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
%------------------------------------------------------------------------------