%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP223_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 : Sat Jun 21 05:12:06 AM UTC 2025
% Result : Theorem 171.82s 172.09s
% Output : Proof 172.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 41 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 6 ~; 2 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 26 ( 24 usr; 24 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 19 con; 0-3 aty)
% Number of variables : 50 ( 45 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(aa_int_int_type,type,
aa_int_int: ( fun_int_int * int ) > int ).
tff(aa_real_int_type,type,
aa_real_int: ( fun_real_int * real ) > int ).
tff(aa_real_real_type,type,
aa_real_real: ( fun_real_real * real ) > real ).
tff(aa_nat_real_type,type,
aa_nat_real: ( fun_nat_real * nat ) > real ).
tff(m_type,type,
m: nat ).
tff(semiri5074537144036343181t_real_type,type,
semiri5074537144036343181t_real: fun_nat_real ).
tff(aa_rea7340605660300375871l_real_type,type,
aa_rea7340605660300375871l_real: ( fun_re7681423839302404990l_real * real ) > fun_real_real ).
tff(aa_num_real_type,type,
aa_num_real: ( fun_num_real * num ) > real ).
tff(aa_num_num_type,type,
aa_num_num: ( fun_num_num * num ) > num ).
tff(one_type,type,
one: num ).
tff(bit0_type,type,
bit0: fun_num_num ).
tff(numeral_numeral_real_type,type,
numeral_numeral_real: fun_num_real ).
tff(log_type,type,
log: fun_re7681423839302404990l_real ).
tff(archim7802044766580827645g_real_type,type,
archim7802044766580827645g_real: fun_real_int ).
tff(aa_int_fun_int_int_type,type,
aa_int_fun_int_int: ( fun_int_fun_int_int * int ) > fun_int_int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(plus_plus_int_type,type,
plus_plus_int: fun_int_fun_int_int ).
tff(aa_nat_int_type,type,
aa_nat_int: ( fun_nat_int * nat ) > int ).
tff(aa_VEBT_VEBT_nat_type,type,
aa_VEBT_VEBT_nat: ( fun_VEBT_VEBT_nat * vEBT_VEBT ) > nat ).
tff(aa_VEB5832953974749077948T_VEBT_type,type,
aa_VEB5832953974749077948T_VEBT: ( fun_VE3165209603783583043T_VEBT * vEBT_VEBT ) > vEBT_VEBT ).
tff(summary_type,type,
summary: vEBT_VEBT ).
tff(vEBT_Node_type,type,
vEBT_Node: ( option4927543243414619207at_nat * nat * list_VEBT_VEBT ) > fun_VE3165209603783583043T_VEBT ).
tff(treeList_type,type,
treeList: list_VEBT_VEBT ).
tff(deg_type,type,
deg: nat ).
tff(none_P5556105721700978146at_nat_type,type,
none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
tff(vEBT_VEBT_height_type,type,
vEBT_VEBT_height: fun_VEBT_VEBT_nat ).
tff(semiri1314217659103216013at_int_type,type,
semiri1314217659103216013at_int: fun_nat_int ).
tff(lattic8265883725875713057ax_nat_type,type,
lattic8265883725875713057ax_nat: set_nat > nat ).
tff(image_VEBT_VEBT_nat_type,type,
image_VEBT_VEBT_nat: ( fun_VEBT_VEBT_nat * set_VEBT_VEBT ) > set_nat ).
tff(aa_set3061394203342972348T_VEBT_type,type,
aa_set3061394203342972348T_VEBT: ( fun_se8977052110697326915T_VEBT * set_VEBT_VEBT ) > set_VEBT_VEBT ).
tff(set_VEBT_VEBT2_type,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
tff(insert_VEBT_VEBT_type,type,
insert_VEBT_VEBT: vEBT_VEBT > fun_se8977052110697326915T_VEBT ).
tff(aa_nat_nat_type,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(suc_type,type,
suc: fun_nat_nat ).
tff(aa_nat_fun_nat_nat_type,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(one_one_nat_type,type,
one_one_nat: nat ).
tff(plus_plus_nat_type,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(na_type,type,
na: nat ).
tff(1,plain,
( ( aa_nat_int(semiri1314217659103216013at_int,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))) = aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m))) )
<=> ( aa_nat_int(semiri1314217659103216013at_int,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))) = aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
aa_nat_int(semiri1314217659103216013at_int,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))) = aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__C3_C) ).
tff(3,plain,
aa_nat_int(semiri1314217659103216013at_int,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))) = aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList)))))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m)))),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
^ [M: nat] :
refl(( ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) )
<=> ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) )
<=> ! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) )
<=> ! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_of__nat__Suc) ).
tff(9,plain,
! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) ),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
( ~ ! [M: nat] : ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) )
| ( aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList)))))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList)))))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList)))))),
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
( ( aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat) = suc )
<=> ( aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat) = suc ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat) = suc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_plus__1__eq__Suc) ).
tff(16,plain,
aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat) = suc,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))) = aa_nat_nat(suc,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
^ [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
refl(( ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) )
<=> ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) )
<=> ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) )
<=> ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_VEBT__internal_Oheight_Osimps_I2_J) ).
tff(22,plain,
! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] : ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(Uu,Deg,TreeList),Summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(Summary),set_VEBT_VEBT2(TreeList))))) )
| ( aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),treeList),summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),treeList),summary)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ( deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m) )
<=> ( deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85__C3_Ohyps_C_I4_J) ).
tff(29,plain,
deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m) = deg,
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
vEBT_Node(none_P5556105721700978146at_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),treeList) = vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),treeList),summary) = aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary) = aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),treeList),summary),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary)) = aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m),treeList),summary)),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary)) = aa_nat_nat(suc,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList))))),
inference(transitivity,[status(thm)],[34,26,17]) ).
tff(36,plain,
aa_nat_int(semiri1314217659103216013at_int,aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary))) = aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,lattic8265883725875713057ax_nat(image_VEBT_VEBT_nat(vEBT_VEBT_height,aa_set3061394203342972348T_VEBT(insert_VEBT_VEBT(summary),set_VEBT_VEBT2(treeList)))))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
aa_nat_int(semiri1314217659103216013at_int,aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m)))),
inference(transitivity,[status(thm)],[36,13,4]) ).
tff(38,plain,
( ( aa_nat_int(semiri1314217659103216013at_int,aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary))) != aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m)))) )
<=> ( aa_nat_int(semiri1314217659103216013at_int,aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary))) != aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
aa_nat_int(semiri1314217659103216013at_int,aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary))) != aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(40,plain,
aa_nat_int(semiri1314217659103216013at_int,aa_VEBT_VEBT_nat(vEBT_VEBT_height,aa_VEB5832953974749077948T_VEBT(vEBT_Node(none_P5556105721700978146at_nat,deg,treeList),summary))) != aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_real_int(archim7802044766580827645g_real,aa_real_real(aa_rea7340605660300375871l_real(log,aa_num_real(numeral_numeral_real,aa_num_num(bit0,one))),aa_nat_real(semiri5074537144036343181t_real,m)))),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP223_1 : TPTP v9.0.0. Released v8.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 18:32:17 EDT 2025
% 0.11/0.32 % CPUTime :
% 171.82/172.09 % SZS status Theorem
% 171.82/172.09 % SZS output start Proof
% See solution above
% 172.59/172.82 % E exiting
%------------------------------------------------------------------------------