%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT171+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 : Fri Sep 25 02:40:57 PM UTC 2026
% Result : Theorem 3.68s 6.39s
% Output : CNFRefutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of types : 0 ( 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 : 39 ( 39 usr; 18 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f141,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('/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) ).
fof(f142,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
fof(f885,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f886,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(negated_conjecture,[status(cth)],[f885]) ).
fof(f887,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(flattening,[],[f886]) ).
fof(f1759,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)))
| 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,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(nnf_transformation,[],[f142]) ).
fof(f2248,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(cnf_transformation,[],[f141]) ).
fof(f2250,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(cnf_transformation,[],[f1759]) ).
fof(f3397,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(cnf_transformation,[],[f887]) ).
tcf(c_232,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(cnf_transformation,[],[f2248]) ).
tcf(c_233,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)))
| ~ 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(cnf_transformation,[],[f2250]) ).
tcf(c_1337,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(cnf_transformation,[],[f3397]) ).
tcf(c_1929,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_233,c_232,c_1337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT171+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 % Computer : n003.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Thu Sep 24 09:01:27 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.47 Running first-order theorem proving
% 0.15/5.48 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.49
% 0.15/5.49 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.49
% 0.15/5.49 % Detected problem language: tptp
% 0.18/5.51 % Proving...
% 3.68/6.39 % SZS status Started for theBenchmark.p
% 3.68/6.39 % SZS status Theorem for theBenchmark.p
% 3.68/6.39
% 3.68/6.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.68/6.39
% 3.68/6.39 % ------ iProver source info
% 3.68/6.39
% 3.68/6.39 % git: date: 2026-07-19 20:42:38 +0200
% 3.68/6.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.68/6.39 % git: non_committed_changes: false
% 3.68/6.39
% 3.68/6.39 % ------ Parsing...
% 3.68/6.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.68/6.39
% 3.68/6.39 % ------ Preprocessing...%
% 3.68/6.39
% 3.68/6.39 % SZS status Theorem for theBenchmark.p
% 3.68/6.39
% 3.68/6.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.68/6.39
% 3.68/6.39
%------------------------------------------------------------------------------