%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP067^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:38 AM UTC 2026
% Result : Theorem 51.67s 15.83s
% Output : Refutation 53.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 146
% Syntax : Number of formulae : 318 ( 107 unt; 0 typ; 0 def)
% Number of atoms : 1114 ( 325 equ; 2 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 5936 ( 154 ~; 23 |; 68 &;5181 @)
% ( 0 <=>; 510 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 251 ( 251 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 17 con; 0-8 aty)
% Number of variables : 1276 ( 57 ^;1207 !; 12 ?;1276 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_decl,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_decl,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_decl,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere516151231imp_le_decl,type,
ordere516151231imp_le:
!>[TA: $tType] : $o ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(heapIm1271749598e_left_decl,type,
heapIm1271749598e_left:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) ) ).
thf(heapIm1434396069_right_decl,type,
heapIm1434396069_right:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) ) ).
thf(heapIm748920189ftDown_decl,type,
heapIm748920189ftDown:
!>[TA: $tType] : ( ( tree @ TA ) > ( tree @ TA ) ) ).
thf(heap_decl,type,
heap:
!>[TA: $tType,TB: $tType] : ( TB > ( TB > $o ) > ( ( list @ TA ) > TB ) > ( TB > ( multiset @ TA ) ) > ( TB > ( tree @ TA ) ) > ( TB > ( product_prod @ TA @ TB ) ) > $o ) ).
thf(heap_axioms_decl,type,
heap_axioms:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( ( list @ TA ) > TB ) > ( TB > ( multiset @ TA ) ) > ( TB > ( tree @ TA ) ) > ( TB > ( product_prod @ TA @ TB ) ) > $o ) ).
thf(e_decl,type,
e:
!>[TA: $tType] : ( tree @ TA ) ).
thf(t_decl,type,
t:
!>[TA: $tType] : ( TA > ( tree @ TA ) > ( tree @ TA ) > ( tree @ TA ) ) ).
thf(case_Tree_decl,type,
case_Tree:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( tree @ TA ) > ( tree @ TA ) > TB ) > ( tree @ TA ) > TB ) ).
thf(pred_Tree_decl,type,
pred_Tree:
!>[TA: $tType] : ( ( TA > $o ) > ( tree @ TA ) > $o ) ).
thf(rec_Tree_decl,type,
rec_Tree:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( tree @ TA ) > ( tree @ TA ) > TB > TB > TB ) > ( tree @ TA ) > TB ) ).
thf(set_Tree_decl,type,
set_Tree:
!>[TA: $tType] : ( ( tree @ TA ) > ( set @ TA ) ) ).
thf(in_tree_decl,type,
in_tree:
!>[TA: $tType] : ( TA > ( tree @ TA ) > $o ) ).
thf(is_heap_decl,type,
is_heap:
!>[TA: $tType] : ( ( tree @ TA ) > $o ) ).
thf(multiset2_decl,type,
multiset2:
!>[TA: $tType] : ( ( tree @ TA ) > ( multiset @ TA ) ) ).
thf(val_decl,type,
val:
!>[TA: $tType] : ( ( tree @ TA ) > TA ) ).
thf(lattic929149872er_Max_decl,type,
lattic929149872er_Max:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(add_mset_decl,type,
add_mset:
!>[TA: $tType] : ( TA > ( multiset @ TA ) > ( multiset @ TA ) ) ).
thf(set_mset_decl,type,
set_mset:
!>[TA: $tType] : ( ( multiset @ TA ) > ( set @ TA ) ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(powp_decl,type,
powp:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) > $o ) ).
thf(collection_decl,type,
collection:
!>[TA: $tType,TB: $tType] : ( TB > ( TB > $o ) > ( ( list @ TA ) > TB ) > ( TB > ( multiset @ TA ) ) > $o ) ).
thf(ball_decl,type,
ball:
!>[TA: $tType] : ( ( set @ TA ) > ( TA > $o ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(l1_decl,type,
l1: tree @ a ).
thf(l2_decl,type,
l2: tree @ a ).
thf(r1_decl,type,
r1: tree @ a ).
thf(r2_decl,type,
r2: tree @ a ).
thf(t2_decl,type,
t2: tree @ a ).
thf(v_decl,type,
v: a ).
thf(v1_decl,type,
v1: a ).
thf(v2_decl,type,
v2: a ).
thf(v3_decl,type,
v3: a ).
thf(139,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( tree @ TA ) > ( tree @ TA ) > TB,C: TA,D: tree @ TA,E: tree @ TA] :
( ( case_Tree @ TB @ TA @ A @ B @ ( t @ TA @ C @ D @ E ) )
= ( B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Tree_Osimps_I5_J) ).
thf(645,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( tree @ TA ) > ( tree @ TA ) > TB,C: TA,D: tree @ TA,E: tree @ TA] :
( ( case_Tree @ TB @ TA @ A @ B @ ( t @ TA @ C @ D @ E ) )
= ( B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(63,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_verit__la__disequality) ).
thf(347,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(36,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_subset__trans) ).
thf(249,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(31,axiom,
! [TA: $tType] :
( ( ball @ TA )
= ( ^ [A: set @ TA,B: TA > $o] : ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Ball__Collect) ).
thf(234,plain,
! [TA: $tType] :
( ( ball @ TA )
= ( ^ [A: set @ TA,B: TA > $o] : ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(74,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ ( multiset2 @ TA @ B ) ) )
=> ( ( is_heap @ TA @ B )
=> ( ord_less_eq @ TA @ A @ ( val @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_heap__top__geq) ).
thf(379,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA] :
( ( member @ TA @ A @ ( set_mset @ TA @ ( multiset2 @ TA @ B ) ) )
=> ( ( is_heap @ TA @ B )
=> ( ord_less_eq @ TA @ A @ ( val @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(143,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: TA,D: tree @ TA] :
( ( member @ TA @ A @ ( set_Tree @ TA @ B ) )
=> ( member @ TA @ A @ ( set_Tree @ TA @ ( t @ TA @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Tree_Oset__intros_I3_J) ).
thf(655,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: TA,D: tree @ TA] :
( ( member @ TA @ A @ ( set_Tree @ TA @ B ) )
=> ( member @ TA @ A @ ( set_Tree @ TA @ ( t @ TA @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(22,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_subset__emptyI) ).
thf(202,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(77,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_add__increasing2) ).
thf(385,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(146,axiom,
in_tree @ a @ v @ ( heapIm748920189ftDown @ a @ t2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062in__tree_Av_A_IsiftDown_At_J_092_060close_062) ).
thf(670,plain,
in_tree @ a @ v @ ( heapIm748920189ftDown @ a @ t2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(84,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_le__iff__add) ).
thf(404,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(118,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( e @ TA ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_siftDown_Osimps_I4_J) ).
thf(565,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( e @ TA ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( e @ TA ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(95,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_mset @ TA @ D ) )
=> ( ord_less_eq @ TA @ E @ C ) )
=> ( A @ ( add_mset @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_multiset__induct__max) ).
thf(436,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_mset @ TA @ D ) )
=> ( ord_less_eq @ TA @ E @ C ) )
=> ( A @ ( add_mset @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(79,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_less__eqE) ).
thf(389,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( collection @ TA @ TB @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Heap_Oaxioms_I1_J) ).
thf(184,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( collection @ TA @ TB @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(196,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(123,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] : ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_is__heap_Osimps_I2_J) ).
thf(587,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] : ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( in_tree @ TA @ A @ ( t @ TA @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree @ TA @ A @ C )
| ( in_tree @ TA @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__tree_Osimps_I2_J) ).
thf(619,plain,
! [TA: $tType,A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( in_tree @ TA @ A @ ( t @ TA @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree @ TA @ A @ C )
| ( in_tree @ TA @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(113,axiom,
~ ( ( v = v3 )
| ( v = v1 )
| ( v = v2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False) ).
thf(534,plain,
~ ( ( v = v3 )
| ( v = v1 )
| ( v = v2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(535,plain,
~ ( ( v = v3 )
| ( v = v1 )
| ( v = v2 ) ),
inference(polarity_switch,[status(thm)],[534]) ).
thf(536,plain,
( ( v != v3 )
& ( v != v1 )
& ( v != v2 ) ),
inference(cnf,[status(esa)],[535]) ).
thf(539,plain,
v != v2,
inference(cnfConj,[status(thm)],[536]) ).
thf(542,plain,
v2 != v,
inference(lifteq,[status(thm)],[539]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_Collect__mono) ).
thf(157,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(50,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_add__left__mono) ).
thf(284,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_le__add__same__cancel1) ).
thf(416,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(4,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_empty__subsetI) ).
thf(152,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( tree @ TA ) > $o ) @ ( pred_Tree @ TA @ A ) @ ( pred_Tree @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Tree_Opred__mono) ).
thf(289,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( tree @ TA ) > $o ) @ ( pred_Tree @ TA @ A ) @ ( pred_Tree @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(8,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_subset__empty) ).
thf(164,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_subset__eq) ).
thf(376,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(132,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( in_tree @ TA @ ( val @ TA @ ( heapIm748920189ftDown @ TA @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_siftDown__in__tree) ).
thf(623,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( in_tree @ TA @ ( val @ TA @ ( heapIm748920189ftDown @ TA @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(105,axiom,
! [TA: $tType,A: TA > $o] : ( pred_Tree @ TA @ A @ ( e @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Tree_Opred__inject_I1_J) ).
thf(485,plain,
! [TA: $tType,A: TA > $o] : ( pred_Tree @ TA @ A @ ( e @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(120,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] : ( member @ TA @ A @ ( set_Tree @ TA @ ( t @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Tree_Oset__intros_I1_J) ).
thf(574,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] : ( member @ TA @ A @ ( set_Tree @ TA @ ( t @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___HOL_Otype) ).
thf(353,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(103,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__cases) ).
thf(480,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(25,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_predicate1I) ).
thf(211,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(38,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_rev__predicate1D) ).
thf(253,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(126,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA,G: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( t @ TA @ E @ F @ G ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ E @ F @ G ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ E @ F @ G ) )
& ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_is__heap_Osimps_I5_J) ).
thf(602,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA,G: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( t @ TA @ E @ F @ G ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ E @ F @ G ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ E @ F @ G ) )
& ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(82,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_add__mono__thms__linordered__semiring_I2_J) ).
thf(397,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(54,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( is_heap @ TA @ ( e @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_is__heap_Osimps_I1_J) ).
thf(293,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( is_heap @ TA @ ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_le__add__same__cancel2) ).
thf(453,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( is_heap @ TB @ ( E @ G ) )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( is_heap @ TB @ ( E @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Heap_Oremove__max__is__heap) ).
thf(265,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( is_heap @ TB @ ( E @ G ) )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( is_heap @ TB @ ( E @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA,G: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( t @ TA @ E @ F @ G ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ E @ F @ G ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ E @ F @ G ) )
& ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_is__heap_Osimps_I6_J) ).
thf(527,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA,E: TA,F: tree @ TA,G: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( t @ TA @ E @ F @ G ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ E @ F @ G ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ E @ F @ G ) )
& ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(53,axiom,
! [TA: $tType] : ( cancel1352612707id_add @ ( multiset @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add) ).
thf(291,plain,
! [TA: $tType] : ( cancel1352612707id_add @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(292,plain,
! [TA: $tType] : ( cancel1352612707id_add @ ( multiset @ TA ) ),
inference(cnf,[status(esa)],[291]) ).
thf(45,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_le__numeral__extra_I3_J) ).
thf(270,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(75,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_subsetD) ).
thf(381,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( H
= ( val @ TB @ ( E @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_Heap_Oremove__max__val) ).
thf(220,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( H
= ( val @ TB @ ( E @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( tree @ TB ) > ( tree @ TB ) > TA > TA > TA] :
( ( rec_Tree @ TA @ TB @ A @ B @ ( e @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Tree_Osimps_I6_J) ).
thf(366,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( tree @ TB ) > ( tree @ TB ) > TA > TA > TA] :
( ( rec_Tree @ TA @ TB @ A @ B @ ( e @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(80,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_add__nonpos__nonpos) ).
thf(392,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(92,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ( is_heap @ TA @ A )
=> ( ( val @ TA @ A )
= ( lattic929149872er_Max @ TA @ ( set_mset @ TA @ ( multiset2 @ TA @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_heap__top__max) ).
thf(424,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ( is_heap @ TA @ A )
=> ( ( val @ TA @ A )
= ( lattic929149872er_Max @ TA @ ( set_mset @ TA @ ( multiset2 @ TA @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( tree @ TA ),F: TB > ( product_prod @ TA @ TB ),G: list @ TA] :
( ( heap @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( is_heap @ TA @ ( E @ ( C @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Heap_Ois__heap__of__list) ).
thf(407,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TA )
=> ! [A: TB,B: TB > $o,C: ( list @ TA ) > TB,D: TB > ( multiset @ TA ),E: TB > ( tree @ TA ),F: TB > ( product_prod @ TA @ TB ),G: list @ TA] :
( ( heap @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( is_heap @ TA @ ( E @ ( C @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(100,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_zero__le) ).
thf(461,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(98,axiom,
! [TA: $tType] :
( ( ball @ TA )
= ( ^ [A: set @ TA,B: TA > $o] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Ball__def) ).
thf(456,plain,
! [TA: $tType] :
( ( ball @ TA )
= ( ^ [A: set @ TA,B: TA > $o] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__le__same__cancel1) ).
thf(324,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(141,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_left_Osimps) ).
thf(650,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(17,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_empty__iff) ).
thf(188,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [TA: $tType] :
( ( set_Tree @ TA @ ( e @ TA ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Tree_Osimps_I14_J) ).
thf(169,plain,
! [TA: $tType] :
( ( set_Tree @ TA @ ( e @ TA ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_bot__empty__eq) ).
thf(193,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(138,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( e @ TA ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_is__heap_Osimps_I4_J) ).
thf(642,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( t @ TA @ B @ C @ D ) @ ( e @ TA ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(136,axiom,
( ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ v3 )
=> ( ( in_tree @ a @ v @ ( heapIm748920189ftDown @ a @ ( t @ a @ v3 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) )
=> ( in_tree @ a @ v @ ( t @ a @ v3 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C5__1_Ohyps_C_I1_J) ).
thf(637,plain,
( ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ v3 )
=> ( ( in_tree @ a @ v @ ( heapIm748920189ftDown @ a @ ( t @ a @ v3 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) )
=> ( in_tree @ a @ v @ ( t @ a @ v3 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > ( multiset @ TB ),B: TA > ( tree @ TB ),C: ( list @ TB ) > TA,D: TA > $o,E: TA > ( product_prod @ TB @ TA )] :
( ! [F: TA] :
( ( A @ F )
= ( multiset2 @ TB @ ( B @ F ) ) )
=> ( ! [F: list @ TB] : ( is_heap @ TB @ ( B @ ( C @ F ) ) )
=> ( ! [F: TA] :
( ( ( B @ F )
= ( e @ TB ) )
= ( D @ F ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( ( add_mset @ TB @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( is_heap @ TB @ ( B @ F ) )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( is_heap @ TB @ ( B @ H ) ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( G
= ( val @ TB @ ( B @ F ) ) ) ) )
=> ( heap_axioms @ TA @ TB @ D @ C @ A @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_Heap__axioms_Ointro) ).
thf(489,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > ( multiset @ TB ),B: TA > ( tree @ TB ),C: ( list @ TB ) > TA,D: TA > $o,E: TA > ( product_prod @ TB @ TA )] :
( ! [F: TA] :
( ( A @ F )
= ( multiset2 @ TB @ ( B @ F ) ) )
=> ( ! [F: list @ TB] : ( is_heap @ TB @ ( B @ ( C @ F ) ) )
=> ( ! [F: TA] :
( ( ( B @ F )
= ( e @ TB ) )
= ( D @ F ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( ( add_mset @ TB @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( is_heap @ TB @ ( B @ F ) )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( is_heap @ TB @ ( B @ H ) ) ) ) )
=> ( ! [F: TA,G: TB,H: TA] :
( ~ ( D @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( G
= ( val @ TB @ ( B @ F ) ) ) ) )
=> ( heap_axioms @ TA @ TB @ D @ C @ A @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(42,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(264,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(354,plain,
! [TA: $tType] :
( ~ ( linorder @ TA )
| ( type @ TA ) ),
inference(cnf,[status(esa)],[353]) ).
thf(677,plain,
! [TA: $tType] :
( ~ $true
| ( type @ TA )
| ( ( linorder @ $o )
!= ( linorder @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[264,354]) ).
thf(678,plain,
! [TA: $tType] :
( ( type @ TA )
| ( ( linorder @ $o )
!= ( linorder @ TA ) ) ),
inference(simp,[status(thm)],[677]) ).
thf(679,plain,
type @ $o,
inference(pattern_uni,[status(thm)],[678:[bind_type(TA,$thf( $o ))]]) ).
thf(131,axiom,
linorder @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(622,plain,
linorder @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(127,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( e @ TA )
!= ( t @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Tree_Odistinct_I1_J) ).
thf(605,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( e @ TA )
!= ( t @ TA @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(32,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_subset__antisym) ).
thf(237,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(68,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_zero__le__double__add__iff__zero__le__single__add) ).
thf(360,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(538,plain,
v != v1,
inference(cnfConj,[status(thm)],[536]) ).
thf(541,plain,
v1 != v,
inference(lifteq,[status(thm)],[538]) ).
thf(144,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ D @ E @ F ) ) ) ) @ ( t @ TA @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( t @ TA @ D @ E @ F ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_siftDown_Osimps_I5_J) ).
thf(657,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ D @ E @ F ) ) ) ) @ ( t @ TA @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( t @ TA @ D @ E @ F ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(111,axiom,
ord_less_eq @ a @ v2 @ v1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_True) ).
thf(530,plain,
ord_less_eq @ a @ v2 @ v1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(56,axiom,
! [TA: $tType,A: tree @ TA,B: tree @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_Tree @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( pred_Tree @ TA @ C @ A )
= ( pred_Tree @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Tree_Opred__cong) ).
thf(298,plain,
! [TA: $tType,A: tree @ TA,B: tree @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_Tree @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( pred_Tree @ TA @ C @ A )
= ( pred_Tree @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(87,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_add__mono) ).
thf(412,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1,conjecture,
in_tree @ a @ v @ ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( in_tree @ a @ v @ ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(148,plain,
~ ( in_tree @ a @ v @ ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_ex__in__conv) ).
thf(161,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(149,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(117,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_is__heap_Ocases) ).
thf(562,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( heap_axioms @ TA @ TB )
= ( ^ [A: TA > $o,B: ( list @ TB ) > TA,C: TA > ( multiset @ TB ),D: TA > ( tree @ TB ),E: TA > ( product_prod @ TB @ TA )] :
( ! [F: TA] :
( ( C @ F )
= ( multiset2 @ TB @ ( D @ F ) ) )
& ! [F: list @ TB] : ( is_heap @ TB @ ( D @ ( B @ F ) ) )
& ! [F: TA] :
( ( ( D @ F )
= ( e @ TB ) )
= ( A @ F ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( ( add_mset @ TB @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( is_heap @ TB @ ( D @ F ) )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( is_heap @ TB @ ( D @ H ) ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( G
= ( val @ TB @ ( D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_Heap__axioms__def) ).
thf(286,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( heap_axioms @ TA @ TB )
= ( ^ [A: TA > $o,B: ( list @ TB ) > TA,C: TA > ( multiset @ TB ),D: TA > ( tree @ TB ),E: TA > ( product_prod @ TB @ TA )] :
( ! [F: TA] :
( ( C @ F )
= ( multiset2 @ TB @ ( D @ F ) ) )
& ! [F: list @ TB] : ( is_heap @ TB @ ( D @ ( B @ F ) ) )
& ! [F: TA] :
( ( ( D @ F )
= ( e @ TB ) )
= ( A @ F ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( ( add_mset @ TB @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( is_heap @ TB @ ( D @ F ) )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( is_heap @ TB @ ( D @ H ) ) ) ) )
& ! [F: TA,G: TB,H: TA] :
( ~ ( A @ F )
=> ( ( ( product_Pair @ TB @ TA @ G @ H )
= ( E @ F ) )
=> ( G
= ( val @ TB @ ( D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(23,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_equals0D) ).
thf(204,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(40,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( ( set_mset @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_set__mset__eq__empty__iff) ).
thf(259,plain,
! [TA: $tType,A: multiset @ TA] :
( ( ( set_mset @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(122,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( A
= ( t @ TA @ B @ C @ D ) )
=> ? [E: tree @ TA,F: TA,G: tree @ TA] :
( ( ( heapIm748920189ftDown @ TA @ A )
= ( t @ TA @ F @ E @ G ) )
& ( ord_less_eq @ TA @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_siftDown__Node) ).
thf(579,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( A
= ( t @ TA @ B @ C @ D ) )
=> ? [E: tree @ TA,F: TA,G: tree @ TA] :
( ( ( heapIm748920189ftDown @ TA @ A )
= ( t @ TA @ F @ E @ G ) )
& ( ord_less_eq @ TA @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(14,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Collect__empty__eq) ).
thf(181,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( tree @ TB ) > ( tree @ TB ) > TA] :
( ( case_Tree @ TA @ TB @ A @ B @ ( e @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Tree_Osimps_I4_J) ).
thf(350,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( tree @ TB ) > ( tree @ TB ) > TA] :
( ( case_Tree @ TA @ TB @ A @ B @ ( e @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(537,plain,
v != v3,
inference(cnfConj,[status(thm)],[536]) ).
thf(540,plain,
v3 != v,
inference(lifteq,[status(thm)],[537]) ).
thf(16,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_emptyE) ).
thf(186,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(187,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[186]) ).
thf(11,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Collect__empty__eq__bot) ).
thf(172,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(47,axiom,
! [TA: $tType] :
( ( pred_Tree @ TA )
= ( ^ [A: TA > $o,B: tree @ TA] :
! [C: TA] :
( ( member @ TA @ C @ ( set_Tree @ TA @ B ) )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Tree_Opred__set) ).
thf(274,plain,
! [TA: $tType] :
( ( pred_Tree @ TA )
= ( ^ [A: TA > $o,B: tree @ TA] :
! [C: TA] :
( ( member @ TA @ C @ ( set_Tree @ TA @ B ) )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( ( E @ G )
= ( e @ TB ) )
= ( B @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Heap_Oas__tree__empty) ).
thf(419,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( ( E @ G )
= ( e @ TB ) )
= ( B @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(35,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_equalityD1) ).
thf(245,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(24,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_all__not__in__conv) ).
thf(208,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(125,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ~ ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_siftDown_Ocases) ).
thf(599,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ( ! [B: TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( e @ TA ) ) )
=> ( ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA] :
( A
!= ( t @ TA @ B @ ( e @ TA ) @ ( t @ TA @ C @ D @ E ) ) )
=> ~ ! [B: TA,C: TA,D: tree @ TA,E: tree @ TA,F: TA,G: tree @ TA,H: tree @ TA] :
( A
!= ( t @ TA @ B @ ( t @ TA @ C @ D @ E ) @ ( t @ TA @ F @ G @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_subset__iff) ).
thf(477,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(78,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add__le__imp__le__right) ).
thf(387,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(62,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add__decreasing2) ).
thf(345,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(129,axiom,
! [TA: $tType,A: TA,B: tree @ TA] :
( ( member @ TA @ A @ ( set_Tree @ TA @ B ) )
=> ( ! [C: tree @ TA,D: tree @ TA] :
( B
!= ( t @ TA @ A @ C @ D ) )
=> ( ! [C: TA,D: tree @ TA] :
( ? [E: tree @ TA] :
( B
= ( t @ TA @ C @ D @ E ) )
=> ~ ( member @ TA @ A @ ( set_Tree @ TA @ D ) ) )
=> ~ ! [C: TA,D: tree @ TA,E: tree @ TA] :
( ( B
= ( t @ TA @ C @ D @ E ) )
=> ~ ( member @ TA @ A @ ( set_Tree @ TA @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Tree_Oset__cases) ).
thf(609,plain,
! [TA: $tType,A: TA,B: tree @ TA] :
( ( member @ TA @ A @ ( set_Tree @ TA @ B ) )
=> ( ! [C: tree @ TA,D: tree @ TA] :
( B
!= ( t @ TA @ A @ C @ D ) )
=> ( ! [C: TA,D: tree @ TA] :
( ? [E: tree @ TA] :
( B
= ( t @ TA @ C @ D @ E ) )
=> ~ ( member @ TA @ A @ ( set_Tree @ TA @ D ) ) )
=> ~ ! [C: TA,D: tree @ TA,E: tree @ TA] :
( ( B
= ( t @ TA @ C @ D @ E ) )
=> ~ ( member @ TA @ A @ ( set_Tree @ TA @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(133,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) )
= ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) @ ( e @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_siftDown_Osimps_I3_J) ).
thf(626,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) )
= ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ D )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( t @ TA @ A @ B @ C ) @ ( e @ TA ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ D @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) @ ( e @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(61,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_le__cases3) ).
thf(330,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(33,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_subset__refl) ).
thf(240,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F )
=> ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Heap_Ointro) ).
thf(251,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
=> ( ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F )
=> ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(108,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_add__le__cancel__left) ).
thf(521,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(142,axiom,
! [TA: $tType,A: TA] :
~ ( in_tree @ TA @ A @ ( e @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_in__tree_Osimps_I1_J) ).
thf(653,plain,
! [TA: $tType,A: TA] :
~ ( in_tree @ TA @ A @ ( e @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(9,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( member @ TA @ B @ ( bot_bot @ ( set @ TA ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_ball__empty) ).
thf(167,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( member @ TA @ B @ ( bot_bot @ ( set @ TA ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_equalityE) ).
thf(223,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(128,axiom,
in_tree @ a @ v @ ( heapIm748920189ftDown @ a @ ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C5__1_Oprems_C) ).
thf(608,plain,
in_tree @ a @ v @ ( heapIm748920189ftDown @ a @ ( t @ a @ v3 @ ( t @ a @ v1 @ l1 @ r1 ) @ ( t @ a @ v2 @ l2 @ r2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( ( add_mset @ TB @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Heap_Oremove__max__multiset_H) ).
thf(394,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA,H: TB,I: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( product_Pair @ TB @ TA @ H @ I )
= ( F @ G ) )
=> ( ( add_mset @ TB @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(57,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_subsetI) ).
thf(306,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(124,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ D @ E @ F ) ) ) ) @ ( t @ TA @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( t @ TA @ D @ E @ F ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_siftDown_Osimps_I6_J) ).
thf(589,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA,G: TA] :
( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ D @ E @ F ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ D @ E @ F ) ) ) ) @ ( t @ TA @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( val @ TA @ ( t @ TA @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ G )
=> ( ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( t @ TA @ D @ E @ F ) @ ( t @ TA @ A @ B @ C ) ) )
= ( t @ TA @ ( val @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( t @ TA @ D @ E @ F ) @ ( heapIm748920189ftDown @ TA @ ( t @ TA @ G @ ( heapIm1271749598e_left @ TA @ ( t @ TA @ A @ B @ C ) ) @ ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( multiset2 @ TA @ ( t @ TA @ A @ B @ C ) )
= ( plus_plus @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) @ ( multiset2 @ TA @ B ) @ ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) ) @ ( multiset2 @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_multiset_Osimps_I2_J) ).
thf(531,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( multiset2 @ TA @ ( t @ TA @ A @ B @ C ) )
= ( plus_plus @ ( multiset @ TA ) @ ( plus_plus @ ( multiset @ TA ) @ ( multiset2 @ TA @ B ) @ ( add_mset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) ) ) @ ( multiset2 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(39,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_equalityD2) ).
thf(255,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(66,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_le__zero__eq) ).
thf(355,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(140,axiom,
( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ v3 )
=> ( ( in_tree @ a @ v @ ( heapIm748920189ftDown @ a @ ( t @ a @ v3 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) )
=> ( in_tree @ a @ v @ ( t @ a @ v3 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__C5__1_Ohyps_C_I2_J) ).
thf(648,plain,
( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( val @ a @ ( t @ a @ v1 @ l1 @ r1 ) ) )
=> ( ~ ( ord_less_eq @ a @ ( val @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ v3 )
=> ( ( in_tree @ a @ v @ ( heapIm748920189ftDown @ a @ ( t @ a @ v3 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) )
=> ( in_tree @ a @ v @ ( t @ a @ v3 @ ( heapIm1271749598e_left @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) @ ( heapIm1434396069_right @ a @ ( t @ a @ v2 @ l2 @ r2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(106,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_add__le__imp__le__left) ).
thf(487,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(115,axiom,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ~ ! [B: TA,C: tree @ TA,D: tree @ TA] :
( A
!= ( t @ TA @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Tree_Oexhaust) ).
thf(557,plain,
! [TA: $tType,A: tree @ TA] :
( ( A
!= ( e @ TA ) )
=> ~ ! [B: TA,C: tree @ TA,D: tree @ TA] :
( A
!= ( t @ TA @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(55,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_add__le__cancel__right) ).
thf(295,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(49,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_add__right__mono) ).
thf(282,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(88,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_in__mono) ).
thf(414,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(60,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add__nonpos__eq__0__iff) ).
thf(327,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(86,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm748920189ftDown @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_siftDown_Osimps_I1_J) ).
thf(409,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( heapIm748920189ftDown @ TA @ ( e @ TA ) )
= ( e @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(58,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_ball__reg) ).
thf(310,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(21,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_equals0I) ).
thf(199,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(101,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_mset @ TA @ D ) )
=> ( ord_less_eq @ TA @ C @ E ) )
=> ( A @ ( add_mset @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_multiset__induct__min) ).
thf(463,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( multiset @ TA ) > $o,B: multiset @ TA] :
( ( A @ ( zero_zero @ ( multiset @ TA ) ) )
=> ( ! [C: TA,D: multiset @ TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set_mset @ TA @ D ) )
=> ( ord_less_eq @ TA @ C @ E ) )
=> ( A @ ( add_mset @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(121,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( t @ TA @ B @ C @ D ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_is__heap_Osimps_I3_J) ).
thf(576,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: tree @ TA,D: tree @ TA] :
( ( is_heap @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( t @ TA @ B @ C @ D ) ) )
= ( ( ord_less_eq @ TA @ ( val @ TA @ ( t @ TA @ B @ C @ D ) ) @ A )
& ( is_heap @ TA @ ( t @ TA @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(154,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_empty__Collect__eq) ).
thf(175,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(119,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( val @ TA @ ( t @ TA @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_val_Osimps) ).
thf(571,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( val @ TA @ ( t @ TA @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(30,axiom,
! [TA: $tType] :
( ( set_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_set__mset__empty) ).
thf(231,plain,
! [TA: $tType] :
( ( set_mset @ TA @ ( zero_zero @ ( multiset @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(96,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add__nonneg__eq__0__iff) ).
thf(450,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( D @ G )
= ( multiset2 @ TB @ ( E @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Heap_Omultiset) ).
thf(363,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA ),G: TA] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( D @ G )
= ( multiset2 @ TB @ ( E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(104,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_verit__sum__simplify) ).
thf(482,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( tree @ TA ) > ( tree @ TA ) > TB > TB > TB,C: TA,D: tree @ TA,E: tree @ TA] :
( ( rec_Tree @ TB @ TA @ A @ B @ ( t @ TA @ C @ D @ E ) )
= ( B @ C @ D @ E @ ( rec_Tree @ TB @ TA @ A @ B @ D ) @ ( rec_Tree @ TB @ TA @ A @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Tree_Osimps_I7_J) ).
thf(671,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( tree @ TA ) > ( tree @ TA ) > TB > TB > TB,C: TA,D: tree @ TA,E: tree @ TA] :
( ( rec_Tree @ TB @ TA @ A @ B @ ( t @ TA @ C @ D @ E ) )
= ( B @ C @ D @ E @ ( rec_Tree @ TB @ TA @ A @ B @ D ) @ ( rec_Tree @ TB @ TA @ A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_right_Osimps) ).
thf(524,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA] :
( ( heapIm1434396069_right @ TA @ ( t @ TA @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(27,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_predicate1D) ).
thf(218,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA] :
( ( ( t @ TA @ A @ B @ C )
= ( t @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Tree_Oinject) ).
thf(632,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: tree @ TA,D: TA,E: tree @ TA,F: tree @ TA] :
( ( ( t @ TA @ A @ B @ C )
= ( t @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(83,axiom,
! [TA: $tType] :
( ( multiset2 @ TA @ ( e @ TA ) )
= ( zero_zero @ ( multiset @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_multiset_Osimps_I1_J) ).
thf(401,plain,
! [TA: $tType] :
( ( multiset2 @ TA @ ( e @ TA ) )
= ( zero_zero @ ( multiset @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(170,plain,
! [TA: $tType] :
( ( set_Tree @ TA @ ( e @ TA ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(171,plain,
! [TA: $tType] :
( ( set_Tree @ TA @ ( e @ TA ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(94,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_add__le__same__cancel2) ).
thf(433,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(145,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: tree @ TA,D: tree @ TA] :
( ( pred_Tree @ TA @ A @ ( t @ TA @ B @ C @ D ) )
= ( ( A @ B )
& ( pred_Tree @ TA @ A @ C )
& ( pred_Tree @ TA @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Tree_Opred__inject_I2_J) ).
thf(667,plain,
! [TA: $tType,A: TA > $o,B: TA,C: tree @ TA,D: tree @ TA] :
( ( pred_Tree @ TA @ A @ ( t @ TA @ B @ C @ D ) )
= ( ( A @ B )
& ( pred_Tree @ TA @ A @ C )
& ( pred_Tree @ TA @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(46,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_add__nonneg__nonneg) ).
thf(272,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(76,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_linear) ).
thf(383,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(194,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(cnf,[status(esa)],[193]) ).
thf(195,plain,
! [TA: $tType] :
( ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= ( bot_bot @ ( TA > $o ) ) ),
inference(lifteq,[status(thm)],[194]) ).
thf(716,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : $false ) ),
inference(rewrite,[status(thm)],[195,187]) ).
thf(150,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(cnf,[status(esa)],[149]) ).
thf(151,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Heap_Oaxioms_I2_J) ).
thf(262,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( heap @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(18,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_bot__set__def) ).
thf(190,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(91,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_add__increasing) ).
thf(422,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(72,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_double__add__le__zero__iff__single__add__le__zero) ).
thf(373,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(34,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_set__eq__subset) ).
thf(242,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(44,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( set @ TA ) > $o ) @ ( powp @ TA @ A ) @ ( powp @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Powp__mono) ).
thf(268,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( set @ TA ) > $o ) @ ( powp @ TA @ A ) @ ( powp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(67,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_add__decreasing) ).
thf(358,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(135,axiom,
! [TA: $tType,A: TA,B: tree @ TA,C: TA,D: tree @ TA] :
( ( member @ TA @ A @ ( set_Tree @ TA @ B ) )
=> ( member @ TA @ A @ ( set_Tree @ TA @ ( t @ TA @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Tree_Oset__intros_I2_J) ).
thf(635,plain,
! [TA: $tType,A: TA,B: tree @ TA,C: TA,D: tree @ TA] :
( ( member @ TA @ A @ ( set_Tree @ TA @ B ) )
=> ( member @ TA @ A @ ( set_Tree @ TA @ ( t @ TA @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(93,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_linorder__wlog) ).
thf(427,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add__mono__thms__linordered__semiring_I1_J) ).
thf(459,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(13,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Collect__mono__iff) ).
thf(178,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(48,axiom,
! [TA: $tType,A: TA > $o,B: tree @ TA,C: TA > $o] :
( ( pred_Tree @ TA @ A @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( set_Tree @ TA @ B ) )
=> ( ( A @ D )
=> ( C @ D ) ) )
=> ( pred_Tree @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Tree_Opred__mono__strong) ).
thf(277,plain,
! [TA: $tType,A: TA > $o,B: tree @ TA,C: TA > $o] :
( ( pred_Tree @ TA @ A @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( set_Tree @ TA @ B ) )
=> ( ( A @ D )
=> ( C @ D ) ) )
=> ( pred_Tree @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_add__mono__thms__linordered__semiring_I3_J) ).
thf(369,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(114,axiom,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( e @ TA ) )
=> ( ! [C: TA,D: tree @ TA,E: tree @ TA] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Tree_Oinduct) ).
thf(543,plain,
! [TA: $tType,A: ( tree @ TA ) > $o,B: tree @ TA] :
( ( A @ ( e @ TA ) )
=> ( ! [C: TA,D: tree @ TA,E: tree @ TA] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t @ TA @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( heap @ TA @ TB )
= ( ^ [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
& ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Heap__def) ).
thf(215,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ( ( heap @ TA @ TB )
= ( ^ [A: TA,B: TA > $o,C: ( list @ TB ) > TA,D: TA > ( multiset @ TB ),E: TA > ( tree @ TB ),F: TA > ( product_prod @ TB @ TA )] :
( ( collection @ TA @ TB @ A @ B @ C @ D )
& ( heap_axioms @ TA @ TB @ B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA] :
( ( in_tree @ TA @ A @ B )
=> ( ( is_heap @ TA @ B )
=> ( ord_less_eq @ TA @ A @ ( val @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_is__heap__max) ).
thf(560,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: tree @ TA] :
( ( in_tree @ TA @ A @ B )
=> ( ( is_heap @ TA @ B )
=> ( ord_less_eq @ TA @ A @ ( val @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(137,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
( ( heapIm748920189ftDown @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) )
= ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_siftDown_Osimps_I2_J) ).
thf(639,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
( ( heapIm748920189ftDown @ TA @ ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) )
= ( t @ TA @ A @ ( e @ TA ) @ ( e @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(674,plain,
! [TA: $tType] :
( ~ $true
| ( type @ TA )
| ( ( linorder @ a )
!= ( linorder @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[622,354]) ).
thf(675,plain,
! [TA: $tType] :
( ( type @ TA )
| ( ( linorder @ a )
!= ( linorder @ TA ) ) ),
inference(simp,[status(thm)],[674]) ).
thf(676,plain,
type @ a,
inference(pattern_uni,[status(thm)],[675:[bind_type(TA,$thf( a ))]]) ).
thf(1276,plain,
$false,
inference(e,[status(thm)],[645,347,249,234,379,655,202,385,670,404,565,436,389,184,196,587,619,542,157,284,416,152,289,164,376,623,485,574,353,480,211,253,602,397,293,453,265,527,292,270,381,534,220,366,392,424,407,461,456,324,650,188,169,193,642,637,489,679,622,605,237,360,541,657,530,298,412,148,264,161,149,562,286,204,259,579,291,181,350,540,187,172,274,419,245,208,599,477,387,345,609,626,330,240,251,521,653,167,223,608,394,306,589,531,255,355,648,487,557,295,282,414,327,409,310,199,463,576,154,175,571,231,450,363,482,671,524,218,186,632,401,171,433,667,272,383,716,151,262,190,422,373,242,268,358,635,427,459,178,277,369,354,543,215,560,639,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP067^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n020.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:47:19 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.69/0.56 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.12/0.96 % [INFO] Parsing done (394ms).
% 2.12/0.98 % [INFO] Running in sequential loop mode.
% 4.06/1.50 % [INFO] eprover registered as external prover.
% 4.06/1.51 % [INFO] Scanning for conjecture ...
% 4.23/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 282 axioms. Running axiom selection ...
% 4.73/1.88 % [INFO] Axiom selection finished. Selected 145 axioms (removed 137 axioms).
% 6.27/2.32 % [INFO] Problem is higher-order (TPTP THF).
% 6.27/2.37 % [INFO] Type checking passed.
% 6.27/2.37 % [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 ...
% 51.67/15.82 % External prover 'e' found a proof!
% 51.67/15.82 % [INFO] Killing All external provers ...
% 51.67/15.83 % Time passed: 15516ms (effective reasoning time: 14838ms)
% 51.67/15.83 % 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)>
% 51.67/15.83 % Axioms used in derivation (145): fact_184_zero__le__double__add__iff__zero__le__single__add, fact_129_Powp__mono, fact_12_Tree_Osimps_I7_J, fact_112_Collect__mono__iff, tfree_0, fact_41_is__heap_Osimps_I6_J, fact_86_predicate1D, tcon_Multiset_Omultiset___Groups_Ocancel__comm__monoid__add, fact_140_multiset_Osimps_I1_J, fact_191_add__le__imp__le__right, fact_104_subset__eq, fact_29_Tree_Oexhaust, fact_65_le__cases3, fact_24_Tree_Opred__cong, fact_226_add__nonneg__eq__0__iff, fact_117_emptyE, fact_128_Heap_Oaxioms_I1_J, fact_167_le__numeral__extra_I3_J, fact_35_Tree_Oset__intros_I1_J, fact_53_is__heap_Osimps_I2_J, fact_4_Tree_Oinject, fact_31_Tree_Odistinct_I1_J, fact_193_le__iff__add, fact_85_predicate1I, fact_120_subset__emptyI, fact_197_add__mono, fact_1__092_060open_062in__tree_Av_A_IsiftDown_At_J_092_060close_062, fact_183_double__add__le__zero__iff__single__add__le__zero, tcon_HOL_Obool___Orderings_Olinorder, fact_225_add__nonpos__nonpos, fact_3__C5__1_Oprems_C, fact_105_equalityD1, fact_155_set__mset__eq__empty__iff, fact_39_is__heap_Osimps_I3_J, fact_224_add__nonneg__nonneg, fact_165_multiset__induct__max, fact_113_bot__set__def, fact_28_is__heap_Ocases, fact_196_add__left__mono, fact_173_add__le__cancel__right, fact_102_subsetD, fact_46_Collect__mem__eq, fact_36_Tree_Oset__intros_I2_J, fact_169_multiset_Osimps_I2_J, fact_96_all__not__in__conv, fact_109_Collect__mono, fact_101_in__mono, fact_25_Tree_Opred__mono__strong, fact_34_Tree_Oset__cases, fact_114_ex__in__conv, fact_11_Tree_Osimps_I5_J, fact_81_Heap_Ois__heap__of__list, fact_87_rev__predicate1D, fact_139_heap__top__max, fact_67_le__cases, fact_6__C5__1_Ohyps_C_I2_J, fact_97_Collect__empty__eq, fact_220_add__decreasing, fact_99_subsetI, fact_13_Tree_Opred__inject_I2_J, fact_130_Heap_Omultiset, fact_79_verit__la__disequality, fact_30_Tree_Oinduct, fact_83_Heap_Oas__tree__empty, fact_135_Heap__axioms__def, fact_223_add__increasing2, fact_45_mem__Collect__eq, fact_123_ball__reg, fact_198_add__mono__thms__linordered__semiring_I1_J, fact_42_is__heap_Osimps_I5_J, fact_222_add__decreasing2, fact_32_siftDown_Osimps_I2_J, fact_190_verit__sum__simplify, fact_16_Tree_Osimps_I6_J, fact_127_Heap__def, fact_10_siftDown_Ocases, fact_40_is__heap__max, fact_82_Tree_Opred__set, fact_182_le__add__same__cancel2, fact_47_Collect__cong, fact_2_True, fact_100_subset__antisym, fact_134_Heap__axioms_Ointro, fact_26_siftDown__in__tree, fact_22_siftDown_Osimps_I3_J, fact_52_is__heap_Osimps_I1_J, fact_124_Collect__empty__eq__bot, fact_69_linear, fact_57_linorder__wlog, fact_227_add__nonpos__eq__0__iff, fact_111_set__eq__subset, fact_9_right_Osimps, fact_94_empty__subsetI, fact_192_add__le__imp__le__left, fact_119_Ball__Collect, fact_125_bot__empty__eq, fact_20_siftDown_Osimps_I5_J, fact_23_siftDown_Osimps_I1_J, fact_180_add__le__same__cancel2, fact_136_heap__top__geq, fact_156_set__mset__empty, fact_132_Heap_Oremove__max__val, fact_21_siftDown_Osimps_I4_J, fact_122_Heap_Oaxioms_I2_J, fact_103_equalityE, fact_159_zero__le, fact_93_subset__empty, fact_179_add__le__same__cancel1, fact_158_le__zero__eq, fact_200_add__mono__thms__linordered__semiring_I3_J, fact_14_in__tree_Osimps_I1_J, fact_0_False, fact_7__C5__1_Ohyps_C_I1_J, fact_106_equalityD2, fact_181_le__add__same__cancel1, fact_17_Tree_Osimps_I4_J, fact_95_empty__iff, fact_138_Heap_Oremove__max__multiset_H, fact_80_Tree_Osimps_I14_J, fact_51_Tree_Opred__mono, fact_166_multiset__induct__min, fact_118_Ball__def, fact_108_subset__refl, fact_194_add__right__mono, fact_221_add__increasing, fact_27_siftDown__Node, fact_115_equals0I, fact_8_left_Osimps, fact_199_add__mono__thms__linordered__semiring_I2_J, subcl_Orderings_Olinorder___HOL_Otype, fact_174_add__le__cancel__left, fact_195_less__eqE, fact_131_Heap_Oremove__max__is__heap, fact_19_siftDown_Osimps_I6_J, fact_18_Tree_Opred__inject_I1_J, fact_107_subset__iff, fact_38_is__heap_Osimps_I4_J, fact_116_equals0D, fact_5_in__tree_Osimps_I2_J, fact_33_val_Osimps, fact_126_Heap_Ointro, fact_98_empty__Collect__eq, fact_110_subset__trans, fact_92_ball__empty, fact_15_Tree_Oset__intros_I3_J
% 51.67/15.83 % No. of inferences in proof: 318
% 51.67/15.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15516 ms resp. 14838 ms w/o parsing
% 53.91/16.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.91/16.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------