TSTP Solution File: SCT171+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT171+1 : 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 : n004.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 14:22:21 EDT 2023
% Result : Theorem 7.11s 1.82s
% Output : Proof 7.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SCT171+1 : TPTP v8.1.2. Released v5.3.0.
% 0.09/0.17 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8042.1875MB
% 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Aug 24 14:53:38 EDT 2023
% 0.12/0.37 % CPUTime :
% 7.11/1.82 Command-line arguments: --no-flatten-goal
% 7.11/1.82
% 7.11/1.82 % SZS status Theorem
% 7.11/1.82
% 7.11/1.83 % SZS output start Proof
% 7.11/1.83 Take the following subset of the input axioms:
% 7.11/1.83 fof(conj_0, conjecture, hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, p)))).
% 7.11/1.83 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_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat, h), n)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop, p), e)), cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat, h), n)), cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above, p), c), e)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot, p), e))))))).
% 7.11/1.83 fof(fact_14_PW, axiom, hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, p))) <=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat, h), n)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop, p), e)), cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat, h), n)), cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above, p), c), e)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot, p), e))))))).
% 7.11/1.83
% 7.11/1.84 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.11/1.84 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.11/1.84 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.11/1.84 fresh(y, y, x1...xn) = u
% 7.11/1.84 C => fresh(s, t, x1...xn) = v
% 7.11/1.84 where fresh is a fresh function symbol and x1..xn are the free
% 7.11/1.84 variables of u and v.
% 7.11/1.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.11/1.84 input problem has no model of domain size 1).
% 7.11/1.84
% 7.11/1.84 The encoding turns the above axioms into the following unit equations and goals:
% 7.11/1.84
% 7.11/1.84 Axiom 1 (fact_14_PW_1): fresh174(X, X) = true2.
% 7.11/1.84 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_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat, h), n)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop, p), e)), cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat, h), n)), cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above, p), c), e)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot, p), e)))))) = true2.
% 7.11/1.84 Axiom 3 (fact_14_PW_1): fresh174(hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat, h), n)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop, p), e)), cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat, h), n)), cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above, p), c), e)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot, p), e)))))), true2) = hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, p))).
% 7.11/1.84
% 7.11/1.84 Goal 1 (conj_0): hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, p))) = true2.
% 7.11/1.84 Proof:
% 7.11/1.84 hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, p)))
% 7.11/1.84 = { by axiom 3 (fact_14_PW_1) R->L }
% 7.11/1.84 fresh174(hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c, d)), hAPP_f695124765t_bool(f, cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat, h), n)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop, p), e)), cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool, cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat, h), n)), cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above, p), c), e)), cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot, p), e)))))), true2)
% 7.11/1.84 = { by axiom 2 (fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) }
% 7.11/1.84 fresh174(true2, true2)
% 7.11/1.84 = { by axiom 1 (fact_14_PW_1) }
% 7.11/1.84 true2
% 7.11/1.84 % SZS output end Proof
% 7.11/1.84
% 7.11/1.84 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------