%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SCT171_3 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:24:37 AM UTC 2025
% Result : Theorem 0.60s 0.79s
% Output : Proof 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 3 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 36 ( 35 usr; 35 prp; 0-1 aty)
% Number of functors : 41 ( 41 usr; 18 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_f52567537l_bool_type,type,
hAPP_f52567537l_bool: ( fun_fu638310559l_bool * fun_Pr2067565481t_bool ) > bool ).
tff(hAPP_f2008608496t_bool_type,type,
hAPP_f2008608496t_bool: ( fun_fu2114379172t_bool * fun_Ar274636406t_bool ) > fun_Pr2067565481t_bool ).
tff(p_type,type,
p: fun_Ar274636406t_bool ).
tff(f_type,type,
f: fun_fu2114379172t_bool ).
tff(hAPP_P38525833l_bool_type,type,
hAPP_P38525833l_bool: ( fun_Pr1085078251l_bool * produc472769767le_alt ) > fun_fu638310559l_bool ).
tff(hAPP_A1299015393le_alt_type,type,
hAPP_A1299015393le_alt: ( fun_Ar245737999le_alt * arrow_1893660431le_alt ) > produc472769767le_alt ).
tff(d_type,type,
d: arrow_1893660431le_alt ).
tff(hAPP_A1146194953le_alt_type,type,
hAPP_A1146194953le_alt: ( fun_Ar2121501495le_alt * arrow_1893660431le_alt ) > fun_Ar245737999le_alt ).
tff(c_type,type,
c: arrow_1893660431le_alt ).
tff(produc1590937303le_alt_type,type,
produc1590937303le_alt: fun_Ar2121501495le_alt ).
tff(member1333168212le_alt_type,type,
member1333168212le_alt: fun_Pr1085078251l_bool ).
tff(hAPP_f1302887663t_bool_type,type,
hAPP_f1302887663t_bool: ( fun_fu1037963345t_bool * fun_Ar274636406t_bool ) > fun_Ar274636406t_bool ).
tff(hAPP_A425126512t_bool_type,type,
hAPP_A425126512t_bool: ( fun_Ar1623257374t_bool * arrow_1893660431le_alt ) > fun_Ar274636406t_bool ).
tff(e_type,type,
e: arrow_1893660431le_alt ).
tff(hAPP_f1631649925t_bool_type,type,
hAPP_f1631649925t_bool: ( fun_fu2128130023t_bool * fun_Ar64685412t_bool ) > fun_Ar1623257374t_bool ).
tff(hAPP_f831214557t_bool_type,type,
hAPP_f831214557t_bool: ( fun_fu1896276031t_bool * fun_Ar274636406t_bool ) > fun_Ar64685412t_bool ).
tff(cOMBB_80760910e_indi_type,type,
cOMBB_80760910e_indi: fun_fu1679793515t_bool > fun_fu1896276031t_bool ).
tff(arrow_1481558583_mkbot_type,type,
arrow_1481558583_mkbot: fun_fu1679793515t_bool ).
tff(cOMBC_1417338747t_bool_type,type,
cOMBC_1417338747t_bool: fun_fu2128130023t_bool ).
tff(cOMBS_1181656689t_bool_type,type,
cOMBS_1181656689t_bool: fun_Ar516759882t_bool > fun_fu1037963345t_bool ).
tff(hAPP_f1001205955t_bool_type,type,
hAPP_f1001205955t_bool: ( fun_fu419698981t_bool * fun_Ar274636406t_bool ) > fun_Ar516759882t_bool ).
tff(hAPP_A1889513822t_bool_type,type,
hAPP_A1889513822t_bool: ( fun_Ar1753411852t_bool * arrow_1893660431le_alt ) > fun_Ar64685412t_bool ).
tff(hAPP_f2102110817t_bool_type,type,
hAPP_f2102110817t_bool: ( fun_fu548876995t_bool * fun_Ar290235730t_bool ) > fun_Ar1753411852t_bool ).
tff(hAPP_f1751344075t_bool_type,type,
hAPP_f1751344075t_bool: ( fun_fu1427663149t_bool * fun_Ar274636406t_bool ) > fun_Ar290235730t_bool ).
tff(cOMBB_1876517692e_indi_type,type,
cOMBB_1876517692e_indi: fun_fu1287834969t_bool > fun_fu1427663149t_bool ).
tff(arrow_216713899_above_type,type,
arrow_216713899_above: fun_fu1287834969t_bool ).
tff(cOMBC_1486904681t_bool_type,type,
cOMBC_1486904681t_bool: fun_fu548876995t_bool ).
tff(cOMBS_1925466437t_bool_type,type,
cOMBS_1925466437t_bool: fun_Ar535288606t_bool > fun_fu419698981t_bool ).
tff(hAPP_f668886383t_bool_type,type,
hAPP_f668886383t_bool: ( fun_fu1821795357t_bool * fun_Ar1809396326i_bool ) > fun_Ar535288606t_bool ).
tff(hAPP_n34002993i_bool_type,type,
hAPP_n34002993i_bool: ( fun_na2037635353i_bool * nat ) > fun_Ar1809396326i_bool ).
tff(n_type,type,
n: nat ).
tff(hAPP_f721434149i_bool_type,type,
hAPP_f721434149i_bool: ( fun_fu1610971917i_bool * fun_Ar603939593t_bool ) > fun_na2037635353i_bool ).
tff(hAPP_f966656047t_bool_type,type,
hAPP_f966656047t_bool: ( fun_fu1372829539t_bool * fun_Ar671024215di_nat ) > fun_Ar603939593t_bool ).
tff(h_type,type,
h: fun_Ar671024215di_nat ).
tff(cOMBB_1869811296e_indi_type,type,
cOMBB_1869811296e_indi: fun_nat_fun_nat_bool > fun_fu1372829539t_bool ).
tff(fequal_nat_type,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(cOMBC_722552198t_bool_type,type,
cOMBC_722552198t_bool: fun_fu1610971917i_bool ).
tff(cOMBB_1061985500e_indi_type,type,
cOMBB_1061985500e_indi: fun_bo1945492389t_bool > fun_fu1821795357t_bool ).
tff(if_fun523439385t_bool_type,type,
if_fun523439385t_bool: fun_bo1945492389t_bool ).
tff(arrow_1630265669_mktop_type,type,
arrow_1630265669_mktop: fun_fu1679793515t_bool ).
tff(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(1,plain,
( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
<=> ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(3,plain,
~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e))))))
<=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_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(6,plain,
hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
<=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) )
<=> ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
<=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
<=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).
tff(9,plain,
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
<=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e))))))
| ~ ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
<=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(11,plain,
( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
| ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ),
inference(unit_resolution,[status(thm)],[10,9]) ).
tff(12,plain,
hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p))),
inference(unit_resolution,[status(thm)],[11,6]) ).
tff(13,plain,
$false,
inference(unit_resolution,[status(thm)],[12,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT171_3 : TPTP v9.0.0. Released v5.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 03:58:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.60/0.79 % SZS status Theorem
% 0.60/0.79 % SZS output start Proof
% See solution above
% 0.74/0.90 % E exiting
%------------------------------------------------------------------------------