TSTP Solution File: SCT171_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SCT171_2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 Sep 20 03:41:50 EDT 2022
% Result : Theorem 0.42s 0.56s
% Output : Proof 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 45
% Syntax : Number of formulae : 53 ( 4 unt; 40 typ; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 18 ( 5 ~; 0 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 39 ( 22 >; 17 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 34 prp; 0-1 aty)
% Number of functors : 39 ( 39 usr; 18 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_f429946033l_bool_type,type,
hAPP_f429946033l_bool: ( fun_fu1015689055l_bool * fun_Pr1055212137t_bool ) > bool ).
tff(hAPP_f792184801t_bool_type,type,
hAPP_f792184801t_bool: ( fun_fu1595299477t_bool * fun_Ar500372357t_bool ) > fun_Pr1055212137t_bool ).
tff(p_type,type,
p: fun_Ar500372357t_bool ).
tff(f_type,type,
f: fun_fu1595299477t_bool ).
tff(hAPP_P840149257l_bool_type,type,
hAPP_P840149257l_bool: ( fun_Pr1228236907l_bool * produc1840315303le_alt ) > fun_fu1015689055l_bool ).
tff(hAPP_A1313367280le_alt_type,type,
hAPP_A1313367280le_alt: ( fun_Ar836847646le_alt * arrow_931160158le_alt ) > produc1840315303le_alt ).
tff(d_type,type,
d: arrow_931160158le_alt ).
tff(hAPP_A1485971815le_alt_type,type,
hAPP_A1485971815le_alt: ( fun_Ar2049444117le_alt * arrow_931160158le_alt ) > fun_Ar836847646le_alt ).
tff(c_type,type,
c: arrow_931160158le_alt ).
tff(produc362059031le_alt_type,type,
produc362059031le_alt: fun_Ar2049444117le_alt ).
tff(member553230100le_alt_type,type,
member553230100le_alt: fun_Pr1228236907l_bool ).
tff(cOMBS_1921392482t_bool_type,type,
cOMBS_1921392482t_bool: ( fun_Ar1492469401t_bool * fun_Ar500372357t_bool ) > fun_Ar500372357t_bool ).
tff(hAPP_A658738638t_bool_type,type,
hAPP_A658738638t_bool: ( fun_Ar421919996t_bool * arrow_931160158le_alt ) > fun_Ar500372357t_bool ).
tff(e_type,type,
e: arrow_931160158le_alt ).
tff(hAPP_f293545699t_bool_type,type,
hAPP_f293545699t_bool: ( fun_fu613599045t_bool * fun_Ar698916836t_bool ) > fun_Ar421919996t_bool ).
tff(hAPP_f842954860t_bool_type,type,
hAPP_f842954860t_bool: ( fun_fu1872020686t_bool * fun_Ar500372357t_bool ) > fun_Ar698916836t_bool ).
tff(cOMBB_117136048e_indi_type,type,
cOMBB_117136048e_indi: fun_fu1628463836t_bool > fun_fu1872020686t_bool ).
tff(arrow_592884904_mkbot_type,type,
arrow_592884904_mkbot: fun_fu1628463836t_bool ).
tff(cOMBC_18834461t_bool_type,type,
cOMBC_18834461t_bool: fun_fu613599045t_bool ).
tff(cOMBS_811328630t_bool_type,type,
cOMBS_811328630t_bool: ( fun_Ar1519997101t_bool * fun_Ar500372357t_bool ) > fun_Ar1492469401t_bool ).
tff(hAPP_A102926893t_bool_type,type,
hAPP_A102926893t_bool: ( fun_Ar2078312923t_bool * arrow_931160158le_alt ) > fun_Ar698916836t_bool ).
tff(hAPP_f141075873t_bool_type,type,
hAPP_f141075873t_bool: ( fun_fu209106563t_bool * fun_Ar1583656131t_bool ) > fun_Ar2078312923t_bool ).
tff(hAPP_f576849227t_bool_type,type,
hAPP_f576849227t_bool: ( fun_fu757621293t_bool * fun_Ar500372357t_bool ) > fun_Ar1583656131t_bool ).
tff(cOMBB_656639247e_indi_type,type,
cOMBB_656639247e_indi: fun_fu699199419t_bool > fun_fu757621293t_bool ).
tff(arrow_1475523868_above_type,type,
arrow_1475523868_above: fun_fu699199419t_bool ).
tff(cOMBC_1505804284t_bool_type,type,
cOMBC_1505804284t_bool: fun_fu209106563t_bool ).
tff(hAPP_f509814255t_bool_type,type,
hAPP_f509814255t_bool: ( fun_fu2115718429t_bool * fun_Ar552120407i_bool ) > fun_Ar1519997101t_bool ).
tff(hAPP_n924210722i_bool_type,type,
hAPP_n924210722i_bool: ( fun_na457272970i_bool * nat ) > fun_Ar552120407i_bool ).
tff(n_type,type,
n: nat ).
tff(hAPP_f62620517i_bool_type,type,
hAPP_f62620517i_bool: ( fun_fu954933197i_bool * fun_Ar2045874810t_bool ) > fun_na457272970i_bool ).
tff(hAPP_f1381130897t_bool_type,type,
hAPP_f1381130897t_bool: ( fun_fu1845850437t_bool * fun_Ar1744566822di_nat ) > fun_Ar2045874810t_bool ).
tff(h_type,type,
h: fun_Ar1744566822di_nat ).
tff(cOMBB_981137617e_indi_type,type,
cOMBB_981137617e_indi: fun_nat_fun_nat_bool > fun_fu1845850437t_bool ).
tff(fequal_nat_type,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(cOMBC_922322901t_bool_type,type,
cOMBC_922322901t_bool: fun_fu954933197i_bool ).
tff(cOMBB_231886989e_indi_type,type,
cOMBB_231886989e_indi: fun_bo462718181t_bool > fun_fu2115718429t_bool ).
tff(if_fun1658569689t_bool_type,type,
if_fun1658569689t_bool: fun_bo462718181t_bool ).
tff(arrow_741591990_mktop_type,type,
arrow_741591990_mktop: fun_fu1628463836t_bool ).
tff(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
<=> $true )
<=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p))) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
tff(4,plain,
( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e))))))
<=> $true ),
inference(iff_true,[status(thm)],[3]) ).
tff(5,plain,
( ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
<=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))))) )
<=> ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
<=> $true ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
<=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))))) )
<=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p))) ),
inference(transitivity,[status(thm)],[5,2]) ).
tff(7,axiom,
( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
<=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).
tff(8,plain,
hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p))),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
<=> $true ),
inference(iff_true,[status(thm)],[8]) ).
tff(10,plain,
( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
<=> ~ $true ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
<=> $false ),
inference(transitivity,[status(thm)],[10,1]) ).
tff(12,axiom,
~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(13,plain,
$false,
inference(modus_ponens,[status(thm)],[12,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT171_2 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.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 : Sat Sep 3 01:00:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.42/0.56 % SZS status Theorem
% 0.42/0.56 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------