TSTP Solution File: SCT171+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT171+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 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 : Thu Aug 31 14:22:22 EDT 2023
% Result : Theorem 39.48s 5.45s
% Output : Proof 39.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT171+2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 16:10:47 EDT 2023
% 0.16/0.35 % CPUTime :
% 39.48/5.45 Command-line arguments: --no-flatten-goal
% 39.48/5.45
% 39.48/5.45 % SZS status Theorem
% 39.48/5.45
% 39.48/5.46 % SZS output start Proof
% 39.48/5.46 Take the following subset of the input axioms:
% 39.48/5.46 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)))).
% 39.48/5.46 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))))))).
% 39.48/5.46 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))))))).
% 39.48/5.46
% 39.48/5.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 39.48/5.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 39.48/5.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 39.48/5.46 fresh(y, y, x1...xn) = u
% 39.48/5.46 C => fresh(s, t, x1...xn) = v
% 39.48/5.46 where fresh is a fresh function symbol and x1..xn are the free
% 39.48/5.46 variables of u and v.
% 39.48/5.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 39.48/5.46 input problem has no model of domain size 1).
% 39.48/5.46
% 39.48/5.46 The encoding turns the above axioms into the following unit equations and goals:
% 39.48/5.46
% 39.48/5.46 Axiom 1 (fact_14_PW_1): fresh726(X, X) = true2.
% 39.48/5.46 Axiom 2 (fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto): 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)))))) = true2.
% 39.48/5.46 Axiom 3 (fact_14_PW_1): fresh726(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)))))), true2) = hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt, hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt, c), d)), hAPP_f1817389232t_bool(f, p))).
% 39.48/5.46
% 39.48/5.46 Goal 1 (conj_0): hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt, hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt, c), d)), hAPP_f1817389232t_bool(f, p))) = true2.
% 39.48/5.46 Proof:
% 39.48/5.46 hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt, hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt, c), d)), hAPP_f1817389232t_bool(f, p)))
% 39.48/5.46 = { by axiom 3 (fact_14_PW_1) R->L }
% 39.48/5.46 fresh726(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)))))), true2)
% 39.48/5.46 = { by axiom 2 (fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) }
% 39.48/5.46 fresh726(true2, true2)
% 39.48/5.46 = { by axiom 1 (fact_14_PW_1) }
% 39.48/5.46 true2
% 39.48/5.46 % SZS output end Proof
% 39.48/5.46
% 39.48/5.46 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------