%------------------------------------------------------------------------------
% 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 : n012.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 05:24:36 AM UTC 2025
% Result : Theorem 0.60s 0.80s
% Output : Proof 0.71s
% 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 : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 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: $i > $o ).
tff(hAPP_f592646513l_bool_type,type,
hAPP_f592646513l_bool: ( $i * $i ) > $i ).
tff(hAPP_f412050202t_bool_type,type,
hAPP_f412050202t_bool: ( $i * $i ) > $i ).
tff(p_type,type,
p: $i ).
tff(f_type,type,
f: $i ).
tff(hAPP_P229966473l_bool_type,type,
hAPP_P229966473l_bool: ( $i * $i ) > $i ).
tff(hAPP_A702847159le_alt_type,type,
hAPP_A702847159le_alt: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(hAPP_A1505516597le_alt_type,type,
hAPP_A1505516597le_alt: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(produc1400112471le_alt_type,type,
produc1400112471le_alt: $i ).
tff(member1441201108le_alt_type,type,
member1441201108le_alt: $i ).
tff(hAPP_f1740414619t_bool_type,type,
hAPP_f1740414619t_bool: ( $i * $i ) > $i ).
tff(hAPP_A1805174428t_bool_type,type,
hAPP_A1805174428t_bool: ( $i * $i ) > $i ).
tff(e_type,type,
e: $i ).
tff(hAPP_f1808153265t_bool_type,type,
hAPP_f1808153265t_bool: ( $i * $i ) > $i ).
tff(hAPP_f721938099t_bool_type,type,
hAPP_f721938099t_bool: ( $i * $i ) > $i ).
tff(cOMBB_2032668066e_indi_type,type,
cOMBB_2032668066e_indi: $i > $i ).
tff(arrow_1495666017_mkbot_type,type,
arrow_1495666017_mkbot: $i ).
tff(cOMBC_1353880399t_bool_type,type,
cOMBC_1353880399t_bool: $i ).
tff(cOMBS_1064524443t_bool_type,type,
cOMBS_1064524443t_bool: $i > $i ).
tff(hAPP_f1842612975t_bool_type,type,
hAPP_f1842612975t_bool: ( $i * $i ) > $i ).
tff(hAPP_A1906441908t_bool_type,type,
hAPP_A1906441908t_bool: ( $i * $i ) > $i ).
tff(hAPP_f248867553t_bool_type,type,
hAPP_f248867553t_bool: ( $i * $i ) > $i ).
tff(hAPP_f210227915t_bool_type,type,
hAPP_f210227915t_bool: ( $i * $i ) > $i ).
tff(cOMBB_1769989562e_indi_type,type,
cOMBB_1769989562e_indi: $i > $i ).
tff(arrow_230821333_above_type,type,
arrow_230821333_above: $i ).
tff(cOMBC_898791271t_bool_type,type,
cOMBC_898791271t_bool: $i ).
tff(cOMBS_131695599t_bool_type,type,
cOMBS_131695599t_bool: $i > $i ).
tff(hAPP_f586238575t_bool_type,type,
hAPP_f586238575t_bool: ( $i * $i ) > $i ).
tff(hAPP_n821919323i_bool_type,type,
hAPP_n821919323i_bool: ( $i * $i ) > $i ).
tff(n_type,type,
n: $i ).
tff(hAPP_f446868133i_bool_type,type,
hAPP_f446868133i_bool: ( $i * $i ) > $i ).
tff(hAPP_f224734595t_bool_type,type,
hAPP_f224734595t_bool: ( $i * $i ) > $i ).
tff(h_type,type,
h: $i ).
tff(cOMBB_1883918730e_indi_type,type,
cOMBB_1883918730e_indi: $i > $i ).
tff(fequal_nat_type,type,
fequal_nat: $i ).
tff(cOMBC_1996607964t_bool_type,type,
cOMBC_1996607964t_bool: $i ).
tff(cOMBB_2107911302e_indi_type,type,
cOMBB_2107911302e_indi: $i > $i ).
tff(if_fun2098446489t_bool_type,type,
if_fun2098446489t_bool: $i ).
tff(arrow_1644373103_mktop_type,type,
arrow_1644373103_mktop: $i ).
tff(ord_less_nat_type,type,
ord_less_nat: $i ).
tff(1,plain,
( ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
<=> ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(3,plain,
~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
file('/export/starexec/sandbox2/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_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) )
<=> ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
tff(9,plain,
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
| ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e))))))
| ~ ( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
<=> hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(11,plain,
( hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p)))
| ~ hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(ord_less_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1644373103_mktop),p)),e))),hAPP_f1740414619t_bool(cOMBS_1064524443t_bool(hAPP_f1842612975t_bool(cOMBS_131695599t_bool(hAPP_f586238575t_bool(cOMBB_2107911302e_indi(if_fun2098446489t_bool),hAPP_n821919323i_bool(hAPP_f446868133i_bool(cOMBC_1996607964t_bool,hAPP_f224734595t_bool(cOMBB_1883918730e_indi(fequal_nat),h)),n))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_A1906441908t_bool(hAPP_f248867553t_bool(cOMBC_898791271t_bool,hAPP_f210227915t_bool(cOMBB_1769989562e_indi(arrow_230821333_above),p)),c)),e))),hAPP_A1805174428t_bool(hAPP_f1808153265t_bool(cOMBC_1353880399t_bool,hAPP_f721938099t_bool(cOMBB_2032668066e_indi(arrow_1495666017_mkbot),p)),e)))))) ),
inference(unit_resolution,[status(thm)],[10,9]) ).
tff(12,plain,
hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt,hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt,c),d)),hAPP_f412050202t_bool(f,p))),
inference(unit_resolution,[status(thm)],[11,6]) ).
tff(13,plain,
$false,
inference(unit_resolution,[status(thm)],[12,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT171+3 : TPTP v9.0.0. Released v5.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 03:57:40 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.60/0.80 % SZS status Theorem
% 0.60/0.80 % SZS output start Proof
% See solution above
% 0.71/0.88 % E exiting
%------------------------------------------------------------------------------