%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP278_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:12:33 AM UTC 2025
% Result : Theorem 3.43s 3.63s
% Output : Proof 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 35 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 20 ( 4 ~; 0 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 17 con; 0-4 aty)
% Number of variables : 1 ( 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
tff(vEBT_Node_type,type,
vEBT_Node: ( option4927543243414619207at_nat * nat * list_VEBT_VEBT * vEBT_VEBT ) > vEBT_VEBT ).
tff(summary2_type,type,
summary2: vEBT_VEBT ).
tff(treeList2_type,type,
treeList2: list_VEBT_VEBT ).
tff(deg_type,type,
deg: nat ).
tff(some_P7363390416028606310at_nat_type,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
tff(aa_nat7603221163087113075at_nat_type,type,
aa_nat7603221163087113075at_nat: ( fun_na1476630412504255114at_nat * nat ) > product_prod_nat_nat ).
tff(ma_type,type,
ma: nat ).
tff(product_Pair_nat_nat_type,type,
product_Pair_nat_nat: nat > fun_na1476630412504255114at_nat ).
tff(mi_type,type,
mi: nat ).
tff(sa_type,type,
sa: vEBT_VEBT ).
tff(summary_type,type,
summary: vEBT_VEBT ).
tff(treeList_type,type,
treeList: list_VEBT_VEBT ).
tff(info_type,type,
info: option4927543243414619207at_nat ).
tff(aa_nat_nat_type,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(m_type,type,
m: nat ).
tff(aa_nat_fun_nat_nat_type,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(na_type,type,
na: nat ).
tff(plus_plus_nat_type,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(aa_num_nat_type,type,
aa_num_nat: ( fun_num_nat * num ) > nat ).
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_nat_type,type,
numeral_numeral_nat: fun_num_nat ).
tff(power_power_nat_type,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(size_s6755466524823107622T_VEBT_type,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
tff(pp_type,type,
pp: bool > $o ).
tff(aa_nat_bool_type,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(vEBT_invar_vebt_type,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_bool ).
tff(aa_set8260762808118238015T_bool_type,type,
aa_set8260762808118238015T_bool: ( fun_se448528567104302406T_bool * set_VEBT_VEBT ) > bool ).
tff(set_VEBT_VEBT2_type,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
tff(aa_VEB289770264548726718T_bool_type,type,
aa_VEB289770264548726718T_bool: ( fun_VE7346385682144900493T_bool * vEBT_VEBT ) > fun_se448528567104302406T_bool ).
tff(member_VEBT_VEBT_type,type,
member_VEBT_VEBT: fun_VE7346385682144900493T_bool ).
tff(1,plain,
( ( summary2 = summary )
<=> ( summary2 = summary ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
summary2 = summary,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062summary_A_061_Asummary_H_092_060close_062) ).
tff(3,plain,
summary2 = summary,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( treeList2 = treeList )
<=> ( treeList2 = treeList ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
treeList2 = treeList,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__092_060open_062treeList_A_061_AtreeList_H_092_060close_062) ).
tff(6,plain,
treeList2 = treeList,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ( info = some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)) )
<=> ( info = some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
info = some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_infsplit) ).
tff(9,plain,
info = some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)) = info,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2) = vEBT_Node(info,deg,treeList,summary),
inference(monotonicity,[status(thm)],[10,6,3]) ).
tff(12,plain,
vEBT_Node(info,deg,treeList,summary) = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ( sa = vEBT_Node(info,deg,treeList,summary) )
<=> ( sa = vEBT_Node(info,deg,treeList,summary) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
( ( sa = vEBT_Node(info,deg,treeList,summary) )
& ( deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m) )
& ( size_s6755466524823107622T_VEBT(treeList) = aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m) )
& pp(aa_nat_bool(vEBT_invar_vebt(summary),m))
& ! [X: vEBT_VEBT] :
( pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X),set_VEBT_VEBT2(treeList)))
=> pp(aa_nat_bool(vEBT_invar_vebt(X),na)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_737_sprop1) ).
tff(15,plain,
( ( sa = vEBT_Node(info,deg,treeList,summary) )
& ( deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m) )
& ( size_s6755466524823107622T_VEBT(treeList) = aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m) )
& pp(aa_nat_bool(vEBT_invar_vebt(summary),m)) ),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
( ( sa = vEBT_Node(info,deg,treeList,summary) )
& ( deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m) )
& ( size_s6755466524823107622T_VEBT(treeList) = aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),m) ) ),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
( ( sa = vEBT_Node(info,deg,treeList,summary) )
& ( deg = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),m) ) ),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
sa = vEBT_Node(info,deg,treeList,summary),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
sa = vEBT_Node(info,deg,treeList,summary),
inference(modus_ponens,[status(thm)],[18,13]) ).
tff(20,plain,
sa = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2),
inference(transitivity,[status(thm)],[19,12]) ).
tff(21,plain,
( ( sa != vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2) )
<=> ( sa != vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
sa != vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(23,plain,
sa != vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ITP278_1 : TPTP v9.0.0. Released v8.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.11/0.34 % Computer : n009.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Thu Jun 19 18:41:18 EDT 2025
% 0.11/0.34 % CPUTime :
% 3.43/3.63 % SZS status Theorem
% 3.43/3.63 % SZS output start Proof
% See solution above
% 4.39/4.57 % E exiting
%------------------------------------------------------------------------------