%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP067^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 16.64s 4.94s
% Output : Refutation 17.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 112
% Syntax : Number of formulae : 226 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 664 ( 238 equ; 6 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2981 ( 128 ~; 16 |; 64 &;2443 @)
% ( 0 <=>; 330 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 14 con; 0-3 aty)
% Number of variables : 696 ( 24 ^; 658 !; 14 ?; 696 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiset_a_type,type,
multiset_a: $tType ).
thf(tree_a_type,type,
tree_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(plus_plus_multiset_a_decl,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(zero_zero_multiset_a_decl,type,
zero_zero_multiset_a: multiset_a ).
thf(heapIm1140443833left_a_decl,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(heapIm1257206334ight_a_decl,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(heapIm1091024090Down_a_decl,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(e_a_decl,type,
e_a: tree_a ).
thf(t_a_decl,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(pred_Tree_a_decl,type,
pred_Tree_a: ( a > $o ) > tree_a > $o ).
thf(set_Tree_a_decl,type,
set_Tree_a: tree_a > set_a ).
thf(in_tree_a_decl,type,
in_tree_a: a > tree_a > $o ).
thf(is_heap_a_decl,type,
is_heap_a: tree_a > $o ).
thf(multiset_a2_decl,type,
multiset_a2: tree_a > multiset_a ).
thf(val_a_decl,type,
val_a: tree_a > a ).
thf(lattic146396397_Max_a_decl,type,
lattic146396397_Max_a: set_a > a ).
thf(add_mset_a_decl,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(set_mset_a_decl,type,
set_mset_a: multiset_a > set_a ).
thf(bot_bot_a_o_decl,type,
bot_bot_a_o: a > $o ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_less_eq_Tree_a_o_decl,type,
ord_less_eq_Tree_a_o: ( tree_a > $o ) > ( tree_a > $o ) > $o ).
thf(ord_less_eq_a_o_decl,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(ord_le1199012836iset_a_decl,type,
ord_le1199012836iset_a: multiset_a > multiset_a > $o ).
thf(ord_less_eq_a_decl,type,
ord_less_eq_a: a > a > $o ).
thf(order_Greatest_a_decl,type,
order_Greatest_a: ( a > $o ) > a ).
thf(ball_a_decl,type,
ball_a: set_a > ( a > $o ) > $o ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(insert_a_decl,type,
insert_a: a > set_a > set_a ).
thf(is_singleton_a_decl,type,
is_singleton_a: set_a > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $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(t_decl,type,
t: 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(109,axiom,
! [A: a,B: tree_a,C: tree_a,D: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ D @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_siftDown_Osimps_I4_J) ).
thf(587,plain,
! [A: a,B: tree_a,C: tree_a,D: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ e_a @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ D @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(5,axiom,
! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_insertI1) ).
thf(122,plain,
! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(88,axiom,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a] :
( ( ( t_a @ A @ B @ C )
= ( t_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Tree_Oinject) ).
thf(479,plain,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a] :
( ( ( t_a @ A @ B @ C )
= ( t_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(97,axiom,
~ ( ( v = v3 )
| ( v = v1 )
| ( v = v2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_False) ).
thf(518,plain,
~ ( ( v = v3 )
| ( v = v1 )
| ( v = v2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(69,axiom,
! [A: a,B: a,C: a > a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_ord__le__eq__subst) ).
thf(408,plain,
! [A: a,B: a,C: a > a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(3,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ? [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
& ~ ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_mk__disjoint__insert) ).
thf(115,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ? [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
& ~ ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,axiom,
! [A: set_a] :
( ( A != bot_bot_set_a )
=> ( ! [B: a,C: a] :
( ( member_a @ B @ A )
=> ( ( member_a @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_is__singletonI_H) ).
thf(308,plain,
! [A: set_a] :
( ( A != bot_bot_set_a )
=> ( ! [B: a,C: a] :
( ( member_a @ B @ A )
=> ( ( member_a @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(4,axiom,
! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_singletonI) ).
thf(120,plain,
! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(58,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ( ord_le1199012836iset_a @ C @ D )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_add__mono) ).
thf(379,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ( ord_le1199012836iset_a @ C @ D )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(60,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mem__Collect__eq) ).
thf(385,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(95,axiom,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a,G: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1257206334ight_a @ ( t_a @ D @ E @ F ) ) ) ) @ ( t_a @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( t_a @ D @ E @ F ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_siftDown_Osimps_I5_J) ).
thf(500,plain,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a,G: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1257206334ight_a @ ( t_a @ D @ E @ F ) ) ) ) @ ( t_a @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( t_a @ D @ E @ F ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(15,axiom,
! [A: a,B: set_a,C: a] :
( ( ~ ( member_a @ A @ B )
=> ( A = C ) )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_insertCI) ).
thf(153,plain,
! [A: a,B: set_a,C: a] :
( ( ~ ( member_a @ A @ B )
=> ( A = C ) )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_equals0D) ).
thf(174,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(23,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_empty__iff) ).
thf(185,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(70,axiom,
! [A: a,B: a] :
( ~ ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_le__cases) ).
thf(417,plain,
! [A: a,B: a] :
( ~ ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(32,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( ord_less_eq_a @ C @ B ) )
=> ( ( order_Greatest_a @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Greatest__equality) ).
thf(257,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( ord_less_eq_a @ C @ B ) )
=> ( ( order_Greatest_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(106,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_siftDown__in__tree) ).
thf(559,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(72,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_order__class_Oorder_Oantisym) ).
thf(421,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(39,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_dual__order_Oantisym) ).
thf(284,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(41,axiom,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ D ) )
=> ( ord_less_eq_a @ E @ C ) )
=> ( A @ ( add_mset_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_multiset__induct__max) ).
thf(289,plain,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ D ) )
=> ( ord_less_eq_a @ E @ C ) )
=> ( A @ ( add_mset_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(80,axiom,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_is__heap_Osimps_I2_J) ).
thf(448,plain,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(17,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_equals0I) ).
thf(164,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [A: a] :
( ( set_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_set__mset__single) ).
thf(179,plain,
! [A: a] :
( ( set_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= ( insert_a @ A @ bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(90,axiom,
! [A: a,B: tree_a] :
( ( in_tree_a @ A @ B )
=> ( ( is_heap_a @ B )
=> ( ord_less_eq_a @ A @ ( val_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_is__heap__max) ).
thf(485,plain,
! [A: a,B: tree_a] :
( ( in_tree_a @ A @ B )
=> ( ( is_heap_a @ B )
=> ( ord_less_eq_a @ A @ ( val_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(96,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ~ ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_siftDown_Ocases) ).
thf(514,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ~ ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(52,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_add__left__mono) ).
thf(348,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ C @ A ) @ ( plus_plus_multiset_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(13,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_singletonD) ).
thf(147,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(65,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_order__class_Oorder_Oeq__iff) ).
thf(396,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(9,axiom,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_insert__ident) ).
thf(133,plain,
! [A: a,B: set_a,C: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
! [A: a,B: a,C: a > a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ ( C @ B ) @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_order__subst2) ).
thf(243,plain,
! [A: a,B: a,C: a > a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ ( C @ B ) @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(98,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( in_tree_a @ A @ ( t_a @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree_a @ A @ C )
| ( in_tree_a @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_in__tree_Osimps_I2_J) ).
thf(527,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( in_tree_a @ A @ ( t_a @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree_a @ A @ C )
| ( in_tree_a @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(83,axiom,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ E @ F @ G ) ) @ A )
& ( is_heap_a @ ( t_a @ E @ F @ G ) )
& ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_is__heap_Osimps_I6_J) ).
thf(452,plain,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ E @ F @ G ) ) @ A )
& ( is_heap_a @ ( t_a @ E @ F @ G ) )
& ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(31,axiom,
! [A: tree_a,B: tree_a,C: a > $o,D: a > $o] :
( ( A = B )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_Tree_a @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( pred_Tree_a @ C @ A )
= ( pred_Tree_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Tree_Opred__cong) ).
thf(248,plain,
! [A: tree_a,B: tree_a,C: a > $o,D: a > $o] :
( ( A = B )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_Tree_a @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( pred_Tree_a @ C @ A )
= ( pred_Tree_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(77,axiom,
! [A: a,B: a] :
( ( A = B )
| ~ ( ord_less_eq_a @ A @ B )
| ~ ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_verit__la__disequality) ).
thf(439,plain,
! [A: a,B: a] :
( ( A = B )
| ~ ( ord_less_eq_a @ A @ B )
| ~ ( ord_less_eq_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(100,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 @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
=> ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C5__1_Ohyps_C_I2_J) ).
thf(534,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 @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) )
=> ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v2 @ l2 @ r2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v2 @ l2 @ r2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(48,axiom,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_siftDown_Osimps_I1_J) ).
thf(334,plain,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(111,axiom,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( member_a @ A @ ( set_Tree_a @ B ) )
=> ( member_a @ A @ ( set_Tree_a @ ( t_a @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Tree_Oset__intros_I3_J) ).
thf(598,plain,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( member_a @ A @ ( set_Tree_a @ B ) )
=> ( member_a @ A @ ( set_Tree_a @ ( t_a @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(63,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Collect__mem__eq) ).
thf(392,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(73,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_add__right__mono) ).
thf(424,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a] :
( ( ord_le1199012836iset_a @ A @ B )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(36,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( ord_le1199012836iset_a @ A @ B )
& ( ord_le1199012836iset_a @ C @ D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_add__mono__thms__linordered__semiring_I1_J) ).
thf(275,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( ord_le1199012836iset_a @ A @ B )
& ( ord_le1199012836iset_a @ C @ D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(10,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_singleton__iff) ).
thf(137,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,axiom,
! [A: a,B: a > a,C: a,D: a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ord__eq__le__subst) ).
thf(317,plain,
! [A: a,B: a > a,C: a,D: a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(24,axiom,
( ( set_mset_a @ zero_zero_multiset_a )
= bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_set__mset__empty) ).
thf(188,plain,
( ( set_mset_a @ zero_zero_multiset_a )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,axiom,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_multiset_Osimps_I1_J) ).
thf(388,plain,
( ( multiset_a2 @ e_a )
= zero_zero_multiset_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(46,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ C @ A )
=> ( ord_less_eq_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dual__order_Otrans) ).
thf(328,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ C @ A )
=> ( ord_less_eq_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(6,axiom,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_insertE) ).
thf(124,plain,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
=> ( ( A != B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,axiom,
! [A: set_a,B: a > $o,C: a > $o] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ( B @ D ) )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_ball__reg) ).
thf(193,plain,
! [A: set_a,B: a > $o,C: a > $o] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ( B @ D ) )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(103,axiom,
! [A: tree_a,B: a,C: tree_a,D: tree_a] :
( ( A
= ( t_a @ B @ C @ D ) )
=> ? [E: tree_a,F: a,G: tree_a] :
( ( ( heapIm1091024090Down_a @ A )
= ( t_a @ F @ E @ G ) )
& ( ord_less_eq_a @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_siftDown__Node) ).
thf(547,plain,
! [A: tree_a,B: a,C: tree_a,D: tree_a] :
( ( A
= ( t_a @ B @ C @ D ) )
=> ? [E: tree_a,F: a,G: tree_a] :
( ( ( heapIm1091024090Down_a @ A )
= ( t_a @ F @ E @ G ) )
& ( ord_less_eq_a @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(33,axiom,
( pred_Tree_a
= ( ^ [A: a > $o,B: tree_a] :
! [C: a] :
( ( member_a @ C @ ( set_Tree_a @ B ) )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_Tree_Opred__set) ).
thf(266,plain,
( pred_Tree_a
= ( ^ [A: a > $o,B: tree_a] :
! [C: a] :
( ( member_a @ C @ ( set_Tree_a @ B ) )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(55,axiom,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_bot__empty__eq) ).
thf(360,plain,
( bot_bot_a_o
= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(66,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_Tree_a_o @ ( pred_Tree_a @ A ) @ ( pred_Tree_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Tree_Opred__mono) ).
thf(398,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_Tree_a_o @ ( pred_Tree_a @ A ) @ ( pred_Tree_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(105,axiom,
in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C5__1_Oprems_C) ).
thf(558,plain,
in_tree_a @ v @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(99,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ~ ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_is__heap_Ocases) ).
thf(530,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( ! [B: a] :
( A
!= ( t_a @ B @ e_a @ e_a ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ e_a @ ( t_a @ C @ D @ E ) ) )
=> ( ! [B: a,C: a,D: tree_a,E: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ e_a ) )
=> ~ ! [B: a,C: a,D: tree_a,E: tree_a,F: a,G: tree_a,H: tree_a] :
( A
!= ( t_a @ B @ ( t_a @ C @ D @ E ) @ ( t_a @ F @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(75,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( ord_le1199012836iset_a @ A @ B )
& ( C = D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_add__mono__thms__linordered__semiring_I3_J) ).
thf(430,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( ord_le1199012836iset_a @ A @ B )
& ( C = D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(108,axiom,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a,G: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1257206334ight_a @ ( t_a @ D @ E @ F ) ) ) ) @ ( t_a @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( t_a @ D @ E @ F ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_siftDown_Osimps_I6_J) ).
thf(573,plain,
! [A: a,B: tree_a,C: tree_a,D: a,E: tree_a,F: tree_a,G: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ D @ E @ F ) ) @ ( heapIm1257206334ight_a @ ( t_a @ D @ E @ F ) ) ) ) @ ( t_a @ A @ B @ C ) ) ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( val_a @ ( t_a @ D @ E @ F ) ) )
=> ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ G )
=> ( ( heapIm1091024090Down_a @ ( t_a @ G @ ( t_a @ D @ E @ F ) @ ( t_a @ A @ B @ C ) ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( t_a @ D @ E @ F ) @ ( heapIm1091024090Down_a @ ( t_a @ G @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(112,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( val_a @ ( t_a @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_val_Osimps) ).
thf(601,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( val_a @ ( t_a @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(107,axiom,
! [A: a,B: tree_a] :
( ( member_a @ A @ ( set_Tree_a @ B ) )
=> ( ! [C: tree_a,D: tree_a] :
( B
!= ( t_a @ A @ C @ D ) )
=> ( ! [C: a,D: tree_a] :
( ? [E: tree_a] :
( B
= ( t_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( set_Tree_a @ D ) ) )
=> ~ ! [C: a,D: tree_a,E: tree_a] :
( ( B
= ( t_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( set_Tree_a @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Tree_Oset__cases) ).
thf(562,plain,
! [A: a,B: tree_a] :
( ( member_a @ A @ ( set_Tree_a @ B ) )
=> ( ! [C: tree_a,D: tree_a] :
( B
!= ( t_a @ A @ C @ D ) )
=> ( ! [C: a,D: tree_a] :
( ? [E: tree_a] :
( B
= ( t_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( set_Tree_a @ D ) ) )
=> ~ ! [C: a,D: tree_a,E: tree_a] :
( ( B
= ( t_a @ C @ D @ E ) )
=> ~ ( member_a @ A @ ( set_Tree_a @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(68,axiom,
! [A: a > $o,B: tree_a,C: a > $o] :
( ( pred_Tree_a @ A @ B )
=> ( ! [D: a] :
( ( member_a @ D @ ( set_Tree_a @ B ) )
=> ( ( A @ D )
=> ( C @ D ) ) )
=> ( pred_Tree_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Tree_Opred__mono__strong) ).
thf(402,plain,
! [A: a > $o,B: tree_a,C: a > $o] :
( ( pred_Tree_a @ A @ B )
=> ( ! [D: a] :
( ( member_a @ D @ ( set_Tree_a @ B ) )
=> ( ( A @ D )
=> ( C @ D ) ) )
=> ( pred_Tree_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(79,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_right_Osimps) ).
thf(445,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(59,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( ( is_heap_a @ A )
=> ( ( val_a @ A )
= ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_heap__top__max) ).
thf(382,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( ( is_heap_a @ A )
=> ( ( val_a @ A )
= ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ~ ! [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Set_Oset__insert) ).
thf(159,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ~ ! [C: set_a] :
( ( B
= ( insert_a @ A @ C ) )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(113,axiom,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( member_a @ A @ ( set_Tree_a @ B ) )
=> ( member_a @ A @ ( set_Tree_a @ ( t_a @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Tree_Oset__intros_I2_J) ).
thf(604,plain,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( member_a @ A @ ( set_Tree_a @ B ) )
=> ( member_a @ A @ ( set_Tree_a @ ( t_a @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(71,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_eq__iff) ).
thf(419,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(57,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_dual__order_Orefl) ).
thf(377,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(76,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_ord__le__eq__trans) ).
thf(434,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(35,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( ord_less_eq_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_eq__refl) ).
thf(271,plain,
! [A: a,B: a] :
( ( A = B )
=> ( ord_less_eq_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(56,axiom,
! [A: a,B: a,C: a] :
( ( ( ord_less_eq_a @ A @ B )
=> ~ ( ord_less_eq_a @ B @ C ) )
=> ( ( ( ord_less_eq_a @ B @ A )
=> ~ ( ord_less_eq_a @ A @ C ) )
=> ( ( ( ord_less_eq_a @ A @ C )
=> ~ ( ord_less_eq_a @ C @ B ) )
=> ( ( ( ord_less_eq_a @ C @ B )
=> ~ ( ord_less_eq_a @ B @ A ) )
=> ( ( ( ord_less_eq_a @ B @ C )
=> ~ ( ord_less_eq_a @ C @ A ) )
=> ~ ( ( ord_less_eq_a @ C @ A )
=> ~ ( ord_less_eq_a @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__cases3) ).
thf(362,plain,
! [A: a,B: a,C: a] :
( ( ( ord_less_eq_a @ A @ B )
=> ~ ( ord_less_eq_a @ B @ C ) )
=> ( ( ( ord_less_eq_a @ B @ A )
=> ~ ( ord_less_eq_a @ A @ C ) )
=> ( ( ( ord_less_eq_a @ A @ C )
=> ~ ( ord_less_eq_a @ C @ B ) )
=> ( ( ( ord_less_eq_a @ C @ B )
=> ~ ( ord_less_eq_a @ B @ A ) )
=> ( ( ( ord_less_eq_a @ B @ C )
=> ~ ( ord_less_eq_a @ C @ A ) )
=> ~ ( ( ord_less_eq_a @ C @ A )
=> ~ ( ord_less_eq_a @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(82,axiom,
ord_less_eq_a @ v2 @ v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_True) ).
thf(451,plain,
ord_less_eq_a @ v2 @ v1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(87,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 @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
=> ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__C5__1_Ohyps_C_I1_J) ).
thf(477,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 @ ( heapIm1091024090Down_a @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) )
=> ( in_tree_a @ v @ ( t_a @ v3 @ ( heapIm1140443833left_a @ ( t_a @ v1 @ l1 @ r1 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(93,axiom,
! [A: a] :
( ( heapIm1091024090Down_a @ ( t_a @ A @ e_a @ e_a ) )
= ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_siftDown_Osimps_I2_J) ).
thf(494,plain,
! [A: a] :
( ( heapIm1091024090Down_a @ ( t_a @ A @ e_a @ e_a ) )
= ( t_a @ A @ e_a @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(51,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_order__trans) ).
thf(345,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(11,axiom,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_insert__iff) ).
thf(140,plain,
! [A: a,B: a,C: set_a] :
( ( member_a @ A @ ( insert_a @ B @ C ) )
= ( ( A = B )
| ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: a,B: set_a,C: a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_insertI2) ).
thf(130,plain,
! [A: a,B: set_a,C: a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( insert_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(84,axiom,
! [A: a > $o,B: a,C: tree_a,D: tree_a] :
( ( pred_Tree_a @ A @ ( t_a @ B @ C @ D ) )
= ( ( A @ B )
& ( pred_Tree_a @ A @ C )
& ( pred_Tree_a @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Tree_Opred__inject_I2_J) ).
thf(455,plain,
! [A: a > $o,B: a,C: tree_a,D: tree_a] :
( ( pred_Tree_a @ A @ ( t_a @ B @ C @ D ) )
= ( ( A @ B )
& ( pred_Tree_a @ A @ C )
& ( pred_Tree_a @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(42,axiom,
! [A: a > $o] : ( pred_Tree_a @ A @ e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Tree_Opred__inject_I1_J) ).
thf(306,plain,
! [A: a > $o] : ( pred_Tree_a @ A @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(29,axiom,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ D ) )
=> ( ord_less_eq_a @ C @ E ) )
=> ( A @ ( add_mset_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_multiset__induct__min) ).
thf(226,plain,
! [A: multiset_a > $o,B: multiset_a] :
( ( A @ zero_zero_multiset_a )
=> ( ! [C: a,D: multiset_a] :
( ( A @ D )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ D ) )
=> ( ord_less_eq_a @ C @ E ) )
=> ( A @ ( add_mset_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(86,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ~ ! [B: a,C: tree_a,D: tree_a] :
( A
!= ( t_a @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Tree_Oexhaust) ).
thf(473,plain,
! [A: tree_a] :
( ( A != e_a )
=> ~ ! [B: a,C: tree_a,D: tree_a] :
( A
!= ( t_a @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(92,axiom,
! [A: a,B: tree_a,C: tree_a] :
( e_a
!= ( t_a @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Tree_Odistinct_I1_J) ).
thf(490,plain,
! [A: a,B: tree_a,C: tree_a] :
( e_a
!= ( t_a @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(91,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( multiset_a2 @ ( t_a @ A @ B @ C ) )
= ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_multiset_Osimps_I2_J) ).
thf(487,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( multiset_a2 @ ( t_a @ A @ B @ C ) )
= ( plus_plus_multiset_a @ ( plus_plus_multiset_a @ ( multiset_a2 @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) @ ( multiset_a2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(85,axiom,
! [A: tree_a > $o,B: tree_a] :
( ( A @ e_a )
=> ( ! [C: a,D: tree_a,E: tree_a] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t_a @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Tree_Oinduct) ).
thf(458,plain,
! [A: tree_a > $o,B: tree_a] :
( ( A @ e_a )
=> ( ! [C: a,D: tree_a,E: tree_a] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t_a @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38,axiom,
( ( set_Tree_a @ e_a )
= bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Tree_Osimps_I14_J) ).
thf(282,plain,
( ( set_Tree_a @ e_a )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(14,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_insert__absorb) ).
thf(150,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ B )
=> ( ( insert_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_emptyE) ).
thf(182,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(47,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_antisym__conv) ).
thf(331,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(7,axiom,
! [A: a] :
( ( lattic146396397_Max_a @ ( insert_a @ A @ bot_bot_set_a ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_Max__singleton) ).
thf(127,plain,
! [A: a] :
( ( lattic146396397_Max_a @ ( insert_a @ A @ bot_bot_set_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(49,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ord__eq__le__trans) ).
thf(336,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(110,axiom,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ E @ F @ G ) ) @ A )
& ( is_heap_a @ ( t_a @ E @ F @ G ) )
& ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_is__heap_Osimps_I5_J) ).
thf(595,plain,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ E @ F @ G ) ) @ A )
& ( is_heap_a @ ( t_a @ E @ F @ G ) )
& ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(12,axiom,
! [A: a,B: set_a,C: a,D: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ C @ D )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_a] :
( ( B
= ( insert_a @ C @ E ) )
& ~ ( member_a @ C @ E )
& ( D
= ( insert_a @ A @ E ) )
& ~ ( member_a @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_insert__eq__iff) ).
thf(143,plain,
! [A: a,B: set_a,C: a,D: set_a] :
( ~ ( member_a @ A @ B )
=> ( ~ ( member_a @ C @ D )
=> ( ( ( insert_a @ A @ B )
= ( insert_a @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_a] :
( ( B
= ( insert_a @ C @ E ) )
& ~ ( member_a @ C @ E )
& ( D
= ( insert_a @ A @ E ) )
& ~ ( member_a @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(94,axiom,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_in__tree_Osimps_I1_J) ).
thf(497,plain,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(81,axiom,
in_tree_a @ v @ ( heapIm1091024090Down_a @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062in__tree_Av_A_IsiftDown_At_J_092_060close_062) ).
thf(450,plain,
in_tree_a @ v @ ( heapIm1091024090Down_a @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(104,axiom,
! [A: a,B: tree_a,C: tree_a] : ( member_a @ A @ ( set_Tree_a @ ( t_a @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Tree_Oset__intros_I1_J) ).
thf(556,plain,
! [A: a,B: tree_a,C: tree_a] : ( member_a @ A @ ( set_Tree_a @ ( t_a @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(102,axiom,
! [A: a,B: tree_a,C: tree_a,D: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) )
= ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1091024090Down_a @ ( t_a @ D @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) @ e_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_siftDown_Osimps_I3_J) ).
thf(539,plain,
! [A: a,B: tree_a,C: tree_a,D: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) )
= ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ D )
=> ( ( heapIm1091024090Down_a @ ( t_a @ D @ ( t_a @ A @ B @ C ) @ e_a ) )
= ( t_a @ ( val_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1091024090Down_a @ ( t_a @ D @ ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) ) @ ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) ) ) ) @ e_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(89,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( is_heap_a @ ( t_a @ A @ e_a @ ( t_a @ B @ C @ D ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_is__heap_Osimps_I3_J) ).
thf(482,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( is_heap_a @ ( t_a @ A @ e_a @ ( t_a @ B @ C @ D ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(53,axiom,
! [A: a > a > $o,B: a,C: a] :
( ! [D: a,E: a] :
( ( ord_less_eq_a @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: a,E: a] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_linorder__wlog) ).
thf(351,plain,
! [A: a > a > $o,B: a,C: a] :
( ! [D: a,E: a] :
( ( ord_less_eq_a @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: a,E: a] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(62,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_order__refl) ).
thf(390,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1,conjecture,
in_tree_a @ v @ ( t_a @ v3 @ ( t_a @ v1 @ l1 @ r1 ) @ ( t_a @ v2 @ l2 @ r2 ) ),
file('/export/starexec/sandbox/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(114,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(19,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_ex__in__conv) ).
thf(171,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_verit__sum__simplify) ).
thf(207,plain,
! [A: multiset_a] :
( ( plus_plus_multiset_a @ A @ zero_zero_multiset_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(101,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_left_Osimps) ).
thf(536,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(40,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
| ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_linear) ).
thf(287,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
| ( ord_less_eq_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_all__not__in__conv) ).
thf(168,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [A: multiset_a] :
( ( ( set_mset_a @ A )
= bot_bot_set_a )
= ( A = zero_zero_multiset_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_set__mset__eq__empty__iff) ).
thf(190,plain,
! [A: multiset_a] :
( ( ( set_mset_a @ A )
= bot_bot_set_a )
= ( A = zero_zero_multiset_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(28,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( ord_less_eq_a @ D @ B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( ord_less_eq_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_GreatestI2__order) ).
thf(210,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( ord_less_eq_a @ D @ B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( ord_less_eq_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(45,axiom,
! [A: a,B: tree_a] :
( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ B ) ) )
=> ( ( is_heap_a @ B )
=> ( ord_less_eq_a @ A @ ( val_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_heap__top__geq) ).
thf(326,plain,
! [A: a,B: tree_a] :
( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ B ) ) )
=> ( ( is_heap_a @ B )
=> ( ord_less_eq_a @ A @ ( val_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(50,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( A = B )
& ( ord_le1199012836iset_a @ C @ D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_add__mono__thms__linordered__semiring_I2_J) ).
thf(341,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( A = B )
& ( ord_le1199012836iset_a @ C @ D ) )
=> ( ord_le1199012836iset_a @ ( plus_plus_multiset_a @ A @ C ) @ ( plus_plus_multiset_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(34,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_order_Otrans) ).
thf(268,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(54,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ B @ A )
& ( ord_less_eq_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_dual__order_Oeq__iff) ).
thf(358,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ B @ A )
& ( ord_less_eq_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(67,axiom,
( ball_a
= ( ^ [A: set_a,B: a > $o] :
! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Ball__def) ).
thf(400,plain,
( ball_a
= ( ^ [A: set_a,B: a > $o] :
! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(64,axiom,
is_heap_a @ e_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_is__heap_Osimps_I1_J) ).
thf(395,plain,
is_heap_a @ e_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(74,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_antisym) ).
thf(427,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(37,axiom,
! [A: a,B: a > a,C: a,D: a] :
( ( ord_less_eq_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_order__subst1) ).
thf(277,plain,
! [A: a,B: a > a,C: a,D: a] :
( ( ord_less_eq_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ! [E: a,F: a] :
( ( ord_less_eq_a @ E @ F )
=> ( ord_less_eq_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(78,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ e_a ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_is__heap_Osimps_I4_J) ).
thf(442,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( is_heap_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ e_a ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ B @ C @ D ) ) @ A )
& ( is_heap_a @ ( t_a @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(742,plain,
$false,
inference(e,[status(thm)],[587,122,479,518,408,115,308,120,379,385,500,153,174,185,417,257,559,421,284,289,448,164,179,485,514,348,147,396,133,243,527,452,248,439,534,334,598,392,424,275,137,317,188,388,328,124,193,547,266,360,398,558,530,430,573,601,562,402,445,382,159,604,419,377,434,271,362,451,477,494,345,140,130,455,306,226,473,490,487,458,282,150,182,331,127,336,595,143,497,450,556,539,482,351,390,114,171,207,536,287,168,190,210,326,341,268,358,400,395,427,277,442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP067^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n005.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 19:46:00 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.06/1.19 % [INFO] Parsing done (383ms).
% 2.38/1.20 % [INFO] Running in sequential loop mode.
% 3.19/1.59 % [INFO] eprover registered as external prover.
% 3.43/1.60 % [INFO] Scanning for conjecture ...
% 3.64/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 168 axioms. Running axiom selection ...
% 3.84/1.86 % [INFO] Axiom selection finished. Selected 111 axioms (removed 57 axioms).
% 4.53/2.07 % [INFO] Problem is higher-order (TPTP THF).
% 4.53/2.09 % [INFO] Type checking passed.
% 4.53/2.10 % [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 ...
% 16.64/4.94 % External prover 'e' found a proof!
% 16.64/4.94 % [INFO] Killing All external provers ...
% 16.64/4.94 % Time passed: 4587ms (effective reasoning time: 3732ms)
% 16.64/4.94 % 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)>
% 16.64/4.94 % Axioms used in derivation (111): fact_35_is__heap_Osimps_I4_J, fact_166_set__mset__single, fact_157_insertE, fact_13_Tree_Oset__intros_I3_J, fact_138_singletonI, fact_28_siftDown_Osimps_I2_J, fact_20_Tree_Opred__cong, fact_54_dual__order_Otrans, fact_156_insertI1, fact_17_siftDown_Osimps_I4_J, fact_159_singleton__iff, fact_148_add__mono__thms__linordered__semiring_I2_J, fact_76_linear, fact_143_verit__sum__simplify, fact_117_Ball__def, fact_46_Tree_Opred__mono, fact_61_order__class_Oorder_Oantisym, fact_59_order__trans, fact_131_set__mset__empty, fact_130_set__mset__eq__empty__iff, fact_73_le__cases, fact_121_heap__top__geq, fact_75_eq__refl, fact_103_verit__la__disequality, fact_4_Tree_Oinject, fact_52_dual__order_Oeq__iff, fact_158_singletonD, fact_70_le__cases3, fact_92_order__subst2, fact_147_add__mono__thms__linordered__semiring_I1_J, fact_152_insert__absorb, fact_104_Tree_Osimps_I14_J, fact_1__092_060open_062in__tree_Av_A_IsiftDown_At_J_092_060close_062, fact_25_Tree_Oexhaust, fact_3__C5__1_Oprems_C, fact_154_Set_Oset__insert, fact_32_Tree_Oset__intros_I2_J, fact_135_multiset_Osimps_I2_J, fact_22_siftDown__in__tree, fact_65_ord__eq__le__trans, fact_30_Tree_Oset__cases, fact_72_order_Otrans, fact_67_order__class_Oorder_Oeq__iff, fact_12_in__tree_Osimps_I1_J, fact_98_Greatest__equality, fact_31_Tree_Oset__intros_I1_J, fact_119_ball__reg, fact_21_Tree_Opred__mono__strong, fact_115_equals0D, fact_6__C5__1_Ohyps_C_I2_J, fact_113_ex__in__conv, fact_120_bot__empty__eq, fact_11_Tree_Opred__inject_I2_J, fact_14_Tree_Opred__inject_I1_J, fact_122_heap__top__max, fact_100_GreatestI2__order, fact_48_is__heap_Osimps_I2_J, fact_15_siftDown_Osimps_I6_J, fact_24_is__heap_Ocases, fact_124_is__singletonI_H, fact_23_siftDown__Node, fact_78_antisym, fact_43_Collect__mem__eq, fact_133_multiset__induct__min, fact_84_ord__le__eq__subst, fact_27_Tree_Odistinct_I1_J, fact_151_insert__eq__iff, fact_146_add__mono, fact_145_add__left__mono, fact_10_siftDown_Ocases, fact_2_True, fact_150_mk__disjoint__insert, fact_55_linorder__wlog, fact_114_equals0I, fact_37_is__heap__max, fact_80_eq__iff, fact_88_ord__eq__le__subst, fact_26_Tree_Oinduct, fact_36_is__heap_Osimps_I3_J, fact_9_right_Osimps, fact_34_order__refl, fact_69_antisym__conv, fact_105_Tree_Opred__set, fact_116_emptyE, fact_57_dual__order_Orefl, fact_39_is__heap_Osimps_I5_J, fact_96_order__subst1, fact_38_is__heap_Osimps_I6_J, fact_149_add__mono__thms__linordered__semiring_I3_J, fact_50_dual__order_Oantisym, fact_106_empty__iff, fact_136_insert__iff, fact_132_multiset__induct__max, fact_153_insert__ident, fact_107_all__not__in__conv, fact_155_insertI2, fact_123_multiset_Osimps_I1_J, fact_0_False, fact_7__C5__1_Ohyps_C_I1_J, fact_18_siftDown_Osimps_I3_J, fact_137_insertCI, fact_16_siftDown_Osimps_I5_J, fact_8_left_Osimps, fact_144_add__right__mono, fact_42_mem__Collect__eq, fact_63_ord__le__eq__trans, fact_167_Max__singleton, fact_47_is__heap_Osimps_I1_J, fact_29_val_Osimps, fact_19_siftDown_Osimps_I1_J, fact_5_in__tree_Osimps_I2_J
% 16.64/4.94 % No. of inferences in proof: 226
% 16.64/4.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4587 ms resp. 3732 ms w/o parsing
% 17.32/5.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.32/5.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------