_old_Opath2__split_I1_J) ).
thf(1114,plain,
! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ E ) ) @ F )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ ( nil @ node ) ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(171,axiom,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_old_Odominates__trans) ).
thf(985,plain,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(217,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( distinct @ TA @ A )
=> ( ( B
= ( hd @ TA @ A ) )
=> ~ ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Misc_Odistinct__hd__tl) ).
thf(1150,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( distinct @ TA @ A )
=> ( ( B
= ( hd @ TA @ A ) )
=> ~ ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(228,axiom,
! [A: node,B: g,C: node] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ D @ A )
=> ( member @ node @ C @ ( set2 @ node @ D ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_old_OdominatesI) ).
thf(1192,plain,
! [A: node,B: g,C: node] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ D @ A )
=> ( member @ node @ C @ ( set2 @ node @ D ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(240,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_split__list__propE) ).
thf(1246,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ~ ! [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(26,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ ( append @ TA @ A @ B ) @ C )
=> ( suffix @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_suffix__appendD) ).
thf(371,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ ( append @ TA @ A @ B ) @ C )
=> ( suffix @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_arg__min__list_Oinduct) ).
thf(647,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(176,axiom,
! [A: g,B: node,C: val] :
( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
= ( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_defAss__def) ).
thf(997,plain,
! [A: g,B: node,C: val] :
( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
= ( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(19,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_neq__Nil__revE) ).
thf(343,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(198,axiom,
! [A: node,B: g,C: val] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ A ) )
=> ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ B @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_defNode__eq) ).
thf(1086,plain,
! [A: node,B: g,C: val] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ A ) )
=> ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ B @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(266,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(193,axiom,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( ( B
!= ( entry @ A ) )
=> ? [C: node] :
( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
& ! [D: node] :
( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_old_Oidom__ex) ).
thf(1071,plain,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( ( B
!= ( entry @ A ) )
=> ? [C: node] :
( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
& ! [D: node] :
( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ ( nil @ TA ) )
= ( append @ TA @ B @ ( cons @ TA @ C @ D ) ) )
= ( ( B
= ( nil @ TA ) )
& ( C = A )
& ( D
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_list__e__eq__lel_I1_J) ).
thf(662,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ ( nil @ TA ) )
= ( append @ TA @ B @ ( cons @ TA @ C @ D ) ) )
= ( ( B
= ( nil @ TA ) )
& ( C = A )
& ( D
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(143,axiom,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( ( B != C )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C ) )
=> ( ( ( C != D )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D ) )
=> ( ( B != D )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_old_Ostrict__dom__trans) ).
thf(888,plain,
! [A: g,B: node,C: node,D: node] :
( ( invar @ A )
=> ( ( ( B != C )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C ) )
=> ( ( ( C != D )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D ) )
=> ( ( B != D )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(214,axiom,
! [A: node,B: g,C: node] :
( ( member @ node @ A @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ C ) ) )
=> ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_old_Osuccessor__is__node) ).
thf(1135,plain,
! [A: node,B: g,C: node] :
( ( member @ node @ A @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ C ) ) )
=> ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(205,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_split__list__last) ).
thf(1103,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1,conjecture,
~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(264,plain,
~ ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(113,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: TA,D: list @ TA,E: TA,F: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) )
= ( cons @ TA @ E @ ( cons @ TA @ F @ ( nil @ TA ) ) ) )
= ( ( A
= ( nil @ TA ) )
& ( E = B )
& ( F = C )
& ( D
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_list__ee__eq__leel_I2_J) ).
thf(745,plain,
! [TA: $tType,A: list @ TA,B: TA,C: TA,D: list @ TA,E: TA,F: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) )
= ( cons @ TA @ E @ ( cons @ TA @ F @ ( nil @ TA ) ) ) )
= ( ( A
= ( nil @ TA ) )
& ( E = B )
& ( F = C )
& ( D
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( TC > TA > TB ) > ( list @ TC ) > ( list @ TA ) > $o,B: TC > TA > TB,C: list @ TC,D: list @ TA] :
( ! [E: TC > TA > TB] : ( A @ E @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TC > TA > TB,F: TC,G: list @ TC,H: TA,I: list @ TA] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons @ TC @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
=> ( ! [E: TC > TA > TB,F: TC,G: list @ TC] : ( A @ E @ ( cons @ TC @ F @ G ) @ ( nil @ TA ) )
=> ( ! [E: TC > TA > TB,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TC ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_zipf_Oinduct) ).
thf(375,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( TC > TA > TB ) > ( list @ TC ) > ( list @ TA ) > $o,B: TC > TA > TB,C: list @ TC,D: list @ TA] :
( ! [E: TC > TA > TB] : ( A @ E @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TC > TA > TB,F: TC,G: list @ TC,H: TA,I: list @ TA] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons @ TC @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
=> ( ! [E: TC > TA > TB,F: TC,G: list @ TC] : ( A @ E @ ( cons @ TC @ F @ G ) @ ( nil @ TA ) )
=> ( ! [E: TC > TA > TB,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TC ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(55,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
& ( suffix @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_suffix__order_Oorder_Oeq__iff) ).
thf(513,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
& ( suffix @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(216,axiom,
! [A: g,B: node,C: val] :
( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ A @ E ) ) ) )
=> ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_defAssI) ).
thf(1146,plain,
! [A: g,B: node,C: val] :
( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ A @ E ) ) ) )
=> ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(37,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_append__Nil) ).
thf(430,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(71,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ord @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oord) ).
thf(562,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ord @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(35,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( suffix @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_suffix__order_Oeq__refl) ).
thf(423,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( suffix @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(178,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ B ) ) )
=> ( member @ TA @ A @ ( set2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_FormalSSA__Misc_Oin__set__tlD) ).
thf(1007,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ B ) ) )
=> ( member @ TA @ A @ ( set2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(111,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_list_Oinducts) ).
thf(732,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(121,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ C @ A )
=> ( suffix @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_suffix__order_Odual__order_Otrans) ).
thf(772,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ C @ A )
=> ( suffix @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(75,axiom,
! [TA: $tType] :
( ( append @ TA @ ( nil @ TA ) )
= ( ^ [A: list @ TA] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_empty__append__eq__id) ).
thf(577,plain,
! [TA: $tType] :
( ( append @ TA @ ( nil @ TA ) )
= ( ^ [A: list @ TA] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ ( append @ TA @ A @ B ) @ B )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_same__suffix__nil) ).
thf(291,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ ( append @ TA @ A @ B ) @ B )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_list__induct__first2) ).
thf(281,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ C )
=> ( suffix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_suffix__order_Oorder__trans) ).
thf(545,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ C )
=> ( suffix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(77,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_suffix__order_Odual__order_Oantisym) ).
thf(584,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(218,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite @ TA @ A )
=> ? [B: list @ TA] :
( ( set2 @ TA @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_finite__list) ).
thf(1154,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite @ TA @ A )
=> ? [B: list @ TA] :
( ( set2 @ TA @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(87,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ ( append @ TA @ A @ B ) @ ( append @ TA @ C @ B ) )
= ( suffix @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_same__suffix__suffix) ).
thf(641,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ ( append @ TA @ A @ B ) @ ( append @ TA @ C @ B ) )
= ( suffix @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(157,axiom,
! [A: g,B: node,C: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( invar @ A )
=> ~ ! [D: list @ node] :
~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_old_Odominates__path) ).
thf(936,plain,
! [A: g,B: node,C: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( invar @ A )
=> ~ ! [D: list @ node] :
~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(30,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_sorted__wrt_Oinduct) ).
thf(382,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(238,axiom,
! [A: g,B: node,C: val,D: list @ node] :
( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_defAssD) ).
thf(1239,plain,
! [A: g,B: node,C: val,D: list @ node] :
( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(199,axiom,
member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_rs_H__props_I3_J) ).
thf(1090,plain,
member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Nil__suffix) ).
thf(704,plain,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(63,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( suffix @ TA @ A @ ( append @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_suffix__appendI) ).
thf(540,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( suffix @ TA @ A @ ( append @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1208,plain,
r != phi_r,
inference(polarity_switch,[status(thm)],[1207]) ).
thf(1209,plain,
r != phi_r,
inference(lifteq,[status(thm)],[1208]) ).
thf(97,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_rev__exhaust) ).
thf(681,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(209,axiom,
! [TA: $tType,A: list @ TA] :
( ( distinct @ TA @ A )
=> ~ ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ ( tl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_FormalSSA__Misc_Odistinct__hd__tl) ).
thf(1117,plain,
! [TA: $tType,A: list @ TA] :
( ( distinct @ TA @ A )
=> ~ ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ ( tl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(175,axiom,
graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_assms_I7_J) ).
thf(996,plain,
graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(73,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_hd__append) ).
thf(567,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(224,axiom,
! [A: g,B: node,C: list @ node,D: node,E: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member @ node @ E @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B ) ) )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons @ node @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_old_OCons__path2) ).
thf(1175,plain,
! [A: g,B: node,C: list @ node,D: node,E: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member @ node @ E @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B ) ) )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons @ node @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(118,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_remdups__adj_Ocases) ).
thf(764,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(169,axiom,
! [A: g,B: node,C: node] :
( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
= ( ( C != B )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
& ! [D: node] :
( ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( ( ( D != B )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_old_OisIdom__def) ).
thf(979,plain,
! [A: g,B: node,C: node] :
( ( graph_graph_isIdom @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
= ( ( C != B )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
& ! [D: node] :
( ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( ( ( D != B )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(54,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( A
= ( append @ TA @ B @ C ) )
=> ( suffix @ TA @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_suffixI) ).
thf(509,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( A
= ( append @ TA @ B @ C ) )
=> ( suffix @ TA @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(140,axiom,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ~ ! [C: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ C @ A )
=> ~ ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_old_OEntry__reachesE) ).
thf(880,plain,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ~ ! [C: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ C @ A )
=> ~ ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(85,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ D ) )
& ( B
= ( append @ TA @ C @ E ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( hd @ TA @ D )
!= ( hd @ TA @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_longest__common__prefix) ).
thf(631,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ D ) )
& ( B
= ( append @ TA @ C @ E ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( hd @ TA @ D )
!= ( hd @ TA @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: list @ TA] :
( ( A @ E @ F )
=> ( A @ ( cons @ TB @ D @ E ) @ F ) )
=> ( ! [D: TA,E: list @ TB,F: list @ TA] :
( ( A @ E @ F )
=> ( A @ E @ ( cons @ TA @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_list__2pre__induct) ).
thf(758,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: list @ TA] :
( ( A @ E @ F )
=> ( A @ ( cons @ TB @ D @ E ) @ F ) )
=> ( ! [D: TA,E: list @ TB,F: list @ TA] :
( ( A @ E @ F )
=> ( A @ E @ ( cons @ TA @ D @ F ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(220,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( tl @ TA @ ( cons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_list_Osel_I3_J) ).
thf(1162,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( tl @ TA @ ( cons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(120,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( suffix @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( ( A
= ( cons @ TA @ B @ C ) )
| ( suffix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_suffix__Cons) ).
thf(769,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( suffix @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( ( A
= ( cons @ TA @ B @ C ) )
| ( suffix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(183,axiom,
! [A: g,B: node,C: node,D: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_dominates__trans_H) ).
thf(1022,plain,
! [A: g,B: node,C: node,D: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(49,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ~ ! [C: list @ TA] :
( B
!= ( append @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_suffixE) ).
thf(494,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ~ ! [C: list @ TA] :
( B
!= ( append @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(195,axiom,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( finite_finite @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_phiUses__finite) ).
thf(1080,plain,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( finite_finite @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA > $o ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA > $o] : ( A @ E @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB > TA > $o,F: TB,G: list @ TB,H: TA,I: list @ TA] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
=> ( ! [E: TB > TA > $o,F: TB,G: list @ TB] : ( A @ E @ ( cons @ TB @ F @ G ) @ ( nil @ TA ) )
=> ( ! [E: TB > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TB ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_list__all__zip_Oinduct) ).
thf(695,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA > $o ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA > $o] : ( A @ E @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB > TA > $o,F: TB,G: list @ TB,H: TA,I: list @ TA] :
( ( A @ E @ G @ I )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
=> ( ! [E: TB > TA > $o,F: TB,G: list @ TB] : ( A @ E @ ( cons @ TB @ F @ G ) @ ( nil @ TA ) )
=> ( ! [E: TB > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TB ) @ ( cons @ TA @ F @ G ) )
=> ( A @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(177,axiom,
~ ! [A: list @ node,B: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ A @ B )
=> ( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ A )
=> ( ( member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ B ) )
=> ~ ( member @ node @ B @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25__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(1000,plain,
~ ! [A: list @ node,B: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ A @ B )
=> ( ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ A )
=> ( ( member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ B ) )
=> ~ ( member @ node @ B @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(92,axiom,
! [TA: $tType] :
( ( suffix @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
? [C: list @ TA] :
( B
= ( append @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_Sublist_Osuffix__def) ).
thf(658,plain,
! [TA: $tType] :
( ( suffix @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
? [C: list @ TA] :
( B
= ( append @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(191,axiom,
! [A: val,B: g,C: node] :
( ( member @ val @ A @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ B @ C ) )
=> ( member @ val @ A @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_phiDefs__in__allDefs) ).
thf(1066,plain,
! [A: val,B: g,C: node] :
( ( member @ val @ A @ ( sSA_CFG_SSA_phiDefs @ g @ node @ val @ phis @ B @ C ) )
=> ( member @ val @ A @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(8,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_suffix__order_Oantisym__conv) ).
thf(278,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(153,axiom,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( finite_finite @ val @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_allDefs__finite) ).
thf(927,plain,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( finite_finite @ val @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(126,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_suffix__order_Oorder_Oantisym) ).
thf(812,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(68,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( suffix @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( B = D )
& ( suffix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_snoc__suffix__snoc) ).
thf(553,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( suffix @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( B = D )
& ( suffix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_append_Oright__neutral) ).
thf(617,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(56,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_neq__Nil__conv) ).
thf(516,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(158,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( A
!= ( hd @ TA @ B ) )
=> ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_not__hd__in__tl) ).
thf(939,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( A
!= ( hd @ TA @ B ) )
=> ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(263,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_in__set__conv__decomp__first) ).
thf(1340,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: list @ TA,D: list @ TA] :
( ( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
& ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(123,axiom,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_suffix__order_Oorder__refl) ).
thf(776,plain,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(108,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( distinct @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ C ) ) )
=> ( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TA @ D @ ( cons @ TA @ B @ E ) ) )
= ( ( A = D )
& ( C = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_distinct__match) ).
thf(712,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( distinct @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ C ) ) )
=> ( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TA @ D @ ( cons @ TA @ B @ E ) ) )
= ( ( A = D )
& ( C = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(100,axiom,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_suffix__bot_Obot_Oextremum) ).
thf(690,plain,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(184,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_split__list__prop) ).
thf(1025,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(245,axiom,
sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_assms_I10_J) ).
thf(1267,plain,
sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(203,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_list_Ocollapse) ).
thf(1098,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(76,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_append__eq__appendI) ).
thf(580,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(133,axiom,
! [TA: $tType,A: list @ TA] : ( finite_finite @ TA @ ( set2 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_List_Ofinite__set) ).
thf(855,plain,
! [TA: $tType,A: list @ TA] : ( finite_finite @ TA @ ( set2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(187,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( tl @ TA @ A ) )
= ( ( A
= ( nil @ TA ) )
| ? [B: TA] :
( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Nil__tl) ).
thf(1053,plain,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( tl @ TA @ A ) )
= ( ( A
= ( nil @ TA ) )
| ? [B: TA] :
( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(243,axiom,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_old_Odominates__refl) ).
thf(1262,plain,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(256,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_split__list) ).
thf(1317,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ? [C: list @ TA,D: list @ TA] :
( B
= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(23,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Cons__eq__appendI) ).
thf(359,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(234,axiom,
! [A: g,B: node,C: list @ node,D: node,E: node > ( list @ node ) > node > $o] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( E @ B @ ( cons @ node @ B @ ( nil @ node ) ) @ B ) )
=> ( ! [F: list @ node,G: node,H: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G )
=> ( ( E @ B @ F @ G )
=> ( ( member @ node @ G @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ H ) ) )
=> ( E @ B @ ( append @ node @ F @ ( cons @ node @ H @ ( nil @ node ) ) ) @ H ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_old_Opath2__rev__induct) ).
thf(1218,plain,
! [A: g,B: node,C: list @ node,D: node,E: node > ( list @ node ) > node > $o] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( E @ B @ ( cons @ node @ B @ ( nil @ node ) ) @ B ) )
=> ( ! [F: list @ node,G: node,H: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G )
=> ( ( E @ B @ F @ G )
=> ( ( member @ node @ G @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ 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)],[234]) ).
thf(242,axiom,
! [A: g,B: node,C: val,D: list @ node] :
( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ~ ! [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
=> ~ ( member @ val @ C @ ( defs @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_defAss_HE) ).
thf(1257,plain,
! [A: g,B: node,C: val,D: list @ node] :
( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ~ ! [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
=> ~ ( member @ val @ C @ ( defs @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(247,axiom,
! [A: g,B: node,C: list @ node,D: node,E: node > ( list @ node ) > node > $o] :
( ( graph_1661282752_path2 @ g @ node @ 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_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D )
=> ( ( E @ H @ F @ D )
=> ( ( member @ node @ G @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ H ) ) )
=> ( E @ G @ ( cons @ node @ G @ F ) @ D ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_old_Opath2__induct) ).
thf(1272,plain,
! [A: g,B: node,C: list @ node,D: node,E: node > ( list @ node ) > node > $o] :
( ( graph_1661282752_path2 @ g @ node @ 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_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D )
=> ( ( E @ H @ F @ D )
=> ( ( member @ node @ G @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ H ) ) )
=> ( E @ G @ ( cons @ node @ G @ F ) @ D ) ) ) )
=> ( E @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(50,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_successively_Oinduct) ).
thf(497,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(201,axiom,
graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_rs_H__props_I2_J) ).
thf(1094,plain,
graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(31,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_list__nonempty__induct) ).
thf(386,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(132,axiom,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( C
= ( cons @ node @ B @ ( nil @ node ) ) )
=> ( D != B ) )
=> ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd @ node @ ( tl @ node @ C ) ) @ ( tl @ node @ C ) @ D )
=> ~ ( member @ node @ B @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ ( tl @ node @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_old_Opath2__cases) ).
thf(845,plain,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( ( C
= ( cons @ node @ B @ ( nil @ node ) ) )
=> ( D != B ) )
=> ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd @ node @ ( tl @ node @ C ) ) @ ( tl @ node @ C ) @ D )
=> ~ ( member @ node @ B @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ ( tl @ node @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(197,axiom,
! [A: g,B: node] : ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( cons @ node @ B @ ( nil @ node ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_old_OEntryPath__triv) ).
thf(1084,plain,
! [A: g,B: node] : ( graph_2081878492ryPath @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ ( cons @ node @ B @ ( nil @ node ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(226,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( tl @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( tl @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_tl__append2) ).
thf(1180,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( tl @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( tl @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(155,axiom,
! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ E ) ) @ F )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ ( cons @ node @ D @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_old_Opath2__split_I2_J) ).
thf(931,plain,
! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ E ) ) @ F )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ ( cons @ node @ D @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(45,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_neq__NilE) ).
thf(482,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(219,axiom,
! [A: g,B: node,C: val,D: node,E: list @ node] :
( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B )
=> ( ! [F: node] :
( ( member @ node @ F @ ( set2 @ node @ ( tl @ node @ E ) ) )
=> ~ ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ A @ F ) ) )
=> ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_defAss__extend) ).
thf(1157,plain,
! [A: g,B: node,C: val,D: node,E: list @ node] :
( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B )
=> ( ! [F: node] :
( ( member @ node @ F @ ( set2 @ node @ ( tl @ node @ E ) ) )
=> ~ ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ A @ F ) ) )
=> ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(249,axiom,
linorder @ val,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_1) ).
thf(1289,plain,
linorder @ val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(206,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) ) )
= ( ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_split__list__first__prop__iff) ).
thf(1108,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) ) )
= ( ? [C: list @ TA,D: TA] :
( ? [E: list @ TA] :
( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ C ) )
=> ~ ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(24,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_append__assoc) ).
thf(363,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(69,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(556,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(168,axiom,
! [A: g,B: node,C: list @ node,D: node,E: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ E ) ) )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ E @ ( nil @ node ) ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_old_Opath2__snoc) ).
thf(976,plain,
! [A: g,B: node,C: list @ node,D: node,E: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ E ) ) )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ E @ ( nil @ node ) ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(146,axiom,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ? [C: list @ node] : ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_old_OEntry__reaches) ).
thf(903,plain,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( invar @ B )
=> ? [C: list @ node] : ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ ( entry @ B ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(259,axiom,
! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( tl @ node @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_old_Opath2__app) ).
thf(1326,plain,
! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
=> ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( tl @ node @ E ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(103,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ B @ A )
& ( suffix @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_suffix__order_Odual__order_Oeq__iff) ).
thf(699,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( suffix @ TA @ B @ A )
& ( suffix @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(165,axiom,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_old_Opath2__tl__in___092_060alpha_062n) ).
thf(961,plain,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(166,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) ) )
= ( ? [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_split__list__last__prop__iff) ).
thf(963,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) ) )
= ( ? [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(12,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_self__append__conv) ).
thf(304,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(239,axiom,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member @ node @ D @ ( set2 @ node @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_old_Opath2__last__in__ns) ).
thf(1244,plain,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member @ node @ D @ ( set2 @ node @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(174,axiom,
linorder @ node,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(995,plain,
linorder @ node,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(144,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite @ TA @ A )
=> ? [B: list @ TA] :
( ( ( set2 @ TA @ B )
= A )
& ( distinct @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_finite__distinct__list) ).
thf(896,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite @ TA @ A )
=> ? [B: list @ TA] :
( ( ( set2 @ TA @ B )
= A )
& ( distinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(114,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_append__Nil2) ).
thf(748,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(160,axiom,
! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_list_Oset__intros_I1_J) ).
thf(946,plain,
! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(204,axiom,
! [A: g] :
( ( invar @ A )
=> ( distinct @ node @ ( alpha_n @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_old_O_092_060alpha_062n__distinct) ).
thf(1101,plain,
! [A: g] :
( ( invar @ A )
=> ( distinct @ node @ ( alpha_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(149,axiom,
! [A: node,B: g,C: node] :
( ( member @ node @ A @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ C ) ) )
=> ( ( invar @ B )
=> ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_old_Opredecessor__is__node) ).
thf(914,plain,
! [A: node,B: g,C: node] :
( ( member @ node @ A @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ C ) ) )
=> ( ( invar @ B )
=> ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(38,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_append__eq__append__conv2) ).
thf(433,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(251,axiom,
! [A: node,B: node,C: g,D: node] :
( ( ( A != B )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ B ) )
=> ( ( ( B != D )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ B @ D ) )
=> ( ( A != D )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_strict__dom__trans_H) ).
thf(1294,plain,
! [A: node,B: node,C: g,D: node] :
( ( ( A != B )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ B ) )
=> ( ( ( B != D )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ B @ D ) )
=> ( ( A != D )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(154,axiom,
! [A: g] : ( member @ node @ ( entry @ A ) @ ( set2 @ node @ ( alpha_n @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_old_OEntry__in__graph) ).
thf(929,plain,
! [A: g] : ( member @ node @ ( entry @ A ) @ ( set2 @ node @ ( alpha_n @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(232,axiom,
! [A: g] :
( ( graph_reducible @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A )
= ( ! [B: node,C: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B )
=> ? [D: node] :
( ( member @ node @ D @ ( set2 @ node @ C ) )
& ! [E: node] :
( ( member @ node @ E @ ( set2 @ node @ C ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_old_Oreducible__def) ).
thf(1212,plain,
! [A: g] :
( ( graph_reducible @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A )
= ( ! [B: node,C: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B )
=> ? [D: node] :
( ( member @ node @ D @ ( set2 @ node @ C ) )
& ! [E: node] :
( ( member @ node @ E @ ( set2 @ node @ C ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_list__induct2_H) ).
thf(272,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(98,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_append__same__eq) ).
thf(684,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(20,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_list__tail__coinc) ).
thf(346,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(67,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ E @ ( cons @ TA @ D @ F ) )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_revg_Oinduct) ).
thf(549,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ E @ ( cons @ TA @ D @ F ) )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(62,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_eq__Nil__appendI) ).
thf(536,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(82,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ( D = F )
=> ( A @ E @ G ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_longest__common__prefix_Oinduct) ).
thf(620,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ( D = F )
=> ( A @ E @ G ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( A
!= ( nil @ TB ) )
=> ( ( B
!= ( nil @ TA ) )
=> ( ! [D: TB,E: TA] : ( C @ ( cons @ TB @ D @ ( nil @ TB ) ) @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TB,E: list @ TB,F: TA] :
( ( E
!= ( nil @ TB ) )
=> ( C @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( cons @ TA @ F @ ( nil @ TA ) ) ) )
=> ( ! [D: TB,E: TA,F: list @ TA] :
( ( F
!= ( nil @ TA ) )
=> ( C @ ( cons @ TB @ D @ ( nil @ TB ) ) @ ( append @ TA @ F @ ( cons @ TA @ E @ ( nil @ TA ) ) ) ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( C @ E @ G )
=> ( ( E
!= ( nil @ TB ) )
=> ( ( G
!= ( nil @ TA ) )
=> ( C @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_rev__nonempty__induct2_H) ).
thf(315,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( A
!= ( nil @ TB ) )
=> ( ( B
!= ( nil @ TA ) )
=> ( ! [D: TB,E: TA] : ( C @ ( cons @ TB @ D @ ( nil @ TB ) ) @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TB,E: list @ TB,F: TA] :
( ( E
!= ( nil @ TB ) )
=> ( C @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( cons @ TA @ F @ ( nil @ TA ) ) ) )
=> ( ! [D: TB,E: TA,F: list @ TA] :
( ( F
!= ( nil @ TA ) )
=> ( C @ ( cons @ TB @ D @ ( nil @ TB ) ) @ ( append @ TA @ F @ ( cons @ TA @ E @ ( nil @ TA ) ) ) ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( C @ E @ G )
=> ( ( E
!= ( nil @ TB ) )
=> ( ( G
!= ( nil @ TA ) )
=> ( C @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(33,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
=> ( ( ( C
= ( nil @ TA ) )
=> ( D
!= ( cons @ TA @ A @ B ) ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ A @ E ) )
=> ( ( append @ TA @ E @ D )
!= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_list__Cons__eq__append__cases) ).
thf(410,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
=> ( ( ( C
= ( nil @ TA ) )
=> ( D
!= ( cons @ TA @ A @ B ) ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ A @ E ) )
=> ( ( append @ TA @ E @ D )
!= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(235,axiom,
! [A: g,B: node,C: node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_old_Odominates__antisymm) ).
thf(1229,plain,
! [A: g,B: node,C: node] :
( ( invar @ A )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(27,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ C )
=> ( suffix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_suffix__order_Oorder_Otrans) ).
thf(373,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( suffix @ TA @ A @ B )
=> ( ( suffix @ TA @ B @ C )
=> ( suffix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(72,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_list_Oinject) ).
thf(564,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( cons @ TA @ C @ D ) ) )
=> ~ ! [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
=> ( ( append @ TA @ E @ B )
!= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_list__append__eq__Cons__cases) ).
thf(294,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( cons @ TA @ C @ D ) ) )
=> ~ ! [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
=> ( ( append @ TA @ E @ B )
!= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(254,axiom,
graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_rs_H__props_I1_J) ).
thf(1314,plain,
graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(188,axiom,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member @ node @ B @ ( set2 @ node @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_old_Opath2__hd__in__ns) ).
thf(1056,plain,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member @ node @ B @ ( set2 @ node @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
( ! [E: list @ TB] : ( A @ E @ ( nil @ TA ) )
=> ( ! [E: list @ TA] : ( A @ ( nil @ TB ) @ E )
=> ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
( ( B @ E @ G )
=> ( ( A @ F @ ( cons @ TA @ G @ H ) )
=> ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
=> ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
( ~ ( B @ E @ G )
=> ( ( A @ ( cons @ TB @ E @ F ) @ H )
=> ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
=> ( A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_mergesort__by__rel__merge__induct) ).
thf(828,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
( ! [E: list @ TB] : ( A @ E @ ( nil @ TA ) )
=> ( ! [E: list @ TA] : ( A @ ( nil @ TB ) @ E )
=> ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
( ( B @ E @ G )
=> ( ( A @ F @ ( cons @ TA @ G @ H ) )
=> ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
=> ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
( ~ ( B @ E @ G )
=> ( ( A @ ( cons @ TB @ E @ F ) @ H )
=> ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
=> ( A @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(164,axiom,
member @ node @ pred_phi_r @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_rs_H__props_I4_J) ).
thf(960,plain,
member @ node @ pred_phi_r @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(221,axiom,
! [A: g,B: node,C: val] :
( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( defs @ A @ E ) ) ) )
=> ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_defAss_HI) ).
thf(1165,plain,
! [A: g,B: node,C: val] :
( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( defs @ A @ E ) ) ) )
=> ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(142,axiom,
! [A: g,B: node] : ( finite_finite @ val @ ( defs @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_defs__finite) ).
thf(886,plain,
! [A: g,B: node] : ( finite_finite @ val @ ( defs @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(53,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_not__Cons__self2) ).
thf(506,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(4,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_2) ).
thf(268,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(223,axiom,
! [A: g,B: node] :
( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B )
!= ( nil @ node ) )
=> ( ( invar @ A )
=> ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_old_Osuccessor__in___092_060alpha_062n) ).
thf(1172,plain,
! [A: g,B: node] :
( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B )
!= ( nil @ node ) )
=> ( ( invar @ A )
=> ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(119,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( suffix @ TA @ A @ B )
=> ( suffix @ TA @ A @ ( cons @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_suffix__ConsI) ).
thf(767,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( suffix @ TA @ A @ B )
=> ( suffix @ TA @ A @ ( cons @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ~ ! [C: list @ TA,D: list @ TA] :
( B
!= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_in__set__list__format) ).
thf(1033,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ~ ! [C: list @ TA,D: list @ TA] :
( B
!= ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(32,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_rev__induct) ).
thf(400,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(229,axiom,
! [A: g,B: node,C: list @ node,D: node,E: node > $o] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ? [F: node] :
( ( member @ node @ F @ ( set2 @ node @ C ) )
& ( E @ F ) )
=> ~ ! [F: node,G: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D )
=> ( ( E @ F )
=> ( ! [H: node] :
( ( member @ node @ H @ ( set2 @ node @ ( tl @ node @ G ) ) )
=> ~ ( E @ H ) )
=> ~ ( suffix @ node @ G @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_old_Opath2__split__last__prop) ).
thf(1197,plain,
! [A: g,B: node,C: list @ node,D: node,E: node > $o] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( ? [F: node] :
( ( member @ node @ F @ ( set2 @ node @ C ) )
& ( E @ F ) )
=> ~ ! [F: node,G: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D )
=> ( ( E @ F )
=> ( ! [H: node] :
( ( member @ node @ H @ ( set2 @ node @ ( tl @ node @ G ) ) )
=> ~ ( E @ H ) )
=> ~ ( suffix @ node @ G @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ~ ( member @ TA @ A @ ( set2 @ TA @ C ) )
=> ( ( ( append @ TA @ B @ ( cons @ TA @ A @ C ) )
= ( append @ TA @ D @ ( cons @ TA @ A @ E ) ) )
= ( ( B = D )
& ( C = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_append__Cons__eq__iff) ).
thf(839,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ~ ( member @ TA @ A @ ( set2 @ TA @ C ) )
=> ( ( ( append @ TA @ B @ ( cons @ TA @ A @ C ) )
= ( append @ TA @ D @ ( cons @ TA @ A @ E ) ) )
= ( ( B = D )
& ( C = E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(237,axiom,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_old_Opath2__hd__in___092_060alpha_062n) ).
thf(1236,plain,
! [A: g,B: node,C: list @ node,D: node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
=> ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(43,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_remdups__adj_Oinduct) ).
thf(464,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(213,axiom,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( A
!= ( entry @ B ) )
=> ~ ! [C: node] :
( ( member @ node @ C @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ A ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_non__dominated__predecessor) ).
thf(1129,plain,
! [A: node,B: g] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( A
!= ( entry @ B ) )
=> ~ ! [C: node] :
( ( member @ node @ C @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ A ) ) )
=> ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(246,axiom,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B )
= ( nil @ node ) )
= ( B
= ( entry @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_old_OEntry__iff__unreachable) ).
thf(1268,plain,
! [A: g,B: node] :
( ( invar @ A )
=> ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
=> ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B )
= ( nil @ node ) )
= ( B
= ( entry @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(36,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( hd @ TA @ ( cons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_list_Osel_I1_J) ).
thf(427,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( hd @ TA @ ( cons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(135,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_split__list__last__prop) ).
thf(860,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ? [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
& ( B @ C ) )
=> ? [C: list @ TA,D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
& ( B @ D )
& ! [F: TA] :
( ( member @ TA @ F @ ( set2 @ TA @ E ) )
=> ~ ( B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(182,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( B
= ( hd @ TA @ A ) )
| ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) ) )
= ( member @ TA @ B @ ( set2 @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_in__hd__or__tl__conv) ).
thf(1019,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( B
= ( hd @ TA @ A ) )
| ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) ) )
= ( member @ TA @ B @ ( set2 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(88,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_same__append__eq) ).
thf(644,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(170,axiom,
! [A: g,B: node,C: val] :
( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
= ( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( defs @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_defAss_H__def) ).
thf(982,plain,
! [A: g,B: node,C: val] :
( ( sSA_CFG_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C )
= ( ! [D: list @ node] :
( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( entry @ A ) @ D @ B )
=> ? [E: node] :
( ( member @ node @ E @ ( set2 @ node @ D ) )
& ( member @ val @ C @ ( defs @ A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(137,axiom,
! [A: g,B: node,C: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_dominates__antisymm_H) ).
thf(871,plain,
! [A: g,B: node,C: node] :
( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C )
=> ( ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(211,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_hd__in__set) ).
thf(1120,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(51,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_self__append__conv2) ).
thf(501,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(80,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_strict__sorted_Oinduct) ).
thf(607,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ! [C: list @ TA] :
( B
!= ( cons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_list_Oset__cases) ).
thf(908,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ! [C: list @ TA] :
( B
!= ( cons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(173,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( tl @ TA @ A )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
| ? [B: TA] :
( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_tl__Nil) ).
thf(992,plain,
! [TA: $tType,A: list @ TA] :
( ( ( tl @ TA @ A )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
| ? [B: TA] :
( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(257,axiom,
! [A: val,B: g,C: node] :
( ( member @ val @ A @ ( defs @ B @ C ) )
=> ( member @ val @ A @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_defs__in__allDefs) ).
thf(1320,plain,
! [A: val,B: g,C: node] :
( ( member @ val @ A @ ( defs @ B @ C ) )
=> ( member @ val @ A @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(17,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( cons @ TA @ B @ ( nil @ TA ) )
= ( append @ TA @ A @ C ) )
= ( ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) )
& ( C
= ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_list__se__match_I3_J) ).
thf(337,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( cons @ TA @ B @ ( nil @ TA ) )
= ( append @ TA @ A @ C ) )
= ( ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) )
& ( C
= ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(179,axiom,
! [A: node,B: g,C: val] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ B @ A @ C )
= ( ? [D: node] :
( ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ B ) ) )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ D @ A )
& ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_defAss__dominating) ).
thf(1009,plain,
! [A: node,B: g,C: val] :
( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
=> ( ( sSA_CFG_SSA_defAss @ g @ node @ edgeD @ val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ B @ A @ C )
= ( ? [D: node] :
( ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ B ) ) )
& ( graph_709200220inates @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ D @ A )
& ( member @ val @ C @ ( sSA_CFG_SSA_allDefs @ g @ node @ val @ defs @ phis @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_list_Odistinct_I1_J) ).
thf(309,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(86,axiom,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_suffix__order_Odual__order_Orefl) ).
thf(639,plain,
! [TA: $tType,A: list @ TA] : ( suffix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(116,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_transpose_Ocases) ).
thf(755,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(48,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_append__is__Nil__conv) ).
thf(491,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(5610,plain,
$false,
inference(e,[status(thm)],[1322,1036,809,1337,628,1315,352,1068,379,269,1305,1290,276,440,655,1078,1137,533,715,1233,340,1095,709,436,1265,1254,651,504,587,1059,542,917,702,751,559,1013,924,1302,443,1334,485,574,966,1183,1283,905,480,602,1215,988,312,1169,687,877,692,1119,774,307,920,942,529,661,366,957,1091,825,778,952,1123,815,729,625,1178,665,522,461,1210,842,874,948,1064,1111,356,869,420,857,519,742,1082,488,933,901,526,679,547,706,884,1329,1016,1207,1114,985,1150,1192,1246,371,647,997,343,1086,266,1071,662,888,1135,1103,264,745,375,513,1146,430,562,423,1007,732,772,577,291,281,545,584,1154,641,936,382,1239,1090,704,540,1209,681,1117,996,567,1175,764,979,509,880,631,758,1162,769,1022,494,1080,695,1000,658,1066,278,927,812,553,617,516,939,1340,776,712,690,1025,1267,1098,580,855,1053,1262,1317,359,1218,1257,1272,497,1094,386,845,1084,1180,931,482,1157,1289,1108,363,556,976,903,1326,699,961,963,304,1244,995,896,748,946,1101,914,433,1294,929,1212,272,684,346,549,536,620,315,410,1229,373,564,294,1314,1056,828,960,1165,886,506,268,1172,767,1033,400,1197,839,1236,464,1129,1268,427,860,1019,644,982,871,1120,501,607,908,992,1320,337,1009,309,639,755,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP080^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n011.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 19:48:46 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.04/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.04/1.49 % [INFO] Parsing done (596ms).
% 3.48/1.51 % [INFO] Running in sequential loop mode.
% 5.15/2.09 % [INFO] eprover registered as external prover.
% 5.15/2.11 % [INFO] Scanning for conjecture ...
% 5.92/2.40 % [INFO] Found a conjecture (or negated_conjecture) and 263 axioms. Running axiom selection ...
% 6.61/2.65 % [INFO] Axiom selection finished. Selected 261 axioms (removed 2 axioms).
% 9.04/3.32 % [INFO] Problem is higher-order (TPTP THF).
% 9.04/3.38 % [INFO] Type checking passed.
% 9.04/3.39 % [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 ...
% 148.06/66.46 % External prover 'e' found a proof!
% 148.06/66.46 % [INFO] Killing All external provers ...
% 148.06/66.47 % Time passed: 66110ms (effective reasoning time: 64947ms)
% 148.06/66.47 % 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)>
% 148.06/66.47 % Axioms used in derivation (261): fact_187_split__list__propE, fact_241_suffixE, fact_56_old_Odominates__antitrans, fact_145_list__2pre__induct, fact_194_split__list__first__propE, fact_17_old_Opath2__in___092_060alpha_062n, fact_31_defAss_HI, fact_28_FormalSSA__Misc_Odistinct__hd__tl, fact_130_zipf_Oinduct, fact_133_neq__Nil__conv, fact_41_phiUses__finite, fact_120_suffix__snoc, tfree_0, fact_27_old_Oidom__ex, fact_84_old_Opath2__induct, fact_43_allDefs__finite, fact_49_old_Opath2__not__Nil2, fact_245_finite__distinct__list, fact_63_old_Odominates__def, fact_114_list__se__match_I2_J, fact_224_suffix__order_Oantisym, fact_106_same__suffix__suffix, fact_132_list_Oinducts, fact_62_old_Odominates__mid, fact_42_old_Opath2__split__last__prop, fact_26_old_OEntry__reaches, fact_24_old_OEntry__reachesE, fact_253_Misc_Odistinct__hd__tl, fact_154_successively_Oinduct, fact_250_hd__append, fact_116_list__se__match_I4_J, fact_39_defAss__dominating, fact_123_rs__def, fact_252_not__hd__in__tl, fact_23_old_Opath2__forget__hd, fact_254_old_OEntry__unreachable, fact_160_longest__common__prefix_Oinduct, fact_1_False, fact_176_Cons__eq__append__conv, fact_171_list__append__eq__Cons__cases, fact_204_tl__obtain__elem, fact_207_not__suffix__induct, fact_100_append__self__conv2, fact_214_suffix__order_Odual__order_Oeq__iff, fact_37_defAssD, fact_230_eq__Nil__appendI, fact_198_split__list__first__prop__iff, fact_22_old_Opredecessor__is__node, fact_117_list__e__eq__lel_I1_J, tcon_fun___Orderings_Oord, fact_94_List_Ofinite__set, fact_173_rev__nonempty__induct2_H, fact_185_xy__in__set__cases, fact_180_rev__exhaust, fact_235_list_Osel_I2_J, fact_247_hd__in__set, fact_199_distinct__singleton, fact_149_append__Cons, fact_70_old_Odominates__extend, fact_57_old_Odominates__antisymm, fact_234_Nil__suffix, fact_139_Cons__eq__appendI, fact_119_snoc__suffix__snoc, tcon_HOL_Obool___Orderings_Olinorder, fact_6_old_O_092_060alpha_062n__distinct, fact_186_split__list__first, fact_87_same__append__eq, fact_9_allDefs__disjoint_H, fact_88_append__same__eq, fact_96_empty__append__eq__id, fact_229_append__Nil, fact_152_list__match__lel__lel, fact_248_list_Oset__sel_I2_J, fact_195_in__set__conv__decomp__last, fact_182_split__list, fact_177_neq__Nil__rev__conv, fact_105_suffix__Nil, fact_66_non__dominated__predecessor, fact_124_old_Oempty__path2, fact_210_not__distinct__split__distinct, fact_86_list_Oinject, fact_10_assms_I7_J, fact_206_not__distinct__conv__prefix, fact_217_suffix__order_Oord__eq__le__trans, fact_46_Collect__mem__eq, fact_169_list_Oset__intros_I1_J, fact_65_old_Odominates__unsnoc, fact_32_defAss_HE, fact_233_suffix__bot_Obot_Oextremum, fact_99_self__append__conv2, fact_16_old_Opath2__hd__in__ns, fact_251_list_Oexpand, fact_118_list__e__eq__lel_I2_J, fact_92_suffix__order_Oorder__refl, fact_143_suffix__ConsD, fact_236_suffix__appendI, fact_36_defAssI, fact_69_old_Odominates__unsnoc_H, fact_167_list_Oset__cases, fact_170_list_Oset__intros_I2_J, fact_237_suffix__appendD, fact_189_in__set__conv__decomp, fact_135_splice_Oinduct, fact_128_list_OdiscI, fact_183_split__list__last, fact_168_set__ConsD, fact_243_distinct__tl, fact_5_old_OEntryPath__distinct, fact_109_old_OEntryPath__triv, fact_81_tl__append2, fact_219_suffix__order_Oorder_Oeq__iff, fact_14_FormalSSA__Misc_Oin__set__tlD, fact_179_neq__Nil__revE, fact_58_dominates__trans_H, fact_80_old_Opath2__rev__induct, fact_156_list__nonempty__induct, fact_134_list__induct2_H, fact_225_suffix__order_Oeq__iff, fact_178_rev__induct2_H, fact_222_suffix__order_Oorder_Otrans, fact_193_split__list__last__propE, fact_85_old_Oelem__set__implies__elem__tl__app__cons, fact_4_rs_H__props_I1_J, fact_73_old_OEntry__dominates, fact_93_old_Opath2__split_I2_J, fact_2_old_OEntry__in__graph, fact_51_defs__finite, fact_231_distinct_Osimps_I1_J, fact_192_split__list__first__prop, fact_95_append_Oright__neutral, fact_201_distinct__match, fact_155_list__all__zip_Oinduct, fact_239_Sublist_Osuffix__def, fact_20_old_Opath2__last__in__ns, fact_190_in__set__list__format, fact_77_in__hd__or__tl__conv, fact_45_mem__Collect__eq, fact_129_revg_Oinduct, fact_11_defNode__eq, fact_18_old_Oinvar, fact_196_in__set__conv__decomp__first, fact_174_rev__nonempty__induct, fact_181_rev__induct, fact_126_list_Odistinct_I1_J, fact_157_map__tailrec__rev_Oinduct, fact_15_old_Opath2__hd__in___092_060alpha_062n, fact_197_split__list__last__prop__iff, fact_121_list_Ocollapse, fact_188_append__Cons__eq__iff, fact_136_induct__list012, fact_249_longest__common__prefix, fact_53_strict__dom__trans_H, fact_13_defs__in__allDefs, fact_71_old_OEntry__no__predecessor, fact_67_old_OisIdom__def, fact_131_list_Oexhaust, fact_72_old_Odominates__refl, fact_103_append__Nil2, fact_151_list__induct__first2, fact_76_old_Oreducible__def, fact_55_old_Odominates__trans, fact_7_rs_H__props_I3_J, fact_208_not__suffix__cases, fact_246_list_Oset__sel_I1_J, fact_142_transpose_Ocases, fact_59_dominates__antisymm_H, fact_90_append_Oassoc, fact_12_rs_H__props_I4_J, fact_220_suffix__order_Oantisym__conv, fact_184_split__list__prop, fact_47_Collect__cong, fact_122_hd__Cons__tl, fact_240_suffixI, fact_107_old_Opath2__split_I1_J, fact_148_sorted__wrt_Oinduct, fact_161_strict__sorted_Oinduct, subcl_Orderings_Olinorder___Orderings_Oord, fact_8_assms_I10_J, fact_158_mergesort__by__rel__merge_Oinduct, fact_102_append__self__conv, fact_89_append__assoc, fact_215_suffix__order_Odual__order_Otrans, fact_218_suffix__order_Oorder_Oantisym, fact_38_phiDefs__in__allDefs, fact_68_old_OEntryPath__suffix, fact_110_append1__eq__conv, fact_112_list__ee__eq__leel_I2_J, fact_202_Nil__tl, fact_19_old_Opath2__tl__in___092_060alpha_062n, fact_111_list__ee__eq__leel_I1_J, fact_52_phiDefs__finite, fact_223_suffix__order_Oeq__refl, fact_141_shuffles_Oinduct, fact_172_list__Cons__eq__append__cases, fact_29_defAss_H__extend, fact_34_assms_I8_J, fact_140_min__list_Oinduct, fact_104_suffix__bot_Obot_Oextremum__unique, fact_64_old_OdominatesE, fact_50_old_Opath2__app, fact_165_not__Cons__self2, fact_175_append__eq__Cons__conv, fact_203_tl__Nil, fact_244_suffix__tl, fact_164_list__tail__coinc, fact_91_suffix__order_Odual__order_Orefl, fact_144_suffix__ConsI, fact_0_old_Opath2__hd, fact_191_split__list__last__prop, tfree_1, fact_33_defAss__extend, fact_98_Nil__is__append__conv, fact_242_distinct__suffix, fact_25__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_232_suffix__bot_Obot_Oextremum__uniqueI, fact_166_distinct__length__2__or__more, fact_211_append__eq__append__conv2, fact_159_mergesort__by__rel__merge__induct, fact_213_suffix__order_Odual__order_Oantisym, fact_40_old_Osuccessor__in___092_060alpha_062n, fact_200_distinct_Osimps_I2_J, fact_60_dominates__refl_H, fact_83_same__suffix__nil, fact_61_old_Odominates__path, fact_21_old_Osuccessor__is__node, fact_228_append_Oleft__neutral, fact_54_old_Ostrict__dom__trans, fact_137_min__list_Ocases, fact_74_old_OdominatesI, fact_138_suffix__Cons, fact_205_not__distinct__decomp, fact_162_list_Osel_I1_J, fact_44_old_Opath2__not__Nil, fact_35_defAss__def, fact_75_old_OEntry__iff__unreachable, fact_221_suffix__order_Oorder__trans, subcl_Orderings_Olinorder___HOL_Otype, fact_216_suffix__order_Oord__le__eq__trans, fact_30_defAss_H__def, fact_78_old_Opath2__cases, fact_101_self__append__conv, fact_147_remdups__adj_Ocases, fact_115_list__se__match_I3_J, fact_226_suffix__same__cases, fact_153_arg__min__list_Oinduct, fact_79_old_Opath2__snoc, fact_82_hd__append2, fact_227_finite__list, fact_209_list_Oexhaust__sel, tcon_HOL_Obool___Orderings_Oord_2, fact_97_append__is__Nil__conv, fact_163_list_Osel_I3_J, fact_125_old_OCons__path2, fact_3_rs_H__props_I2_J, fact_127_neq__NilE, fact_150_remdups__adj_Oinduct, fact_146_suffix__ConsD2, fact_212_append__eq__appendI, fact_108_old_OEntry__loop, fact_113_list__se__match_I1_J, fact_238_suffix__append
% 148.06/66.47 % No. of inferences in proof: 528
% 148.06/66.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 66110 ms resp. 64947 ms w/o parsing
% 149.09/66.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 149.09/66.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------