%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT171+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:28:38 AM UTC 2026
% Result : Theorem 1.57s 0.91s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 11 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 39 ( 39 usr; 18 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_14_PW,axiom,
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))) ),
file('theBenchmark.p',fact_14_PW) ).
fof(conj_0,conjecture,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))),
file('theBenchmark.p',conj_0) ).
fof(conj_0_neg,negated_conjecture,
~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
file('theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
cnf(c_1301,plain,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e)))))),
inference(clausify,[status(thm)],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]) ).
cnf(c_1302,plain,
( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(ord_less_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_312654597_mktop),p)),e)),cOMBS_178315313t_bool(cOMBS_995062533t_bool(hAPP_f1931036015t_bool(cOMBB_810329756e_indi(if_fun1158274329t_bool),hAPP_n1600508401i_bool(hAPP_f595617317i_bool(cOMBC_70761414t_bool,hAPP_f1882280879t_bool(cOMBB_552200224e_indi(fequal_nat),h)),n)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(cOMBB_930893948e_indi(arrow_1046586475_above),p)),c)),e)),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_f2027600413t_bool(cOMBB_640263118e_indi(arrow_163947511_mkbot),p)),e))))))
| hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))) ),
inference(clausify,[status(thm)],[fact_14_PW]) ).
cnf(c_1303,plain,
hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))),
inference(resolve,[status(thm)],[c_1301,c_1302]) ).
cnf(c_1921,negated_conjecture,
~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,c),d)),hAPP_f1817389232t_bool(f,p))),
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_1922,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1303,c_1921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT171+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 06:40:06 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3968667 was started by sandbox on n018,
% 0.16/0.42 % Sat Sep 26 06:40:06 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.38/0.67
% 0.38/0.67 % From the command line: assign(max_seconds, 300).
% 0.38/0.67
% 0.38/0.67 % SInE: 607 to sos, 277 to usable, of 884 axioms (tolerance 2.00, depth 0 fixpoint).
% 1.57/0.91
% 1.57/0.91 % SZS status Theorem for theBenchmark
% 1.57/0.91
% 1.57/0.91 % Proof 1 at 0.11 (+ 0.05) seconds.
% 1.57/0.91 % Length of proof is 7.
% 1.57/0.91 % Level of proof is 3.
% 1.57/0.91 % Maximum clause weight is 91.000.
% 1.57/0.91 % Given clauses 0.
% 1.57/0.91
% 1.57/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------