%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV668+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 : Sun Sep 27 08:48:19 AM UTC 2026
% Result : Theorem 11.41s 4.86s
% Output : Refutation 11.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 54
% Syntax : Number of formulae : 110 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 1222 ( 449 equ; 0 cnn)
% Maximal formula atoms : 369 ( 11 avg)
% Number of connectives : 4613 ( 21 ~; 136 |; 620 &;3480 @)
% ( 20 <=>; 336 =>; 0 <=; 0 <~>)
% Maximal formula depth : 105 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 50 usr; 19 con; 0-5 aty)
% Number of variables : 624 ( 0 ^; 294 !; 330 ?; 624 :)
% Comments :
%------------------------------------------------------------------------------
thf(cRedblack_2ecolor___24t_decl,type,
cRedblack_2ecolor___24t: $i > $o ).
thf(cRedblack_2eTREES_2etree___24t_decl,type,
cRedblack_2eTREES_2etree___24t: $i > $o ).
thf(cRedblack_2ekey___24t_decl,type,
cRedblack_2ekey___24t: $i > $o ).
thf(cV___24t_decl,type,
cV___24t: $i > $o ).
thf(cRedblack_2eTREES_2eT___24a5_decl,type,
cRedblack_2eTREES_2eT___24a5: $i > $i > $i > $i > $i > $i ).
thf(cRedblack_2eTREES_2eE_decl,type,
cRedblack_2eTREES_2eE: $i ).
thf(cProp___24t_decl,type,
cProp___24t: $i > $o ).
thf(p_decl,type,
p: $i > $o ).
thf(c_24__type__3076___24t_decl,type,
c_24__type__3076___24t: $i > $o ).
thf(cType___24t_decl,type,
cType___24t: $i > $o ).
thf(happ_decl,type,
happ: $i > $i > $i ).
thf(c_24__type__3002___24t_decl,type,
c_24__type__3002___24t: $i > $o ).
thf(cRedblack_2eTREES_2ebalance_decl,type,
cRedblack_2eTREES_2ebalance: $i ).
thf(c_24__type__144___24t_decl,type,
c_24__type__144___24t: $i > $o ).
thf(cRedblack_2eTREES_2eins_decl,type,
cRedblack_2eTREES_2eins: $i ).
thf(c_24__type__3074___24t_decl,type,
c_24__type__3074___24t: $i > $o ).
thf(cRedblack_2eTREES_2etree__rect_decl,type,
cRedblack_2eTREES_2etree__rect: $i ).
thf(c_24__type__3031___24t_decl,type,
c_24__type__3031___24t: $i > $o ).
thf(cRedblack_2eTREES_2elookup_decl,type,
cRedblack_2eTREES_2elookup: $i ).
thf(c_24__type__3218___24t_decl,type,
c_24__type__3218___24t: $i > $o ).
thf(c_24__type__3216___24t_decl,type,
c_24__type__3216___24t: $i > $o ).
thf(cRedblack_2eRed_decl,type,
cRedblack_2eRed: $i ).
thf(cRedblack_2eBlack_decl,type,
cRedblack_2eBlack: $i ).
thf(cRedblack_2eTREES_2ebalance___24a5_decl,type,
cRedblack_2eTREES_2ebalance___24a5: $i > $i > $i > $i > $i > $i ).
thf(cVFA_2eExtract_2eint___24t_decl,type,
cVFA_2eExtract_2eint___24t: $i > $o ).
thf(t_decl,type,
t: $i > $i > $o ).
thf(cVFA_2eExtract_2eint_decl,type,
cVFA_2eExtract_2eint: $i ).
thf(c_24__type__3106___24t_decl,type,
c_24__type__3106___24t: $i > $i > $o ).
thf(c_24__type__3106___24a1_decl,type,
c_24__type__3106___24a1: $i > $i ).
thf(c_24__type__3031_decl,type,
c_24__type__3031: $i ).
thf(c_24__type__144_decl,type,
c_24__type__144: $i ).
thf(cRedblack_2eTREES_2eins___24a3_decl,type,
cRedblack_2eTREES_2eins___24a3: $i > $i > $i > $i ).
thf(cCoq_2eInit_2eDatatypes_2etrue_decl,type,
cCoq_2eInit_2eDatatypes_2etrue: $i ).
thf(cCoq_2eInit_2eDatatypes_2efalse_decl,type,
cCoq_2eInit_2eDatatypes_2efalse: $i ).
thf(cRedblack_2eTREES_2emakeBlack_decl,type,
cRedblack_2eTREES_2emakeBlack: $i ).
thf(cRedblack_2eTREES_2emakeBlack___24a1_decl,type,
cRedblack_2eTREES_2emakeBlack___24a1: $i > $i ).
thf(cRedblack_2eTREES_2elookup___24a2_decl,type,
cRedblack_2eTREES_2elookup___24a2: $i > $i > $i ).
thf(c_24__type__3214___24t_decl,type,
c_24__type__3214___24t: $i > $o ).
thf(c_24__type__3002_decl,type,
c_24__type__3002: $i ).
thf(cCoq_2eLists_2eSetoidList_2etranspose___24a4_decl,type,
cCoq_2eLists_2eSetoidList_2etranspose___24a4: $i > $i > $i > $i > $o ).
thf(c_24__type__3134___24t_decl,type,
c_24__type__3134___24t: $i > $i > $o ).
thf(c_24__type__3134___24a1_decl,type,
c_24__type__3134___24a1: $i > $i ).
thf(cRedblack_2eTREES_2einsert___24a3_decl,type,
cRedblack_2eTREES_2einsert___24a3: $i > $i > $i > $i ).
thf(c_24__type__3108___24t_decl,type,
c_24__type__3108___24t: $i > $o ).
thf(c_24__type__3108_decl,type,
c_24__type__3108: $i ).
thf(cVFA_2eExtract_2eltb_decl,type,
cVFA_2eExtract_2eltb: $i ).
thf(cVFA_2eExtract_2eltb___24a2_decl,type,
cVFA_2eExtract_2eltb___24a2: $i > $i > $i ).
thf(cRedblack_2eTREES_2etree__rect___24a4_decl,type,
cRedblack_2eTREES_2etree__rect___24a4: $i > $i > $i > $i > $i ).
thf(cdefault_decl,type,
cdefault: $i ).
thf(cRedblack_2eTREES_2eempty__tree_decl,type,
cRedblack_2eTREES_2eempty__tree: $i ).
thf(39,axiom,
cRedblack_2eBlack @ cRedblack_2ecolor___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Redblack.Black') ).
thf(565,plain,
cRedblack_2eBlack @ cRedblack_2ecolor___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cRedblack_2ecolor___24t )
=> ( ( A = cRedblack_2eBlack )
| ( A = cRedblack_2eRed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Redblack.color') ).
thf(216,plain,
! [A: $i] :
( ( A @ cRedblack_2ecolor___24t )
=> ( ( A = cRedblack_2eBlack )
| ( A = cRedblack_2eRed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cRedblack_2eTREES_2eins @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Redblack.TREES.ins_$a3') ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cRedblack_2eTREES_2eins @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cVFA_2eExtract_2eint___24t )
<=> ( cVFA_2eExtract_2eint @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_VFA.Extract.int') ).
thf(105,plain,
! [A: $i] :
( ( ( cVFA_2eExtract_2eint @ ( A @ t ) )
=> ( A @ cVFA_2eExtract_2eint___24t ) )
& ( ( A @ cVFA_2eExtract_2eint___24t )
=> ( cVFA_2eExtract_2eint @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cRedblack_2ekey___24t )
<=> ( A @ cVFA_2eExtract_2eint___24t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Redblack.key') ).
thf(584,plain,
! [A: $i] :
( ( ( A @ cVFA_2eExtract_2eint___24t )
=> ( A @ cRedblack_2ekey___24t ) )
& ( ( A @ cRedblack_2ekey___24t )
=> ( A @ cVFA_2eExtract_2eint___24t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(23,axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Bool.Bool.diff_true_false') ).
thf(155,plain,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ c_24__type__144___24t )
<=> ( c_24__type__144 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_144') ).
thf(123,plain,
! [A: $i] :
( ( ( c_24__type__144 @ ( A @ t ) )
=> ( A @ c_24__type__144___24t ) )
& ( ( A @ c_24__type__144___24t )
=> ( c_24__type__144 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cRedblack_2eTREES_2einsert___24a3 ) ) )
= ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) @ cRedblack_2eTREES_2emakeBlack___24a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Redblack.TREES.insert') ).
thf(207,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cRedblack_2eTREES_2einsert___24a3 ) ) )
= ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) @ cRedblack_2eTREES_2emakeBlack___24a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ c_24__type__3076___24t )
<=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3076') ).
thf(69,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) )
=> ( A @ c_24__type__3076___24t ) )
& ( ( A @ c_24__type__3076___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cRedblack_2ecolor___24t )
=> ( ( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( ( F @ cRedblack_2ecolor___24t )
=> ( ( ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eBlack ) )
| ( ( L @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( O @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( V @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( O
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( O = cRedblack_2eTREES_2eE ) ) )
& ( P = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( O @ ( N @ ( M @ ( T @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( L
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( O @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Q @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( O
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( O = cRedblack_2eTREES_2eE ) ) )
& ( L = cRedblack_2eTREES_2eE ) ) ) )
& ( K = cRedblack_2eRed ) ) ) )
& ( E
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( F = cRedblack_2eBlack ) ) )
| ( ( G @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( J @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( V @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [Z: $i] :
( ? [ZA: $i] :
( ? [ZB: $i] :
( ? [ZC: $i] :
( ? [ZD: $i] :
( ( ( Z @ cRedblack_2ecolor___24t )
=> ( ( ( ( Y @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [ZE: $i] :
( ? [ZF: $i] :
( ? [ZG: $i] :
( ? [ZH: $i] :
( ? [ZI: $i] :
( ( ( ZE @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( ZE = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( X @ ( W @ ( V @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( ZE = cRedblack_2eRed ) ) )
& ( Y
= ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZI @ cRedblack_2eTREES_2etree___24t ) )
& ( ZH @ cV___24t ) )
& ( ZG @ cRedblack_2ekey___24t ) )
& ( ZF @ cRedblack_2eTREES_2etree___24t ) )
& ( ZE @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Y = cRedblack_2eTREES_2eE ) ) )
& ( Z = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( ZD @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( ZC @ ( ZB @ ( ZA @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eRed ) ) )
& ( V
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZD @ cRedblack_2eTREES_2etree___24t ) )
& ( ZC @ cV___24t ) )
& ( ZB @ cRedblack_2ekey___24t ) )
& ( ZA @ cRedblack_2eTREES_2etree___24t ) )
& ( Z @ cRedblack_2ecolor___24t ) )
| ( ( Y @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [Z: $i] :
( ? [ZA: $i] :
( ? [ZB: $i] :
( ? [ZC: $i] :
( ? [ZD: $i] :
( ( ( Z @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( X @ ( W @ ( V @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eRed ) ) )
& ( Y
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZD @ cRedblack_2eTREES_2etree___24t ) )
& ( ZC @ cV___24t ) )
& ( ZB @ cRedblack_2ekey___24t ) )
& ( ZA @ cRedblack_2eTREES_2etree___24t ) )
& ( Z @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Y = cRedblack_2eTREES_2eE ) ) )
& ( V = cRedblack_2eTREES_2eE ) ) ) )
& ( U = cRedblack_2eRed ) ) ) )
& ( E
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( P = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( T @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( I @ ( H @ ( G @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( J
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( Q @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( T @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [Z: $i] :
( ? [ZA: $i] :
( ? [ZB: $i] :
( ? [ZC: $i] :
( ? [ZD: $i] :
( ( ( Z @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eRed ) ) )
& ( T
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZD @ cRedblack_2eTREES_2etree___24t ) )
& ( ZC @ cV___24t ) )
& ( ZB @ cRedblack_2ekey___24t ) )
& ( ZA @ cRedblack_2eTREES_2etree___24t ) )
& ( Z @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( T = cRedblack_2eTREES_2eE ) ) )
& ( U = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Y @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( X @ ( W @ ( V @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( Q
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( T @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( V @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( T
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( T = cRedblack_2eTREES_2eE ) ) )
& ( Q = cRedblack_2eTREES_2eE ) ) ) )
& ( P = cRedblack_2eRed ) ) ) )
& ( E
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( J = cRedblack_2eTREES_2eE ) ) ) )
& ( K = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( J @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( I @ ( H @ ( O @ ( N @ ( M @ ( L @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eRed ) ) )
& ( G
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( J @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( Q @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( T @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [Z: $i] :
( ? [ZA: $i] :
( ? [ZB: $i] :
( ? [ZC: $i] :
( ? [ZD: $i] :
( ( ( Z @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eRed ) ) )
& ( T
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZD @ cRedblack_2eTREES_2etree___24t ) )
& ( ZC @ cV___24t ) )
& ( ZB @ cRedblack_2ekey___24t ) )
& ( ZA @ cRedblack_2eTREES_2etree___24t ) )
& ( Z @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( T = cRedblack_2eTREES_2eE ) ) )
& ( U = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Y @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( X @ ( W @ ( V @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( Q
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( T @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( V @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( T
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( T = cRedblack_2eTREES_2eE ) ) )
& ( Q = cRedblack_2eTREES_2eE ) ) ) )
& ( P = cRedblack_2eRed ) ) ) )
& ( E
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( K = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( O @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( I @ ( H @ ( G @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eRed ) ) )
& ( J
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eBlack ) )
| ( ( L @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( O @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( V @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( O
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( O = cRedblack_2eTREES_2eE ) ) )
& ( P = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( O @ ( N @ ( M @ ( T @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( L
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( O @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Q @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( O
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( O = cRedblack_2eTREES_2eE ) ) )
& ( L = cRedblack_2eTREES_2eE ) ) ) )
& ( K = cRedblack_2eRed ) ) ) )
& ( E
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( J = cRedblack_2eTREES_2eE ) ) ) )
& ( G = cRedblack_2eTREES_2eE ) ) ) )
& ( F = cRedblack_2eRed ) ) ) )
& ( B
= ( J @ ( I @ ( H @ ( G @ ( F @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( J @ cRedblack_2eTREES_2etree___24t ) )
& ( I @ cV___24t ) )
& ( H @ cRedblack_2ekey___24t ) )
& ( G @ cRedblack_2eTREES_2etree___24t ) )
& ( F @ cRedblack_2ecolor___24t ) )
| ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( ( F @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( F = cRedblack_2eBlack ) )
| ( ( G @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( J @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Q @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( I @ ( H @ ( G @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( J
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( J = cRedblack_2eTREES_2eE ) ) )
& ( K = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( J @ ( I @ ( H @ ( O @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eRed ) ) )
& ( G
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( J @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( O @ ( N @ ( M @ ( L @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( I @ ( H @ ( G @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eRed ) ) )
& ( J
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( J = cRedblack_2eTREES_2eE ) ) )
& ( G = cRedblack_2eTREES_2eE ) ) ) )
& ( F = cRedblack_2eRed ) ) ) )
& ( E
= ( J @ ( I @ ( H @ ( G @ ( F @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( J @ cRedblack_2eTREES_2etree___24t ) )
& ( I @ cV___24t ) )
& ( H @ cRedblack_2ekey___24t ) )
& ( G @ cRedblack_2eTREES_2etree___24t ) )
& ( F @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( B = cRedblack_2eTREES_2eE ) ) ) )
& ( A = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( A = cRedblack_2eRed ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Redblack.TREES.balance') ).
thf(234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cRedblack_2ecolor___24t )
=> ( ( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( ( F @ cRedblack_2ecolor___24t )
=> ( ( ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eBlack ) )
| ( ( L @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( O @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( V @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( O
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( O = cRedblack_2eTREES_2eE ) ) )
& ( P = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( O @ ( N @ ( M @ ( T @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( L
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( O @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Q @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( O
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( O = cRedblack_2eTREES_2eE ) ) )
& ( L = cRedblack_2eTREES_2eE ) ) ) )
& ( K = cRedblack_2eRed ) ) ) )
& ( E
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( F = cRedblack_2eBlack ) ) )
| ( ( G @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( J @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( V @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [Z: $i] :
( ? [ZA: $i] :
( ? [ZB: $i] :
( ? [ZC: $i] :
( ? [ZD: $i] :
( ( ( Z @ cRedblack_2ecolor___24t )
=> ( ( ( ( Y @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [ZE: $i] :
( ? [ZF: $i] :
( ? [ZG: $i] :
( ? [ZH: $i] :
( ? [ZI: $i] :
( ( ( ZE @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( ZE = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( X @ ( W @ ( V @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( ZE = cRedblack_2eRed ) ) )
& ( Y
= ( ZI @ ( ZH @ ( ZG @ ( ZF @ ( ZE @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZI @ cRedblack_2eTREES_2etree___24t ) )
& ( ZH @ cV___24t ) )
& ( ZG @ cRedblack_2ekey___24t ) )
& ( ZF @ cRedblack_2eTREES_2etree___24t ) )
& ( ZE @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Y = cRedblack_2eTREES_2eE ) ) )
& ( Z = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( ZD @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( ZC @ ( ZB @ ( ZA @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eRed ) ) )
& ( V
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZD @ cRedblack_2eTREES_2etree___24t ) )
& ( ZC @ cV___24t ) )
& ( ZB @ cRedblack_2ekey___24t ) )
& ( ZA @ cRedblack_2eTREES_2etree___24t ) )
& ( Z @ cRedblack_2ecolor___24t ) )
| ( ( Y @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [Z: $i] :
( ? [ZA: $i] :
( ? [ZB: $i] :
( ? [ZC: $i] :
( ? [ZD: $i] :
( ( ( Z @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( X @ ( W @ ( V @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eRed ) ) )
& ( Y
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZD @ cRedblack_2eTREES_2etree___24t ) )
& ( ZC @ cV___24t ) )
& ( ZB @ cRedblack_2ekey___24t ) )
& ( ZA @ cRedblack_2eTREES_2etree___24t ) )
& ( Z @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Y = cRedblack_2eTREES_2eE ) ) )
& ( V = cRedblack_2eTREES_2eE ) ) ) )
& ( U = cRedblack_2eRed ) ) ) )
& ( E
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( P = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( T @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( I @ ( H @ ( G @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( J
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( Q @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( T @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [Z: $i] :
( ? [ZA: $i] :
( ? [ZB: $i] :
( ? [ZC: $i] :
( ? [ZD: $i] :
( ( ( Z @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eRed ) ) )
& ( T
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZD @ cRedblack_2eTREES_2etree___24t ) )
& ( ZC @ cV___24t ) )
& ( ZB @ cRedblack_2ekey___24t ) )
& ( ZA @ cRedblack_2eTREES_2etree___24t ) )
& ( Z @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( T = cRedblack_2eTREES_2eE ) ) )
& ( U = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Y @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( X @ ( W @ ( V @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( Q
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( T @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( V @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( T
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( T = cRedblack_2eTREES_2eE ) ) )
& ( Q = cRedblack_2eTREES_2eE ) ) ) )
& ( P = cRedblack_2eRed ) ) ) )
& ( E
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( J = cRedblack_2eTREES_2eE ) ) ) )
& ( K = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( J @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( I @ ( H @ ( O @ ( N @ ( M @ ( L @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eRed ) ) )
& ( G
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( J @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( Q @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( T @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [Z: $i] :
( ? [ZA: $i] :
( ? [ZB: $i] :
( ? [ZC: $i] :
( ? [ZD: $i] :
( ( ( Z @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( Z = cRedblack_2eRed ) ) )
& ( T
= ( ZD @ ( ZC @ ( ZB @ ( ZA @ ( Z @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( ZD @ cRedblack_2eTREES_2etree___24t ) )
& ( ZC @ cV___24t ) )
& ( ZB @ cRedblack_2ekey___24t ) )
& ( ZA @ cRedblack_2eTREES_2etree___24t ) )
& ( Z @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( T = cRedblack_2eTREES_2eE ) ) )
& ( U = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Y @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( X @ ( W @ ( V @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( Q
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( T @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( V @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( T
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( T = cRedblack_2eTREES_2eE ) ) )
& ( Q = cRedblack_2eTREES_2eE ) ) ) )
& ( P = cRedblack_2eRed ) ) ) )
& ( E
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( K = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( O @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( I @ ( H @ ( G @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eRed ) ) )
& ( J
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eBlack ) )
| ( ( L @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( O @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [U: $i] :
( ? [V: $i] :
( ? [W: $i] :
( ? [X: $i] :
( ? [Y: $i] :
( ( ( U @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( Y @ ( X @ ( W @ ( V @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( U = cRedblack_2eRed ) ) )
& ( O
= ( Y @ ( X @ ( W @ ( V @ ( U @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( Y @ cRedblack_2eTREES_2etree___24t ) )
& ( X @ cV___24t ) )
& ( W @ cRedblack_2ekey___24t ) )
& ( V @ cRedblack_2eTREES_2etree___24t ) )
& ( U @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( O = cRedblack_2eTREES_2eE ) ) )
& ( P = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( O @ ( N @ ( M @ ( T @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( S @ ( R @ ( Q @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( L
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( O @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Q @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( O
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( O = cRedblack_2eTREES_2eE ) ) )
& ( L = cRedblack_2eTREES_2eE ) ) ) )
& ( K = cRedblack_2eRed ) ) ) )
& ( E
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( J = cRedblack_2eTREES_2eE ) ) ) )
& ( G = cRedblack_2eTREES_2eE ) ) ) )
& ( F = cRedblack_2eRed ) ) ) )
& ( B
= ( J @ ( I @ ( H @ ( G @ ( F @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( J @ cRedblack_2eTREES_2etree___24t ) )
& ( I @ cV___24t ) )
& ( H @ cRedblack_2ekey___24t ) )
& ( G @ cRedblack_2eTREES_2etree___24t ) )
& ( F @ cRedblack_2ecolor___24t ) )
| ( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( ( F @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( F = cRedblack_2eBlack ) )
| ( ( G @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( J @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [P: $i] :
( ? [Q: $i] :
( ? [R: $i] :
( ? [S: $i] :
( ? [T: $i] :
( ( ( P @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( T @ ( S @ ( R @ ( Q @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( I @ ( H @ ( G @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( P = cRedblack_2eRed ) ) )
& ( J
= ( T @ ( S @ ( R @ ( Q @ ( P @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( T @ cRedblack_2eTREES_2etree___24t ) )
& ( S @ cV___24t ) )
& ( R @ cRedblack_2ekey___24t ) )
& ( Q @ cRedblack_2eTREES_2etree___24t ) )
& ( P @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( J = cRedblack_2eTREES_2eE ) ) )
& ( K = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( J @ ( I @ ( H @ ( O @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( N @ ( M @ ( L @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eRed ) ) )
& ( G
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( J @ cRedblack_2eTREES_2etree___24t )
=> ( ( ? [K: $i] :
( ? [L: $i] :
( ? [M: $i] :
( ? [N: $i] :
( ? [O: $i] :
( ( ( K @ cRedblack_2ecolor___24t )
=> ( ( ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eBlack ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( O @ ( N @ ( M @ ( L @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( I @ ( H @ ( G @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( K = cRedblack_2eRed ) ) )
& ( J
= ( O @ ( N @ ( M @ ( L @ ( K @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( O @ cRedblack_2eTREES_2etree___24t ) )
& ( N @ cV___24t ) )
& ( M @ cRedblack_2ekey___24t ) )
& ( L @ cRedblack_2eTREES_2etree___24t ) )
& ( K @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( J = cRedblack_2eTREES_2eE ) ) )
& ( G = cRedblack_2eTREES_2eE ) ) ) )
& ( F = cRedblack_2eRed ) ) ) )
& ( E
= ( J @ ( I @ ( H @ ( G @ ( F @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) )
& ( J @ cRedblack_2eTREES_2etree___24t ) )
& ( I @ cV___24t ) )
& ( H @ cRedblack_2ekey___24t ) )
& ( G @ cRedblack_2eTREES_2etree___24t ) )
& ( F @ cRedblack_2ecolor___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( E = cRedblack_2eTREES_2eE ) ) )
& ( B = cRedblack_2eTREES_2eE ) ) ) )
& ( A = cRedblack_2eBlack ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( A = cRedblack_2eRed ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(42,axiom,
cRedblack_2eTREES_2eempty__tree = cRedblack_2eTREES_2eE,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Redblack.TREES.empty_tree') ).
thf(582,plain,
cRedblack_2eTREES_2eempty__tree = cRedblack_2eTREES_2eE,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( cRedblack_2eTREES_2eE
!= ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_discrim_Redblack.TREES.E$Redblack.TREES.T') ).
thf(730,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( cRedblack_2eTREES_2eE
!= ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(49,axiom,
cRedblack_2eTREES_2eempty__tree @ cRedblack_2eTREES_2etree___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Redblack.TREES.empty_tree') ).
thf(655,plain,
cRedblack_2eTREES_2eempty__tree @ cRedblack_2eTREES_2etree___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ cRedblack_2ecolor___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2ekey___24t )
=> ! [D: $i] :
( ( D @ cV___24t )
=> ! [E: $i] :
( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) )
!= cRedblack_2eTREES_2eE ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ cRedblack_2ecolor___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2ekey___24t )
=> ! [D: $i] :
( ( D @ cV___24t )
=> ! [E: $i] :
( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) )
!= cRedblack_2eTREES_2eE ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(56,plain,
~ ! [A: $i] :
( ( A @ cRedblack_2ecolor___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2ekey___24t )
=> ! [D: $i] :
( ( D @ cV___24t )
=> ! [E: $i] :
( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) )
!= cRedblack_2eTREES_2eE ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( A @ cRedblack_2ekey___24t )
=> ( ( E @ cRedblack_2ekey___24t )
=> ( ( ( ( A @ cRedblack_2ekey___24t )
=> ( ( E @ cRedblack_2ekey___24t )
=> ( ( ( ( ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) )
= F )
& ( ( A @ ( E @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2efalse ) )
| ( ( ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) )
= ( G @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) ) )
& ( ( A @ ( E @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2etrue ) ) )
& ( ( E @ ( A @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( ( ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) )
= ( D @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) ) )
& ( ( E @ ( A @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2etrue ) ) )
& ( B
= ( G @ ( F @ ( E @ ( D @ ( C @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) ) )
& ( G @ cRedblack_2eTREES_2etree___24t ) )
& ( F @ cV___24t ) )
& ( E @ cRedblack_2ekey___24t ) )
& ( D @ cRedblack_2eTREES_2etree___24t ) )
& ( C @ cRedblack_2ecolor___24t ) )
| ( ( ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) )
= cdefault )
& ( B = cRedblack_2eTREES_2eE ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Redblack.TREES.lookup') ).
thf(533,plain,
! [A: $i,B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( A @ cRedblack_2ekey___24t )
=> ( ( E @ cRedblack_2ekey___24t )
=> ( ( ( ( A @ cRedblack_2ekey___24t )
=> ( ( E @ cRedblack_2ekey___24t )
=> ( ( ( ( ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) )
= F )
& ( ( A @ ( E @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2efalse ) )
| ( ( ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) )
= ( G @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) ) )
& ( ( A @ ( E @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2etrue ) ) )
& ( ( E @ ( A @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( ( ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) )
= ( D @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) ) )
& ( ( E @ ( A @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2etrue ) ) )
& ( B
= ( G @ ( F @ ( E @ ( D @ ( C @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) ) )
& ( G @ cRedblack_2eTREES_2etree___24t ) )
& ( F @ cV___24t ) )
& ( E @ cRedblack_2ekey___24t ) )
& ( D @ cRedblack_2eTREES_2etree___24t ) )
& ( C @ cRedblack_2ecolor___24t ) )
| ( ( ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) )
= cdefault )
& ( B = cRedblack_2eTREES_2eE ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( ( A @ cRedblack_2ekey___24t )
=> ( ( F @ cRedblack_2ekey___24t )
=> ( ( ( ( A @ cRedblack_2ekey___24t )
=> ( ( F @ cRedblack_2ekey___24t )
=> ( ( ( ( ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) )
= ( H @ ( B @ ( A @ ( E @ ( D @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( ( A @ ( F @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2efalse ) )
| ( ( ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) )
= ( H @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) @ ( G @ ( F @ ( E @ ( D @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) ) )
& ( ( A @ ( F @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2etrue ) ) )
& ( ( F @ ( A @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( ( ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) )
= ( H @ ( G @ ( F @ ( E @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) @ ( D @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) ) )
& ( ( F @ ( A @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2etrue ) ) )
& ( C
= ( H @ ( G @ ( F @ ( E @ ( D @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) ) )
& ( H @ cRedblack_2eTREES_2etree___24t ) )
& ( G @ cV___24t ) )
& ( F @ cRedblack_2ekey___24t ) )
& ( E @ cRedblack_2eTREES_2etree___24t ) )
& ( D @ cRedblack_2ecolor___24t ) )
| ( ( ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) )
= ( cRedblack_2eTREES_2eE @ ( B @ ( A @ ( cRedblack_2eTREES_2eE @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( C = cRedblack_2eTREES_2eE ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Redblack.TREES.ins') ).
thf(698,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( ( A @ cRedblack_2ekey___24t )
=> ( ( F @ cRedblack_2ekey___24t )
=> ( ( ( ( A @ cRedblack_2ekey___24t )
=> ( ( F @ cRedblack_2ekey___24t )
=> ( ( ( ( ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) )
= ( H @ ( B @ ( A @ ( E @ ( D @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( ( A @ ( F @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2efalse ) )
| ( ( ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) )
= ( H @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) @ ( G @ ( F @ ( E @ ( D @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) ) )
& ( ( A @ ( F @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2etrue ) ) )
& ( ( F @ ( A @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( ( ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) )
= ( H @ ( G @ ( F @ ( E @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) @ ( D @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) ) )
& ( ( F @ ( A @ cVFA_2eExtract_2eltb___24a2 ) )
= cCoq_2eInit_2eDatatypes_2etrue ) ) )
& ( C
= ( H @ ( G @ ( F @ ( E @ ( D @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) ) ) ) )
& ( H @ cRedblack_2eTREES_2etree___24t ) )
& ( G @ cV___24t ) )
& ( F @ cRedblack_2ekey___24t ) )
& ( E @ cRedblack_2eTREES_2etree___24t ) )
& ( D @ cRedblack_2ecolor___24t ) )
| ( ( ( C @ ( B @ ( A @ cRedblack_2eTREES_2eins___24a3 ) ) )
= ( cRedblack_2eTREES_2eE @ ( B @ ( A @ ( cRedblack_2eTREES_2eE @ ( cRedblack_2eRed @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( C = cRedblack_2eTREES_2eE ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(22,axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Bool.Bool.diff_false_true') ).
thf(152,plain,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
cRedblack_2eTREES_2eins @ c_24__type__144___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Redblack.TREES.ins') ).
thf(78,plain,
cRedblack_2eTREES_2eins @ c_24__type__144___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ cRedblack_2eTREES_2etree___24t )
=> ( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( F @ cRedblack_2eTREES_2etree___24t ) )
& ( E @ cV___24t ) )
& ( D @ cRedblack_2ekey___24t ) )
& ( C @ cRedblack_2eTREES_2etree___24t ) )
& ( B @ cRedblack_2ecolor___24t ) )
| ( A = cRedblack_2eTREES_2eE ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Redblack.TREES.tree') ).
thf(734,plain,
! [A: $i] :
( ( A @ cRedblack_2eTREES_2etree___24t )
=> ( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( F @ cRedblack_2eTREES_2etree___24t ) )
& ( E @ cV___24t ) )
& ( D @ cRedblack_2ekey___24t ) )
& ( C @ cRedblack_2eTREES_2etree___24t ) )
& ( B @ cRedblack_2ecolor___24t ) )
| ( A = cRedblack_2eTREES_2eE ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(19,axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false') ).
thf(132,plain,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ c_24__type__3216___24t )
<=> ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3216') ).
thf(89,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) )
=> ( A @ c_24__type__3216___24t ) )
& ( ( A @ c_24__type__3216___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,axiom,
cdefault @ cV___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_default') ).
thf(233,plain,
cdefault @ cV___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ c_24__type__3031___24t )
<=> ( c_24__type__3031 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_3031') ).
thf(117,plain,
! [A: $i] :
( ( ( c_24__type__3031 @ ( A @ t ) )
=> ( A @ c_24__type__3031___24t ) )
& ( ( A @ c_24__type__3031___24t )
=> ( c_24__type__3031 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( cRedblack_2eTREES_2ebalance @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Redblack.TREES.balance_$a5') ).
thf(102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( cRedblack_2eTREES_2ebalance @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2ebalance___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(40,axiom,
cRedblack_2eTREES_2eE @ cRedblack_2eTREES_2etree___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Redblack.TREES.E') ).
thf(566,plain,
cRedblack_2eTREES_2eE @ cRedblack_2eTREES_2etree___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cProp___24t )
=> ! [B: $i] :
( ( B @ cProp___24t )
=> ( ~ ( ( B @ p )
| ( A @ p ) )
=> ( ~ ( B @ p )
& ~ ( A @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.Decidable.not_or') ).
thf(65,plain,
! [A: $i] :
( ( A @ cProp___24t )
=> ! [B: $i] :
( ( B @ cProp___24t )
=> ( ~ ( ( B @ p )
| ( A @ p ) )
=> ( ~ ( B @ p )
& ~ ( A @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ c_24__type__3218___24t )
=> ( ( cRedblack_2eRed @ ( A @ happ ) @ p )
=> ( ( cRedblack_2eBlack @ ( A @ happ ) @ p )
=> ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ( B @ ( A @ happ ) @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Redblack.color_ind') ).
thf(97,plain,
! [A: $i] :
( ( A @ c_24__type__3218___24t )
=> ( ( cRedblack_2eRed @ ( A @ happ ) @ p )
=> ( ( cRedblack_2eBlack @ ( A @ happ ) @ p )
=> ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ( B @ ( A @ happ ) @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
cRedblack_2eTREES_2ebalance @ c_24__type__3002___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Redblack.TREES.balance') ).
thf(77,plain,
cRedblack_2eTREES_2ebalance @ c_24__type__3002___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__3134___24t ) )
<=> ( A @ c_24__type__3134___24a1 @ ( B @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_3134') ).
thf(193,plain,
! [A: $i,B: $i] :
( ( ( A @ c_24__type__3134___24a1 @ ( B @ t ) )
=> ( B @ ( A @ c_24__type__3134___24t ) ) )
& ( ( B @ ( A @ c_24__type__3134___24t ) )
=> ( A @ c_24__type__3134___24a1 @ ( B @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(47,axiom,
cRedblack_2eRed @ cRedblack_2ecolor___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Redblack.Red') ).
thf(642,plain,
cRedblack_2eRed @ cRedblack_2ecolor___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( I @ ( G @ ( E @ ( C @ ( A @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) )
= ( J @ ( H @ ( F @ ( D @ ( B @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F )
& ( G = H )
& ( I = J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_Redblack.TREES.T') ).
thf(590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( I @ ( G @ ( E @ ( C @ ( A @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) )
= ( J @ ( H @ ( F @ ( D @ ( B @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F )
& ( G = H )
& ( I = J ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ c_24__type__3214___24t )
<=> ! [B: $i] :
( ( B @ c_24__type__3216___24t )
=> ! [C: $i] :
( ( cRedblack_2eRed @ ( B @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( cRedblack_2eBlack @ ( B @ happ ) @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ cRedblack_2ecolor___24t )
=> ( E @ ( B @ happ ) @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3214') ).
thf(161,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ c_24__type__3216___24t )
=> ! [C: $i] :
( ( cRedblack_2eRed @ ( B @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( cRedblack_2eBlack @ ( B @ happ ) @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ cRedblack_2ecolor___24t )
=> ( E @ ( B @ happ ) @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) )
=> ( A @ c_24__type__3214___24t ) )
& ( ( A @ c_24__type__3214___24t )
=> ! [B: $i] :
( ( B @ c_24__type__3216___24t )
=> ! [C: $i] :
( ( cRedblack_2eRed @ ( B @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( cRedblack_2eBlack @ ( B @ happ ) @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ cRedblack_2ecolor___24t )
=> ( E @ ( B @ happ ) @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ( cRedblack_2eTREES_2emakeBlack @ happ ) )
= ( A @ cRedblack_2eTREES_2emakeBlack___24a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Redblack.TREES.makeBlack_$a1') ).
thf(149,plain,
! [A: $i] :
( ( A @ ( cRedblack_2eTREES_2emakeBlack @ happ ) )
= ( A @ cRedblack_2eTREES_2emakeBlack___24a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose___24a4 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ( G @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.SetoidList.transpose') ).
thf(181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ( G @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ( G @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( A @ c_24__type__3134___24t ) )
=> ( ( D @ cRedblack_2eTREES_2etree___24t )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) )
= ( I @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) @ ( I @ ( H @ ( G @ ( F @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) @ ( F @ ( E @ ( C @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) ) )
& ( D
= ( I @ ( H @ ( G @ ( F @ ( E @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( I @ cRedblack_2eTREES_2etree___24t ) )
& ( H @ cV___24t ) )
& ( G @ cRedblack_2ekey___24t ) )
& ( F @ cRedblack_2eTREES_2etree___24t ) )
& ( E @ cRedblack_2ecolor___24t ) )
| ( ( ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) )
= B )
& ( D = cRedblack_2eTREES_2eE ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Redblack.TREES.tree_rect') ).
thf(672,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( A @ c_24__type__3134___24t ) )
=> ( ( D @ cRedblack_2eTREES_2etree___24t )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) )
= ( I @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) @ ( I @ ( H @ ( G @ ( F @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) @ ( F @ ( E @ ( C @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) ) )
& ( D
= ( I @ ( H @ ( G @ ( F @ ( E @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( I @ cRedblack_2eTREES_2etree___24t ) )
& ( H @ cV___24t ) )
& ( G @ cRedblack_2ekey___24t ) )
& ( F @ cRedblack_2eTREES_2etree___24t ) )
& ( E @ cRedblack_2ecolor___24t ) )
| ( ( ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) )
= B )
& ( D = cRedblack_2eTREES_2eE ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ c_24__type__3108___24t )
<=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( B @ ( A @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3108') ).
thf(219,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( B @ ( A @ happ ) @ cProp___24t ) )
=> ( A @ c_24__type__3108___24t ) )
& ( ( A @ c_24__type__3108___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( B @ ( A @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ c_24__type__3218___24t )
<=> ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ( B @ ( A @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3218') ).
thf(81,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ( B @ ( A @ happ ) @ cProp___24t ) )
=> ( A @ c_24__type__3218___24t ) )
& ( ( A @ c_24__type__3218___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ( B @ ( A @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( cRedblack_2eTREES_2etree__rect @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Redblack.TREES.tree_rect_$a4') ).
thf(230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( cRedblack_2eTREES_2etree__rect @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ cRedblack_2eTREES_2etree__rect___24a4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ cRedblack_2eTREES_2etree___24t )
=> ( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( ( A @ cRedblack_2eTREES_2emakeBlack___24a1 )
= ( F @ ( E @ ( D @ ( C @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( F @ cRedblack_2eTREES_2etree___24t ) )
& ( E @ cV___24t ) )
& ( D @ cRedblack_2ekey___24t ) )
& ( C @ cRedblack_2eTREES_2etree___24t ) )
& ( B @ cRedblack_2ecolor___24t ) )
| ( ( ( A @ cRedblack_2eTREES_2emakeBlack___24a1 )
= cRedblack_2eTREES_2eE )
& ( A = cRedblack_2eTREES_2eE ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Redblack.TREES.makeBlack') ).
thf(567,plain,
! [A: $i] :
( ( A @ cRedblack_2eTREES_2etree___24t )
=> ( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( ( A @ cRedblack_2eTREES_2emakeBlack___24a1 )
= ( F @ ( E @ ( D @ ( C @ ( cRedblack_2eBlack @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( A
= ( F @ ( E @ ( D @ ( C @ ( B @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) ) )
& ( F @ cRedblack_2eTREES_2etree___24t ) )
& ( E @ cV___24t ) )
& ( D @ cRedblack_2ekey___24t ) )
& ( C @ cRedblack_2eTREES_2etree___24t ) )
& ( B @ cRedblack_2ecolor___24t ) )
| ( ( ( A @ cRedblack_2eTREES_2emakeBlack___24a1 )
= cRedblack_2eTREES_2eE )
& ( A = cRedblack_2eTREES_2eE ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ c_24__type__3074___24t )
<=> ! [B: $i] :
( ( B @ c_24__type__3076___24t )
=> ! [C: $i] :
( ( cRedblack_2eTREES_2eE @ ( B @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ c_24__type__3106___24t ) )
=> ! [E: $i] :
( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( E @ ( B @ happ ) @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3074') ).
thf(135,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ c_24__type__3076___24t )
=> ! [C: $i] :
( ( cRedblack_2eTREES_2eE @ ( B @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ c_24__type__3106___24t ) )
=> ! [E: $i] :
( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( E @ ( B @ happ ) @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) )
=> ( A @ c_24__type__3074___24t ) )
& ( ( A @ c_24__type__3074___24t )
=> ! [B: $i] :
( ( B @ c_24__type__3076___24t )
=> ! [C: $i] :
( ( cRedblack_2eTREES_2eE @ ( B @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ c_24__type__3106___24t ) )
=> ! [E: $i] :
( ( E @ cRedblack_2eTREES_2etree___24t )
=> ( E @ ( B @ happ ) @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
cRedblack_2eTREES_2elookup @ c_24__type__3031___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Redblack.TREES.lookup') ).
thf(80,plain,
cRedblack_2eTREES_2elookup @ c_24__type__3031___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__3134___24t ) )
<=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( C @ ( B @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3134') ).
thf(199,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( C @ ( B @ happ ) @ cType___24t ) )
=> ( B @ ( A @ c_24__type__3134___24t ) ) )
& ( ( B @ ( A @ c_24__type__3134___24t ) )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( C @ ( B @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ c_24__type__144___24t )
<=> ! [B: $i] :
( ( B @ cRedblack_2ekey___24t )
=> ! [C: $i] :
( ( C @ cV___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2eTREES_2etree___24t )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cRedblack_2eTREES_2etree___24t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_144') ).
thf(643,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cRedblack_2ekey___24t )
=> ! [C: $i] :
( ( C @ cV___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2eTREES_2etree___24t )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cRedblack_2eTREES_2etree___24t ) ) ) )
=> ( A @ c_24__type__144___24t ) )
& ( ( A @ c_24__type__144___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2ekey___24t )
=> ! [C: $i] :
( ( C @ cV___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2eTREES_2etree___24t )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cRedblack_2eTREES_2etree___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ c_24__type__3002___24t )
<=> ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2ekey___24t )
=> ! [E: $i] :
( ( E @ cV___24t )
=> ! [F: $i] :
( ( F @ cRedblack_2eTREES_2etree___24t )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ cRedblack_2eTREES_2etree___24t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3002') ).
thf(656,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2ekey___24t )
=> ! [E: $i] :
( ( E @ cV___24t )
=> ! [F: $i] :
( ( F @ cRedblack_2eTREES_2etree___24t )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ cRedblack_2eTREES_2etree___24t ) ) ) ) ) )
=> ( A @ c_24__type__3002___24t ) )
& ( ( A @ c_24__type__3002___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2ekey___24t )
=> ! [E: $i] :
( ( E @ cV___24t )
=> ! [F: $i] :
( ( F @ cRedblack_2eTREES_2etree___24t )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ cRedblack_2eTREES_2etree___24t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ c_24__type__3002___24t )
<=> ( c_24__type__3002 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_3002') ).
thf(175,plain,
! [A: $i] :
( ( ( c_24__type__3002 @ ( A @ t ) )
=> ( A @ c_24__type__3002___24t ) )
& ( ( A @ c_24__type__3002___24t )
=> ( c_24__type__3002 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__3106___24t ) )
<=> ! [C: $i] :
( ( C @ cRedblack_2ecolor___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2eTREES_2etree___24t )
=> ! [E: $i] :
( ( D @ ( A @ happ ) @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ cRedblack_2ekey___24t )
=> ! [G: $i] :
( ( G @ cV___24t )
=> ! [H: $i] :
( ( H @ cRedblack_2eTREES_2etree___24t )
=> ! [I: $i] :
( ( H @ ( A @ happ ) @ ( I @ t ) )
=> ( H @ ( G @ ( F @ ( D @ ( C @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( A @ happ ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3106') ).
thf(612,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cRedblack_2ecolor___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2eTREES_2etree___24t )
=> ! [E: $i] :
( ( D @ ( A @ happ ) @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ cRedblack_2ekey___24t )
=> ! [G: $i] :
( ( G @ cV___24t )
=> ! [H: $i] :
( ( H @ cRedblack_2eTREES_2etree___24t )
=> ! [I: $i] :
( ( H @ ( A @ happ ) @ ( I @ t ) )
=> ( H @ ( G @ ( F @ ( D @ ( C @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( A @ happ ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ) )
=> ( B @ ( A @ c_24__type__3106___24t ) ) )
& ( ( B @ ( A @ c_24__type__3106___24t ) )
=> ! [C: $i] :
( ( C @ cRedblack_2ecolor___24t )
=> ! [D: $i] :
( ( D @ cRedblack_2eTREES_2etree___24t )
=> ! [E: $i] :
( ( D @ ( A @ happ ) @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ cRedblack_2ekey___24t )
=> ! [G: $i] :
( ( G @ cV___24t )
=> ! [H: $i] :
( ( H @ cRedblack_2eTREES_2etree___24t )
=> ! [I: $i] :
( ( H @ ( A @ happ ) @ ( I @ t ) )
=> ( H @ ( G @ ( F @ ( D @ ( C @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( A @ happ ) @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(12,axiom,
cRedblack_2eRed != cRedblack_2eBlack,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_discrim_Redblack.Red$Redblack.Black') ).
thf(99,plain,
cRedblack_2eRed != cRedblack_2eBlack,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ c_24__type__3031___24t )
<=> ! [B: $i] :
( ( B @ cRedblack_2ekey___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cV___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3031') ).
thf(688,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cRedblack_2ekey___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cV___24t ) ) )
=> ( A @ c_24__type__3031___24t ) )
& ( ( A @ c_24__type__3031___24t )
=> ! [B: $i] :
( ( B @ cRedblack_2ekey___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cV___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cRedblack_2eTREES_2elookup @ happ ) @ happ ) )
= ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Redblack.TREES.lookup_$a2') ).
thf(158,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cRedblack_2eTREES_2elookup @ happ ) @ happ ) )
= ( B @ ( A @ cRedblack_2eTREES_2elookup___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ c_24__type__3108___24t )
=> ( ( cRedblack_2eTREES_2eE @ ( A @ happ ) @ p )
=> ( ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( ( C @ ( A @ happ ) @ p )
=> ! [D: $i] :
( ( D @ cRedblack_2ekey___24t )
=> ! [E: $i] :
( ( E @ cV___24t )
=> ! [F: $i] :
( ( F @ cRedblack_2eTREES_2etree___24t )
=> ( ( F @ ( A @ happ ) @ p )
=> ( F @ ( E @ ( D @ ( C @ ( B @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( A @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( B @ ( A @ happ ) @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Redblack.TREES.tree_ind') ).
thf(632,plain,
! [A: $i] :
( ( A @ c_24__type__3108___24t )
=> ( ( cRedblack_2eTREES_2eE @ ( A @ happ ) @ p )
=> ( ! [B: $i] :
( ( B @ cRedblack_2ecolor___24t )
=> ! [C: $i] :
( ( C @ cRedblack_2eTREES_2etree___24t )
=> ( ( C @ ( A @ happ ) @ p )
=> ! [D: $i] :
( ( D @ cRedblack_2ekey___24t )
=> ! [E: $i] :
( ( E @ cV___24t )
=> ! [F: $i] :
( ( F @ cRedblack_2eTREES_2etree___24t )
=> ( ( F @ ( A @ happ ) @ p )
=> ( F @ ( E @ ( D @ ( C @ ( B @ cRedblack_2eTREES_2eT___24a5 ) ) ) ) @ ( A @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [B: $i] :
( ( B @ cRedblack_2eTREES_2etree___24t )
=> ( B @ ( A @ happ ) @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ c_24__type__3108___24t )
<=> ( c_24__type__3108 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_3108') ).
thf(210,plain,
! [A: $i] :
( ( ( c_24__type__3108 @ ( A @ t ) )
=> ( A @ c_24__type__3108___24t ) )
& ( ( A @ c_24__type__3108___24t )
=> ( c_24__type__3108 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
cRedblack_2eTREES_2etree__rect @ c_24__type__3074___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Redblack.TREES.tree_rect') ).
thf(79,plain,
cRedblack_2eTREES_2etree__rect @ c_24__type__3074___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__3106___24t ) )
<=> ( A @ c_24__type__3106___24a1 @ ( B @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_3106') ).
thf(111,plain,
! [A: $i,B: $i] :
( ( ( A @ c_24__type__3106___24a1 @ ( B @ t ) )
=> ( B @ ( A @ c_24__type__3106___24t ) ) )
& ( ( B @ ( A @ c_24__type__3106___24t ) )
=> ( A @ c_24__type__3106___24a1 @ ( B @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cVFA_2eExtract_2eltb @ happ ) @ happ ) )
= ( B @ ( A @ cVFA_2eExtract_2eltb___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_VFA.Extract.ltb_$a2') ).
thf(227,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cVFA_2eExtract_2eltb @ happ ) @ happ ) )
= ( B @ ( A @ cVFA_2eExtract_2eltb___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(754,plain,
$false,
inference(e,[status(thm)],[565,216,129,105,584,155,123,207,69,234,582,730,655,56,533,698,152,78,734,132,89,233,117,102,566,65,97,77,193,642,590,161,149,181,672,219,81,230,567,135,80,199,643,656,175,612,99,688,158,632,210,79,111,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV668+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sat Sep 26 11:34:35 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.37/0.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/0.97 % [INFO] Parsing done (365ms).
% 1.56/0.98 % [INFO] Running in sequential loop mode.
% 2.22/1.17 % [INFO] eprover registered as external prover.
% 2.22/1.17 % [INFO] Scanning for conjecture ...
% 2.79/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 2820 axioms. Running axiom selection ...
% 3.69/1.51 % [INFO] Axiom selection finished. Selected 53 axioms (removed 2767 axioms).
% 4.19/1.70 % [INFO] Problem is first-order (TPTP FOF).
% 4.19/1.72 % [INFO] Type checking passed.
% 4.19/1.72 % [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 ...
% 11.41/4.85 % External prover 'e' found a proof!
% 11.41/4.86 % [INFO] Killing All external provers ...
% 11.41/4.86 % Time passed: 4457ms (effective reasoning time: 3871ms)
% 11.41/4.86 % 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)>
% 11.41/4.86 % Axioms used in derivation (53): $adef_Redblack.TREES.makeBlack_$a1, $_type_3002, $_typeof_Redblack.TREES.empty_tree, $_def_Redblack.TREES.balance, $_type_3218, $_type_3074, $_typeof_Redblack.TREES.ins, $_type_3134, $tdef_$_type_3002, $_def_Redblack.TREES.insert, $_inversion_Redblack.color, $tdef_$_type_3106, $adef_Redblack.TREES.ins_$a3, $_typeof_Redblack.TREES.tree_rect, $_def_Redblack.key, Coq.Logic.Decidable.not_or, $_type_3108, $_typeof_Redblack.TREES.lookup, $adef_VFA.Extract.ltb_$a2, $_typeof_default, $_type_3214, $_type_3031, Coq.Bool.Bool.diff_true_false, $_def_Redblack.TREES.makeBlack, $_def_Redblack.TREES.ins, $_def_Redblack.TREES.lookup, $_typeof_Redblack.Red, $_typeof_Redblack.Black, $_discrim_Redblack.Red$Redblack.Black, $_type_144, $adef_Redblack.TREES.balance_$a5, $adef_Redblack.TREES.tree_rect_$a4, Redblack.TREES.tree_ind, Coq.Bool.Bool.diff_false_true, $_def_Redblack.TREES.tree_rect, $_discrim_Redblack.TREES.E$Redblack.TREES.T, Redblack.color_ind, $tdef_VFA.Extract.int, $_def_Coq.Lists.SetoidList.transpose, $_type_3106, $adef_Redblack.TREES.lookup_$a2, $_inversion_Redblack.TREES.tree, $tdef_$_type_3134, $tdef_$_type_3108, $tdef_$_type_144, $_typeof_Redblack.TREES.E, $_type_3076, $_def_Redblack.TREES.empty_tree, $_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false, $_typeof_Redblack.TREES.balance, $_inj_Redblack.TREES.T, $tdef_$_type_3031, $_type_3216
% 11.41/4.86 % No. of inferences in proof: 110
% 11.41/4.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4457 ms resp. 3871 ms w/o parsing
% 11.85/4.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.85/4.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------