TSTP Solution File: SWW478+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW478+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 : n001.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 : Fri Sep 1 00:55:19 EDT 2023
% Result : Theorem 4.28s 0.93s
% Output : Proof 4.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW478+1 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 22:19:48 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.28/0.93 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 4.28/0.93
% 4.28/0.93 % SZS status Theorem
% 4.28/0.93
% 4.28/0.93 % SZS output start Proof
% 4.28/0.93 Take the following subset of the input axioms:
% 4.28/0.93 fof(conj_0, conjecture, hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val, hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, ea), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, ha), fun_up1149430426on_val(la, v_1, some_val(v))))), hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, e_a), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, h_a), l_a))), red(p)))).
% 4.28/0.93 fof(fact_1_InitBlockRed_I1_J, axiom, hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val, hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, ea), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, ha), fun_up1149430426on_val(la, v_1, some_val(v))))), hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, e_a), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, h_a), l_a))), red(p)))).
% 4.28/0.93
% 4.28/0.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.28/0.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.28/0.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.28/0.93 fresh(y, y, x1...xn) = u
% 4.28/0.93 C => fresh(s, t, x1...xn) = v
% 4.28/0.93 where fresh is a fresh function symbol and x1..xn are the free
% 4.28/0.93 variables of u and v.
% 4.28/0.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.28/0.93 input problem has no model of domain size 1).
% 4.28/0.93
% 4.28/0.93 The encoding turns the above axioms into the following unit equations and goals:
% 4.28/0.93
% 4.28/0.93 Axiom 1 (fact_1_InitBlockRed_I1_J): hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val, hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, ea), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, ha), fun_up1149430426on_val(la, v_1, some_val(v))))), hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, e_a), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, h_a), l_a))), red(p))) = true2.
% 4.28/0.93
% 4.28/0.93 Goal 1 (conj_0): hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val, hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, ea), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, ha), fun_up1149430426on_val(la, v_1, some_val(v))))), hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, e_a), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, h_a), l_a))), red(p))) = true2.
% 4.28/0.93 Proof:
% 4.28/0.93 hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val, hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, ea), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, ha), fun_up1149430426on_val(la, v_1, some_val(v))))), hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val, e_a), hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val, h_a), l_a))), red(p)))
% 4.28/0.94 = { by axiom 1 (fact_1_InitBlockRed_I1_J) }
% 4.28/0.94 true2
% 4.28/0.94 % SZS output end Proof
% 4.28/0.94
% 4.28/0.94 RESULT: Theorem (the conjecture is true).
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