TSTP Solution File: ITP278_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP278_1 : TPTP v8.1.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 Sep 17 04:18:16 EDT 2022
% Result : Theorem 2.89s 2.84s
% Output : Proof 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 53 ( 8 unt; 33 typ; 0 def)
% Number of atoms : 39 ( 28 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 27 ( 8 ~; 0 |; 10 &)
% ( 8 <=>; 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 : 26 ( 15 >; 11 *; 0 +; 0 <<)
% Number of predicates : 20 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 18 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(aa_nat_nat_type,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(na_type,type,
na: 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(info_type,type,
info: option4927543243414619207at_nat ).
tff(m_type,type,
m: 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,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),na)),treeList,summary) = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),na)),treeList,summary) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2) = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),na)),treeList,summary),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
vEBT_Node(info,deg,treeList,summary) = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),na)),treeList,summary),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( sa = vEBT_Node(info,deg,treeList,summary) )
<=> ( sa = vEBT_Node(info,deg,treeList,summary) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,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/sandbox2/benchmark/theBenchmark.p',fact_737_sprop1) ).
tff(7,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)],[6]) ).
tff(8,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)],[7]) ).
tff(9,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)],[8]) ).
tff(10,plain,
sa = vEBT_Node(info,deg,treeList,summary),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
sa = vEBT_Node(info,deg,treeList,summary),
inference(modus_ponens,[status(thm)],[10,5]) ).
tff(12,plain,
sa = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),na)),treeList,summary),
inference(transitivity,[status(thm)],[11,4]) ).
tff(13,plain,
( ( sa = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2) )
<=> ( vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),na)),treeList,summary) = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),na)),treeList,summary) ) ),
inference(monotonicity,[status(thm)],[12,3]) ).
tff(14,plain,
( ( sa = vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2) )
<=> $true ),
inference(transitivity,[status(thm)],[13,2]) ).
tff(15,plain,
( ( sa != vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ( sa != vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2) )
<=> $false ),
inference(transitivity,[status(thm)],[15,1]) ).
tff(17,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(18,axiom,
sa != vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(19,plain,
sa != vEBT_Node(some_P7363390416028606310at_nat(aa_nat7603221163087113075at_nat(product_Pair_nat_nat(mi),ma)),deg,treeList2,summary2),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(modus_ponens,[status(thm)],[19,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP278_1 : TPTP v8.1.0. Released v8.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 07:04:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 2.89/2.84 % SZS status Theorem
% 2.89/2.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------