%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP071^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:35 AM UTC 2026
% Result : Theorem 0.67s 0.43s
% Output : Refutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 104 ( 7 ~; 4 |; 0 &; 93 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 376 ( 373 usr; 5 con; 0-6 aty)
% Number of variables : 29 ( 18 ^; 11 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
produc1689254567Tree_a: $tType ).
thf(type_def_6,type,
set_Pr1070816379Tree_a: $tType ).
thf(type_def_7,type,
set_Pr921883667ee_a_a: $tType ).
thf(type_def_8,type,
produc143150363Tree_a: $tType ).
thf(type_def_9,type,
produc981471411ee_a_a: $tType ).
thf(type_def_10,type,
set_Product_prod_a_a: $tType ).
thf(type_def_11,type,
product_prod_a_a: $tType ).
thf(type_def_12,type,
multiset_a: $tType ).
thf(type_def_13,type,
list_a: $tType ).
thf(type_def_14,type,
tree_a: $tType ).
thf(type_def_15,type,
set_a: $tType ).
thf(type_def_16,type,
a: $tType ).
thf(type_def_17,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,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(func_def_1,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(func_def_2,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(func_def_3,type,
bNF_fstOp_Tree_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_4,type,
bNF_fs1579355852Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_5,type,
bNF_fstOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc143150363Tree_a ).
thf(func_def_6,type,
bNF_fstOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > product_prod_a_a ).
thf(func_def_7,type,
bNF_pi1059296282ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > tree_a > a > tree_a ).
thf(func_def_8,type,
bNF_pi1407460238_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > tree_a > a > a ).
thf(func_def_9,type,
bNF_pi1536086554Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > tree_a ).
thf(func_def_10,type,
bNF_pi207687054Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > a ).
thf(func_def_11,type,
bNF_sn210385162ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_12,type,
bNF_sn687175434Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc1689254567Tree_a ).
thf(func_def_13,type,
bNF_sndOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc981471411ee_a_a ).
thf(func_def_14,type,
bNF_sndOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_15,type,
bNF_Gr2005589581ee_a_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > tree_a ) > ( produc143150363Tree_a > a ) > set_Pr921883667ee_a_a ).
thf(func_def_16,type,
bNF_Gr2042500789Tree_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > tree_a ) > set_Pr1070816379Tree_a ).
thf(func_def_17,type,
bNF_Gr614734384ee_a_a: set_a > ( a > tree_a ) > ( a > a ) > set_Pr921883667ee_a_a ).
thf(func_def_18,type,
bNF_Gr651645592Tree_a: set_a > ( a > a ) > ( a > tree_a ) > set_Pr1070816379Tree_a ).
thf(func_def_19,type,
comp_T59512783Tree_a: ( tree_a > tree_a ) > ( tree_a > tree_a ) > tree_a > tree_a ).
thf(func_def_20,type,
comp_T1074491280ee_a_a: ( tree_a > tree_a ) > ( produc981471411ee_a_a > tree_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_21,type,
comp_T236170232Tree_a: ( tree_a > tree_a ) > ( produc143150363Tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_22,type,
comp_P1066590417ee_a_a: ( produc981471411ee_a_a > tree_a ) > ( produc981471411ee_a_a > produc981471411ee_a_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_23,type,
comp_P228269369Tree_a: ( produc981471411ee_a_a > tree_a ) > ( produc143150363Tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_24,type,
comp_P342079405Tree_a: ( produc981471411ee_a_a > a ) > ( produc143150363Tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > a ).
thf(func_def_25,type,
comp_P1663859001ee_a_a: ( produc143150363Tree_a > tree_a ) > ( produc981471411ee_a_a > produc143150363Tree_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_26,type,
comp_P825537953Tree_a: ( produc143150363Tree_a > tree_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_27,type,
comp_P1103783853ee_a_a: ( produc143150363Tree_a > a ) > ( produc981471411ee_a_a > produc143150363Tree_a ) > produc981471411ee_a_a > a ).
thf(func_def_28,type,
comp_P265462805Tree_a: ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > produc143150363Tree_a > a ).
thf(func_def_29,type,
comp_a608639864Tree_a: ( a > a ) > ( produc143150363Tree_a > a ) > produc143150363Tree_a > a ).
thf(func_def_30,type,
heapIm970322378pify_a: tree_a > tree_a ).
thf(func_def_31,type,
heapIm229596386mpty_a: tree_a > $o ).
thf(func_def_32,type,
heapIm915766629_max_a: tree_a > produc143150363Tree_a ).
thf(func_def_33,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(func_def_34,type,
heapIm837449470Leaf_a: tree_a > produc143150363Tree_a ).
thf(func_def_35,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(func_def_36,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(func_def_37,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(func_def_38,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(func_def_39,type,
e_a: tree_a ).
thf(func_def_40,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(func_def_41,type,
in_tree_a: a > tree_a > $o ).
thf(func_def_42,type,
is_heap_a: tree_a > $o ).
thf(func_def_43,type,
multiset_a2: tree_a > multiset_a ).
thf(func_def_44,type,
val_a: tree_a > a ).
thf(func_def_45,type,
if_Pro1144176865Tree_a: $o > produc143150363Tree_a > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_46,type,
lattic146396397_Max_a: set_a > a ).
thf(func_def_47,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(func_def_48,type,
set_mset_a: multiset_a > set_a ).
thf(func_def_49,type,
ord_le1748873858_a_a_o: ( tree_a > a > $o ) > ( tree_a > a > $o ) > $o ).
thf(func_def_50,type,
ord_le1601593986ee_a_o: ( produc143150363Tree_a > $o ) > ( produc143150363Tree_a > $o ) > $o ).
thf(func_def_51,type,
ord_le1327026842ee_a_o: ( a > tree_a > $o ) > ( a > tree_a > $o ) > $o ).
thf(func_def_52,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_53,type,
ord_le864074675ee_a_a: set_Pr921883667ee_a_a > set_Pr921883667ee_a_a > $o ).
thf(func_def_54,type,
ord_le1013007387Tree_a: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > $o ).
thf(func_def_55,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_56,type,
ord_less_eq_a: a > a > $o ).
thf(func_def_57,type,
order_Greatest_a: ( a > $o ) > a ).
thf(func_def_58,type,
produc649172771ee_a_a: tree_a > a > produc981471411ee_a_a ).
thf(func_def_59,type,
produc686083979Tree_a: a > tree_a > produc143150363Tree_a ).
thf(func_def_60,type,
produc569472578ee_a_a: ( tree_a > tree_a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_61,type,
produc606383786Tree_a: ( tree_a > a ) > produc1689254567Tree_a > produc143150363Tree_a ).
thf(func_def_62,type,
produc159857078_a_a_a: ( tree_a > a ) > produc981471411ee_a_a > product_prod_a_a ).
thf(func_def_63,type,
produc1046262850Tree_a: ( a > tree_a ) > produc143150363Tree_a > produc1689254567Tree_a ).
thf(func_def_64,type,
produc1070656334ee_a_a: ( a > tree_a ) > product_prod_a_a > produc981471411ee_a_a ).
thf(func_def_65,type,
produc1107567542Tree_a: ( a > a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_66,type,
produc819961216ee_a_a: ( tree_a > tree_a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_67,type,
produc856872424Tree_a: ( tree_a > a ) > produc1689254567Tree_a > produc981471411ee_a_a ).
thf(func_def_68,type,
produc21534708_a_a_a: ( tree_a > a ) > produc143150363Tree_a > product_prod_a_a ).
thf(func_def_69,type,
produc1296751488Tree_a: ( a > tree_a ) > produc981471411ee_a_a > produc1689254567Tree_a ).
thf(func_def_70,type,
produc932333964ee_a_a: ( a > tree_a ) > product_prod_a_a > produc143150363Tree_a ).
thf(func_def_71,type,
produc969245172Tree_a: ( a > a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_72,type,
produc1205515265_a_a_o: ( produc981471411ee_a_a > $o ) > tree_a > a > $o ).
thf(func_def_73,type,
produc1808426884Tree_a: ( produc981471411ee_a_a > produc143150363Tree_a ) > tree_a > a > produc143150363Tree_a ).
thf(func_def_74,type,
produc1291432345ee_a_o: ( produc143150363Tree_a > $o ) > a > tree_a > $o ).
thf(func_def_75,type,
produc740705523Tree_a: ( produc143150363Tree_a > tree_a ) > a > tree_a > tree_a ).
thf(func_def_76,type,
produc623433908ee_a_a: ( produc143150363Tree_a > produc981471411ee_a_a ) > a > tree_a > produc981471411ee_a_a ).
thf(func_def_77,type,
produc126329485Tree_a: ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > produc143150363Tree_a ).
thf(func_def_78,type,
produc1405823650ee_a_o: ( a > tree_a > $o ) > produc143150363Tree_a > $o ).
thf(func_def_79,type,
produc534868220Tree_a: ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_80,type,
produc1088820157ee_a_a: ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > produc981471411ee_a_a ).
thf(func_def_81,type,
produc1587316832_a_a_o: ( tree_a > a > $o ) > produc981471411ee_a_a > $o ).
thf(func_def_82,type,
produc433477818Tree_a: ( tree_a > a > tree_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_83,type,
produc1207340411ee_a_a: ( tree_a > a > produc981471411ee_a_a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_84,type,
produc369019363Tree_a: ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > produc143150363Tree_a ).
thf(func_def_85,type,
produc951236931Tree_a: ( tree_a > a > set_Pr1070816379Tree_a ) > produc981471411ee_a_a > set_Pr1070816379Tree_a ).
thf(func_def_86,type,
produc136688934_set_a: ( tree_a > a > set_a ) > produc981471411ee_a_a > set_a ).
thf(func_def_87,type,
produc1673233912ee_a_o: ( a > tree_a > $o ) > produc143150363Tree_a > $o ).
thf(func_def_88,type,
produc873356882Tree_a: ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_89,type,
produc1331510035ee_a_a: ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > produc981471411ee_a_a ).
thf(func_def_90,type,
produc493188987Tree_a: ( a > tree_a > produc143150363Tree_a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_91,type,
produc802621147Tree_a: ( a > tree_a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > set_Pr1070816379Tree_a ).
thf(func_def_92,type,
produc1902270_set_a: ( a > tree_a > set_a ) > produc143150363Tree_a > set_a ).
thf(func_def_93,type,
produc950721886ee_a_a: ( a > tree_a > a ) > produc143150363Tree_a > a ).
thf(func_def_94,type,
produc1206152067Tree_a: produc1689254567Tree_a > tree_a ).
thf(func_def_95,type,
product_fst_Tree_a_a: produc981471411ee_a_a > tree_a ).
thf(func_def_96,type,
product_fst_a_Tree_a: produc143150363Tree_a > a ).
thf(func_def_97,type,
product_snd_Tree_a_a: produc981471411ee_a_a > a ).
thf(func_def_98,type,
product_snd_a_Tree_a: produc143150363Tree_a > tree_a ).
thf(func_def_99,type,
product_snd_a_a: product_prod_a_a > a ).
thf(func_def_100,type,
produc1478296771ee_a_a: produc981471411ee_a_a > produc143150363Tree_a ).
thf(func_def_101,type,
produc1515207979Tree_a: produc143150363Tree_a > produc981471411ee_a_a ).
thf(func_def_102,type,
relcom439193229Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > $o ).
thf(func_def_103,type,
relcompp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > a > a > $o ).
thf(func_def_104,type,
relcompp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > $o ).
thf(func_def_105,type,
collec1324690334ee_a_a: ( produc981471411ee_a_a > $o ) > set_Pr921883667ee_a_a ).
thf(func_def_106,type,
collec486369286Tree_a: ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a ).
thf(func_def_107,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(func_def_108,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_109,type,
member1092636252ee_a_a: produc981471411ee_a_a > set_Pr921883667ee_a_a > $o ).
thf(func_def_110,type,
member254315204Tree_a: produc143150363Tree_a > set_Pr1070816379Tree_a > $o ).
thf(func_def_111,type,
member_a: a > set_a > $o ).
thf(func_def_112,type,
t: tree_a ).
thf(func_def_113,type,
v: a ).
thf(func_def_117,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_118,type,
vAND: $o > $o > $o ).
thf(func_def_119,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_120,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_121,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_122,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
vOR: $o > $o > $o ).
thf(func_def_124,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_126,type,
vIMP: $o > $o > $o ).
thf(func_def_127,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
vNOT: $o > $o ).
thf(func_def_131,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
sP0: ( tree_a > $o ) > $o ).
thf(func_def_133,type,
sP1: ( tree_a > $o ) > $o ).
thf(func_def_134,type,
sP2: ( tree_a > $o ) > $o ).
thf(func_def_135,type,
sP3: a > a > a > $o ).
thf(func_def_136,type,
sP4: a > a > a > $o ).
thf(func_def_137,type,
sP5: a > a > a > $o ).
thf(func_def_138,type,
sP6: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > tree_a ) > $o ).
thf(func_def_139,type,
sP7: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > multiset_a ) > $o ).
thf(func_def_140,type,
sK8: tree_a > a ).
thf(func_def_141,type,
sK9: tree_a > a ).
thf(func_def_142,type,
sK10: tree_a > tree_a ).
thf(func_def_143,type,
sK11: tree_a > tree_a ).
thf(func_def_144,type,
sK12: tree_a > a ).
thf(func_def_145,type,
sK13: tree_a > tree_a ).
thf(func_def_146,type,
sK14: tree_a > tree_a ).
thf(func_def_147,type,
sK15: tree_a > a ).
thf(func_def_148,type,
sK16: tree_a > a ).
thf(func_def_149,type,
sK17: tree_a > tree_a ).
thf(func_def_150,type,
sK18: tree_a > tree_a ).
thf(func_def_151,type,
sK19: tree_a > a ).
thf(func_def_152,type,
sK20: tree_a > a ).
thf(func_def_153,type,
sK21: tree_a > tree_a ).
thf(func_def_154,type,
sK22: tree_a > tree_a ).
thf(func_def_155,type,
sK23: tree_a > a ).
thf(func_def_156,type,
sK24: tree_a > a ).
thf(func_def_157,type,
sK25: tree_a > a ).
thf(func_def_158,type,
sK26: tree_a > tree_a ).
thf(func_def_159,type,
sK27: tree_a > tree_a ).
thf(func_def_160,type,
sK28: tree_a > a ).
thf(func_def_161,type,
sK29: tree_a > tree_a ).
thf(func_def_162,type,
sK30: tree_a > tree_a ).
thf(func_def_163,type,
sK31: tree_a > a ).
thf(func_def_164,type,
sK32: tree_a > a ).
thf(func_def_165,type,
sK33: tree_a > tree_a ).
thf(func_def_166,type,
sK34: tree_a > tree_a ).
thf(func_def_167,type,
sK35: tree_a > a ).
thf(func_def_168,type,
sK36: tree_a > tree_a ).
thf(func_def_169,type,
sK37: tree_a > tree_a ).
thf(func_def_170,type,
sK38: tree_a > a ).
thf(func_def_171,type,
sK39: tree_a > a ).
thf(func_def_172,type,
sK40: tree_a > tree_a ).
thf(func_def_173,type,
sK41: tree_a > tree_a ).
thf(func_def_174,type,
sK42: tree_a > a ).
thf(func_def_175,type,
sK43: tree_a > a ).
thf(func_def_176,type,
sK44: tree_a > tree_a ).
thf(func_def_177,type,
sK45: tree_a > tree_a ).
thf(func_def_178,type,
sK46: tree_a > a ).
thf(func_def_179,type,
sK47: ( tree_a > $o ) > a ).
thf(func_def_180,type,
sK48: ( tree_a > $o ) > a ).
thf(func_def_181,type,
sK49: ( tree_a > $o ) > tree_a ).
thf(func_def_182,type,
sK50: ( tree_a > $o ) > tree_a ).
thf(func_def_183,type,
sK51: ( tree_a > $o ) > a ).
thf(func_def_184,type,
sK52: ( tree_a > $o ) > tree_a ).
thf(func_def_185,type,
sK53: ( tree_a > $o ) > tree_a ).
thf(func_def_186,type,
sK54: ( tree_a > $o ) > a ).
thf(func_def_187,type,
sK55: ( tree_a > $o ) > a ).
thf(func_def_188,type,
sK56: ( tree_a > $o ) > tree_a ).
thf(func_def_189,type,
sK57: ( tree_a > $o ) > tree_a ).
thf(func_def_190,type,
sK58: ( tree_a > $o ) > a ).
thf(func_def_191,type,
sK59: ( tree_a > $o ) > a ).
thf(func_def_192,type,
sK60: ( tree_a > $o ) > tree_a ).
thf(func_def_193,type,
sK61: ( tree_a > $o ) > tree_a ).
thf(func_def_194,type,
sK62: ( tree_a > $o ) > a ).
thf(func_def_195,type,
sK63: ( tree_a > $o ) > a ).
thf(func_def_196,type,
sK64: ( tree_a > $o ) > tree_a ).
thf(func_def_197,type,
sK65: ( tree_a > $o ) > tree_a ).
thf(func_def_198,type,
sK66: ( tree_a > $o ) > a ).
thf(func_def_199,type,
sK67: ( tree_a > $o ) > tree_a ).
thf(func_def_200,type,
sK68: ( tree_a > $o ) > tree_a ).
thf(func_def_201,type,
sK69: ( tree_a > $o ) > a ).
thf(func_def_202,type,
sK70: ( tree_a > $o ) > a ).
thf(func_def_203,type,
sK71: ( tree_a > $o ) > tree_a ).
thf(func_def_204,type,
sK72: ( tree_a > $o ) > tree_a ).
thf(func_def_205,type,
sK73: tree_a > a ).
thf(func_def_206,type,
sK74: tree_a > tree_a ).
thf(func_def_207,type,
sK75: tree_a > tree_a ).
thf(func_def_208,type,
sK76: tree_a > a ).
thf(func_def_209,type,
sK77: tree_a > a ).
thf(func_def_210,type,
sK78: tree_a > tree_a ).
thf(func_def_211,type,
sK79: tree_a > tree_a ).
thf(func_def_212,type,
sK80: tree_a > a ).
thf(func_def_213,type,
sK81: tree_a > tree_a ).
thf(func_def_214,type,
sK82: tree_a > tree_a ).
thf(func_def_215,type,
sK83: tree_a > a ).
thf(func_def_216,type,
sK84: tree_a > a ).
thf(func_def_217,type,
sK85: tree_a > tree_a ).
thf(func_def_218,type,
sK86: tree_a > tree_a ).
thf(func_def_219,type,
sK87: tree_a > a ).
thf(func_def_220,type,
sK88: tree_a > a ).
thf(func_def_221,type,
sK89: tree_a > tree_a ).
thf(func_def_222,type,
sK90: tree_a > tree_a ).
thf(func_def_223,type,
sK91: tree_a > a ).
thf(func_def_224,type,
sK92: ( produc143150363Tree_a > $o ) > a ).
thf(func_def_225,type,
sK93: ( produc143150363Tree_a > $o ) > tree_a ).
thf(func_def_226,type,
sK94: ( produc981471411ee_a_a > $o ) > tree_a ).
thf(func_def_227,type,
sK95: ( produc981471411ee_a_a > $o ) > a ).
thf(func_def_228,type,
sK96: ( produc143150363Tree_a > $o ) > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_229,type,
sK97: produc143150363Tree_a > a ).
thf(func_def_230,type,
sK98: produc143150363Tree_a > tree_a ).
thf(func_def_231,type,
sK99: produc981471411ee_a_a > tree_a ).
thf(func_def_232,type,
sK100: produc981471411ee_a_a > a ).
thf(func_def_233,type,
sK101: ( produc143150363Tree_a > $o ) > a ).
thf(func_def_234,type,
sK102: ( produc143150363Tree_a > $o ) > tree_a ).
thf(func_def_235,type,
sK103: ( produc981471411ee_a_a > $o ) > tree_a ).
thf(func_def_236,type,
sK104: ( produc981471411ee_a_a > $o ) > a ).
thf(func_def_237,type,
sK105: produc143150363Tree_a > a ).
thf(func_def_238,type,
sK106: produc143150363Tree_a > tree_a ).
thf(func_def_239,type,
sK107: produc981471411ee_a_a > tree_a ).
thf(func_def_240,type,
sK108: produc981471411ee_a_a > a ).
thf(func_def_241,type,
sK109: ( a > tree_a > $o ) > tree_a ).
thf(func_def_242,type,
sK110: ( a > tree_a > $o ) > a ).
thf(func_def_243,type,
sK111: ( tree_a > a > $o ) > a ).
thf(func_def_244,type,
sK112: ( tree_a > a > $o ) > tree_a ).
thf(func_def_245,type,
sK113: a > tree_a > tree_a ).
thf(func_def_246,type,
sK114: a > tree_a > a ).
thf(func_def_247,type,
sK115: a > tree_a > tree_a ).
thf(func_def_248,type,
sK116: ( a > a > $o ) > a ).
thf(func_def_249,type,
sK117: ( a > a > $o ) > a ).
thf(func_def_250,type,
sK118: ( a > a > $o ) > a ).
thf(func_def_251,type,
sK119: ( a > a > $o ) > a ).
thf(func_def_252,type,
sK120: ( a > a ) > a ).
thf(func_def_253,type,
sK121: ( a > a ) > a ).
thf(func_def_254,type,
sK122: ( a > a ) > a ).
thf(func_def_255,type,
sK123: ( a > a ) > a ).
thf(func_def_256,type,
sK124: ( a > a ) > a ).
thf(func_def_257,type,
sK125: ( a > a ) > a ).
thf(func_def_258,type,
sK126: ( a > a ) > a ).
thf(func_def_259,type,
sK127: ( a > a ) > a ).
thf(func_def_260,type,
sK128: ( a > $o ) > ( a > $o ) > set_a > a ).
thf(func_def_261,type,
sK129: ( produc143150363Tree_a > $o ) > ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_262,type,
sK130: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > a ).
thf(func_def_263,type,
sK131: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > tree_a ).
thf(func_def_264,type,
sK132: set_Pr921883667ee_a_a > set_Pr921883667ee_a_a > tree_a ).
thf(func_def_265,type,
sK133: set_Pr921883667ee_a_a > set_Pr921883667ee_a_a > a ).
thf(func_def_266,type,
sK134: set_a > set_a > a ).
thf(func_def_267,type,
sK135: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_268,type,
sK136: ( produc143150363Tree_a > $o ) > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_269,type,
sK137: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_270,type,
sK138: a > ( a > $o ) > a ).
thf(func_def_271,type,
sK139: a > ( a > $o ) > a ).
thf(func_def_272,type,
sK140: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > multiset_a ) > tree_a ).
thf(func_def_273,type,
sK141: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > multiset_a ) > a ).
thf(func_def_274,type,
sK142: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > multiset_a ) > tree_a ).
thf(func_def_275,type,
sK143: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > tree_a ) > tree_a ).
thf(func_def_276,type,
sK144: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > tree_a ) > a ).
thf(func_def_277,type,
sK145: ( tree_a > $o ) > ( tree_a > produc143150363Tree_a ) > ( tree_a > tree_a ) > tree_a ).
thf(func_def_278,type,
sK146: ( tree_a > produc143150363Tree_a ) > ( tree_a > $o ) > ( tree_a > tree_a ) > tree_a ).
thf(func_def_279,type,
sK147: ( tree_a > produc143150363Tree_a ) > ( tree_a > $o ) > ( tree_a > tree_a ) > a ).
thf(func_def_280,type,
sK148: ( tree_a > produc143150363Tree_a ) > ( tree_a > $o ) > ( tree_a > tree_a ) > tree_a ).
thf(func_def_281,type,
sK149: ( tree_a > $o ) > ( tree_a > tree_a ) > tree_a ).
thf(func_def_282,type,
sK150: ( list_a > tree_a ) > ( tree_a > tree_a ) > list_a ).
thf(func_def_283,type,
sK151: ( tree_a > tree_a ) > ( tree_a > multiset_a ) > tree_a ).
thf(func_def_284,type,
sK152: ( a > tree_a > set_a ) > a > produc143150363Tree_a > a ).
thf(func_def_285,type,
sK153: ( a > tree_a > set_a ) > a > produc143150363Tree_a > tree_a ).
thf(func_def_286,type,
sK154: ( a > tree_a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > produc143150363Tree_a > a ).
thf(func_def_287,type,
sK155: ( a > tree_a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > produc143150363Tree_a > tree_a ).
thf(func_def_288,type,
sK156: ( tree_a > a > set_a ) > a > produc981471411ee_a_a > tree_a ).
thf(func_def_289,type,
sK157: ( tree_a > a > set_a ) > a > produc981471411ee_a_a > a ).
thf(func_def_290,type,
sK158: ( tree_a > a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > produc981471411ee_a_a > tree_a ).
thf(func_def_291,type,
sK159: ( tree_a > a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > produc981471411ee_a_a > a ).
thf(func_def_292,type,
sK160: ( tree_a > a > $o ) > produc981471411ee_a_a > tree_a ).
thf(func_def_293,type,
sK161: ( tree_a > a > $o ) > produc981471411ee_a_a > a ).
thf(func_def_294,type,
sK162: ( a > tree_a > $o ) > produc143150363Tree_a > a ).
thf(func_def_295,type,
sK163: ( a > tree_a > $o ) > produc143150363Tree_a > tree_a ).
thf(func_def_296,type,
sK164: produc981471411ee_a_a > ( tree_a > a > $o ) > tree_a ).
thf(func_def_297,type,
sK165: produc981471411ee_a_a > ( tree_a > a > $o ) > a ).
thf(func_def_298,type,
sK166: produc143150363Tree_a > ( a > tree_a > $o ) > a ).
thf(func_def_299,type,
sK167: produc143150363Tree_a > ( a > tree_a > $o ) > tree_a ).
thf(func_def_300,type,
sK168: produc143150363Tree_a > ( a > tree_a > set_a ) > a > a ).
thf(func_def_301,type,
sK169: produc143150363Tree_a > ( a > tree_a > set_a ) > a > tree_a ).
thf(func_def_302,type,
sK170: produc143150363Tree_a > ( a > tree_a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > a ).
thf(func_def_303,type,
sK171: produc143150363Tree_a > ( a > tree_a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_304,type,
sK172: produc981471411ee_a_a > ( tree_a > a > set_a ) > a > tree_a ).
thf(func_def_305,type,
sK173: produc981471411ee_a_a > ( tree_a > a > set_a ) > a > a ).
thf(func_def_306,type,
sK174: produc981471411ee_a_a > ( tree_a > a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_307,type,
sK175: produc981471411ee_a_a > ( tree_a > a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > a ).
thf(func_def_308,type,
sK176: produc143150363Tree_a > ( a > tree_a > $o ) > ( $o > $o ) > a ).
thf(func_def_309,type,
sK177: produc143150363Tree_a > ( a > tree_a > $o ) > ( $o > $o ) > tree_a ).
thf(func_def_310,type,
sK178: produc143150363Tree_a > ( a > tree_a > tree_a ) > ( tree_a > $o ) > a ).
thf(func_def_311,type,
sK179: produc143150363Tree_a > ( a > tree_a > tree_a ) > ( tree_a > $o ) > tree_a ).
thf(func_def_312,type,
sK180: produc981471411ee_a_a > ( tree_a > a > produc143150363Tree_a ) > ( produc143150363Tree_a > $o ) > tree_a ).
thf(func_def_313,type,
sK181: produc981471411ee_a_a > ( tree_a > a > produc143150363Tree_a ) > ( produc143150363Tree_a > $o ) > a ).
thf(func_def_314,type,
sK182: produc143150363Tree_a > ( a > tree_a > produc981471411ee_a_a ) > ( produc981471411ee_a_a > $o ) > a ).
thf(func_def_315,type,
sK183: produc143150363Tree_a > ( a > tree_a > produc981471411ee_a_a ) > ( produc981471411ee_a_a > $o ) > tree_a ).
thf(func_def_316,type,
sK184: ( produc143150363Tree_a > $o ) > ( a > tree_a > $o ) > a ).
thf(func_def_317,type,
sK185: ( produc143150363Tree_a > $o ) > ( a > tree_a > $o ) > tree_a ).
thf(func_def_318,type,
sK186: ( produc143150363Tree_a > tree_a ) > ( a > tree_a > tree_a ) > a ).
thf(func_def_319,type,
sK187: ( produc143150363Tree_a > tree_a ) > ( a > tree_a > tree_a ) > tree_a ).
thf(func_def_320,type,
sK188: ( produc981471411ee_a_a > produc143150363Tree_a ) > ( tree_a > a > produc143150363Tree_a ) > tree_a ).
thf(func_def_321,type,
sK189: ( produc981471411ee_a_a > produc143150363Tree_a ) > ( tree_a > a > produc143150363Tree_a ) > a ).
thf(func_def_322,type,
sK190: ( produc143150363Tree_a > produc981471411ee_a_a ) > ( a > tree_a > produc981471411ee_a_a ) > a ).
thf(func_def_323,type,
sK191: ( produc143150363Tree_a > produc981471411ee_a_a ) > ( a > tree_a > produc981471411ee_a_a ) > tree_a ).
thf(func_def_324,type,
sK192: ( a > tree_a > $o ) > ( $o > $o ) > ( tree_a > a > $o ) > a ).
thf(func_def_325,type,
sK193: ( a > tree_a > $o ) > ( $o > $o ) > ( tree_a > a > $o ) > tree_a ).
thf(func_def_326,type,
sK194: ( a > tree_a > tree_a ) > ( tree_a > $o ) > ( tree_a > a > $o ) > a ).
thf(func_def_327,type,
sK195: ( a > tree_a > tree_a ) > ( tree_a > $o ) > ( tree_a > a > $o ) > tree_a ).
thf(func_def_328,type,
sK196: ( tree_a > a > produc143150363Tree_a ) > ( produc143150363Tree_a > $o ) > ( a > tree_a > $o ) > tree_a ).
thf(func_def_329,type,
sK197: ( tree_a > a > produc143150363Tree_a ) > ( produc143150363Tree_a > $o ) > ( a > tree_a > $o ) > a ).
thf(func_def_330,type,
sK198: ( a > tree_a > produc981471411ee_a_a ) > ( produc981471411ee_a_a > $o ) > ( tree_a > a > $o ) > a ).
thf(func_def_331,type,
sK199: ( a > tree_a > produc981471411ee_a_a ) > ( produc981471411ee_a_a > $o ) > ( tree_a > a > $o ) > tree_a ).
thf(func_def_332,type,
sK200: ( a > tree_a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > a ).
thf(func_def_333,type,
sK201: ( a > tree_a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > tree_a ).
thf(func_def_334,type,
sK202: ( a > tree_a > tree_a ) > ( a > tree_a > tree_a ) > produc143150363Tree_a > a ).
thf(func_def_335,type,
sK203: ( a > tree_a > tree_a ) > ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_336,type,
sK204: ( tree_a > a > produc143150363Tree_a ) > ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_337,type,
sK205: ( tree_a > a > produc143150363Tree_a ) > ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > a ).
thf(func_def_338,type,
sK206: ( a > tree_a > produc981471411ee_a_a ) > ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > a ).
thf(func_def_339,type,
sK207: ( a > tree_a > produc981471411ee_a_a ) > ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_340,type,
sK208: ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_341,type,
sK209: ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_342,type,
sK210: set_Pr1070816379Tree_a > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_343,type,
sK211: ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_344,type,
sK212: ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_345,type,
sK213: ( a > $o ) > set_a > set_a > a ).
thf(func_def_346,type,
sK214: ( produc143150363Tree_a > $o ) > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_347,type,
sK215: ( produc143150363Tree_a > $o ) > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_348,type,
sK216: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_349,type,
sK217: set_a > set_a > a ).
thf(func_def_350,type,
sK218: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_351,type,
sK219: set_a > set_a > a ).
thf(func_def_352,type,
sK220: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_353,type,
sK221: set_a > set_a > a ).
thf(func_def_354,type,
sK222: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_355,type,
sK223: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_356,type,
sK224: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_357,type,
sK225: set_a > set_a > a ).
thf(func_def_358,type,
sK226: set_a > set_a > a ).
thf(func_def_359,type,
sK227: set_a > set_a > a ).
thf(func_def_360,type,
sK228: set_Pr1070816379Tree_a > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_361,type,
sK229: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_362,type,
sK230: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_363,type,
sK231: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_364,type,
sK232: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > ( produc143150363Tree_a > $o ) > produc143150363Tree_a ).
thf(func_def_365,type,
sK233: set_a > ( a > $o ) > a ).
thf(func_def_366,type,
sK234: set_a > set_a > a ).
thf(func_def_367,type,
sK235: set_a > set_a > a ).
thf(func_def_368,type,
sK236: set_a > set_a > a ).
thf(func_def_369,type,
sK237: set_a > set_a > ( a > $o ) > a ).
thf(func_def_370,type,
sK238: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > produc143150363Tree_a ).
thf(func_def_371,type,
sK239: produc981471411ee_a_a > tree_a > a ).
thf(func_def_372,type,
sK240: produc143150363Tree_a > a > tree_a ).
thf(func_def_373,type,
sK241: produc143150363Tree_a > tree_a > a ).
thf(func_def_374,type,
sK242: produc981471411ee_a_a > a > tree_a ).
thf(f11,axiom,
is_heap_a @ e_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_is__heap_Osimps_I1_J) ).
thf(f17,axiom,
! [X0: a] :
( ( heapIm837449470Leaf_a @ ( t_a @ X0 @ e_a @ e_a ) )
= ( produc686083979Tree_a @ X0 @ e_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_removeLeaf_Osimps_I1_J) ).
thf(f30,axiom,
! [X0: a,X1: tree_a] :
( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X0 @ X1 ) )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_snd__conv) ).
thf(f246,axiom,
( product_snd_a_Tree_a
= ( produc873356882Tree_a
@ ^ [X0: a,X1: tree_a] : X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_snd__def) ).
thf(f355,axiom,
! [X0: $o] :
( ( X0 = $false )
| ( X0 = $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T) ).
thf(f358,conjecture,
is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f359,negated_conjecture,
~ ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f370,plain,
is_heap_a @ e_a,
inference(rectify,[],[f11]) ).
thf(f371,plain,
( ( is_heap_a @ e_a )
= $true ),
inference(fool_elimination,[],[f370]) ).
thf(f693,plain,
( product_snd_a_Tree_a
= ( produc873356882Tree_a
@ ^ [X0: a,X1: tree_a] : X1 ) ),
inference(rectify,[],[f246]) ).
thf(f694,plain,
( product_snd_a_Tree_a
= ( produc873356882Tree_a
@ ^ [Y0: a,Y1: tree_a] : Y1 ) ),
inference(fool_elimination,[],[f693]) ).
thf(f773,plain,
! [X0: $o] :
( ( $false = X0 )
| ( $true = X0 ) ),
inference(fool_elimination,[],[f355]) ).
thf(f778,plain,
~ ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ),
inference(rectify,[],[f359]) ).
thf(f779,plain,
( ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) )
!= $true ),
inference(fool_elimination,[],[f778]) ).
thf(f806,plain,
( ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) )
!= $true ),
inference(flattening,[],[f779]) ).
thf(f1135,plain,
( ( is_heap_a @ e_a )
= $true ),
inference(cnf_transformation,[],[f371]) ).
thf(f1143,plain,
! [X0: a] :
( ( heapIm837449470Leaf_a @ ( t_a @ X0 @ e_a @ e_a ) )
= ( produc686083979Tree_a @ X0 @ e_a ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f1156,plain,
! [X0: a,X1: tree_a] :
( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X0 @ X1 ) )
= X1 ),
inference(cnf_transformation,[],[f30]) ).
thf(f1441,plain,
( product_snd_a_Tree_a
= ( produc873356882Tree_a
@ ^ [Y0: a,Y1: tree_a] : Y1 ) ),
inference(cnf_transformation,[],[f694]) ).
thf(f1562,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
inference(cnf_transformation,[],[f773]) ).
thf(f1565,plain,
( ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f806]) ).
thf(f1586,plain,
! [X0: a,X1: tree_a] :
( ( produc873356882Tree_a
@ ^ [Y0: a,Y1: tree_a] : Y1
@ ( produc686083979Tree_a @ X0 @ X1 ) )
= X1 ),
inference(definition_unfolding,[],[f1156,f1441]) ).
thf(f1779,plain,
( $true
!= ( is_heap_a
@ ( produc873356882Tree_a
@ ^ [Y0: a,Y1: tree_a] : Y1
@ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ) ),
inference(definition_unfolding,[],[f1565,f1441]) ).
thf(f2812,plain,
( ( $true != $true )
| ( $false
= ( is_heap_a
@ ( produc873356882Tree_a
@ ^ [Y0: a,Y1: tree_a] : Y1
@ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ) ) ),
inference(constrained_superposition,[],[f1779,f1562]) ).
thf(f2814,plain,
( $false
= ( is_heap_a
@ ( produc873356882Tree_a
@ ^ [Y0: a,Y1: tree_a] : Y1
@ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ) ),
inference(trivial_inequality_removal,[],[f2812]) ).
thf(f3184,plain,
( $false
= ( is_heap_a
@ ( produc873356882Tree_a
@ ^ [Y0: a,Y1: tree_a] : Y1
@ ( produc686083979Tree_a @ v @ e_a ) ) ) ),
inference(constrained_superposition,[],[f2814,f1143]) ).
thf(f3428,plain,
( ( is_heap_a @ e_a )
= $false ),
inference(constrained_superposition,[],[f3184,f1586]) ).
thf(f3435,plain,
$true = $false,
inference(constrained_superposition,[],[f1135,f3428]) ).
thf(f3446,plain,
$false,
inference(trivial_inequality_removal,[],[f3435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP071^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:46:46 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/0.43 % (552601)Will run a generic schedule for satisfiability detection.
% 0.67/0.43 % (552610)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=850099487:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.67/0.43 % (552607)% WARNING: option uhcvi not known.
% 0.67/0.43 % (552606)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2676498319_2999 on theBenchmark for (2999ds/0Mi)
% 0.67/0.43 % (552607)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3081497325:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.67/0.43 % (552611)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2209512782:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.67/0.43 % (552608)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1629357552:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.67/0.43 % (552612)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=74368273:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.67/0.43 % (552609)dis+10_1_sil=32000:sp=arity:random_seed=1884709278:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.67/0.43 % (552610)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.67/0.43 % (552610)Instruction limit reached!
% 0.67/0.43 % (552610)------------------------------
% 0.67/0.43 % (552610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (552610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (552610)CaDiCaL version: 2.1.3
% 0.67/0.43 % (552610)Termination reason: Instruction limit
% 0.67/0.43 % (552610)Termination phase: Property scanning
% 0.67/0.43 % (552610)Time elapsed: 0.026 s
% 0.67/0.43 % (552610)Peak memory usage: 11 MB
% 0.67/0.43 % (552610)Instructions burned: 117 (million)
% 0.67/0.43 % (552607)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.67/0.43 % (552620)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2666813666:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.67/0.43 % (552609)Instruction limit reached!
% 0.67/0.43 % (552609)------------------------------
% 0.67/0.43 % (552609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (552609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (552609)CaDiCaL version: 2.1.3
% 0.67/0.43 % (552609)Termination reason: Instruction limit
% 0.67/0.43 % (552609)Termination phase: Property scanning
% 0.67/0.43 % (552609)Time elapsed: 0.044 s
% 0.67/0.43 % (552609)Peak memory usage: 11 MB
% 0.67/0.43 % (552609)Instructions burned: 105 (million)
% 0.67/0.43 % (552607)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.67/0.43 % (552611)Instruction limit reached!
% 0.67/0.43 % (552611)------------------------------
% 0.67/0.43 % (552611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (552611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (552611)CaDiCaL version: 2.1.3
% 0.67/0.43 % (552611)Termination reason: Instruction limit
% 0.67/0.43 % (552611)Termination phase: Saturation
% 0.67/0.43 % (552611)Time elapsed: 0.055 s
% 0.67/0.43 % (552611)Peak memory usage: 13 MB
% 0.67/0.43 % (552611)Instructions burned: 132 (million)
% 0.67/0.43 % Exception at run slice level
% 0.67/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.67/0.43 % (552622)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3408490951:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.67/0.43 % (552612)Instruction limit reached!
% 0.67/0.43 % (552612)------------------------------
% 0.67/0.43 % (552612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (552612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (552612)CaDiCaL version: 2.1.3
% 0.67/0.43 % (552612)Termination reason: Instruction limit
% 0.67/0.43 % (552612)Termination phase: Saturation
% 0.67/0.43 % (552612)Time elapsed: 0.067 s
% 0.67/0.43 % (552612)Peak memory usage: 13 MB
% 0.67/0.43 % (552612)Instructions burned: 160 (million)
% 0.67/0.43 % (552624)ott-21_1_sil=16000:fs=off:random_seed=3743351118:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.67/0.43 % (552623)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2594532868:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.67/0.43 % (552626)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1272122476:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.67/0.43 % Exception at run slice level
% 0.67/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.67/0.43 % (552623)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.67/0.43 % (552630)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3462608784:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.67/0.43 % (552624)Instruction limit reached!
% 0.67/0.43 % (552624)------------------------------
% 0.67/0.43 % (552624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (552624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (552624)CaDiCaL version: 2.1.3
% 0.67/0.43 % (552624)Termination reason: Instruction limit
% 0.67/0.43 % (552624)Termination phase: Saturation
% 0.67/0.43 % (552624)Time elapsed: 0.040 s
% 0.67/0.43 % (552624)Peak memory usage: 13 MB
% 0.67/0.43 % (552624)Instructions burned: 182 (million)
% 0.67/0.43 % (552607) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-552601-552607"...
% 0.67/0.43 % (552622)Instruction limit reached!
% 0.67/0.43 % (552622)------------------------------
% 0.67/0.43 % (552622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (552622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (552622)CaDiCaL version: 2.1.3
% 0.67/0.43 % (552622)Termination reason: Instruction limit
% 0.67/0.43 % (552622)Termination phase: Saturation
% 0.67/0.43 % (552622)Time elapsed: 0.055 s
% 0.67/0.43 % (552622)Peak memory usage: 13 MB
% 0.67/0.43 % (552622)Instructions burned: 131 (million)
% 0.67/0.43 % (552607)...printing done.
% 0.67/0.43 % (552607)Refutation found. Thanks to Tanya!
% 0.67/0.43 % SZS status Theorem for theBenchmark
% 0.67/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.67/0.43 % (552607)------------------------------
% 0.67/0.43 % (552607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.43 % (552607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.43 % (552607)CaDiCaL version: 2.1.3
% 0.67/0.43 % (552607)Termination reason: Refutation
% 0.67/0.43 % (552607)Time elapsed: 0.119 s
% 0.67/0.43 % (552607)Peak memory usage: 14 MB
% 0.67/0.43 % (552607)Instructions burned: 256 (million)
% 0.67/0.43 % (552601)Success in time 0.189 s
% 0.67/0.43 % Vampire exiting
%------------------------------------------------------------------------------