TSTP Solution File: SCT171+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT171+3 : 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 : n028.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 14:22:23 EDT 2023
% Result : Theorem 153.31s 20.18s
% Output : Proof 153.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT171+3 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 16:36:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 153.31/20.18 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 153.31/20.18
% 153.31/20.18 % SZS status Theorem
% 153.31/20.18
% 153.31/20.18 % SZS output start Proof
% 153.31/20.18 Take the following subset of the input axioms:
% 153.31/20.18 fof(conj_0, conjecture, hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt, hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt, c), d)), hAPP_f412050202t_bool(f, p)))).
% 153.31/20.18 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_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))))))).
% 153.31/20.18 fof(fact_14_PW, 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))))))).
% 153.31/20.18
% 153.31/20.18 Now clausify the problem and encode Horn clauses using encoding 3 of
% 153.31/20.18 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 153.31/20.18 We repeatedly replace C & s=t => u=v by the two clauses:
% 153.31/20.18 fresh(y, y, x1...xn) = u
% 153.31/20.18 C => fresh(s, t, x1...xn) = v
% 153.31/20.18 where fresh is a fresh function symbol and x1..xn are the free
% 153.31/20.18 variables of u and v.
% 153.31/20.18 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 153.31/20.18 input problem has no model of domain size 1).
% 153.31/20.18
% 153.31/20.18 The encoding turns the above axioms into the following unit equations and goals:
% 153.31/20.18
% 153.31/20.19 Axiom 1 (fact_14_PW_1): fresh1061(X, X) = true2.
% 153.31/20.19 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_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)))))) = true2.
% 153.31/20.19 Axiom 3 (fact_14_PW_1): fresh1061(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)))))), true2) = hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt, hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt, c), d)), hAPP_f412050202t_bool(f, p))).
% 153.31/20.19
% 153.31/20.19 Goal 1 (conj_0): hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt, hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt, c), d)), hAPP_f412050202t_bool(f, p))) = true2.
% 153.31/20.19 Proof:
% 153.31/20.19 hBOOL(hAPP_f592646513l_bool(hAPP_P229966473l_bool(member1441201108le_alt, hAPP_A702847159le_alt(hAPP_A1505516597le_alt(produc1400112471le_alt, c), d)), hAPP_f412050202t_bool(f, p)))
% 153.31/20.19 = { by axiom 3 (fact_14_PW_1) R->L }
% 153.31/20.19 fresh1061(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)))))), true2)
% 153.31/20.19 = { by axiom 2 (fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) }
% 153.31/20.19 fresh1061(true2, true2)
% 153.31/20.19 = { by axiom 1 (fact_14_PW_1) }
% 153.31/20.19 true2
% 153.31/20.19 % SZS output end Proof
% 153.31/20.19
% 153.31/20.19 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------