TSTP Solution File: ITP071^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP071^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:35 EDT 2024
% Result : Theorem 20.43s 6.23s
% Output : Refutation 21.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 457
% Syntax : Number of formulae : 798 ( 425 unt; 118 typ; 0 def)
% Number of atoms : 1437 ( 834 equ; 10 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 6571 ( 188 ~; 7 |; 102 &;5642 @)
% ( 0 <=>; 632 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 1325 (1325 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 107 usr; 7 con; 0-6 aty)
% Number of variables : 2333 ( 306 ^2005 !; 22 ?;2333 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc1689254567Tree_a_type,type,
produc1689254567Tree_a: $tType ).
thf(set_Pr1070816379Tree_a_type,type,
set_Pr1070816379Tree_a: $tType ).
thf(set_Pr921883667ee_a_a_type,type,
set_Pr921883667ee_a_a: $tType ).
thf(produc143150363Tree_a_type,type,
produc143150363Tree_a: $tType ).
thf(produc981471411ee_a_a_type,type,
produc981471411ee_a_a: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(multiset_a_type,type,
multiset_a: $tType ).
thf(list_a_type,type,
list_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(bNF_cs1091007358Tree_a_type,type,
bNF_cs1091007358Tree_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > tree_a ) > ( produc1689254567Tree_a > tree_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > ( produc143150363Tree_a > produc1689254567Tree_a ) > $o ).
thf(bNF_cs739966834Tree_a_type,type,
bNF_cs739966834Tree_a: set_Pr1070816379Tree_a > ( product_prod_a_a > a ) > ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > product_prod_a_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > $o ).
thf(bNF_cs1095035134ee_a_a_type,type,
bNF_cs1095035134ee_a_a: set_Product_prod_a_a > ( produc143150363Tree_a > tree_a ) > ( produc981471411ee_a_a > tree_a ) > ( product_prod_a_a > produc143150363Tree_a ) > ( product_prod_a_a > produc981471411ee_a_a ) > $o ).
thf(bNF_fstOp_Tree_a_a_a_type,type,
bNF_fstOp_Tree_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(bNF_fs1579355852Tree_a_type,type,
bNF_fs1579355852Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(bNF_fstOp_a_Tree_a_a_type,type,
bNF_fstOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc143150363Tree_a ).
thf(bNF_fstOp_a_a_Tree_a_type,type,
bNF_fstOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > product_prod_a_a ).
thf(bNF_pi1059296282ee_a_a_type,type,
bNF_pi1059296282ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > tree_a > a > tree_a ).
thf(bNF_pi1407460238_a_a_a_type,type,
bNF_pi1407460238_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > tree_a > a > a ).
thf(bNF_pi1536086554Tree_a_type,type,
bNF_pi1536086554Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > tree_a ).
thf(bNF_pi207687054Tree_a_type,type,
bNF_pi207687054Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > a ).
thf(bNF_sn210385162ee_a_a_type,type,
bNF_sn210385162ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(bNF_sn687175434Tree_a_type,type,
bNF_sn687175434Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc1689254567Tree_a ).
thf(bNF_sndOp_a_Tree_a_a_type,type,
bNF_sndOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc981471411ee_a_a ).
thf(bNF_sndOp_a_a_Tree_a_type,type,
bNF_sndOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(bNF_Gr2005589581ee_a_a_type,type,
bNF_Gr2005589581ee_a_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > tree_a ) > ( produc143150363Tree_a > a ) > set_Pr921883667ee_a_a ).
thf(bNF_Gr2042500789Tree_a_type,type,
bNF_Gr2042500789Tree_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > tree_a ) > set_Pr1070816379Tree_a ).
thf(bNF_Gr614734384ee_a_a_type,type,
bNF_Gr614734384ee_a_a: set_a > ( a > tree_a ) > ( a > a ) > set_Pr921883667ee_a_a ).
thf(bNF_Gr651645592Tree_a_type,type,
bNF_Gr651645592Tree_a: set_a > ( a > a ) > ( a > tree_a ) > set_Pr1070816379Tree_a ).
thf(comp_T59512783Tree_a_type,type,
comp_T59512783Tree_a: ( tree_a > tree_a ) > ( tree_a > tree_a ) > tree_a > tree_a ).
thf(comp_T236170232Tree_a_type,type,
comp_T236170232Tree_a: ( tree_a > tree_a ) > ( produc143150363Tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(comp_P228269369Tree_a_type,type,
comp_P228269369Tree_a: ( produc981471411ee_a_a > tree_a ) > ( produc143150363Tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > tree_a ).
thf(comp_P342079405Tree_a_type,type,
comp_P342079405Tree_a: ( produc981471411ee_a_a > a ) > ( produc143150363Tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > a ).
thf(comp_P1663859001ee_a_a_type,type,
comp_P1663859001ee_a_a: ( produc143150363Tree_a > tree_a ) > ( produc981471411ee_a_a > produc143150363Tree_a ) > produc981471411ee_a_a > tree_a ).
thf(comp_P825537953Tree_a_type,type,
comp_P825537953Tree_a: ( produc143150363Tree_a > tree_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > produc143150363Tree_a > tree_a ).
thf(comp_P1103783853ee_a_a_type,type,
comp_P1103783853ee_a_a: ( produc143150363Tree_a > a ) > ( produc981471411ee_a_a > produc143150363Tree_a ) > produc981471411ee_a_a > a ).
thf(comp_P265462805Tree_a_type,type,
comp_P265462805Tree_a: ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > produc143150363Tree_a > a ).
thf(comp_a608639864Tree_a_type,type,
comp_a608639864Tree_a: ( a > a ) > ( produc143150363Tree_a > a ) > produc143150363Tree_a > a ).
thf(heapIm970322378pify_a_type,type,
heapIm970322378pify_a: tree_a > tree_a ).
thf(heapIm229596386mpty_a_type,type,
heapIm229596386mpty_a: tree_a > $o ).
thf(heapIm915766629_max_a_type,type,
heapIm915766629_max_a: tree_a > produc143150363Tree_a ).
thf(heapIm1140443833left_a_type,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(heapIm837449470Leaf_a_type,type,
heapIm837449470Leaf_a: tree_a > produc143150363Tree_a ).
thf(heapIm1257206334ight_a_type,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(heapIm1091024090Down_a_type,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(heap_Tree_a_a_type,type,
heap_Tree_a_a: tree_a > ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > tree_a ) > ( tree_a > produc143150363Tree_a ) > $o ).
thf(heap_axioms_Tree_a_a_type,type,
heap_axioms_Tree_a_a: ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > tree_a ) > ( tree_a > produc143150363Tree_a ) > $o ).
thf(e_a_type,type,
e_a: tree_a ).
thf(t_a_type,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(in_tree_a_type,type,
in_tree_a: a > tree_a > $o ).
thf(is_heap_a_type,type,
is_heap_a: tree_a > $o ).
thf(multiset_a2_type,type,
multiset_a2: tree_a > multiset_a ).
thf(val_a_type,type,
val_a: tree_a > a ).
thf(if_Pro1144176865Tree_a_type,type,
if_Pro1144176865Tree_a: $o > produc143150363Tree_a > produc143150363Tree_a > produc143150363Tree_a ).
thf(lattic146396397_Max_a_type,type,
lattic146396397_Max_a: set_a > a ).
thf(add_mset_a_type,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(set_mset_a_type,type,
set_mset_a: multiset_a > set_a ).
thf(ord_le1327026842ee_a_o_type,type,
ord_le1327026842ee_a_o: ( a > tree_a > $o ) > ( a > tree_a > $o ) > $o ).
thf(ord_le1013007387Tree_a_type,type,
ord_le1013007387Tree_a: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > $o ).
thf(ord_less_eq_a_type,type,
ord_less_eq_a: a > a > $o ).
thf(order_Greatest_a_type,type,
order_Greatest_a: ( a > $o ) > a ).
thf(produc649172771ee_a_a_type,type,
produc649172771ee_a_a: tree_a > a > produc981471411ee_a_a ).
thf(produc686083979Tree_a_type,type,
produc686083979Tree_a: a > tree_a > produc143150363Tree_a ).
thf(produc569472578ee_a_a_type,type,
produc569472578ee_a_a: ( tree_a > tree_a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(produc606383786Tree_a_type,type,
produc606383786Tree_a: ( tree_a > a ) > produc1689254567Tree_a > produc143150363Tree_a ).
thf(produc159857078_a_a_a_type,type,
produc159857078_a_a_a: ( tree_a > a ) > produc981471411ee_a_a > product_prod_a_a ).
thf(produc1046262850Tree_a_type,type,
produc1046262850Tree_a: ( a > tree_a ) > produc143150363Tree_a > produc1689254567Tree_a ).
thf(produc1070656334ee_a_a_type,type,
produc1070656334ee_a_a: ( a > tree_a ) > product_prod_a_a > produc981471411ee_a_a ).
thf(produc1107567542Tree_a_type,type,
produc1107567542Tree_a: ( a > a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(produc819961216ee_a_a_type,type,
produc819961216ee_a_a: ( tree_a > tree_a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(produc856872424Tree_a_type,type,
produc856872424Tree_a: ( tree_a > a ) > produc1689254567Tree_a > produc981471411ee_a_a ).
thf(produc21534708_a_a_a_type,type,
produc21534708_a_a_a: ( tree_a > a ) > produc143150363Tree_a > product_prod_a_a ).
thf(produc1296751488Tree_a_type,type,
produc1296751488Tree_a: ( a > tree_a ) > produc981471411ee_a_a > produc1689254567Tree_a ).
thf(produc932333964ee_a_a_type,type,
produc932333964ee_a_a: ( a > tree_a ) > product_prod_a_a > produc143150363Tree_a ).
thf(produc969245172Tree_a_type,type,
produc969245172Tree_a: ( a > a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(produc1205515265_a_a_o_type,type,
produc1205515265_a_a_o: ( produc981471411ee_a_a > $o ) > tree_a > a > $o ).
thf(produc1808426884Tree_a_type,type,
produc1808426884Tree_a: ( produc981471411ee_a_a > produc143150363Tree_a ) > tree_a > a > produc143150363Tree_a ).
thf(produc1291432345ee_a_o_type,type,
produc1291432345ee_a_o: ( produc143150363Tree_a > $o ) > a > tree_a > $o ).
thf(produc740705523Tree_a_type,type,
produc740705523Tree_a: ( produc143150363Tree_a > tree_a ) > a > tree_a > tree_a ).
thf(produc623433908ee_a_a_type,type,
produc623433908ee_a_a: ( produc143150363Tree_a > produc981471411ee_a_a ) > a > tree_a > produc981471411ee_a_a ).
thf(produc126329485Tree_a_type,type,
produc126329485Tree_a: ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > produc143150363Tree_a ).
thf(produc1405823650ee_a_o_type,type,
produc1405823650ee_a_o: ( a > tree_a > $o ) > produc143150363Tree_a > $o ).
thf(produc534868220Tree_a_type,type,
produc534868220Tree_a: ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(produc1088820157ee_a_a_type,type,
produc1088820157ee_a_a: ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > produc981471411ee_a_a ).
thf(produc1587316832_a_a_o_type,type,
produc1587316832_a_a_o: ( tree_a > a > $o ) > produc981471411ee_a_a > $o ).
thf(produc433477818Tree_a_type,type,
produc433477818Tree_a: ( tree_a > a > tree_a ) > produc981471411ee_a_a > tree_a ).
thf(produc1207340411ee_a_a_type,type,
produc1207340411ee_a_a: ( tree_a > a > produc981471411ee_a_a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(produc369019363Tree_a_type,type,
produc369019363Tree_a: ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > produc143150363Tree_a ).
thf(produc951236931Tree_a_type,type,
produc951236931Tree_a: ( tree_a > a > set_Pr1070816379Tree_a ) > produc981471411ee_a_a > set_Pr1070816379Tree_a ).
thf(produc136688934_set_a_type,type,
produc136688934_set_a: ( tree_a > a > set_a ) > produc981471411ee_a_a > set_a ).
thf(produc1673233912ee_a_o_type,type,
produc1673233912ee_a_o: ( a > tree_a > $o ) > produc143150363Tree_a > $o ).
thf(produc873356882Tree_a_type,type,
produc873356882Tree_a: ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(produc1331510035ee_a_a_type,type,
produc1331510035ee_a_a: ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > produc981471411ee_a_a ).
thf(produc493188987Tree_a_type,type,
produc493188987Tree_a: ( a > tree_a > produc143150363Tree_a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(produc802621147Tree_a_type,type,
produc802621147Tree_a: ( a > tree_a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > set_Pr1070816379Tree_a ).
thf(produc1902270_set_a_type,type,
produc1902270_set_a: ( a > tree_a > set_a ) > produc143150363Tree_a > set_a ).
thf(produc950721886ee_a_a_type,type,
produc950721886ee_a_a: ( a > tree_a > a ) > produc143150363Tree_a > a ).
thf(produc1206152067Tree_a_type,type,
produc1206152067Tree_a: produc1689254567Tree_a > tree_a ).
thf(product_fst_Tree_a_a_type,type,
product_fst_Tree_a_a: produc981471411ee_a_a > tree_a ).
thf(product_fst_a_Tree_a_type,type,
product_fst_a_Tree_a: produc143150363Tree_a > a ).
thf(product_snd_Tree_a_a_type,type,
product_snd_Tree_a_a: produc981471411ee_a_a > a ).
thf(product_snd_a_Tree_a_type,type,
product_snd_a_Tree_a: produc143150363Tree_a > tree_a ).
thf(product_snd_a_a_type,type,
product_snd_a_a: product_prod_a_a > a ).
thf(produc1478296771ee_a_a_type,type,
produc1478296771ee_a_a: produc981471411ee_a_a > produc143150363Tree_a ).
thf(produc1515207979Tree_a_type,type,
produc1515207979Tree_a: produc143150363Tree_a > produc981471411ee_a_a ).
thf(relcom439193229Tree_a_type,type,
relcom439193229Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > $o ).
thf(relcompp_a_a_Tree_a_type,type,
relcompp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > $o ).
thf(collec1324690334ee_a_a_type,type,
collec1324690334ee_a_a: ( produc981471411ee_a_a > $o ) > set_Pr921883667ee_a_a ).
thf(collec486369286Tree_a_type,type,
collec486369286Tree_a: ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a ).
thf(collec645855634od_a_a_type,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(member1092636252ee_a_a_type,type,
member1092636252ee_a_a: produc981471411ee_a_a > set_Pr921883667ee_a_a > $o ).
thf(member254315204Tree_a_type,type,
member254315204Tree_a: produc143150363Tree_a > set_Pr1070816379Tree_a > $o ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(t_type,type,
t: tree_a ).
thf(v_type,type,
v: a ).
thf(172,axiom,
! [A: a > tree_a > $o,B: a > tree_a > $o] :
( ( ord_le1327026842ee_a_o @ A @ B )
=> ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ A ) ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_Collect__case__prod__mono) ).
thf(892,plain,
! [A: a > tree_a > $o,B: a > tree_a > $o] :
( ( ord_le1327026842ee_a_o @ A @ B )
=> ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ A ) ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',fact_97_siftDown__Node) ).
thf(1411,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)],[314]) ).
thf(5,axiom,
! [A: a > tree_a > $o,B: produc981471411ee_a_a] :
( ( A @ ( product_snd_Tree_a_a @ B ) @ ( product_fst_Tree_a_a @ B ) )
=> ~ ! [C: tree_a,D: a] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_exE__realizer_H) ).
thf(347,plain,
! [A: a > tree_a > $o,B: produc981471411ee_a_a] :
( ( A @ ( product_snd_Tree_a_a @ B ) @ ( product_fst_Tree_a_a @ B ) )
=> ~ ! [C: tree_a,D: a] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(257,axiom,
( produc1331510035ee_a_a
= ( ^ [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_prod_Ocase__eq__if) ).
thf(1237,plain,
( produc1331510035ee_a_a
= ( ^ [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(90,axiom,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( A @ B @ C )
=> ( produc1673233912ee_a_o @ A @ ( produc686083979Tree_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_case__prodI) ).
thf(628,plain,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( A @ B @ C )
=> ( produc1673233912ee_a_o @ A @ ( produc686083979Tree_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(192,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( ( add_mset_a @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_Heap_Oremove__max__multiset_H) ).
thf(962,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( ( add_mset_a @ H @ ( D @ I ) )
= ( D @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(186,axiom,
! [A: produc981471411ee_a_a > $o,B: tree_a,C: a] :
( ( produc1205515265_a_a_o @ A @ B @ C )
=> ( A @ ( produc649172771ee_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_curryE) ).
thf(941,plain,
! [A: produc981471411ee_a_a > $o,B: tree_a,C: a] :
( ( produc1205515265_a_a_o @ A @ B @ C )
=> ( A @ ( produc649172771ee_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(228,axiom,
( in_tree_a
= ( ^ [A: a,B: tree_a] : ( in_tree_a @ A @ ( heapIm1091024090Down_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_siftDown__in__tree__set) ).
thf(1110,plain,
( in_tree_a
= ( ^ [A: a,B: tree_a] : ( in_tree_a @ A @ ( heapIm1091024090Down_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(49,axiom,
! [A: set_Pr1070816379Tree_a] :
( ( collec486369286Tree_a
@ ^ [B: produc143150363Tree_a] : ( member254315204Tree_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Collect__mem__eq) ).
thf(481,plain,
! [A: set_Pr1070816379Tree_a] :
( ( collec486369286Tree_a
@ ^ [B: produc143150363Tree_a] : ( member254315204Tree_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(134,axiom,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( produc1673233912ee_a_o @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_case__prod__conv) ).
thf(777,plain,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( produc1673233912ee_a_o @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(70,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_antisym__conv) ).
thf(555,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)],[70]) ).
thf(62,axiom,
! [A: tree_a > tree_a] :
( ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( produc819961216ee_a_a @ A ) )
= product_fst_a_Tree_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_fst__comp__apsnd) ).
thf(523,plain,
! [A: tree_a > tree_a] :
( ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( produc819961216ee_a_a @ A ) )
= product_fst_a_Tree_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(312,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ e_a ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ e_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_removeLeaf_Osimps_I2_J) ).
thf(1406,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ e_a ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ e_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(104,axiom,
! [A: produc143150363Tree_a,B: a > tree_a > $o] :
( ! [C: a,D: tree_a] :
( ( A
= ( produc686083979Tree_a @ C @ D ) )
=> ( B @ C @ D ) )
=> ( produc1673233912ee_a_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_case__prodI2) ).
thf(683,plain,
! [A: produc143150363Tree_a,B: a > tree_a > $o] :
( ! [C: a,D: tree_a] :
( ( A
= ( produc686083979Tree_a @ C @ D ) )
=> ( B @ C @ D ) )
=> ( produc1673233912ee_a_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(276,axiom,
! [A: tree_a > a > $o,B: produc143150363Tree_a,C: produc981471411ee_a_a > $o,D: a > tree_a > produc981471411ee_a_a] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ( ! [E: a,F: tree_a] :
( ( A @ F @ E )
=> ( C @ ( D @ E @ F ) ) )
=> ( C @ ( produc1331510035ee_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_exE__realizer) ).
thf(1290,plain,
! [A: tree_a > a > $o,B: produc143150363Tree_a,C: produc981471411ee_a_a > $o,D: a > tree_a > produc981471411ee_a_a] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ( ! [E: a,F: tree_a] :
( ( A @ F @ E )
=> ( C @ ( D @ E @ F ) ) )
=> ( C @ ( produc1331510035ee_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(217,axiom,
! [A: produc981471411ee_a_a > $o,B: produc981471411ee_a_a] :
( ! [C: tree_a,D: a] : ( A @ ( produc649172771ee_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_old_Oprod_Oinducts) ).
thf(1068,plain,
! [A: produc981471411ee_a_a > $o,B: produc981471411ee_a_a] :
( ! [C: tree_a,D: a] : ( A @ ( produc649172771ee_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(334,axiom,
! [A: a,B: tree_a,C: tree_a] :
( e_a
!= ( t_a @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Tree_Odistinct_I1_J) ).
thf(1522,plain,
! [A: a,B: tree_a,C: tree_a] :
( e_a
!= ( t_a @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(316,axiom,
! [A: produc143150363Tree_a] :
( ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_prod_Ocollapse) ).
thf(1422,plain,
! [A: produc143150363Tree_a] :
( ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(340,axiom,
! [A: produc143150363Tree_a] :
( A
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_surjective__pairing) ).
thf(1544,plain,
! [A: produc143150363Tree_a] :
( A
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(41,axiom,
! [A: produc143150363Tree_a,B: a > tree_a > set_Pr1070816379Tree_a,C: a,D: tree_a] :
( ( member254315204Tree_a @ A @ ( B @ C @ D ) )
=> ( member254315204Tree_a @ A @ ( produc802621147Tree_a @ B @ ( produc686083979Tree_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_mem__case__prodI) ).
thf(449,plain,
! [A: produc143150363Tree_a,B: a > tree_a > set_Pr1070816379Tree_a,C: a,D: tree_a] :
( ( member254315204Tree_a @ A @ ( B @ C @ D ) )
=> ( member254315204Tree_a @ A @ ( produc802621147Tree_a @ B @ ( produc686083979Tree_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',fact_100_is__heap_Osimps_I5_J) ).
thf(1142,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)],[239]) ).
thf(58,axiom,
! [A: produc143150363Tree_a > produc981471411ee_a_a] :
( ( produc1331510035ee_a_a
@ ^ [B: a,C: tree_a] : ( A @ ( produc686083979Tree_a @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_case__prod__eta) ).
thf(511,plain,
! [A: produc143150363Tree_a > produc981471411ee_a_a] :
( ( produc1331510035ee_a_a
@ ^ [B: a,C: tree_a] : ( A @ ( produc686083979Tree_a @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(337,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( val_a @ ( t_a @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_val_Osimps) ).
thf(1533,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)],[337]) ).
thf(82,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_order__class_Oorder_Oantisym) ).
thf(597,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)],[82]) ).
thf(162,axiom,
! [A: a,B: tree_a > a > set_a,C: produc981471411ee_a_a] :
( ( member_a @ A @ ( produc136688934_set_a @ B @ C ) )
=> ~ ! [D: tree_a,E: a] :
( ( C
= ( produc649172771ee_a_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_mem__case__prodE) ).
thf(861,plain,
! [A: a,B: tree_a > a > set_a,C: produc981471411ee_a_a] :
( ( member_a @ A @ ( produc136688934_set_a @ B @ C ) )
=> ~ ! [D: tree_a,E: a] :
( ( C
= ( produc649172771ee_a_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(220,axiom,
! [A: produc981471411ee_a_a > produc143150363Tree_a] :
( ( produc369019363Tree_a
@ ^ [B: tree_a,C: a] : ( A @ ( produc649172771ee_a_a @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_case__prod__eta) ).
thf(1078,plain,
! [A: produc981471411ee_a_a > produc143150363Tree_a] :
( ( produc369019363Tree_a
@ ^ [B: tree_a,C: a] : ( A @ ( produc649172771ee_a_a @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(18,axiom,
! [A: set_Pr1070816379Tree_a,B: produc143150363Tree_a > $o,C: produc143150363Tree_a > $o] :
( ( ord_le1013007387Tree_a @ A
@ ( collec486369286Tree_a
@ ^ [D: produc143150363Tree_a] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le1013007387Tree_a @ A @ ( collec486369286Tree_a @ B ) )
& ( ord_le1013007387Tree_a @ A @ ( collec486369286Tree_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_conj__subset__def) ).
thf(384,plain,
! [A: set_Pr1070816379Tree_a,B: produc143150363Tree_a > $o,C: produc143150363Tree_a > $o] :
( ( ord_le1013007387Tree_a @ A
@ ( collec486369286Tree_a
@ ^ [D: produc143150363Tree_a] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le1013007387Tree_a @ A @ ( collec486369286Tree_a @ B ) )
& ( ord_le1013007387Tree_a @ A @ ( collec486369286Tree_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(237,axiom,
( produc873356882Tree_a
= ( ^ [A: a > tree_a > tree_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_case__prod__unfold) ).
thf(1137,plain,
( produc873356882Tree_a
= ( ^ [A: a > tree_a > tree_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',fact_182_Greatest__equality) ).
thf(550,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)],[69]) ).
thf(140,axiom,
! [A: tree_a > tree_a,B: tree_a,C: a] :
( ( produc569472578ee_a_a @ A @ ( produc649172771ee_a_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_apfst__conv) ).
thf(797,plain,
! [A: tree_a > tree_a,B: tree_a,C: a] :
( ( produc569472578ee_a_a @ A @ ( produc649172771ee_a_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(269,axiom,
( produc873356882Tree_a
= ( ^ [A: a > tree_a > tree_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_prod_Ocase__eq__if) ).
thf(1260,plain,
( produc873356882Tree_a
= ( ^ [A: a > tree_a > tree_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(178,axiom,
! [A: tree_a > a > produc143150363Tree_a] :
( ( produc1808426884Tree_a @ ( produc369019363Tree_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_curry__case__prod) ).
thf(913,plain,
! [A: tree_a > a > produc143150363Tree_a] :
( ( produc1808426884Tree_a @ ( produc369019363Tree_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(215,axiom,
! [A: a,B: tree_a > a > set_a,C: tree_a,D: a] :
( ( member_a @ A @ ( B @ C @ D ) )
=> ( member_a @ A @ ( produc136688934_set_a @ B @ ( produc649172771ee_a_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_mem__case__prodI) ).
thf(1063,plain,
! [A: a,B: tree_a > a > set_a,C: tree_a,D: a] :
( ( member_a @ A @ ( B @ C @ D ) )
=> ( member_a @ A @ ( produc136688934_set_a @ B @ ( produc649172771ee_a_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(201,axiom,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
( ! [C: a,D: tree_a] :
( ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ A )
=> ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ B ) )
=> ( ord_le1013007387Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_subrelI) ).
thf(1001,plain,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
( ! [C: a,D: tree_a] :
( ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ A )
=> ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ B ) )
=> ( ord_le1013007387Tree_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(112,axiom,
! [A: a,B: a > tree_a > set_a,C: a,D: tree_a] :
( ( member_a @ A @ ( B @ C @ D ) )
=> ( member_a @ A @ ( produc1902270_set_a @ B @ ( produc686083979Tree_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_mem__case__prodI) ).
thf(709,plain,
! [A: a,B: a > tree_a > set_a,C: a,D: tree_a] :
( ( member_a @ A @ ( B @ C @ D ) )
=> ( member_a @ A @ ( produc1902270_set_a @ B @ ( produc686083979Tree_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(295,axiom,
! [A: tree_a > a > $o,B: tree_a,C: a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ C @ B ) ) @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_exI__realizer) ).
thf(1359,plain,
! [A: tree_a > a > $o,B: tree_a,C: a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ C @ B ) ) @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(298,axiom,
( produc1673233912ee_a_o
= ( ^ [A: a > tree_a > $o,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_case__prod__unfold) ).
thf(1366,plain,
( produc1673233912ee_a_o
= ( ^ [A: a > tree_a > $o,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(336,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ~ ! [B: a,C: tree_a,D: tree_a] :
( A
!= ( t_a @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Tree_Oexhaust) ).
thf(1529,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)],[336]) ).
thf(36,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
| ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_linear) ).
thf(436,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)],[36]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',fact_106_siftDown_Osimps_I6_J) ).
thf(1482,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)],[330]) ).
thf(97,axiom,
! [A: produc143150363Tree_a > $o] :
( ( produc1673233912ee_a_o @ ( produc1291432345ee_a_o @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_case__prod__curry) ).
thf(651,plain,
! [A: produc143150363Tree_a > $o] :
( ( produc1673233912ee_a_o @ ( produc1291432345ee_a_o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(224,axiom,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a] :
( ! [C: a,D: tree_a] : ( A @ ( produc686083979Tree_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_prod__cases) ).
thf(1095,plain,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a] :
( ! [C: a,D: tree_a] : ( A @ ( produc686083979Tree_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(25,axiom,
! [A: a,B: produc981471411ee_a_a] :
( ( A
= ( product_snd_Tree_a_a @ B ) )
= ( ? [C: tree_a] :
( B
= ( produc649172771ee_a_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_eq__snd__iff) ).
thf(404,plain,
! [A: a,B: produc981471411ee_a_a] :
( ( A
= ( product_snd_Tree_a_a @ B ) )
= ( ? [C: tree_a] :
( B
= ( produc649172771ee_a_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(313,axiom,
( produc1673233912ee_a_o
= ( ^ [A: a > tree_a > $o,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_case__prod__beta) ).
thf(1409,plain,
( produc1673233912ee_a_o
= ( ^ [A: a > tree_a > $o,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(275,axiom,
! [A: tree_a > $o,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
=> ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_prod_Osplit__sel) ).
thf(1287,plain,
! [A: tree_a > $o,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
=> ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(278,axiom,
( produc1673233912ee_a_o
= ( ^ [A: a > tree_a > $o,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_case__prod__beta_H) ).
thf(1298,plain,
( produc1673233912ee_a_o
= ( ^ [A: a > tree_a > $o,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(288,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ A @ B @ C ) )
= ( heapIm1091024090Down_a @ ( t_a @ A @ ( heapIm970322378pify_a @ B ) @ ( heapIm970322378pify_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_heapify_Osimps_I2_J) ).
thf(1330,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ A @ B @ C ) )
= ( heapIm1091024090Down_a @ ( t_a @ A @ ( heapIm970322378pify_a @ B ) @ ( heapIm970322378pify_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(272,axiom,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_removeLeaf_Osimps_I4_J) ).
thf(1279,plain,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(324,axiom,
! [A: a > $o,B: a,C: tree_a > $o,D: tree_a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ B @ D ) ) )
& ( C @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_conjI__realizer) ).
thf(1455,plain,
! [A: a > $o,B: a,C: tree_a > $o,D: tree_a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ B @ D ) ) )
& ( C @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(184,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( H
= ( val_a @ ( E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_Heap_Oremove__max__val) ).
thf(934,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( H
= ( val_a @ ( E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(287,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/sandbox2/benchmark/theBenchmark.p',fact_105_siftDown_Osimps_I4_J) ).
thf(1323,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)],[287]) ).
thf(87,axiom,
! [A: tree_a] :
( ( multiset_a2 @ ( heapIm970322378pify_a @ A ) )
= ( multiset_a2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_multiset__heapify) ).
thf(619,plain,
! [A: tree_a] :
( ( multiset_a2 @ ( heapIm970322378pify_a @ A ) )
= ( multiset_a2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(154,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ B @ A )
& ( ord_less_eq_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_dual__order_Oeq__iff) ).
thf(838,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)],[154]) ).
thf(146,axiom,
( bNF_fstOp_Tree_a_a_a
= ( ^ [A: tree_a > a > $o,B: a > a > $o,C: produc981471411ee_a_a] : ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ C ) @ ( bNF_pi1407460238_a_a_a @ A @ B @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_fstOp__def) ).
thf(817,plain,
( bNF_fstOp_Tree_a_a_a
= ( ^ [A: tree_a > a > $o,B: a > a > $o,C: produc981471411ee_a_a] : ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ C ) @ ( bNF_pi1407460238_a_a_a @ A @ B @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',fact_113_linorder__wlog) ).
thf(638,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)],[94]) ).
thf(262,axiom,
( product_fst_Tree_a_a
= ( comp_P1663859001ee_a_a @ product_snd_a_Tree_a
@ ( produc369019363Tree_a
@ ^ [A: tree_a,B: a] : ( produc686083979Tree_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_fst__snd__flip) ).
thf(1247,plain,
( product_fst_Tree_a_a
= ( comp_P1663859001ee_a_a @ product_snd_a_Tree_a
@ ( produc369019363Tree_a
@ ^ [A: tree_a,B: a] : ( produc686083979Tree_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(329,axiom,
! [A: a > a] :
( ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( produc1107567542Tree_a @ A ) )
= product_snd_a_Tree_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_snd__comp__apfst) ).
thf(1479,plain,
! [A: a > a] :
( ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( produc1107567542Tree_a @ A ) )
= product_snd_a_Tree_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(29,axiom,
! [A: tree_a > a > $o,B: tree_a,C: a] :
( ( produc1587316832_a_a_o @ A @ ( produc649172771ee_a_a @ B @ C ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_case__prodD) ).
thf(416,plain,
! [A: tree_a > a > $o,B: tree_a,C: a] :
( ( produc1587316832_a_a_o @ A @ ( produc649172771ee_a_a @ B @ C ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(194,axiom,
! [A: produc143150363Tree_a > $o,B: tree_a > a > produc143150363Tree_a,C: produc981471411ee_a_a] :
( ( A @ ( produc369019363Tree_a @ B @ C ) )
= ( ~ ( ( C
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) )
& ~ ( A @ ( B @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_prod_Osplit__sel__asm) ).
thf(969,plain,
! [A: produc143150363Tree_a > $o,B: tree_a > a > produc143150363Tree_a,C: produc981471411ee_a_a] :
( ( A @ ( produc369019363Tree_a @ B @ C ) )
= ( ~ ( ( C
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) )
& ~ ( A @ ( B @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(85,axiom,
! [A: produc143150363Tree_a > $o] :
( ( produc1673233912ee_a_o
@ ^ [B: a,C: tree_a] : ( A @ ( produc686083979Tree_a @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_case__prod__eta) ).
thf(606,plain,
! [A: produc143150363Tree_a > $o] :
( ( produc1673233912ee_a_o
@ ^ [B: a,C: tree_a] : ( A @ ( produc686083979Tree_a @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(47,axiom,
! [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] :
( ( produc493188987Tree_a
@ ^ [C: a,D: tree_a] : ( A @ D @ C )
@ ( produc1478296771ee_a_a @ B ) )
= ( produc369019363Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_case__swap) ).
thf(475,plain,
! [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] :
( ( produc493188987Tree_a
@ ^ [C: a,D: tree_a] : ( A @ D @ C )
@ ( produc1478296771ee_a_a @ B ) )
= ( produc369019363Tree_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(128,axiom,
produc1088820157ee_a_a = produc1331510035ee_a_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_internal__case__prod__def) ).
thf(756,plain,
produc1088820157ee_a_a = produc1331510035ee_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(80,axiom,
! [A: tree_a > tree_a,B: produc981471411ee_a_a] :
( ( product_fst_Tree_a_a @ ( produc569472578ee_a_a @ A @ B ) )
= ( A @ ( product_fst_Tree_a_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_fst__apfst) ).
thf(591,plain,
! [A: tree_a > tree_a,B: produc981471411ee_a_a] :
( ( product_fst_Tree_a_a @ ( produc569472578ee_a_a @ A @ B ) )
= ( A @ ( product_fst_Tree_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(301,axiom,
! [A: tree_a > a,B: a > tree_a,C: produc143150363Tree_a] :
( ( produc856872424Tree_a @ A @ ( produc1046262850Tree_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( B @ ( product_fst_a_Tree_a @ C ) ) @ ( A @ ( product_snd_a_Tree_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_apsnd__apfst) ).
thf(1373,plain,
! [A: tree_a > a,B: a > tree_a,C: produc143150363Tree_a] :
( ( produc856872424Tree_a @ A @ ( produc1046262850Tree_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( B @ ( product_fst_a_Tree_a @ C ) ) @ ( A @ ( product_snd_a_Tree_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(59,axiom,
! [A: a > tree_a > $o] :
( ( produc1291432345ee_a_o @ ( produc1673233912ee_a_o @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_curry__case__prod) ).
thf(514,plain,
! [A: a > tree_a > $o] :
( ( produc1291432345ee_a_o @ ( produc1673233912ee_a_o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(305,axiom,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( is_heap_a @ ( E @ G ) )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( is_heap_a @ ( E @ I ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_Heap_Oremove__max__is__heap) ).
thf(1383,plain,
! [A: tree_a,B: tree_a > $o,C: list_a > tree_a,D: tree_a > multiset_a,E: tree_a > tree_a,F: tree_a > produc143150363Tree_a,G: tree_a,H: a,I: tree_a] :
( ( heap_Tree_a_a @ A @ B @ C @ D @ E @ F )
=> ( ~ ( B @ G )
=> ( ( is_heap_a @ ( E @ G ) )
=> ( ( ( produc686083979Tree_a @ H @ I )
= ( F @ G ) )
=> ( is_heap_a @ ( E @ I ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(148,axiom,
! [A: produc981471411ee_a_a > tree_a,B: produc143150363Tree_a > produc981471411ee_a_a,C: produc143150363Tree_a,D: produc981471411ee_a_a > tree_a,E: produc143150363Tree_a > produc981471411ee_a_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P228269369Tree_a @ A @ B @ C )
= ( comp_P228269369Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_comp__apply__eq) ).
thf(821,plain,
! [A: produc981471411ee_a_a > tree_a,B: produc143150363Tree_a > produc981471411ee_a_a,C: produc143150363Tree_a,D: produc981471411ee_a_a > tree_a,E: produc143150363Tree_a > produc981471411ee_a_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P228269369Tree_a @ A @ B @ C )
= ( comp_P228269369Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(52,axiom,
( product_fst_a_Tree_a
= ( comp_P342079405Tree_a @ product_snd_Tree_a_a
@ ( produc1331510035ee_a_a
@ ^ [A: a,B: tree_a] : ( produc649172771ee_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_fst__snd__flip) ).
thf(492,plain,
( product_fst_a_Tree_a
= ( comp_P342079405Tree_a @ product_snd_Tree_a_a
@ ( produc1331510035ee_a_a
@ ^ [A: a,B: tree_a] : ( produc649172771ee_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',fact_57_in__tree_Osimps_I2_J) ).
thf(1465,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)],[325]) ).
thf(7,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T) ).
thf(353,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(193,axiom,
! [A: a > tree_a > produc981471411ee_a_a] :
( ( produc623433908ee_a_a @ ( produc1331510035ee_a_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_curry__case__prod) ).
thf(966,plain,
! [A: a > tree_a > produc981471411ee_a_a] :
( ( produc623433908ee_a_a @ ( produc1331510035ee_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(198,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( if_Pro1144176865Tree_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T) ).
thf(981,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( if_Pro1144176865Tree_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(105,axiom,
! [A: a > a] :
( ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( produc1107567542Tree_a @ A ) )
= ( comp_a608639864Tree_a @ A @ product_fst_a_Tree_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_fst__comp__apfst) ).
thf(687,plain,
! [A: a > a] :
( ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( produc1107567542Tree_a @ A ) )
= ( comp_a608639864Tree_a @ A @ product_fst_a_Tree_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(167,axiom,
( product_fst_a_Tree_a
= ( produc950721886ee_a_a
@ ^ [A: a,B: tree_a] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_fst__def) ).
thf(877,plain,
( product_fst_a_Tree_a
= ( produc950721886ee_a_a
@ ^ [A: a,B: tree_a] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(121,axiom,
! [A: $o > tree_a,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( produc873356882Tree_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_prod_Ocase__distrib) ).
thf(734,plain,
! [A: $o > tree_a,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( produc873356882Tree_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',fact_129_ord__eq__le__subst) ).
thf(453,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)],[43]) ).
thf(133,axiom,
! [A: produc981471411ee_a_a] :
( ( product_fst_a_Tree_a @ ( produc1478296771ee_a_a @ A ) )
= ( product_snd_Tree_a_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_fst__swap) ).
thf(774,plain,
! [A: produc981471411ee_a_a] :
( ( product_fst_a_Tree_a @ ( produc1478296771ee_a_a @ A ) )
= ( product_snd_Tree_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(335,axiom,
! [A: produc981471411ee_a_a] :
( ( product_snd_a_Tree_a @ ( produc1478296771ee_a_a @ A ) )
= ( product_fst_Tree_a_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_snd__swap) ).
thf(1526,plain,
! [A: produc981471411ee_a_a] :
( ( product_snd_a_Tree_a @ ( produc1478296771ee_a_a @ A ) )
= ( product_fst_Tree_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(292,axiom,
( bNF_sndOp_a_a_Tree_a
= ( ^ [A: a > a > $o,B: a > tree_a > $o,C: produc143150363Tree_a] : ( produc686083979Tree_a @ ( bNF_pi207687054Tree_a @ A @ B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) @ ( product_snd_a_Tree_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_sndOp__def) ).
thf(1351,plain,
( bNF_sndOp_a_a_Tree_a
= ( ^ [A: a > a > $o,B: a > tree_a > $o,C: produc143150363Tree_a] : ( produc686083979Tree_a @ ( bNF_pi207687054Tree_a @ A @ B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) @ ( product_snd_a_Tree_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(100,axiom,
! [A: set_Pr1070816379Tree_a,B: produc143150363Tree_a > $o] :
( ord_le1013007387Tree_a
@ ( collec486369286Tree_a
@ ^ [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Collect__restrict) ).
thf(660,plain,
! [A: set_Pr1070816379Tree_a,B: produc143150363Tree_a > $o] :
( ord_le1013007387Tree_a
@ ( collec486369286Tree_a
@ ^ [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(200,axiom,
! [A: produc981471411ee_a_a] :
( A
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_surjective__pairing) ).
thf(998,plain,
! [A: produc981471411ee_a_a] :
( A
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(260,axiom,
( produc1673233912ee_a_o
= ( ^ [A: a > tree_a > $o,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_prod_Ocase__eq__if) ).
thf(1242,plain,
( produc1673233912ee_a_o
= ( ^ [A: a > tree_a > $o,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(158,axiom,
! [A: produc143150363Tree_a] :
( ( produc493188987Tree_a @ produc686083979Tree_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_case__prod__Pair__iden) ).
thf(849,plain,
! [A: produc143150363Tree_a] :
( ( produc493188987Tree_a @ produc686083979Tree_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(252,axiom,
! [A: tree_a] :
( ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) )
!= e_a )
=> ( ( A != e_a )
=> ( ( val_a @ A )
= ( val_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_removeLeaf__val__val) ).
thf(1206,plain,
! [A: tree_a] :
( ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) )
!= e_a )
=> ( ( A != e_a )
=> ( ( val_a @ A )
= ( val_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(180,axiom,
! [A: $o > produc981471411ee_a_a,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( produc1331510035ee_a_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_prod_Ocase__distrib) ).
thf(920,plain,
! [A: $o > produc981471411ee_a_a,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( produc1331510035ee_a_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(64,axiom,
! [A: produc981471411ee_a_a > $o,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( produc1673233912ee_a_o
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_prod_Ocase__distrib) ).
thf(529,plain,
! [A: produc981471411ee_a_a > $o,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( produc1673233912ee_a_o
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(139,axiom,
! [A: a,B: a > tree_a > set_a,C: produc143150363Tree_a] :
( ( member_a @ A @ ( produc1902270_set_a @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_mem__case__prodE) ).
thf(793,plain,
! [A: a,B: a > tree_a > set_a,C: produc143150363Tree_a] :
( ( member_a @ A @ ( produc1902270_set_a @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(143,axiom,
( product_fst_Tree_a_a
= ( produc433477818Tree_a
@ ^ [A: tree_a,B: a] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_fst__def) ).
thf(810,plain,
( product_fst_Tree_a_a
= ( produc433477818Tree_a
@ ^ [A: tree_a,B: a] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',fact_107_siftDown_Osimps_I5_J) ).
thf(1338,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)],[291]) ).
thf(17,axiom,
! [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
=> ( ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_prod__eqI) ).
thf(381,plain,
! [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
=> ( ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: produc981471411ee_a_a,B: tree_a > a > $o] :
( ! [C: tree_a,D: a] :
( ( A
= ( produc649172771ee_a_a @ C @ D ) )
=> ( B @ C @ D ) )
=> ( produc1587316832_a_a_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_case__prodI2) ).
thf(366,plain,
! [A: produc981471411ee_a_a,B: tree_a > a > $o] :
( ! [C: tree_a,D: a] :
( ( A
= ( produc649172771ee_a_a @ C @ D ) )
=> ( B @ C @ D ) )
=> ( produc1587316832_a_a_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(114,axiom,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
( ( ( ^ [C: a,D: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ A ) )
= ( ^ [C: a,D: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_pred__equals__eq2) ).
thf(714,plain,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
( ( ( ^ [C: a,D: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ A ) )
= ( ^ [C: a,D: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(213,axiom,
! [A: tree_a > tree_a,B: produc143150363Tree_a > tree_a,C: produc143150363Tree_a,D: tree_a > tree_a,E: produc143150363Tree_a > tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_T236170232Tree_a @ A @ B @ C )
= ( comp_T236170232Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_comp__apply__eq) ).
thf(1057,plain,
! [A: tree_a > tree_a,B: produc143150363Tree_a > tree_a,C: produc143150363Tree_a,D: tree_a > tree_a,E: produc143150363Tree_a > tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_T236170232Tree_a @ A @ B @ C )
= ( comp_T236170232Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(243,axiom,
( produc873356882Tree_a
= ( ^ [A: a > tree_a > tree_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_case__prod__beta) ).
thf(1153,plain,
( produc873356882Tree_a
= ( ^ [A: a > tree_a > tree_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(130,axiom,
( produc369019363Tree_a
= ( ^ [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] : ( A @ ( product_fst_Tree_a_a @ B ) @ ( product_snd_Tree_a_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_case__prod__unfold) ).
thf(761,plain,
( produc369019363Tree_a
= ( ^ [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] : ( A @ ( product_fst_Tree_a_a @ B ) @ ( product_snd_Tree_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(306,axiom,
! [A: a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ e_a @ e_a ) )
= ( produc686083979Tree_a @ A @ e_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_removeLeaf_Osimps_I1_J) ).
thf(1387,plain,
! [A: a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ e_a @ e_a ) )
= ( produc686083979Tree_a @ A @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(125,axiom,
! [A: a > tree_a > $o,B: produc143150363Tree_a > $o] :
( ! [C: a,D: tree_a] :
( ( A @ C @ D )
= ( B @ ( produc686083979Tree_a @ C @ D ) ) )
=> ( ( produc1673233912ee_a_o @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_cond__case__prod__eta) ).
thf(746,plain,
! [A: a > tree_a > $o,B: produc143150363Tree_a > $o] :
( ! [C: a,D: tree_a] :
( ( A @ C @ D )
= ( B @ ( produc686083979Tree_a @ C @ D ) ) )
=> ( ( produc1673233912ee_a_o @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',fact_14_is__heap_Ocases) ).
thf(1355,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)],[294]) ).
thf(232,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/sandbox2/benchmark/theBenchmark.p',fact_115_order__trans) ).
thf(1123,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)],[232]) ).
thf(72,axiom,
! [A: produc981471411ee_a_a] :
? [B: tree_a,C: a] :
( A
= ( produc649172771ee_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_surj__pair) ).
thf(561,plain,
! [A: produc981471411ee_a_a] :
? [B: tree_a,C: a] :
( A
= ( produc649172771ee_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(21,axiom,
( ord_le1013007387Tree_a
= ( ^ [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
! [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_subset__eq) ).
thf(392,plain,
( ord_le1013007387Tree_a
= ( ^ [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
! [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(32,axiom,
! [A: produc981471411ee_a_a] :
( A
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_prod_Oexhaust__sel) ).
thf(424,plain,
! [A: produc981471411ee_a_a] :
( A
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(300,axiom,
! [A: a > a > $o,B: a > tree_a > $o] :
( product_snd_a_Tree_a
= ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( bNF_sndOp_a_a_Tree_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_snd__sndOp) ).
thf(1370,plain,
! [A: a > a > $o,B: a > tree_a > $o] :
( product_snd_a_Tree_a
= ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( bNF_sndOp_a_a_Tree_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(145,axiom,
produc126329485Tree_a = produc369019363Tree_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_internal__case__prod__def) ).
thf(815,plain,
produc126329485Tree_a = produc369019363Tree_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(119,axiom,
! [A: produc981471411ee_a_a > $o,B: tree_a,C: a] :
( ( A @ ( produc649172771ee_a_a @ B @ C ) )
=> ( produc1205515265_a_a_o @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_curryI) ).
thf(729,plain,
! [A: produc981471411ee_a_a > $o,B: tree_a,C: a] :
( ( A @ ( produc649172771ee_a_a @ B @ C ) )
=> ( produc1205515265_a_a_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(190,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_dual__order_Orefl) ).
thf(957,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(173,axiom,
! [A: tree_a,B: a] :
( ( produc1478296771ee_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= ( produc686083979Tree_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_swap__simp) ).
thf(894,plain,
! [A: tree_a,B: a] :
( ( produc1478296771ee_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= ( produc686083979Tree_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(26,axiom,
! [A: tree_a,B: a] :
( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_snd__conv) ).
thf(407,plain,
! [A: tree_a,B: a] :
( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(91,axiom,
! [A: a > tree_a > tree_a,B: produc143150363Tree_a > tree_a] :
( ! [C: a,D: tree_a] :
( ( A @ C @ D )
= ( B @ ( produc686083979Tree_a @ C @ D ) ) )
=> ( ( produc873356882Tree_a @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_cond__case__prod__eta) ).
thf(630,plain,
! [A: a > tree_a > tree_a,B: produc143150363Tree_a > tree_a] :
( ! [C: a,D: tree_a] :
( ( A @ C @ D )
= ( B @ ( produc686083979Tree_a @ C @ D ) ) )
=> ( ( produc873356882Tree_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(50,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( ord_less_eq_a @ B @ C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_ord__eq__le__trans) ).
thf(484,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)],[50]) ).
thf(89,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_dual__order_Oantisym) ).
thf(625,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)],[89]) ).
thf(168,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( if_Pro1144176865Tree_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T) ).
thf(879,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( if_Pro1144176865Tree_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(159,axiom,
! [A: a,B: tree_a,C: a] :
( ( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_fst__eqD) ).
thf(852,plain,
! [A: a,B: tree_a,C: a] :
( ( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(151,axiom,
! [A: produc143150363Tree_a] :
? [B: a,C: tree_a] :
( A
= ( produc686083979Tree_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_surj__pair) ).
thf(830,plain,
! [A: produc143150363Tree_a] :
? [B: a,C: tree_a] :
( A
= ( produc686083979Tree_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(171,axiom,
! [A: produc981471411ee_a_a > produc981471411ee_a_a,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( produc1331510035ee_a_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_prod_Ocase__distrib) ).
thf(889,plain,
! [A: produc981471411ee_a_a > produc981471411ee_a_a,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( produc1331510035ee_a_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(179,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a,C: a > tree_a > set_Pr1070816379Tree_a] :
( ! [D: a,E: tree_a] :
( ( A
= ( produc686083979Tree_a @ D @ E ) )
=> ( member254315204Tree_a @ B @ ( C @ D @ E ) ) )
=> ( member254315204Tree_a @ B @ ( produc802621147Tree_a @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_mem__case__prodI2) ).
thf(916,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a,C: a > tree_a > set_Pr1070816379Tree_a] :
( ! [D: a,E: tree_a] :
( ( A
= ( produc686083979Tree_a @ D @ E ) )
=> ( member254315204Tree_a @ B @ ( C @ D @ E ) ) )
=> ( member254315204Tree_a @ B @ ( produc802621147Tree_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(46,axiom,
! [A: produc143150363Tree_a,B: a > tree_a > $o,C: a > tree_a > $o,D: produc143150363Tree_a] :
( ! [E: a,F: tree_a] :
( ( ( produc686083979Tree_a @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( produc1673233912ee_a_o @ B @ D )
= ( produc1673233912ee_a_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_split__cong) ).
thf(467,plain,
! [A: produc143150363Tree_a,B: a > tree_a > $o,C: a > tree_a > $o,D: produc143150363Tree_a] :
( ! [E: a,F: tree_a] :
( ( ( produc686083979Tree_a @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( produc1673233912ee_a_o @ B @ D )
= ( produc1673233912ee_a_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(246,axiom,
! [A: a > a,B: produc143150363Tree_a] :
( ( product_snd_a_Tree_a @ ( produc1107567542Tree_a @ A @ B ) )
= ( product_snd_a_Tree_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_snd__apfst) ).
thf(1159,plain,
! [A: a > a,B: produc143150363Tree_a] :
( ( product_snd_a_Tree_a @ ( produc1107567542Tree_a @ A @ B ) )
= ( product_snd_a_Tree_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(44,axiom,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_prod_Oinject) ).
thf(461,plain,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(311,axiom,
! [A: tree_a > a > $o,B: produc143150363Tree_a,C: $o > $o,D: a > tree_a > $o] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ( ! [E: a,F: tree_a] :
( ( A @ F @ E )
=> ( C @ ( D @ E @ F ) ) )
=> ( C @ ( produc1673233912ee_a_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_exE__realizer) ).
thf(1402,plain,
! [A: tree_a > a > $o,B: produc143150363Tree_a,C: $o > $o,D: a > tree_a > $o] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ( ! [E: a,F: tree_a] :
( ( A @ F @ E )
=> ( C @ ( D @ E @ F ) ) )
=> ( C @ ( produc1673233912ee_a_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(166,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_antisym) ).
thf(874,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)],[166]) ).
thf(268,axiom,
is_heap_a @ ( t_a @ v @ e_a @ e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C1_Oprems_C_I1_J) ).
thf(1259,plain,
is_heap_a @ ( t_a @ v @ e_a @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(188,axiom,
! [A: produc981471411ee_a_a,B: tree_a,C: a] :
( ( A
= ( produc649172771ee_a_a @ B @ C ) )
=> ( ( product_fst_Tree_a_a @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_fstI) ).
thf(948,plain,
! [A: produc981471411ee_a_a,B: tree_a,C: a] :
( ( A
= ( produc649172771ee_a_a @ B @ C ) )
=> ( ( product_fst_Tree_a_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(205,axiom,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a,C: produc143150363Tree_a > $o,D: produc143150363Tree_a > $o] :
( ( ord_le1013007387Tree_a @ A @ B )
=> ( ! [E: produc143150363Tree_a] :
( ( member254315204Tree_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1013007387Tree_a
@ ( collec486369286Tree_a
@ ^ [E: produc143150363Tree_a] :
( ( member254315204Tree_a @ E @ A )
& ( C @ E ) ) )
@ ( collec486369286Tree_a
@ ^ [E: produc143150363Tree_a] :
( ( member254315204Tree_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_subset__CollectI) ).
thf(1017,plain,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a,C: produc143150363Tree_a > $o,D: produc143150363Tree_a > $o] :
( ( ord_le1013007387Tree_a @ A @ B )
=> ( ! [E: produc143150363Tree_a] :
( ( member254315204Tree_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1013007387Tree_a
@ ( collec486369286Tree_a
@ ^ [E: produc143150363Tree_a] :
( ( member254315204Tree_a @ E @ A )
& ( C @ E ) ) )
@ ( collec486369286Tree_a
@ ^ [E: produc143150363Tree_a] :
( ( member254315204Tree_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(332,axiom,
( ( heapIm970322378pify_a @ e_a )
= e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_heapify_Osimps_I1_J) ).
thf(1498,plain,
( ( heapIm970322378pify_a @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(317,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
& ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_prod_Oexpand) ).
thf(1425,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
& ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(9,axiom,
! [A: tree_a > a > $o,B: tree_a,C: a] :
( ( A @ B @ C )
=> ( produc1587316832_a_a_o @ A @ ( produc649172771ee_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_case__prodI) ).
thf(356,plain,
! [A: tree_a > a > $o,B: tree_a,C: a] :
( ( A @ B @ C )
=> ( produc1587316832_a_a_o @ A @ ( produc649172771ee_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(136,axiom,
! [A: produc143150363Tree_a > produc143150363Tree_a,B: tree_a > a > produc143150363Tree_a,C: produc981471411ee_a_a] :
( ( A @ ( produc369019363Tree_a @ B @ C ) )
= ( produc369019363Tree_a
@ ^ [D: tree_a,E: a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_prod_Ocase__distrib) ).
thf(783,plain,
! [A: produc143150363Tree_a > produc143150363Tree_a,B: tree_a > a > produc143150363Tree_a,C: produc981471411ee_a_a] :
( ( A @ ( produc369019363Tree_a @ B @ C ) )
= ( produc369019363Tree_a
@ ^ [D: tree_a,E: a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(309,axiom,
! [A: produc981471411ee_a_a > $o,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
=> ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_prod_Osplit__sel) ).
thf(1397,plain,
! [A: produc981471411ee_a_a > $o,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
=> ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(108,axiom,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( produc1673233912ee_a_o @ A @ ( produc686083979Tree_a @ B @ C ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_case__prodD) ).
thf(697,plain,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( produc1673233912ee_a_o @ A @ ( produc686083979Tree_a @ B @ C ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(256,axiom,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_in__tree_Osimps_I1_J) ).
thf(1234,plain,
! [A: a] :
~ ( in_tree_a @ A @ e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(339,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/sandbox2/benchmark/theBenchmark.p',fact_101_is__heap_Osimps_I6_J) ).
thf(1541,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)],[339]) ).
thf(296,axiom,
! [A: tree_a,B: produc143150363Tree_a] :
( ( A
= ( product_snd_a_Tree_a @ B ) )
= ( ? [C: a] :
( B
= ( produc686083979Tree_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_eq__snd__iff) ).
thf(1361,plain,
! [A: tree_a,B: produc143150363Tree_a] :
( ( A
= ( product_snd_a_Tree_a @ B ) )
= ( ? [C: a] :
( B
= ( produc686083979Tree_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(127,axiom,
! [A: produc143150363Tree_a > tree_a,B: produc981471411ee_a_a > produc143150363Tree_a,C: produc981471411ee_a_a,D: produc143150363Tree_a > tree_a,E: produc981471411ee_a_a > produc143150363Tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P1663859001ee_a_a @ A @ B @ C )
= ( comp_P1663859001ee_a_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_comp__apply__eq) ).
thf(753,plain,
! [A: produc143150363Tree_a > tree_a,B: produc981471411ee_a_a > produc143150363Tree_a,C: produc981471411ee_a_a,D: produc143150363Tree_a > tree_a,E: produc981471411ee_a_a > produc143150363Tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P1663859001ee_a_a @ A @ B @ C )
= ( comp_P1663859001ee_a_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(66,axiom,
! [A: produc981471411ee_a_a,B: tree_a > a > produc143150363Tree_a,C: tree_a > a > produc143150363Tree_a,D: produc981471411ee_a_a] :
( ! [E: tree_a,F: a] :
( ( ( produc649172771ee_a_a @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( produc369019363Tree_a @ B @ D )
= ( produc369019363Tree_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_split__cong) ).
thf(537,plain,
! [A: produc981471411ee_a_a,B: tree_a > a > produc143150363Tree_a,C: tree_a > a > produc143150363Tree_a,D: produc981471411ee_a_a] :
( ! [E: tree_a,F: a] :
( ( ( produc649172771ee_a_a @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( produc369019363Tree_a @ B @ D )
= ( produc369019363Tree_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(63,axiom,
! [A: a > tree_a,B: tree_a > a,C: produc981471411ee_a_a] :
( ( produc932333964ee_a_a @ A @ ( produc159857078_a_a_a @ B @ C ) )
= ( produc686083979Tree_a @ ( B @ ( product_fst_Tree_a_a @ C ) ) @ ( A @ ( product_snd_Tree_a_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_apsnd__apfst) ).
thf(526,plain,
! [A: a > tree_a,B: tree_a > a,C: produc981471411ee_a_a] :
( ( produc932333964ee_a_a @ A @ ( produc159857078_a_a_a @ B @ C ) )
= ( produc686083979Tree_a @ ( B @ ( product_fst_Tree_a_a @ C ) ) @ ( A @ ( product_snd_Tree_a_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(51,axiom,
! [A: tree_a > a,B: a > tree_a,C: produc981471411ee_a_a] :
( ( produc606383786Tree_a @ A @ ( produc1296751488Tree_a @ B @ C ) )
= ( produc686083979Tree_a @ ( A @ ( product_fst_Tree_a_a @ C ) ) @ ( B @ ( product_snd_Tree_a_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_apfst__apsnd) ).
thf(489,plain,
! [A: tree_a > a,B: a > tree_a,C: produc981471411ee_a_a] :
( ( produc606383786Tree_a @ A @ ( produc1296751488Tree_a @ B @ C ) )
= ( produc686083979Tree_a @ ( A @ ( product_fst_Tree_a_a @ C ) ) @ ( B @ ( product_snd_Tree_a_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(111,axiom,
! [A: tree_a,B: produc981471411ee_a_a] :
( ( A
= ( product_fst_Tree_a_a @ B ) )
= ( ? [C: a] :
( B
= ( produc649172771ee_a_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_eq__fst__iff) ).
thf(706,plain,
! [A: tree_a,B: produc981471411ee_a_a] :
( ( A
= ( product_fst_Tree_a_a @ B ) )
= ( ? [C: a] :
( B
= ( produc649172771ee_a_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',fact_293_heap__top__max) ).
thf(1419,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)],[315]) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',fact_188_heap__top__geq) ).
thf(1155,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)],[244]) ).
thf(68,axiom,
! [A: produc981471411ee_a_a] :
( ( produc1515207979Tree_a @ ( produc1478296771ee_a_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_swap__swap) ).
thf(547,plain,
! [A: produc981471411ee_a_a] :
( ( produc1515207979Tree_a @ ( produc1478296771ee_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(88,axiom,
! [A: a > tree_a > $o,B: produc143150363Tree_a] :
( ( produc1587316832_a_a_o
@ ^ [C: tree_a,D: a] : ( A @ D @ C )
@ ( produc1515207979Tree_a @ B ) )
= ( produc1673233912ee_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_case__swap) ).
thf(622,plain,
! [A: a > tree_a > $o,B: produc143150363Tree_a] :
( ( produc1587316832_a_a_o
@ ^ [C: tree_a,D: a] : ( A @ D @ C )
@ ( produc1515207979Tree_a @ B ) )
= ( produc1673233912ee_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(230,axiom,
! [A: a > tree_a > tree_a,B: a,C: tree_a] :
( ( produc873356882Tree_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_old_Oprod_Ocase) ).
thf(1114,plain,
! [A: a > tree_a > tree_a,B: a,C: tree_a] :
( ( produc873356882Tree_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(96,axiom,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a,C: produc143150363Tree_a > $o] :
( ( ord_le1013007387Tree_a @ A @ B )
=> ( ( ord_le1013007387Tree_a @ A
@ ( collec486369286Tree_a
@ ^ [D: produc143150363Tree_a] :
( ( member254315204Tree_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: produc143150363Tree_a] :
( ( member254315204Tree_a @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_subset__Collect__iff) ).
thf(647,plain,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a,C: produc143150363Tree_a > $o] :
( ( ord_le1013007387Tree_a @ A @ B )
=> ( ( ord_le1013007387Tree_a @ A
@ ( collec486369286Tree_a
@ ^ [D: produc143150363Tree_a] :
( ( member254315204Tree_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: produc143150363Tree_a] :
( ( member254315204Tree_a @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(322,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/sandbox2/benchmark/theBenchmark.p',fact_102_is__heap__max) ).
thf(1451,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)],[322]) ).
thf(271,axiom,
! [A: $o > $o,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
=> ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_prod_Osplit__sel) ).
thf(1266,plain,
! [A: $o > $o,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
=> ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',fact_121_le__cases3) ).
thf(984,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)],[199]) ).
thf(308,axiom,
! [A: tree_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 ) ) )
=> ( ! [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 ) ) )
=> ( A = e_a ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_removeLeaf_Ocases) ).
thf(1393,plain,
! [A: tree_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 ) ) )
=> ( ! [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 ) ) )
=> ( A = e_a ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(242,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
=> ( ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_prod__eqI) ).
thf(1150,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
=> ( ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(263,axiom,
( produc1331510035ee_a_a
= ( ^ [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_case__prod__unfold) ).
thf(1249,plain,
( produc1331510035ee_a_a
= ( ^ [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(235,axiom,
! [A: a > a,B: produc981471411ee_a_a] :
( ( product_fst_Tree_a_a @ ( produc969245172Tree_a @ A @ B ) )
= ( product_fst_Tree_a_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_fst__apsnd) ).
thf(1131,plain,
! [A: a > a,B: produc981471411ee_a_a] :
( ( product_fst_Tree_a_a @ ( produc969245172Tree_a @ A @ B ) )
= ( product_fst_Tree_a_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(98,axiom,
! [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a > produc981471411ee_a_a] :
( ! [C: a,D: tree_a] :
( ( A @ C @ D )
= ( B @ ( produc686083979Tree_a @ C @ D ) ) )
=> ( ( produc1331510035ee_a_a @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_cond__case__prod__eta) ).
thf(654,plain,
! [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a > produc981471411ee_a_a] :
( ! [C: a,D: tree_a] :
( ( A @ C @ D )
= ( B @ ( produc686083979Tree_a @ C @ D ) ) )
=> ( ( produc1331510035ee_a_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(214,axiom,
! [A: a > tree_a > tree_a,B: produc143150363Tree_a] :
( ( produc433477818Tree_a
@ ^ [C: tree_a,D: a] : ( A @ D @ C )
@ ( produc1515207979Tree_a @ B ) )
= ( produc873356882Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_case__swap) ).
thf(1060,plain,
! [A: a > tree_a > tree_a,B: produc143150363Tree_a] :
( ( produc433477818Tree_a
@ ^ [C: tree_a,D: a] : ( A @ D @ C )
@ ( produc1515207979Tree_a @ B ) )
= ( produc873356882Tree_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(211,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/sandbox2/benchmark/theBenchmark.p',fact_130_order__subst2) ).
thf(1050,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)],[211]) ).
thf(289,axiom,
t != e_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(1333,plain,
t != e_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(251,axiom,
! [A: produc143150363Tree_a,B: a,C: tree_a] :
( ( A
= ( produc686083979Tree_a @ B @ C ) )
=> ( ( product_snd_a_Tree_a @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_sndI) ).
thf(1202,plain,
! [A: produc143150363Tree_a,B: a,C: tree_a] :
( ( A
= ( produc686083979Tree_a @ B @ C ) )
=> ( ( product_snd_a_Tree_a @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(92,axiom,
! [A: produc143150363Tree_a] :
( produc1673233912ee_a_o
@ ^ [B: a,C: tree_a] : $true
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_prod_Odisc__eq__case) ).
thf(633,plain,
! [A: produc143150363Tree_a] :
( produc1673233912ee_a_o
@ ^ [B: a,C: tree_a] : $true
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(57,axiom,
! [A: produc981471411ee_a_a] :
( ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_prod_Ocollapse) ).
thf(508,plain,
! [A: produc981471411ee_a_a] :
( ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(99,axiom,
! [A: produc143150363Tree_a > tree_a,B: produc143150363Tree_a > produc143150363Tree_a,C: produc143150363Tree_a,D: produc981471411ee_a_a > tree_a,E: produc143150363Tree_a > produc981471411ee_a_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P825537953Tree_a @ A @ B @ C )
= ( comp_P228269369Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_comp__apply__eq) ).
thf(657,plain,
! [A: produc143150363Tree_a > tree_a,B: produc143150363Tree_a > produc143150363Tree_a,C: produc143150363Tree_a,D: produc981471411ee_a_a > tree_a,E: produc143150363Tree_a > produc981471411ee_a_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P825537953Tree_a @ A @ B @ C )
= ( comp_P228269369Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(212,axiom,
! [A: a > tree_a > $o,B: tree_a > tree_a > $o] :
( product_fst_a_Tree_a
= ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( bNF_fs1579355852Tree_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_fst__fstOp) ).
thf(1054,plain,
! [A: a > tree_a > $o,B: tree_a > tree_a > $o] :
( product_fst_a_Tree_a
= ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( bNF_fs1579355852Tree_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(250,axiom,
! [A: tree_a > multiset_a,B: tree_a > tree_a,C: list_a > tree_a,D: tree_a > $o,E: tree_a > produc143150363Tree_a] :
( ! [F: tree_a] :
( ( A @ F )
= ( multiset_a2 @ ( B @ F ) ) )
=> ( ! [F: list_a] : ( is_heap_a @ ( B @ ( C @ F ) ) )
=> ( ! [F: tree_a] :
( ( ( B @ F )
= e_a )
= ( D @ F ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( is_heap_a @ ( B @ F ) )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( B @ H ) ) ) ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( B @ F ) ) ) ) )
=> ( heap_axioms_Tree_a_a @ D @ C @ A @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Heap__axioms_Ointro) ).
thf(1170,plain,
! [A: tree_a > multiset_a,B: tree_a > tree_a,C: list_a > tree_a,D: tree_a > $o,E: tree_a > produc143150363Tree_a] :
( ! [F: tree_a] :
( ( A @ F )
= ( multiset_a2 @ ( B @ F ) ) )
=> ( ! [F: list_a] : ( is_heap_a @ ( B @ ( C @ F ) ) )
=> ( ! [F: tree_a] :
( ( ( B @ F )
= e_a )
= ( D @ F ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( A @ H ) )
= ( A @ F ) ) ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( is_heap_a @ ( B @ F ) )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( B @ H ) ) ) ) )
=> ( ! [F: tree_a,G: a,H: tree_a] :
( ~ ( D @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( B @ F ) ) ) ) )
=> ( heap_axioms_Tree_a_a @ D @ C @ A @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(249,axiom,
! [A: tree_a > $o,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( ~ ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
& ~ ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_prod_Osplit__sel__asm) ).
thf(1167,plain,
! [A: tree_a > $o,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( ~ ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
& ~ ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(189,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( ord_less_eq_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_eq__refl) ).
thf(953,plain,
! [A: a,B: a] :
( ( A = B )
=> ( ord_less_eq_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(101,axiom,
! [A: produc143150363Tree_a,B: a > a > $o,C: a > tree_a > $o] :
( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ ( relcompp_a_a_Tree_a @ B @ C ) ) ) )
=> ( member254315204Tree_a @ ( bNF_sndOp_a_a_Tree_a @ B @ C @ A ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_sndOp__in) ).
thf(662,plain,
! [A: produc143150363Tree_a,B: a > a > $o,C: a > tree_a > $o] :
( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ ( relcompp_a_a_Tree_a @ B @ C ) ) ) )
=> ( member254315204Tree_a @ ( bNF_sndOp_a_a_Tree_a @ B @ C @ A ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',fact_181_GreatestI2__order) ).
thf(1086,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)],[222]) ).
thf(185,axiom,
! [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] :
( ( produc1207340411ee_a_a
@ ^ [C: tree_a,D: a] : ( A @ D @ C )
@ ( produc1515207979Tree_a @ B ) )
= ( produc1331510035ee_a_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_case__swap) ).
thf(938,plain,
! [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] :
( ( produc1207340411ee_a_a
@ ^ [C: tree_a,D: a] : ( A @ D @ C )
@ ( produc1515207979Tree_a @ B ) )
= ( produc1331510035ee_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(23,axiom,
! [A: set_Pr921883667ee_a_a,B: set_Pr921883667ee_a_a] :
( ( ( ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ A ) )
= ( ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_pred__equals__eq2) ).
thf(398,plain,
! [A: set_Pr921883667ee_a_a,B: set_Pr921883667ee_a_a] :
( ( ( ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ A ) )
= ( ^ [C: tree_a,D: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(207,axiom,
! [A: a > tree_a > tree_a,B: a,C: tree_a] :
( ( produc873356882Tree_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_case__prod__conv) ).
thf(1035,plain,
! [A: a > tree_a > tree_a,B: a,C: tree_a] :
( ( produc873356882Tree_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(71,axiom,
! [A: tree_a > produc981471411ee_a_a,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( produc1331510035ee_a_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_prod_Ocase__distrib) ).
thf(558,plain,
! [A: tree_a > produc981471411ee_a_a,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( produc1331510035ee_a_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(218,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_ord__le__eq__trans) ).
thf(1071,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)],[218]) ).
thf(177,axiom,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Pair__inject) ).
thf(906,plain,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(264,axiom,
( produc873356882Tree_a
= ( ^ [A: a > tree_a > tree_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_case__prod__beta_H) ).
thf(1251,plain,
( produc873356882Tree_a
= ( ^ [A: a > tree_a > tree_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(160,axiom,
! [A: produc143150363Tree_a,B: tree_a > a > set_Pr1070816379Tree_a,C: tree_a,D: a] :
( ( member254315204Tree_a @ A @ ( B @ C @ D ) )
=> ( member254315204Tree_a @ A @ ( produc951236931Tree_a @ B @ ( produc649172771ee_a_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_mem__case__prodI) ).
thf(856,plain,
! [A: produc143150363Tree_a,B: tree_a > a > set_Pr1070816379Tree_a,C: tree_a,D: a] :
( ( member254315204Tree_a @ A @ ( B @ C @ D ) )
=> ( member254315204Tree_a @ A @ ( produc951236931Tree_a @ B @ ( produc649172771ee_a_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(39,axiom,
! [A: a,B: a] :
( ~ ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_le__cases) ).
thf(444,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)],[39]) ).
thf(255,axiom,
! [A: $o > $o,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( ~ ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
& ~ ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_prod_Osplit__sel__asm) ).
thf(1219,plain,
! [A: $o > $o,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( ~ ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
& ~ ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(149,axiom,
! [A: produc143150363Tree_a > $o,B: tree_a > a > produc143150363Tree_a,C: produc981471411ee_a_a] :
( ( A @ ( produc369019363Tree_a @ B @ C ) )
=> ~ ! [D: tree_a,E: a] :
( ( C
= ( produc649172771ee_a_a @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_case__prodE2) ).
thf(824,plain,
! [A: produc143150363Tree_a > $o,B: tree_a > a > produc143150363Tree_a,C: produc981471411ee_a_a] :
( ( A @ ( produc369019363Tree_a @ B @ C ) )
=> ~ ! [D: tree_a,E: a] :
( ( C
= ( produc649172771ee_a_a @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(147,axiom,
( produc369019363Tree_a
= ( ^ [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] : ( A @ ( product_fst_Tree_a_a @ B ) @ ( product_snd_Tree_a_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_case__prod__beta_H) ).
thf(819,plain,
( produc369019363Tree_a
= ( ^ [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] : ( A @ ( product_fst_Tree_a_a @ B ) @ ( product_snd_Tree_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(156,axiom,
( product_snd_Tree_a_a
= ( comp_P1103783853ee_a_a @ product_fst_a_Tree_a
@ ( produc369019363Tree_a
@ ^ [A: tree_a,B: a] : ( produc686083979Tree_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_snd__fst__flip) ).
thf(843,plain,
( product_snd_Tree_a_a
= ( comp_P1103783853ee_a_a @ product_fst_a_Tree_a
@ ( produc369019363Tree_a
@ ^ [A: tree_a,B: a] : ( produc686083979Tree_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(124,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Collect__mem__eq) ).
thf(743,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(28,axiom,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a > $o] :
( ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ A ) @ ( collec486369286Tree_a @ B ) )
= ( ! [C: produc143150363Tree_a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Collect__mono__iff) ).
thf(413,plain,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a > $o] :
( ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ A ) @ ( collec486369286Tree_a @ B ) )
= ( ! [C: produc143150363Tree_a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(203,axiom,
! [A: produc981471411ee_a_a > $o,B: tree_a,C: a] :
( ( produc1205515265_a_a_o @ A @ B @ C )
=> ( A @ ( produc649172771ee_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_curryD) ).
thf(1007,plain,
! [A: produc981471411ee_a_a > $o,B: tree_a,C: a] :
( ( produc1205515265_a_a_o @ A @ B @ C )
=> ( A @ ( produc649172771ee_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(107,axiom,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( produc1673233912ee_a_o @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_old_Oprod_Ocase) ).
thf(694,plain,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( produc1673233912ee_a_o @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(76,axiom,
! [A: a > tree_a > $o,B: produc143150363Tree_a] :
( ( produc1673233912ee_a_o @ A @ B )
=> ~ ! [C: a,D: tree_a] :
( ( B
= ( produc686083979Tree_a @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_case__prodE) ).
thf(577,plain,
! [A: a > tree_a > $o,B: produc143150363Tree_a] :
( ( produc1673233912ee_a_o @ A @ B )
=> ~ ! [C: a,D: tree_a] :
( ( B
= ( produc686083979Tree_a @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(113,axiom,
! [A: a,B: produc143150363Tree_a] :
( ( A
= ( product_fst_a_Tree_a @ B ) )
= ( ? [C: tree_a] :
( B
= ( produc686083979Tree_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_eq__fst__iff) ).
thf(711,plain,
! [A: a,B: produc143150363Tree_a] :
( ( A
= ( product_fst_a_Tree_a @ B ) )
= ( ? [C: tree_a] :
( B
= ( produc686083979Tree_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(266,axiom,
( heap_axioms_Tree_a_a
= ( ^ [A: tree_a > $o,B: list_a > tree_a,C: tree_a > multiset_a,D: tree_a > tree_a,E: tree_a > produc143150363Tree_a] :
( ! [F: tree_a] :
( ( C @ F )
= ( multiset_a2 @ ( D @ F ) ) )
& ! [F: list_a] : ( is_heap_a @ ( D @ ( B @ F ) ) )
& ! [F: tree_a] :
( ( ( D @ F )
= e_a )
= ( A @ F ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( is_heap_a @ ( D @ F ) )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( D @ H ) ) ) ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( D @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Heap__axioms__def) ).
thf(1256,plain,
( heap_axioms_Tree_a_a
= ( ^ [A: tree_a > $o,B: list_a > tree_a,C: tree_a > multiset_a,D: tree_a > tree_a,E: tree_a > produc143150363Tree_a] :
( ! [F: tree_a] :
( ( C @ F )
= ( multiset_a2 @ ( D @ F ) ) )
& ! [F: list_a] : ( is_heap_a @ ( D @ ( B @ F ) ) )
& ! [F: tree_a] :
( ( ( D @ F )
= e_a )
= ( A @ F ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( ( add_mset_a @ G @ ( C @ H ) )
= ( C @ F ) ) ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( is_heap_a @ ( D @ F ) )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( is_heap_a @ ( D @ H ) ) ) ) )
& ! [F: tree_a,G: a,H: tree_a] :
( ~ ( A @ F )
=> ( ( ( produc686083979Tree_a @ G @ H )
= ( E @ F ) )
=> ( G
= ( val_a @ ( D @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(67,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_order__refl) ).
thf(545,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(318,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/sandbox2/benchmark/theBenchmark.p',fact_12_Tree_Oinduct) ).
thf(1428,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)],[318]) ).
thf(238,axiom,
! [A: a > a,B: tree_a > tree_a,C: produc143150363Tree_a] :
( ( produc1107567542Tree_a @ A @ ( produc819961216ee_a_a @ B @ C ) )
= ( produc686083979Tree_a @ ( A @ ( product_fst_a_Tree_a @ C ) ) @ ( B @ ( product_snd_a_Tree_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_apfst__apsnd) ).
thf(1139,plain,
! [A: a > a,B: tree_a > tree_a,C: produc143150363Tree_a] :
( ( produc1107567542Tree_a @ A @ ( produc819961216ee_a_a @ B @ C ) )
= ( produc686083979Tree_a @ ( A @ ( product_fst_a_Tree_a @ C ) ) @ ( B @ ( product_snd_a_Tree_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(75,axiom,
! [A: a,B: a > a,C: a,D: tree_a,E: a > tree_a,F: set_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_a @ C @ F )
=> ( member254315204Tree_a @ ( produc686083979Tree_a @ A @ D ) @ ( bNF_Gr651645592Tree_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_image2__eqI) ).
thf(572,plain,
! [A: a,B: a > a,C: a,D: tree_a,E: a > tree_a,F: set_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_a @ C @ F )
=> ( member254315204Tree_a @ ( produc686083979Tree_a @ A @ D ) @ ( bNF_Gr651645592Tree_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(283,axiom,
( ( (=) @ produc143150363Tree_a )
= ( ^ [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
& ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_prod__eq__iff) ).
thf(1312,plain,
( ( (=) @ produc143150363Tree_a )
= ( ^ [A: produc143150363Tree_a,B: produc143150363Tree_a] :
( ( ( product_fst_a_Tree_a @ A )
= ( product_fst_a_Tree_a @ B ) )
& ( ( product_snd_a_Tree_a @ A )
= ( product_snd_a_Tree_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(227,axiom,
! [A: tree_a > tree_a,B: a,C: tree_a] :
( ( produc819961216ee_a_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( produc686083979Tree_a @ B @ ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_apsnd__conv) ).
thf(1107,plain,
! [A: tree_a > tree_a,B: a,C: tree_a] :
( ( produc819961216ee_a_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( produc686083979Tree_a @ B @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(258,axiom,
is_heap_a @ e_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_is__heap_Osimps_I1_J) ).
thf(1239,plain,
is_heap_a @ e_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(267,axiom,
is_heap_a @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(1258,plain,
is_heap_a @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(6,axiom,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a > $o] :
( ! [C: produc143150363Tree_a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ A ) @ ( collec486369286Tree_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Collect__mono) ).
thf(350,plain,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a > $o] :
( ! [C: produc143150363Tree_a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ A ) @ ( collec486369286Tree_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(197,axiom,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ C @ B ) ) @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_exI__realizer) ).
thf(979,plain,
! [A: a > tree_a > $o,B: a,C: tree_a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ C @ B ) ) @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',fact_104_siftDown_Osimps_I3_J) ).
thf(1209,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)],[253]) ).
thf(175,axiom,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_prod_Oinject) ).
thf(900,plain,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(103,axiom,
( produc1478296771ee_a_a
= ( ^ [A: produc981471411ee_a_a] : ( produc686083979Tree_a @ ( product_snd_Tree_a_a @ A ) @ ( product_fst_Tree_a_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_prod_Oswap__def) ).
thf(681,plain,
( produc1478296771ee_a_a
= ( ^ [A: produc981471411ee_a_a] : ( produc686083979Tree_a @ ( product_snd_Tree_a_a @ A ) @ ( product_fst_Tree_a_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(273,axiom,
( produc1331510035ee_a_a
= ( ^ [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_case__prod__beta) ).
thf(1282,plain,
( produc1331510035ee_a_a
= ( ^ [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(231,axiom,
! [A: $o,B: a > tree_a > $o] :
( ( produc1673233912ee_a_o
@ ^ [C: a,D: tree_a] :
( A
& ( B @ C @ D ) ) )
= ( ^ [C: produc143150363Tree_a] :
( A
& ( produc1673233912ee_a_o @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_split__part) ).
thf(1117,plain,
! [A: $o,B: a > tree_a > $o] :
( ( produc1673233912ee_a_o
@ ^ [C: a,D: tree_a] :
( A
& ( B @ C @ D ) ) )
= ( ^ [C: produc143150363Tree_a] :
( A
& ( produc1673233912ee_a_o @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(210,axiom,
! [A: produc143150363Tree_a,B: a > tree_a > $o,C: tree_a > tree_a > $o] :
( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ ( relcom439193229Tree_a @ B @ C ) ) ) )
=> ( member254315204Tree_a @ ( bNF_fs1579355852Tree_a @ B @ C @ A ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_fstOp__in) ).
thf(1048,plain,
! [A: produc143150363Tree_a,B: a > tree_a > $o,C: tree_a > tree_a > $o] :
( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ ( relcom439193229Tree_a @ B @ C ) ) ) )
=> ( member254315204Tree_a @ ( bNF_fs1579355852Tree_a @ B @ C @ A ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(122,axiom,
! [A: a > tree_a > produc981471411ee_a_a,B: a,C: tree_a] :
( ( produc1331510035ee_a_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_case__prod__conv) ).
thf(737,plain,
! [A: a > tree_a > produc981471411ee_a_a,B: a,C: tree_a] :
( ( produc1331510035ee_a_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(302,axiom,
( product_snd_a_Tree_a
= ( produc873356882Tree_a
@ ^ [A: a,B: tree_a] : B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_snd__def) ).
thf(1376,plain,
( product_snd_a_Tree_a
= ( produc873356882Tree_a
@ ^ [A: a,B: tree_a] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(281,axiom,
( bNF_fs1579355852Tree_a
= ( ^ [A: a > tree_a > $o,B: tree_a > tree_a > $o,C: produc143150363Tree_a] : ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( bNF_pi1536086554Tree_a @ A @ B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_fstOp__def) ).
thf(1307,plain,
( bNF_fs1579355852Tree_a
= ( ^ [A: a > tree_a > $o,B: tree_a > tree_a > $o,C: produc143150363Tree_a] : ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( bNF_pi1536086554Tree_a @ A @ B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(11,axiom,
! [A: produc143150363Tree_a > $o,B: a,C: tree_a] :
( ( A @ ( produc686083979Tree_a @ B @ C ) )
=> ( produc1291432345ee_a_o @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_curryI) ).
thf(362,plain,
! [A: produc143150363Tree_a > $o,B: a,C: tree_a] :
( ( A @ ( produc686083979Tree_a @ B @ C ) )
=> ( produc1291432345ee_a_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(42,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_eq__iff) ).
thf(451,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)],[42]) ).
thf(19,axiom,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
( ! [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) )
=> ( ord_le1013007387Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_subsetI) ).
thf(387,plain,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
( ! [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) )
=> ( ord_le1013007387Tree_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(327,axiom,
! [A: tree_a,B: tree_a,C: tree_a,D: a] :
( ( is_heap_a @ A )
=> ( ( is_heap_a @ B )
=> ( ( C
= ( t_a @ D @ A @ B ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_siftDown__heap__is__heap) ).
thf(1471,plain,
! [A: tree_a,B: tree_a,C: tree_a,D: a] :
( ( is_heap_a @ A )
=> ( ( is_heap_a @ B )
=> ( ( C
= ( t_a @ D @ A @ B ) )
=> ( is_heap_a @ ( heapIm1091024090Down_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(53,axiom,
! [A: produc981471411ee_a_a > tree_a,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( produc873356882Tree_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_prod_Ocase__distrib) ).
thf(494,plain,
! [A: produc981471411ee_a_a > tree_a,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( produc873356882Tree_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(129,axiom,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
( ( ord_le1327026842ee_a_o
@ ^ [C: a,D: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ A )
@ ^ [C: a,D: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ B ) )
= ( ord_le1013007387Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_pred__subset__eq2) ).
thf(758,plain,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
( ( ord_le1327026842ee_a_o
@ ^ [C: a,D: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ A )
@ ^ [C: a,D: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ C @ D ) @ B ) )
= ( ord_le1013007387Tree_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(86,axiom,
! [A: tree_a > $o,B: tree_a,C: a > $o,D: a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ B @ D ) ) )
& ( C @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_conjI__realizer) ).
thf(609,plain,
! [A: tree_a > $o,B: tree_a,C: a > $o,D: a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ B @ D ) ) )
& ( C @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(81,axiom,
! [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a > produc143150363Tree_a] :
( ! [C: tree_a,D: a] :
( ( A @ C @ D )
= ( B @ ( produc649172771ee_a_a @ C @ D ) ) )
=> ( ( produc369019363Tree_a @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_cond__case__prod__eta) ).
thf(594,plain,
! [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a > produc143150363Tree_a] :
( ! [C: tree_a,D: a] :
( ( A @ C @ D )
= ( B @ ( produc649172771ee_a_a @ C @ D ) ) )
=> ( ( produc369019363Tree_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(61,axiom,
! [A: a > tree_a > tree_a] :
( ( produc740705523Tree_a @ ( produc873356882Tree_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_curry__case__prod) ).
thf(520,plain,
! [A: a > tree_a > tree_a] :
( ( produc740705523Tree_a @ ( produc873356882Tree_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(304,axiom,
! [A: produc143150363Tree_a,B: a > tree_a > $o] :
( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ B ) ) )
=> ( B @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Product__Type_OCollect__case__prodD) ).
thf(1381,plain,
! [A: produc143150363Tree_a,B: a > tree_a > $o] :
( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ B ) ) )
=> ( B @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(229,axiom,
produc1405823650ee_a_o = produc1673233912ee_a_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_internal__case__prod__def) ).
thf(1112,plain,
produc1405823650ee_a_o = produc1673233912ee_a_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(4,axiom,
( ord_le1013007387Tree_a
= ( ^ [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
! [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_subset__iff) ).
thf(345,plain,
( ord_le1013007387Tree_a
= ( ^ [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a] :
! [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_112_dual__order_Otrans) ).
thf(858,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)],[161]) ).
thf(247,axiom,
( ( t_a @ v @ e_a @ e_a )
!= e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__C1_Oprems_C_I2_J) ).
thf(1162,plain,
( ( t_a @ v @ e_a @ e_a )
!= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(118,axiom,
! [A: produc981471411ee_a_a > tree_a,B: produc143150363Tree_a > produc981471411ee_a_a,C: produc143150363Tree_a,D: tree_a > tree_a,E: produc143150363Tree_a > tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P228269369Tree_a @ A @ B @ C )
= ( comp_T236170232Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_comp__apply__eq) ).
thf(726,plain,
! [A: produc981471411ee_a_a > tree_a,B: produc143150363Tree_a > produc981471411ee_a_a,C: produc143150363Tree_a,D: tree_a > tree_a,E: produc143150363Tree_a > tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P228269369Tree_a @ A @ B @ C )
= ( comp_T236170232Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(187,axiom,
! [A: produc143150363Tree_a,B: a,C: tree_a] :
( ( A
= ( produc686083979Tree_a @ B @ C ) )
=> ( ( product_fst_a_Tree_a @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_fstI) ).
thf(943,plain,
! [A: produc143150363Tree_a,B: a,C: tree_a] :
( ( A
= ( produc686083979Tree_a @ B @ C ) )
=> ( ( product_fst_a_Tree_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(206,axiom,
! [A: $o > $o,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( produc1673233912ee_a_o
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_prod_Ocase__distrib) ).
thf(1022,plain,
! [A: $o > $o,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
= ( produc1673233912ee_a_o
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(191,axiom,
! [A: tree_a > tree_a,B: produc143150363Tree_a] :
( ( product_fst_a_Tree_a @ ( produc819961216ee_a_a @ A @ B ) )
= ( product_fst_a_Tree_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_fst__apsnd) ).
thf(959,plain,
! [A: tree_a > tree_a,B: produc143150363Tree_a] :
( ( product_fst_a_Tree_a @ ( produc819961216ee_a_a @ A @ B ) )
= ( product_fst_a_Tree_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(135,axiom,
! [A: produc143150363Tree_a > tree_a] :
( ( produc873356882Tree_a @ ( produc740705523Tree_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_case__prod__curry) ).
thf(780,plain,
! [A: produc143150363Tree_a > tree_a] :
( ( produc873356882Tree_a @ ( produc740705523Tree_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(22,axiom,
! [A: tree_a > a > $o,B: produc981471411ee_a_a] :
( ( produc1587316832_a_a_o @ A @ B )
=> ~ ! [C: tree_a,D: a] :
( ( B
= ( produc649172771ee_a_a @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_case__prodE) ).
thf(394,plain,
! [A: tree_a > a > $o,B: produc981471411ee_a_a] :
( ( produc1587316832_a_a_o @ A @ B )
=> ~ ! [C: tree_a,D: a] :
( ( B
= ( produc649172771ee_a_a @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(297,axiom,
! [A: ( a > a > $o ) > product_prod_a_a > $o,B: a > tree_a > $o,C: tree_a > a > $o] : ( bNF_cs1095035134ee_a_a @ ( collec645855634od_a_a @ ( A @ ( relcompp_a_Tree_a_a @ B @ C ) ) ) @ product_snd_a_Tree_a @ product_fst_Tree_a_a @ ( bNF_fstOp_a_Tree_a_a @ B @ C ) @ ( bNF_sndOp_a_Tree_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_csquare__fstOp__sndOp) ).
thf(1364,plain,
! [A: ( a > a > $o ) > product_prod_a_a > $o,B: a > tree_a > $o,C: tree_a > a > $o] : ( bNF_cs1095035134ee_a_a @ ( collec645855634od_a_a @ ( A @ ( relcompp_a_Tree_a_a @ B @ C ) ) ) @ product_snd_a_Tree_a @ product_fst_Tree_a_a @ ( bNF_fstOp_a_Tree_a_a @ B @ C ) @ ( bNF_sndOp_a_Tree_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(226,axiom,
! [A: a,B: produc143150363Tree_a > a,C: produc143150363Tree_a,D: tree_a,E: produc143150363Tree_a > tree_a,F: set_Pr1070816379Tree_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member254315204Tree_a @ C @ F )
=> ( member254315204Tree_a @ ( produc686083979Tree_a @ A @ D ) @ ( bNF_Gr2042500789Tree_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_image2__eqI) ).
thf(1102,plain,
! [A: a,B: produc143150363Tree_a > a,C: produc143150363Tree_a,D: tree_a,E: produc143150363Tree_a > tree_a,F: set_Pr1070816379Tree_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member254315204Tree_a @ C @ F )
=> ( member254315204Tree_a @ ( produc686083979Tree_a @ A @ D ) @ ( bNF_Gr2042500789Tree_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(34,axiom,
produc534868220Tree_a = produc873356882Tree_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_internal__case__prod__def) ).
thf(431,plain,
produc534868220Tree_a = produc873356882Tree_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(320,axiom,
! [A: a,B: tree_a] :
( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_snd__conv) ).
thf(1445,plain,
! [A: a,B: tree_a] :
( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(164,axiom,
! [A: a > a,B: produc143150363Tree_a] :
( ( product_fst_a_Tree_a @ ( produc1107567542Tree_a @ A @ B ) )
= ( A @ ( product_fst_a_Tree_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_fst__apfst) ).
thf(868,plain,
! [A: a > a,B: produc143150363Tree_a] :
( ( product_fst_a_Tree_a @ ( produc1107567542Tree_a @ A @ B ) )
= ( A @ ( product_fst_a_Tree_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(56,axiom,
! [A: a > a,B: tree_a,C: a] :
( ( produc969245172Tree_a @ A @ ( produc649172771ee_a_a @ B @ C ) )
= ( produc649172771ee_a_a @ B @ ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_apsnd__conv) ).
thf(505,plain,
! [A: a > a,B: tree_a,C: a] :
( ( produc969245172Tree_a @ A @ ( produc649172771ee_a_a @ B @ C ) )
= ( produc649172771ee_a_a @ B @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(37,axiom,
! [A: tree_a > tree_a,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( produc873356882Tree_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_prod_Ocase__distrib) ).
thf(438,plain,
! [A: tree_a > tree_a,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( produc873356882Tree_a
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(219,axiom,
( bNF_sn210385162ee_a_a
= ( ^ [A: tree_a > tree_a > $o,B: tree_a > a > $o,C: produc981471411ee_a_a] : ( produc649172771ee_a_a @ ( bNF_pi1059296282ee_a_a @ A @ B @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) @ ( product_snd_Tree_a_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_sndOp__def) ).
thf(1076,plain,
( bNF_sn210385162ee_a_a
= ( ^ [A: tree_a > tree_a > $o,B: tree_a > a > $o,C: produc981471411ee_a_a] : ( produc649172771ee_a_a @ ( bNF_pi1059296282ee_a_a @ A @ B @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) @ ( product_snd_Tree_a_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(236,axiom,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_removeLeaf_Osimps_I5_J) ).
thf(1134,plain,
! [A: a,B: a,C: tree_a,D: tree_a,E: a,F: tree_a,G: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ ( t_a @ B @ C @ D ) @ ( t_a @ E @ F @ G ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(144,axiom,
! [A: a > a,B: produc143150363Tree_a,C: a > a] :
( ( ( produc1107567542Tree_a @ A @ B )
= ( produc1107567542Tree_a @ C @ B ) )
= ( ( A @ ( product_fst_a_Tree_a @ B ) )
= ( C @ ( product_fst_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_apfst__eq__conv) ).
thf(812,plain,
! [A: a > a,B: produc143150363Tree_a,C: a > a] :
( ( ( produc1107567542Tree_a @ A @ B )
= ( produc1107567542Tree_a @ C @ B ) )
= ( ( A @ ( product_fst_a_Tree_a @ B ) )
= ( C @ ( product_fst_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(3,axiom,
! [A: a > a,B: tree_a > tree_a,C: produc981471411ee_a_a] :
( ( produc969245172Tree_a @ A @ ( produc569472578ee_a_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( B @ ( product_fst_Tree_a_a @ C ) ) @ ( A @ ( product_snd_Tree_a_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_apsnd__apfst) ).
thf(342,plain,
! [A: a > a,B: tree_a > tree_a,C: produc981471411ee_a_a] :
( ( produc969245172Tree_a @ A @ ( produc569472578ee_a_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( B @ ( product_fst_Tree_a_a @ C ) ) @ ( A @ ( product_snd_Tree_a_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(240,axiom,
! [A: tree_a > tree_a,B: a > a,C: produc143150363Tree_a] :
( ( produc819961216ee_a_a @ A @ ( produc1107567542Tree_a @ B @ C ) )
= ( produc686083979Tree_a @ ( B @ ( product_fst_a_Tree_a @ C ) ) @ ( A @ ( product_snd_a_Tree_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_apsnd__apfst) ).
thf(1145,plain,
! [A: tree_a > tree_a,B: a > a,C: produc143150363Tree_a] :
( ( produc819961216ee_a_a @ A @ ( produc1107567542Tree_a @ B @ C ) )
= ( produc686083979Tree_a @ ( B @ ( product_fst_a_Tree_a @ C ) ) @ ( A @ ( product_snd_a_Tree_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(221,axiom,
! [A: tree_a,B: produc143150363Tree_a > tree_a,C: produc143150363Tree_a,D: a,E: produc143150363Tree_a > a,F: set_Pr1070816379Tree_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member254315204Tree_a @ C @ F )
=> ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ A @ D ) @ ( bNF_Gr2005589581ee_a_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_image2__eqI) ).
thf(1081,plain,
! [A: tree_a,B: produc143150363Tree_a > tree_a,C: produc143150363Tree_a,D: a,E: produc143150363Tree_a > a,F: set_Pr1070816379Tree_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member254315204Tree_a @ C @ F )
=> ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ A @ D ) @ ( bNF_Gr2005589581ee_a_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',fact_131_order__subst1) ).
thf(749,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)],[126]) ).
thf(106,axiom,
! [A: a > tree_a > $o,B: produc981471411ee_a_a,C: produc143150363Tree_a > $o,D: tree_a > a > produc143150363Tree_a] :
( ( A @ ( product_snd_Tree_a_a @ B ) @ ( product_fst_Tree_a_a @ B ) )
=> ( ! [E: tree_a,F: a] :
( ( A @ F @ E )
=> ( C @ ( D @ E @ F ) ) )
=> ( C @ ( produc369019363Tree_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_exE__realizer) ).
thf(690,plain,
! [A: a > tree_a > $o,B: produc981471411ee_a_a,C: produc143150363Tree_a > $o,D: tree_a > a > produc143150363Tree_a] :
( ( A @ ( product_snd_Tree_a_a @ B ) @ ( product_fst_Tree_a_a @ B ) )
=> ( ! [E: tree_a,F: a] :
( ( A @ F @ E )
=> ( C @ ( D @ E @ F ) ) )
=> ( C @ ( produc369019363Tree_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(310,axiom,
! [A: ( a > tree_a > $o ) > produc143150363Tree_a > $o,B: a > tree_a > $o,C: tree_a > tree_a > $o] : ( bNF_cs1091007358Tree_a @ ( collec486369286Tree_a @ ( A @ ( relcom439193229Tree_a @ B @ C ) ) ) @ product_snd_a_Tree_a @ produc1206152067Tree_a @ ( bNF_fs1579355852Tree_a @ B @ C ) @ ( bNF_sn687175434Tree_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_csquare__fstOp__sndOp) ).
thf(1400,plain,
! [A: ( a > tree_a > $o ) > produc143150363Tree_a > $o,B: a > tree_a > $o,C: tree_a > tree_a > $o] : ( bNF_cs1091007358Tree_a @ ( collec486369286Tree_a @ ( A @ ( relcom439193229Tree_a @ B @ C ) ) ) @ product_snd_a_Tree_a @ produc1206152067Tree_a @ ( bNF_fs1579355852Tree_a @ B @ C ) @ ( bNF_sn687175434Tree_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(299,axiom,
( product_snd_a_Tree_a
= ( comp_P228269369Tree_a @ product_fst_Tree_a_a
@ ( produc1331510035ee_a_a
@ ^ [A: a,B: tree_a] : ( produc649172771ee_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_snd__fst__flip) ).
thf(1368,plain,
( product_snd_a_Tree_a
= ( comp_P228269369Tree_a @ product_fst_Tree_a_a
@ ( produc1331510035ee_a_a
@ ^ [A: a,B: tree_a] : ( produc649172771ee_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(225,axiom,
! [A: produc143150363Tree_a,B: a > tree_a > set_Pr1070816379Tree_a,C: produc143150363Tree_a] :
( ( member254315204Tree_a @ A @ ( produc802621147Tree_a @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( member254315204Tree_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_mem__case__prodE) ).
thf(1098,plain,
! [A: produc143150363Tree_a,B: a > tree_a > set_Pr1070816379Tree_a,C: produc143150363Tree_a] :
( ( member254315204Tree_a @ A @ ( produc802621147Tree_a @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( member254315204Tree_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(279,axiom,
! [A: tree_a > a > $o,B: produc143150363Tree_a] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ~ ! [C: a,D: tree_a] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_exE__realizer_H) ).
thf(1300,plain,
! [A: tree_a > a > $o,B: produc143150363Tree_a] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ~ ! [C: a,D: tree_a] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(38,axiom,
! [A: produc981471411ee_a_a > produc143150363Tree_a] :
( ( produc369019363Tree_a @ ( produc1808426884Tree_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_case__prod__curry) ).
thf(441,plain,
! [A: produc981471411ee_a_a > produc143150363Tree_a] :
( ( produc369019363Tree_a @ ( produc1808426884Tree_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(115,axiom,
! [A: produc981471411ee_a_a] :
( ( produc1207340411ee_a_a @ produc649172771ee_a_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_case__prod__Pair__iden) ).
thf(717,plain,
! [A: produc981471411ee_a_a] :
( ( produc1207340411ee_a_a @ produc649172771ee_a_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(55,axiom,
! [A: produc143150363Tree_a,B: set_Pr1070816379Tree_a,C: set_Pr1070816379Tree_a,D: produc143150363Tree_a > $o] :
( ( member254315204Tree_a @ A @ B )
=> ( ( ord_le1013007387Tree_a @ B
@ ( collec486369286Tree_a
@ ^ [E: produc143150363Tree_a] :
( ( member254315204Tree_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_prop__restrict) ).
thf(502,plain,
! [A: produc143150363Tree_a,B: set_Pr1070816379Tree_a,C: set_Pr1070816379Tree_a,D: produc143150363Tree_a > $o] :
( ( member254315204Tree_a @ A @ B )
=> ( ( ord_le1013007387Tree_a @ B
@ ( collec486369286Tree_a
@ ^ [E: produc143150363Tree_a] :
( ( member254315204Tree_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(155,axiom,
! [A: produc143150363Tree_a > tree_a,B: produc143150363Tree_a > produc143150363Tree_a,C: produc143150363Tree_a,D: tree_a > tree_a,E: produc143150363Tree_a > tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P825537953Tree_a @ A @ B @ C )
= ( comp_T236170232Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_comp__apply__eq) ).
thf(840,plain,
! [A: produc143150363Tree_a > tree_a,B: produc143150363Tree_a > produc143150363Tree_a,C: produc143150363Tree_a,D: tree_a > tree_a,E: produc143150363Tree_a > tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P825537953Tree_a @ A @ B @ C )
= ( comp_T236170232Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(270,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/sandbox2/benchmark/theBenchmark.p',fact_4_siftDown_Ocases) ).
thf(1262,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)],[270]) ).
thf(285,axiom,
! [A: tree_a > tree_a,B: produc143150363Tree_a,C: tree_a > tree_a] :
( ( ( produc819961216ee_a_a @ A @ B )
= ( produc819961216ee_a_a @ C @ B ) )
= ( ( A @ ( product_snd_a_Tree_a @ B ) )
= ( C @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_apsnd__eq__conv) ).
thf(1317,plain,
! [A: tree_a > tree_a,B: produc143150363Tree_a,C: tree_a > tree_a] :
( ( ( produc819961216ee_a_a @ A @ B )
= ( produc819961216ee_a_a @ C @ B ) )
= ( ( A @ ( product_snd_a_Tree_a @ B ) )
= ( C @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(142,axiom,
! [A: ( a > tree_a > $o ) > produc143150363Tree_a > $o,B: a > a > $o,C: a > tree_a > $o] : ( bNF_cs739966834Tree_a @ ( collec486369286Tree_a @ ( A @ ( relcompp_a_a_Tree_a @ B @ C ) ) ) @ product_snd_a_a @ product_fst_a_Tree_a @ ( bNF_fstOp_a_a_Tree_a @ B @ C ) @ ( bNF_sndOp_a_a_Tree_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_csquare__fstOp__sndOp) ).
thf(808,plain,
! [A: ( a > tree_a > $o ) > produc143150363Tree_a > $o,B: a > a > $o,C: a > tree_a > $o] : ( bNF_cs739966834Tree_a @ ( collec486369286Tree_a @ ( A @ ( relcompp_a_a_Tree_a @ B @ C ) ) ) @ product_snd_a_a @ product_fst_a_Tree_a @ ( bNF_fstOp_a_a_Tree_a @ B @ C ) @ ( bNF_sndOp_a_a_Tree_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(290,axiom,
( produc1331510035ee_a_a
= ( ^ [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_case__prod__beta_H) ).
thf(1336,plain,
( produc1331510035ee_a_a
= ( ^ [A: a > tree_a > produc981471411ee_a_a,B: produc143150363Tree_a] : ( A @ ( product_fst_a_Tree_a @ B ) @ ( product_snd_a_Tree_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(208,axiom,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Pair__inject) ).
thf(1038,plain,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(78,axiom,
! [A: tree_a] :
( ( multiset_a2 @ ( heapIm1091024090Down_a @ A ) )
= ( multiset_a2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_siftDown__multiset) ).
thf(585,plain,
! [A: tree_a] :
( ( multiset_a2 @ ( heapIm1091024090Down_a @ A ) )
= ( multiset_a2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(14,axiom,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a,C: produc143150363Tree_a] :
( ( ord_le1013007387Tree_a @ A @ B )
=> ( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_in__mono) ).
thf(370,plain,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a,C: produc143150363Tree_a] :
( ( ord_le1013007387Tree_a @ A @ B )
=> ( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(110,axiom,
! [A: tree_a > tree_a,B: tree_a > tree_a,C: produc143150363Tree_a] :
( ( produc819961216ee_a_a @ A @ ( produc819961216ee_a_a @ B @ C ) )
= ( produc819961216ee_a_a @ ( comp_T59512783Tree_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_apsnd__compose) ).
thf(703,plain,
! [A: tree_a > tree_a,B: tree_a > tree_a,C: produc143150363Tree_a] :
( ( produc819961216ee_a_a @ A @ ( produc819961216ee_a_a @ B @ C ) )
= ( produc819961216ee_a_a @ ( comp_T59512783Tree_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(338,axiom,
! [A: a > tree_a > $o,B: a,C: tree_a,D: produc143150363Tree_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc686083979Tree_a @ B @ C ) )
=> ( A @ ( product_fst_a_Tree_a @ D ) @ ( product_snd_a_Tree_a @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(1536,plain,
! [A: a > tree_a > $o,B: a,C: tree_a,D: produc143150363Tree_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc686083979Tree_a @ B @ C ) )
=> ( A @ ( product_fst_a_Tree_a @ D ) @ ( product_snd_a_Tree_a @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(274,axiom,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_siftDown__in__tree) ).
thf(1284,plain,
! [A: tree_a] :
( ( A != e_a )
=> ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(40,axiom,
! [A: produc981471411ee_a_a > tree_a,B: produc143150363Tree_a > produc981471411ee_a_a,C: produc143150363Tree_a,D: produc143150363Tree_a > tree_a,E: produc143150363Tree_a > produc143150363Tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P228269369Tree_a @ A @ B @ C )
= ( comp_P825537953Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_comp__apply__eq) ).
thf(446,plain,
! [A: produc981471411ee_a_a > tree_a,B: produc143150363Tree_a > produc981471411ee_a_a,C: produc143150363Tree_a,D: produc143150363Tree_a > tree_a,E: produc143150363Tree_a > produc143150363Tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P228269369Tree_a @ A @ B @ C )
= ( comp_P825537953Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(54,axiom,
! [A: a,B: tree_a,C: set_Pr1070816379Tree_a,D: tree_a] :
( ( member254315204Tree_a @ ( produc686083979Tree_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member254315204Tree_a @ ( produc686083979Tree_a @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_ssubst__Pair__rhs) ).
thf(497,plain,
! [A: a,B: tree_a,C: set_Pr1070816379Tree_a,D: tree_a] :
( ( member254315204Tree_a @ ( produc686083979Tree_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member254315204Tree_a @ ( produc686083979Tree_a @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(259,axiom,
! [A: tree_a] : ( is_heap_a @ ( heapIm970322378pify_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_heapify__heap__is__heap) ).
thf(1240,plain,
! [A: tree_a] : ( is_heap_a @ ( heapIm970322378pify_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(293,axiom,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_siftDown_Osimps_I1_J) ).
thf(1353,plain,
( ( heapIm1091024090Down_a @ e_a )
= e_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(83,axiom,
! [A: produc143150363Tree_a] :
( ( produc1478296771ee_a_a @ ( produc1515207979Tree_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_swap__swap) ).
thf(600,plain,
! [A: produc143150363Tree_a] :
( ( produc1478296771ee_a_a @ ( produc1515207979Tree_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(157,axiom,
! [A: produc981471411ee_a_a > $o,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_case__prodE2) ).
thf(845,plain,
! [A: produc981471411ee_a_a > $o,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(183,axiom,
! [A: tree_a > tree_a,B: produc143150363Tree_a > tree_a,C: produc143150363Tree_a,D: produc143150363Tree_a > tree_a,E: produc143150363Tree_a > produc143150363Tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_T236170232Tree_a @ A @ B @ C )
= ( comp_P825537953Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_comp__apply__eq) ).
thf(931,plain,
! [A: tree_a > tree_a,B: produc143150363Tree_a > tree_a,C: produc143150363Tree_a,D: produc143150363Tree_a > tree_a,E: produc143150363Tree_a > produc143150363Tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_T236170232Tree_a @ A @ B @ C )
= ( comp_P825537953Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(245,axiom,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_is__heap_Osimps_I2_J) ).
thf(1157,plain,
! [A: a] : ( is_heap_a @ ( t_a @ A @ e_a @ e_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(77,axiom,
! [A: produc143150363Tree_a,B: tree_a > a > set_Pr1070816379Tree_a,C: produc981471411ee_a_a] :
( ( member254315204Tree_a @ A @ ( produc951236931Tree_a @ B @ C ) )
=> ~ ! [D: tree_a,E: a] :
( ( C
= ( produc649172771ee_a_a @ D @ E ) )
=> ~ ( member254315204Tree_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_mem__case__prodE) ).
thf(581,plain,
! [A: produc143150363Tree_a,B: tree_a > a > set_Pr1070816379Tree_a,C: produc981471411ee_a_a] :
( ( member254315204Tree_a @ A @ ( produc951236931Tree_a @ B @ C ) )
=> ~ ! [D: tree_a,E: a] :
( ( C
= ( produc649172771ee_a_a @ D @ E ) )
=> ~ ( member254315204Tree_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(254,axiom,
! [A: a > tree_a,B: tree_a > a,C: produc143150363Tree_a] :
( ( produc1070656334ee_a_a @ A @ ( produc21534708_a_a_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( A @ ( product_fst_a_Tree_a @ C ) ) @ ( B @ ( product_snd_a_Tree_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_apfst__apsnd) ).
thf(1216,plain,
! [A: a > tree_a,B: tree_a > a,C: produc143150363Tree_a] :
( ( produc1070656334ee_a_a @ A @ ( produc21534708_a_a_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( A @ ( product_fst_a_Tree_a @ C ) ) @ ( B @ ( product_snd_a_Tree_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(233,axiom,
! [A: a > tree_a > produc143150363Tree_a,B: produc143150363Tree_a] :
( ( produc369019363Tree_a
@ ^ [C: tree_a,D: a] : ( A @ D @ C )
@ ( produc1515207979Tree_a @ B ) )
= ( produc493188987Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_case__swap) ).
thf(1126,plain,
! [A: a > tree_a > produc143150363Tree_a,B: produc143150363Tree_a] :
( ( produc369019363Tree_a
@ ^ [C: tree_a,D: a] : ( A @ D @ C )
@ ( produc1515207979Tree_a @ B ) )
= ( produc493188987Tree_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(321,axiom,
! [A: produc143150363Tree_a] :
( ( product_fst_Tree_a_a @ ( produc1515207979Tree_a @ A ) )
= ( product_snd_a_Tree_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_fst__swap) ).
thf(1448,plain,
! [A: produc143150363Tree_a] :
( ( product_fst_Tree_a_a @ ( produc1515207979Tree_a @ A ) )
= ( product_snd_a_Tree_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(307,axiom,
! [A: tree_a > tree_a] :
( ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( produc819961216ee_a_a @ A ) )
= ( comp_T236170232Tree_a @ A @ product_snd_a_Tree_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_snd__comp__apsnd) ).
thf(1390,plain,
! [A: tree_a > tree_a] :
( ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( produc819961216ee_a_a @ A ) )
= ( comp_T236170232Tree_a @ A @ product_snd_a_Tree_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(323,axiom,
( heapIm229596386mpty_a
= ( ^ [A: tree_a] : ( A = e_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_hs__is__empty__def) ).
thf(1453,plain,
( heapIm229596386mpty_a
= ( ^ [A: tree_a] : ( A = e_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(132,axiom,
! [A: a,B: tree_a] :
( ( produc1515207979Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= ( produc649172771ee_a_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_swap__simp) ).
thf(771,plain,
! [A: a,B: tree_a] :
( ( produc1515207979Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= ( produc649172771ee_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(196,axiom,
! [A: produc143150363Tree_a] :
( ( product_snd_Tree_a_a @ ( produc1515207979Tree_a @ A ) )
= ( product_fst_a_Tree_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_snd__swap) ).
thf(976,plain,
! [A: produc143150363Tree_a] :
( ( product_snd_Tree_a_a @ ( produc1515207979Tree_a @ A ) )
= ( product_fst_a_Tree_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(176,axiom,
! [A: produc143150363Tree_a,B: produc143150363Tree_a > $o] :
( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mem__Collect__eq) ).
thf(903,plain,
! [A: produc143150363Tree_a,B: produc143150363Tree_a > $o] :
( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(60,axiom,
! [A: tree_a > a > produc143150363Tree_a,B: tree_a,C: a] :
( ( produc369019363Tree_a @ A @ ( produc649172771ee_a_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_old_Oprod_Ocase) ).
thf(517,plain,
! [A: tree_a > a > produc143150363Tree_a,B: tree_a,C: a] :
( ( produc369019363Tree_a @ A @ ( produc649172771ee_a_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(328,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_left_Osimps) ).
thf(1476,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)],[328]) ).
thf(20,axiom,
! [A: produc143150363Tree_a > $o,B: a,C: tree_a] :
( ( produc1291432345ee_a_o @ A @ B @ C )
=> ( A @ ( produc686083979Tree_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_curryE) ).
thf(390,plain,
! [A: produc143150363Tree_a > $o,B: a,C: tree_a] :
( ( produc1291432345ee_a_o @ A @ B @ C )
=> ( A @ ( produc686083979Tree_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
! [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
& ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_prod_Oexpand) ).
thf(401,plain,
! [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
& ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(261,axiom,
! [A: produc981471411ee_a_a > $o,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( ~ ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
& ~ ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_prod_Osplit__sel__asm) ).
thf(1244,plain,
! [A: produc981471411ee_a_a > $o,B: a > tree_a > produc981471411ee_a_a,C: produc143150363Tree_a] :
( ( A @ ( produc1331510035ee_a_a @ B @ C ) )
= ( ~ ( ( C
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) )
& ~ ( A @ ( B @ ( product_fst_a_Tree_a @ C ) @ ( product_snd_a_Tree_a @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(79,axiom,
! [A: tree_a > a > produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( produc1331510035ee_a_a
@ ^ [C: a,D: tree_a] : ( A @ D @ C )
@ ( produc1478296771ee_a_a @ B ) )
= ( produc1207340411ee_a_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_case__swap) ).
thf(588,plain,
! [A: tree_a > a > produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( produc1331510035ee_a_a
@ ^ [C: a,D: tree_a] : ( A @ D @ C )
@ ( produc1478296771ee_a_a @ B ) )
= ( produc1207340411ee_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(265,axiom,
! [A: tree_a > tree_a,B: produc143150363Tree_a] :
( ( product_snd_a_Tree_a @ ( produc819961216ee_a_a @ A @ B ) )
= ( A @ ( product_snd_a_Tree_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_snd__apsnd) ).
thf(1253,plain,
! [A: tree_a > tree_a,B: produc143150363Tree_a] :
( ( product_snd_a_Tree_a @ ( produc819961216ee_a_a @ A @ B ) )
= ( A @ ( product_snd_a_Tree_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(109,axiom,
! [A: produc981471411ee_a_a] :
~ ! [B: tree_a,C: a] :
( A
!= ( produc649172771ee_a_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_old_Oprod_Oexhaust) ).
thf(699,plain,
! [A: produc981471411ee_a_a] :
~ ! [B: tree_a,C: a] :
( A
!= ( produc649172771ee_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(120,axiom,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a > $o] :
( ! [C: produc143150363Tree_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec486369286Tree_a @ A )
= ( collec486369286Tree_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Collect__cong) ).
thf(731,plain,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a > $o] :
( ! [C: produc143150363Tree_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec486369286Tree_a @ A )
= ( collec486369286Tree_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(30,axiom,
! [A: produc981471411ee_a_a,B: tree_a,C: a] :
( ( A
= ( produc649172771ee_a_a @ B @ C ) )
=> ( ( product_snd_Tree_a_a @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_sndI) ).
thf(418,plain,
! [A: produc981471411ee_a_a,B: tree_a,C: a] :
( ( A
= ( produc649172771ee_a_a @ B @ C ) )
=> ( ( product_snd_Tree_a_a @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(137,axiom,
! [A: tree_a > $o,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_case__prodE2) ).
thf(786,plain,
! [A: tree_a > $o,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(74,axiom,
! [A: produc143150363Tree_a,B: a,C: a > tree_a > set_a] :
( ! [D: a,E: tree_a] :
( ( A
= ( produc686083979Tree_a @ D @ E ) )
=> ( member_a @ B @ ( C @ D @ E ) ) )
=> ( member_a @ B @ ( produc1902270_set_a @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_mem__case__prodI2) ).
thf(568,plain,
! [A: produc143150363Tree_a,B: a,C: a > tree_a > set_a] :
( ! [D: a,E: tree_a] :
( ( A
= ( produc686083979Tree_a @ D @ E ) )
=> ( member_a @ B @ ( C @ D @ E ) ) )
=> ( member_a @ B @ ( produc1902270_set_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(16,axiom,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a,C: produc143150363Tree_a] :
( ( ord_le1013007387Tree_a @ A @ B )
=> ( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_subsetD) ).
thf(378,plain,
! [A: set_Pr1070816379Tree_a,B: set_Pr1070816379Tree_a,C: produc143150363Tree_a] :
( ( ord_le1013007387Tree_a @ A @ B )
=> ( ( member254315204Tree_a @ C @ A )
=> ( member254315204Tree_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(35,axiom,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a] :
( ! [C: a,D: tree_a] : ( A @ ( produc686083979Tree_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_old_Oprod_Oinducts) ).
thf(433,plain,
! [A: produc143150363Tree_a > $o,B: produc143150363Tree_a] :
( ! [C: a,D: tree_a] : ( A @ ( produc686083979Tree_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(277,axiom,
! [A: tree_a > a > $o,B: produc143150363Tree_a,C: tree_a > $o,D: a > tree_a > tree_a] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ( ! [E: a,F: tree_a] :
( ( A @ F @ E )
=> ( C @ ( D @ E @ F ) ) )
=> ( C @ ( produc873356882Tree_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_exE__realizer) ).
thf(1294,plain,
! [A: tree_a > a > $o,B: produc143150363Tree_a,C: tree_a > $o,D: a > tree_a > tree_a] :
( ( A @ ( product_snd_a_Tree_a @ B ) @ ( product_fst_a_Tree_a @ B ) )
=> ( ! [E: a,F: tree_a] :
( ( A @ F @ E )
=> ( C @ ( D @ E @ F ) ) )
=> ( C @ ( produc873356882Tree_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(48,axiom,
! [A: a > tree_a > produc981471411ee_a_a,B: a,C: tree_a] :
( ( produc1331510035ee_a_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_old_Oprod_Ocase) ).
thf(478,plain,
! [A: a > tree_a > produc981471411ee_a_a,B: a,C: tree_a] :
( ( produc1331510035ee_a_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(131,axiom,
! [A: produc143150363Tree_a,B: a > tree_a > tree_a,C: a > tree_a > tree_a,D: produc143150363Tree_a] :
( ! [E: a,F: tree_a] :
( ( ( produc686083979Tree_a @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( produc873356882Tree_a @ B @ D )
= ( produc873356882Tree_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_split__cong) ).
thf(763,plain,
! [A: produc143150363Tree_a,B: a > tree_a > tree_a,C: a > tree_a > tree_a,D: produc143150363Tree_a] :
( ! [E: a,F: tree_a] :
( ( ( produc686083979Tree_a @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( produc873356882Tree_a @ B @ D )
= ( produc873356882Tree_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(282,axiom,
! [A: a] :
( ( heapIm1091024090Down_a @ ( t_a @ A @ e_a @ e_a ) )
= ( t_a @ A @ e_a @ e_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_siftDown_Osimps_I2_J) ).
thf(1309,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)],[282]) ).
thf(319,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/sandbox2/benchmark/theBenchmark.p',fact_88_is__heap_Osimps_I3_J) ).
thf(1442,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)],[319]) ).
thf(209,axiom,
! [A: produc143150363Tree_a > produc981471411ee_a_a] :
( ( produc1331510035ee_a_a @ ( produc623433908ee_a_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_case__prod__curry) ).
thf(1045,plain,
! [A: produc143150363Tree_a > produc981471411ee_a_a] :
( ( produc1331510035ee_a_a @ ( produc623433908ee_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(141,axiom,
! [A: produc143150363Tree_a,B: a > tree_a > produc981471411ee_a_a,C: a > tree_a > produc981471411ee_a_a,D: produc143150363Tree_a] :
( ! [E: a,F: tree_a] :
( ( ( produc686083979Tree_a @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( produc1331510035ee_a_a @ B @ D )
= ( produc1331510035ee_a_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_split__cong) ).
thf(800,plain,
! [A: produc143150363Tree_a,B: a > tree_a > produc981471411ee_a_a,C: a > tree_a > produc981471411ee_a_a,D: produc143150363Tree_a] :
( ! [E: a,F: tree_a] :
( ( ( produc686083979Tree_a @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( produc1331510035ee_a_a @ B @ D )
= ( produc1331510035ee_a_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(153,axiom,
! [A: tree_a,B: a] :
( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_fst__conv) ).
thf(835,plain,
! [A: tree_a,B: a] :
( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(280,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_snd__eqD) ).
thf(1303,plain,
! [A: a,B: tree_a,C: tree_a] :
( ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(241,axiom,
( heapIm915766629_max_a
= ( ^ [A: tree_a] :
( if_Pro1144176865Tree_a
@ ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) )
= e_a )
@ ( produc686083979Tree_a @ ( val_a @ A ) @ e_a )
@ ( produc686083979Tree_a @ ( val_a @ A ) @ ( heapIm1091024090Down_a @ ( t_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) @ ( heapIm1140443833left_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) @ ( heapIm1257206334ight_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_hs__remove__max__def) ).
thf(1148,plain,
( heapIm915766629_max_a
= ( ^ [A: tree_a] :
( if_Pro1144176865Tree_a
@ ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) )
= e_a )
@ ( produc686083979Tree_a @ ( val_a @ A ) @ e_a )
@ ( produc686083979Tree_a @ ( val_a @ A ) @ ( heapIm1091024090Down_a @ ( t_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) @ ( heapIm1140443833left_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) @ ( heapIm1257206334ight_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(163,axiom,
! [A: produc143150363Tree_a > $o,B: tree_a > a > produc143150363Tree_a,C: produc981471411ee_a_a] :
( ( A @ ( produc369019363Tree_a @ B @ C ) )
= ( ( C
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) )
=> ( A @ ( B @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_prod_Osplit__sel) ).
thf(865,plain,
! [A: produc143150363Tree_a > $o,B: tree_a > a > produc143150363Tree_a,C: produc981471411ee_a_a] :
( ( A @ ( produc369019363Tree_a @ B @ C ) )
= ( ( C
= ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) )
=> ( A @ ( B @ ( product_fst_Tree_a_a @ C ) @ ( product_snd_Tree_a_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(152,axiom,
( produc369019363Tree_a
= ( ^ [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] : ( A @ ( product_fst_Tree_a_a @ B ) @ ( product_snd_Tree_a_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_case__prod__beta) ).
thf(833,plain,
( produc369019363Tree_a
= ( ^ [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] : ( A @ ( product_fst_Tree_a_a @ B ) @ ( product_snd_Tree_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(27,axiom,
! [A: tree_a > tree_a,B: a > a,C: produc981471411ee_a_a] :
( ( produc569472578ee_a_a @ A @ ( produc969245172Tree_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( A @ ( product_fst_Tree_a_a @ C ) ) @ ( B @ ( product_snd_Tree_a_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_apfst__apsnd) ).
thf(410,plain,
! [A: tree_a > tree_a,B: a > a,C: produc981471411ee_a_a] :
( ( produc569472578ee_a_a @ A @ ( produc969245172Tree_a @ B @ C ) )
= ( produc649172771ee_a_a @ ( A @ ( product_fst_Tree_a_a @ C ) ) @ ( B @ ( product_snd_Tree_a_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(31,axiom,
! [A: produc981471411ee_a_a,B: tree_a > a > $o] :
( ( member1092636252ee_a_a @ A @ ( collec1324690334ee_a_a @ ( produc1587316832_a_a_o @ B ) ) )
=> ( B @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Product__Type_OCollect__case__prodD) ).
thf(422,plain,
! [A: produc981471411ee_a_a,B: tree_a > a > $o] :
( ( member1092636252ee_a_a @ A @ ( collec1324690334ee_a_a @ ( produc1587316832_a_a_o @ B ) ) )
=> ( B @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(138,axiom,
! [A: a,B: tree_a] :
( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_fst__conv) ).
thf(790,plain,
! [A: a,B: tree_a] :
( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(15,axiom,
! [A: tree_a,B: a,C: set_Pr921883667ee_a_a,D: a] :
( ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_ssubst__Pair__rhs) ).
thf(373,plain,
! [A: tree_a,B: a,C: set_Pr921883667ee_a_a,D: a] :
( ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(84,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mem__Collect__eq) ).
thf(603,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(73,axiom,
! [A: produc981471411ee_a_a,B: a,C: tree_a > a > set_a] :
( ! [D: tree_a,E: a] :
( ( A
= ( produc649172771ee_a_a @ D @ E ) )
=> ( member_a @ B @ ( C @ D @ E ) ) )
=> ( member_a @ B @ ( produc136688934_set_a @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_mem__case__prodI2) ).
thf(564,plain,
! [A: produc981471411ee_a_a,B: a,C: tree_a > a > set_a] :
( ! [D: tree_a,E: a] :
( ( A
= ( produc649172771ee_a_a @ D @ E ) )
=> ( member_a @ B @ ( C @ D @ E ) ) )
=> ( member_a @ B @ ( produc136688934_set_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',fact_8_Tree_Oinject) ).
thf(1314,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)],[284]) ).
thf(10,axiom,
! [A: tree_a,B: a,C: a] :
( ( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_snd__eqD) ).
thf(358,plain,
! [A: tree_a,B: a,C: a] :
( ( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(174,axiom,
! [A: tree_a > tree_a,B: produc143150363Tree_a > tree_a,C: produc143150363Tree_a,D: produc981471411ee_a_a > tree_a,E: produc143150363Tree_a > produc981471411ee_a_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_T236170232Tree_a @ A @ B @ C )
= ( comp_P228269369Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_comp__apply__eq) ).
thf(897,plain,
! [A: tree_a > tree_a,B: produc143150363Tree_a > tree_a,C: produc143150363Tree_a,D: produc981471411ee_a_a > tree_a,E: produc143150363Tree_a > produc981471411ee_a_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_T236170232Tree_a @ A @ B @ C )
= ( comp_P228269369Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(102,axiom,
! [A: $o > $o,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_case__prodE2) ).
thf(664,plain,
! [A: $o > $o,B: a > tree_a > $o,C: produc143150363Tree_a] :
( ( A @ ( produc1673233912ee_a_o @ B @ C ) )
=> ~ ! [D: a,E: tree_a] :
( ( C
= ( produc686083979Tree_a @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(150,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_order__class_Oorder_Oeq__iff) ).
thf(828,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)],[150]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',fact_122_order_Otrans) ).
thf(635,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)],[93]) ).
thf(1,conjecture,
is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(341,plain,
~ ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(331,axiom,
! [A: a,B: tree_a,C: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_right_Osimps) ).
thf(1495,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)],[331]) ).
thf(65,axiom,
! [A: tree_a,B: a > tree_a,C: a,D: a,E: a > a,F: set_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_a @ C @ F )
=> ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ A @ D ) @ ( bNF_Gr614734384ee_a_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_image2__eqI) ).
thf(532,plain,
! [A: tree_a,B: a > tree_a,C: a,D: a,E: a > a,F: set_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_a @ C @ F )
=> ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ A @ D ) @ ( bNF_Gr614734384ee_a_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(216,axiom,
! [A: produc981471411ee_a_a > $o,B: produc981471411ee_a_a] :
( ! [C: tree_a,D: a] : ( A @ ( produc649172771ee_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_prod__cases) ).
thf(1065,plain,
! [A: produc981471411ee_a_a > $o,B: produc981471411ee_a_a] :
( ! [C: tree_a,D: a] : ( A @ ( produc649172771ee_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(116,axiom,
! [A: a > a,B: a,C: tree_a] :
( ( produc1107567542Tree_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( produc686083979Tree_a @ ( A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_apfst__conv) ).
thf(720,plain,
! [A: a > a,B: a,C: tree_a] :
( ( produc1107567542Tree_a @ A @ ( produc686083979Tree_a @ B @ C ) )
= ( produc686083979Tree_a @ ( A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(248,axiom,
( produc1515207979Tree_a
= ( ^ [A: produc143150363Tree_a] : ( produc649172771ee_a_a @ ( product_snd_a_Tree_a @ A ) @ ( product_fst_a_Tree_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_prod_Oswap__def) ).
thf(1165,plain,
( produc1515207979Tree_a
= ( ^ [A: produc143150363Tree_a] : ( produc649172771ee_a_a @ ( product_snd_a_Tree_a @ A ) @ ( product_fst_a_Tree_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(170,axiom,
! [A: tree_a > a > $o,B: produc981471411ee_a_a] :
( ( produc1673233912ee_a_o
@ ^ [C: a,D: tree_a] : ( A @ D @ C )
@ ( produc1478296771ee_a_a @ B ) )
= ( produc1587316832_a_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_case__swap) ).
thf(886,plain,
! [A: tree_a > a > $o,B: produc981471411ee_a_a] :
( ( produc1673233912ee_a_o
@ ^ [C: a,D: tree_a] : ( A @ D @ C )
@ ( produc1478296771ee_a_a @ B ) )
= ( produc1587316832_a_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(182,axiom,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_old_Oprod_Oinject) ).
thf(928,plain,
! [A: a,B: tree_a,C: a,D: tree_a] :
( ( ( produc686083979Tree_a @ A @ B )
= ( produc686083979Tree_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(223,axiom,
! [A: set_Pr1070816379Tree_a,B: produc143150363Tree_a > $o] :
( ord_le1013007387Tree_a
@ ( collec486369286Tree_a
@ ^ [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Collect__subset) ).
thf(1093,plain,
! [A: set_Pr1070816379Tree_a,B: produc143150363Tree_a > $o] :
( ord_le1013007387Tree_a
@ ( collec486369286Tree_a
@ ^ [C: produc143150363Tree_a] :
( ( member254315204Tree_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(123,axiom,
! [A: produc143150363Tree_a > tree_a,B: produc143150363Tree_a > produc143150363Tree_a,C: produc143150363Tree_a,D: produc143150363Tree_a > tree_a,E: produc143150363Tree_a > produc143150363Tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P825537953Tree_a @ A @ B @ C )
= ( comp_P825537953Tree_a @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_comp__apply__eq) ).
thf(740,plain,
! [A: produc143150363Tree_a > tree_a,B: produc143150363Tree_a > produc143150363Tree_a,C: produc143150363Tree_a,D: produc143150363Tree_a > tree_a,E: produc143150363Tree_a > produc143150363Tree_a] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_P825537953Tree_a @ A @ B @ C )
= ( comp_P825537953Tree_a @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(45,axiom,
! [A: tree_a > $o,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( produc1673233912ee_a_o
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_prod_Ocase__distrib) ).
thf(464,plain,
! [A: tree_a > $o,B: a > tree_a > tree_a,C: produc143150363Tree_a] :
( ( A @ ( produc873356882Tree_a @ B @ C ) )
= ( produc1673233912ee_a_o
@ ^ [D: a,E: tree_a] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(234,axiom,
( produc369019363Tree_a
= ( ^ [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] : ( A @ ( product_fst_Tree_a_a @ B ) @ ( product_snd_Tree_a_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_prod_Ocase__eq__if) ).
thf(1129,plain,
( produc369019363Tree_a
= ( ^ [A: tree_a > a > produc143150363Tree_a,B: produc981471411ee_a_a] : ( A @ ( product_fst_Tree_a_a @ B ) @ ( product_snd_Tree_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(33,axiom,
! [A: produc981471411ee_a_a,B: produc143150363Tree_a,C: tree_a > a > set_Pr1070816379Tree_a] :
( ! [D: tree_a,E: a] :
( ( A
= ( produc649172771ee_a_a @ D @ E ) )
=> ( member254315204Tree_a @ B @ ( C @ D @ E ) ) )
=> ( member254315204Tree_a @ B @ ( produc951236931Tree_a @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_mem__case__prodI2) ).
thf(427,plain,
! [A: produc981471411ee_a_a,B: produc143150363Tree_a,C: tree_a > a > set_Pr1070816379Tree_a] :
( ! [D: tree_a,E: a] :
( ( A
= ( produc649172771ee_a_a @ D @ E ) )
=> ( member254315204Tree_a @ B @ ( C @ D @ E ) ) )
=> ( member254315204Tree_a @ B @ ( produc951236931Tree_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(303,axiom,
! [A: produc143150363Tree_a] :
( A
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_prod_Oexhaust__sel) ).
thf(1378,plain,
! [A: produc143150363Tree_a] :
( A
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(95,axiom,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_old_Oprod_Oinject) ).
thf(644,plain,
! [A: tree_a,B: a,C: tree_a,D: a] :
( ( ( produc649172771ee_a_a @ A @ B )
= ( produc649172771ee_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(202,axiom,
! [A: tree_a > a > produc143150363Tree_a,B: tree_a,C: a] :
( ( produc369019363Tree_a @ A @ ( produc649172771ee_a_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_case__prod__conv) ).
thf(1004,plain,
! [A: tree_a > a > produc143150363Tree_a,B: tree_a,C: a] :
( ( produc369019363Tree_a @ A @ ( produc649172771ee_a_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(165,axiom,
! [A: tree_a > a > tree_a,B: produc981471411ee_a_a] :
( ( produc873356882Tree_a
@ ^ [C: a,D: tree_a] : ( A @ D @ C )
@ ( produc1478296771ee_a_a @ B ) )
= ( produc433477818Tree_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_case__swap) ).
thf(871,plain,
! [A: tree_a > a > tree_a,B: produc981471411ee_a_a] :
( ( produc873356882Tree_a
@ ^ [C: a,D: tree_a] : ( A @ D @ C )
@ ( produc1478296771ee_a_a @ B ) )
= ( produc433477818Tree_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(333,axiom,
! [A: tree_a > $o,B: tree_a] :
( ! [C: a] : ( A @ ( t_a @ C @ e_a @ e_a ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ e_a ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ e_a @ ( t_a @ D @ E @ F ) ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a,G: a,H: tree_a,I: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ ( t_a @ G @ H @ I ) ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a,G: a,H: tree_a,I: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ ( t_a @ G @ H @ I ) ) ) ) )
=> ( ( A @ e_a )
=> ( A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_removeLeaf_Oinduct) ).
thf(1500,plain,
! [A: tree_a > $o,B: tree_a] :
( ! [C: a] : ( A @ ( t_a @ C @ e_a @ e_a ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ e_a ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ e_a @ ( t_a @ D @ E @ F ) ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a,G: a,H: tree_a,I: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ ( t_a @ G @ H @ I ) ) ) ) )
=> ( ! [C: a,D: a,E: tree_a,F: tree_a,G: a,H: tree_a,I: tree_a] :
( ( A @ ( t_a @ D @ E @ F ) )
=> ( ( A @ ( t_a @ D @ E @ F ) )
=> ( A @ ( t_a @ C @ ( t_a @ D @ E @ F ) @ ( t_a @ G @ H @ I ) ) ) ) )
=> ( ( A @ e_a )
=> ( A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(117,axiom,
! [A: produc143150363Tree_a > tree_a] :
( ( produc873356882Tree_a
@ ^ [B: a,C: tree_a] : ( A @ ( produc686083979Tree_a @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_case__prod__eta) ).
thf(723,plain,
! [A: produc143150363Tree_a > tree_a] :
( ( produc873356882Tree_a
@ ^ [B: a,C: tree_a] : ( A @ ( produc686083979Tree_a @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',fact_87_is__heap_Osimps_I4_J) ).
thf(1320,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)],[286]) ).
thf(8,axiom,
! [A: produc143150363Tree_a > $o,B: a,C: tree_a] :
( ( produc1291432345ee_a_o @ A @ B @ C )
=> ( A @ ( produc686083979Tree_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_curryD) ).
thf(354,plain,
! [A: produc143150363Tree_a > $o,B: a,C: tree_a] :
( ( produc1291432345ee_a_o @ A @ B @ C )
=> ( A @ ( produc686083979Tree_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(204,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/sandbox2/benchmark/theBenchmark.p',fact_128_ord__le__eq__subst) ).
thf(1009,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)],[204]) ).
thf(181,axiom,
! [A: tree_a > a > $o,B: tree_a,C: a,D: produc981471411ee_a_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc649172771ee_a_a @ B @ C ) )
=> ( A @ ( product_fst_Tree_a_a @ D ) @ ( product_snd_Tree_a_a @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(923,plain,
! [A: tree_a > a > $o,B: tree_a,C: a,D: produc981471411ee_a_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc649172771ee_a_a @ B @ C ) )
=> ( A @ ( product_fst_Tree_a_a @ D ) @ ( product_snd_Tree_a_a @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(326,axiom,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ e_a @ ( t_a @ B @ C @ D ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ e_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_removeLeaf_Osimps_I3_J) ).
thf(1468,plain,
! [A: a,B: a,C: tree_a,D: tree_a] :
( ( heapIm837449470Leaf_a @ ( t_a @ A @ e_a @ ( t_a @ B @ C @ D ) ) )
= ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) @ ( t_a @ A @ e_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(12,axiom,
( ( (=) @ produc981471411ee_a_a )
= ( ^ [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
& ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_prod__eq__iff) ).
thf(364,plain,
( ( (=) @ produc981471411ee_a_a )
= ( ^ [A: produc981471411ee_a_a,B: produc981471411ee_a_a] :
( ( ( product_fst_Tree_a_a @ A )
= ( product_fst_Tree_a_a @ B ) )
& ( ( product_snd_Tree_a_a @ A )
= ( product_snd_Tree_a_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(169,axiom,
! [A: produc143150363Tree_a] :
~ ! [B: a,C: tree_a] :
( A
!= ( produc686083979Tree_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_old_Oprod_Oexhaust) ).
thf(882,plain,
! [A: produc143150363Tree_a] :
~ ! [B: a,C: tree_a] :
( A
!= ( produc686083979Tree_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(195,axiom,
! [A: tree_a,B: a,C: tree_a] :
( ( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_fst__eqD) ).
thf(972,plain,
! [A: tree_a,B: a,C: tree_a] :
( ( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1549,plain,
$false,
inference(e,[status(thm)],[892,1411,347,1237,628,962,941,1110,481,777,555,523,1406,683,1290,1068,1522,1422,1544,449,1142,511,1533,597,861,1078,384,1137,550,797,1260,913,1063,1001,709,1359,1366,1529,436,1482,651,1095,404,1409,1287,1298,1330,1279,1455,934,1323,619,838,817,638,1247,1479,416,969,606,475,756,591,1373,514,1383,821,492,1465,353,966,981,687,877,734,453,774,1526,1351,660,998,1242,849,1206,920,529,793,810,1338,381,366,714,1057,1153,761,1387,746,1355,1123,561,392,424,1370,815,729,957,894,407,630,484,625,879,852,830,889,916,467,1159,461,1402,874,1259,948,1017,1498,1425,356,783,1397,697,1234,1541,1361,753,537,526,489,706,1419,1155,547,622,1114,647,1451,1266,984,1393,1150,1249,1131,654,1060,1050,1333,1202,633,508,657,1054,1170,1167,953,662,1086,938,398,1035,558,1071,906,1251,856,444,1219,824,819,843,743,413,1007,694,577,711,1256,545,1428,1139,572,1312,1107,1239,1258,350,979,1209,900,681,1282,1117,1048,737,1376,1307,362,451,387,1471,494,758,609,594,520,1381,1112,345,858,1162,726,943,1022,959,780,394,1364,1102,431,1445,868,505,438,1076,1134,812,342,1145,1081,749,690,1400,1368,1098,1300,441,717,502,840,1262,1317,808,1336,1038,585,370,703,1536,1284,446,497,1240,1353,600,845,931,1157,581,1216,1126,1448,1390,1453,771,976,903,517,1476,390,401,1244,588,1253,699,731,418,786,568,378,433,1294,478,763,1309,1442,1045,800,835,1303,1148,865,833,410,422,790,373,603,564,1314,358,897,664,828,635,341,1495,532,1065,720,1165,886,928,1093,740,464,1129,427,1378,644,1004,871,1500,723,1320,354,1009,923,1468,364,882,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP071^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n008.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 14:24:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.89/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.90/1.11 % [INFO] Parsing done (252ms).
% 1.90/1.12 % [INFO] Running in sequential loop mode.
% 2.66/1.35 % [INFO] eprover registered as external prover.
% 2.66/1.35 % [INFO] cvc4 registered as external prover.
% 2.66/1.35 % [INFO] Scanning for conjecture ...
% 2.81/1.46 % [INFO] Found a conjecture and 357 axioms. Running axiom selection ...
% 3.24/1.56 % [INFO] Axiom selection finished. Selected 338 axioms (removed 19 axioms).
% 3.80/1.76 % [INFO] Problem is higher-order (TPTP THF).
% 4.12/1.78 % [INFO] Type checking passed.
% 4.12/1.78 % [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 ...
% 20.43/6.23 % External prover 'e' found a proof!
% 20.43/6.23 % [INFO] Killing All external provers ...
% 20.43/6.23 % Time passed: 5704ms (effective reasoning time: 5104ms)
% 20.43/6.23 % 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)>
% 20.43/6.23 % Axioms used in derivation (338): fact_287_exE__realizer, fact_109_right_Osimps, fact_126_antisym, fact_222_Product__Type_OCollect__case__prodD, fact_144_csquare__fstOp__sndOp, fact_269_case__prod__beta, fact_274_internal__case__prod__def, fact_346_apfst__apsnd, fact_223_prod_Ocase__distrib, fact_183_Heap__axioms__def, fact_87_is__heap_Osimps_I4_J, fact_203_mem__case__prodI2, fact_233_case__prodE, fact_348_apfst__apsnd, fact_216_case__swap, fact_5_removeLeaf_Ocases, fact_267_case__prod__beta, fact_245_snd__def, fact_211_case__prod__conv, fact_270_case__prod__beta, fact_139_pred__subset__eq2, fact_0_assms_I2_J, fact_138_fstOp__def, fact_122_order_Otrans, fact_212_case__prod__conv, fact_46_fstI, fact_255_case__prod__eta, fact_40_eq__fst__iff, fact_350_apsnd__apfst, fact_24_old_Oprod_Oinject, fact_83_exE__realizer_H, fact_214_case__swap, fact_79_conjI__realizer, fact_163_subsetD, fact_180_image2__eqI, fact_190_prod_Osplit__sel__asm, fact_262_Collect__case__prod__mono, fact_120_antisym__conv, fact_248_case__prodE2, fact_353_apsnd__compose, fact_53_surjective__pairing, fact_226_prod_Ocase__distrib, fact_161_in__mono, fact_3__C1_Oprems_C_I1_J, fact_323_comp__apply__eq, fact_17_siftDown__heap__is__heap, fact_285_exE__realizer, fact_312_snd__fst__flip, fact_28_snd__conv, fact_123_le__cases, fact_114_dual__order_Orefl, fact_2__C1_Oprems_C_I2_J, fact_229_prod_Ocase__distrib, fact_181_GreatestI2__order, fact_339_fst__apsnd, fact_240_old_Oprod_Ocase, fact_142_pred__equals__eq2, fact_49_prod_Oexpand, fact_29_snd__conv, fact_195_prod_Osplit__sel, fact_242_mem__case__prodE, fact_184_siftDown__multiset, fact_283_case__prod__unfold, fact_178_image2__eqI, fact_72_prod__cases, fact_112_dual__order_Otrans, fact_310_fst__snd__flip, fact_67_old_Oprod_Oexhaust, fact_321_comp__apply__eq, fact_243_mem__case__prodE, fact_135_sndOp__def, fact_234_case__prodE, fact_256_cond__case__prod__eta, fact_230_prod_Ocase__distrib, fact_280_case__prod__beta_H, fact_320_comp__apply__eq, fact_85_prod_Oswap__def, fact_111_dual__order_Oeq__iff, fact_343_fst__comp__apsnd, fact_116_order__class_Oorder_Oantisym, fact_80_exI__realizer, fact_201_mem__case__prodI2, fact_31_snd__eqD, fact_275_fstOp__in, fact_220_case__swap, fact_169_Collect__mono__iff, fact_258_cond__case__prod__eta, fact_35_removeLeaf_Osimps_I3_J, fact_168_Collect__mono, fact_300_split__part, fact_341_snd__apsnd, fact_204_mem__case__prodI2, fact_7_is__heap_Osimps_I2_J, fact_299_curryI, fact_52_prod__eq__iff, fact_104_siftDown_Osimps_I3_J, fact_159_ssubst__Pair__rhs, fact_349_apsnd__apfst, fact_132_hs__remove__max__def, fact_1_assms_I1_J, fact_196_prod_Osplit__sel, fact_325_comp__apply__eq, fact_276_sndOp__in, fact_293_heap__top__max, fact_265_prod_Ocase__eq__if, fact_308_curryE, fact_19_val_Osimps, fact_11_Tree_Odistinct_I1_J, fact_102_is__heap__max, fact_54_surjective__pairing, fact_74_surj__pair, fact_191_prod_Osplit__sel__asm, help_If_3_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T, fact_290_split__cong, fact_57_in__tree_Osimps_I2_J, fact_44_fst__eqD, fact_179_image2__eqI, fact_225_prod_Ocase__distrib, fact_246_fst__def, fact_124_eq__refl, fact_338_fst__apsnd, fact_259_cond__case__prod__eta, fact_23_old_Oprod_Oinject, fact_14_is__heap_Ocases, fact_20_siftDown_Osimps_I1_J, fact_38_prod_Ocollapse, fact_15_removeLeaf__val__val, fact_90_swap__swap, fact_250_case__prodE2, fact_351_apsnd__apfst, fact_56_prod_Oexhaust__sel, fact_215_case__swap, fact_301_case__prod__curry, fact_167_subset__iff, fact_118_ord__eq__le__trans, fact_264_prod_Ocase__eq__if, help_If_1_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T, fact_304_case__prod__curry, fact_333_apsnd__conv, fact_278_case__prod__beta_H, fact_272_internal__case__prod__def, fact_128_ord__le__eq__subst, fact_313_snd__fst__flip, fact_47_prod__eqI, fact_8_Tree_Oinject, fact_319_comp__apply__eq, fact_182_Greatest__equality, fact_113_linorder__wlog, fact_107_siftDown_Osimps_I5_J, fact_143_csquare__fstOp__sndOp, fact_61_old_Oprod_Oinducts, fact_186_multiset__heapify, fact_335_fst__apfst, fact_324_comp__apply__eq, fact_105_siftDown_Osimps_I4_J, fact_327_snd__comp__apsnd, fact_332_apsnd__conv, fact_45_fstI, fact_238_old_Oprod_Ocase, fact_347_apfst__apsnd, fact_218_case__swap, fact_55_prod_Oexhaust__sel, fact_318_comp__apply__eq, fact_271_internal__case__prod__def, fact_337_snd__apfst, fact_268_case__prod__beta, fact_194_prod_Osplit__sel, fact_192_prod_Osplit__sel__asm, fact_177_image2__eqI, fact_326_comp__apply__eq, fact_84_prod_Oswap__def, fact_205_case__prodI, fact_69_Pair__inject, fact_235_case__prodD, fact_12_Tree_Oinduct, fact_249_case__prodE2, fact_314_fst__fstOp, fact_50_prod_Oexpand, fact_100_is__heap_Osimps_I5_J, fact_252_case__prod__eta, fact_78_conjI__realizer, fact_101_is__heap_Osimps_I6_J, fact_127_eq__iff, fact_71_prod__cases, fact_134_Heap_Oremove__max__val, fact_197_mem__case__prodI, fact_244_mem__case__prodE, fact_296_curry__case__prod, fact_136_sndOp__def, fact_155_subsetI, fact_93_fst__swap, fact_34_removeLeaf_Osimps_I2_J, fact_68_old_Oprod_Oexhaust, fact_42_fst__conv, fact_340_apsnd__eq__conv, fact_336_apfst__eq__conv, fact_253_case__prod__eta, fact_97_siftDown__Node, fact_224_prod_Ocase__distrib, fact_251_case__prodE2, fact_98_heapify_Osimps_I1_J, fact_77_BNF__Greatest__Fixpoint_Osubst__Pair, fact_39_eq__fst__iff, fact_25_siftDown__in__tree, fact_208_case__prodI2, fact_236_case__prodD, fact_241_mem__case__prodE, fact_82_exE__realizer_H, fact_331_apfst__conv, fact_117_ord__le__eq__trans, fact_260_case__prod__Pair__iden, fact_43_fst__eqD, fact_237_old_Oprod_Ocase, fact_62_mem__Collect__eq, fact_257_cond__case__prod__eta, fact_94_fst__swap, fact_18_siftDown_Osimps_I2_J, fact_48_prod__eqI, fact_13_Tree_Oexhaust, fact_115_order__trans, fact_16_removeLeaf_Osimps_I1_J, fact_228_prod_Ocase__distrib, fact_108_left_Osimps, fact_213_case__swap, fact_21_prod_Oinject, fact_145_csquare__fstOp__sndOp, fact_110_dual__order_Oantisym, fact_121_le__cases3, fact_88_is__heap_Osimps_I3_J, fact_200_mem__case__prodI, fact_92_swap__simp, fact_239_old_Oprod_Ocase, fact_152_subrelI, fact_254_case__prod__eta, fact_282_case__prod__unfold, fact_106_siftDown_Osimps_I6_J, fact_231_prod_Ocase__distrib, fact_103_order__refl, fact_206_case__prodI, fact_302_case__prod__curry, fact_281_case__prod__unfold, fact_75_removeLeaf_Osimps_I5_J, fact_298_curryI, fact_295_curry__case__prod, fact_149_subset__CollectI, fact_209_case__prod__conv, fact_202_mem__case__prodI2, fact_322_comp__apply__eq, fact_81_exI__realizer, fact_273_internal__case__prod__def, fact_51_prod__eq__iff, fact_227_prod_Ocase__distrib, fact_193_prod_Osplit__sel, fact_165_subset__eq, fact_37_prod_Ocollapse, fact_334_fst__apfst, fact_22_prod_Oinject, fact_207_case__prodI2, fact_266_prod_Ocase__eq__if, fact_99_heapify__heap__is__heap, fact_309_curryE, fact_317_comp__apply__eq, fact_10_is__heap_Osimps_I1_J, fact_330_apfst__conv, fact_66_Collect__cong, fact_279_case__prod__beta_H, fact_76_BNF__Greatest__Fixpoint_Osubst__Pair, fact_303_case__prod__curry, fact_89_swap__swap, fact_288_exE__realizer, fact_64_Collect__mem__eq, fact_133_Heap_Oremove__max__is__heap, fact_292_split__cong, fact_158_ssubst__Pair__rhs, fact_9_hs__is__empty__def, fact_284_case__prod__unfold, fact_36_removeLeaf_Osimps_I4_J, fact_175_prop__restrict, fact_157_Collect__restrict, fact_60_old_Oprod_Oinducts, fact_119_order__class_Oorder_Oeq__iff, fact_58_in__tree_Osimps_I1_J, fact_59_siftDown__in__tree__set, fact_187_Heap__axioms_Ointro, fact_316_snd__sndOp, fact_73_surj__pair, fact_141_pred__equals__eq2, fact_311_fst__snd__flip, fact_176_conj__subset__def, fact_4_siftDown_Ocases, fact_95_snd__swap, fact_86_heapify_Osimps_I2_J, fact_217_case__swap, fact_297_curry__case__prod, fact_30_snd__eqD, fact_198_mem__case__prodI, fact_129_ord__eq__le__subst, fact_307_curryD, fact_26_eq__snd__iff, fact_131_order__subst1, fact_291_split__cong, fact_219_case__swap, fact_188_heap__top__geq, fact_125_linear, fact_91_swap__simp, fact_70_Pair__inject, fact_277_case__prod__beta_H, help_If_2_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T, fact_345_apfst__apsnd, fact_352_apsnd__apfst, fact_286_exE__realizer, fact_137_fstOp__def, fact_294_curry__case__prod, fact_328_fst__comp__apfst, fact_210_case__prod__conv, fact_65_Collect__mem__eq, fact_41_fst__conv, fact_130_order__subst2, fact_221_Product__Type_OCollect__case__prodD, fact_33_sndI, fact_263_prod_Ocase__eq__if, fact_247_fst__def, fact_171_Collect__subset, fact_185_Heap_Oremove__max__multiset_H, fact_342_snd__comp__apfst, fact_289_split__cong, fact_199_mem__case__prodI, fact_305_prod_Odisc__eq__case, fact_63_mem__Collect__eq, fact_261_case__prod__Pair__iden, fact_147_subset__Collect__iff, fact_232_prod_Ocase__distrib, fact_27_eq__snd__iff, fact_189_prod_Osplit__sel__asm, fact_6_removeLeaf_Oinduct, fact_96_snd__swap, fact_306_curryD, fact_32_sndI
% 20.43/6.23 % No. of inferences in proof: 680
% 20.43/6.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5704 ms resp. 5104 ms w/o parsing
% 21.39/6.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.39/6.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------