TSTP Solution File: LCL848-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL848-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n006.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 08:20:57 EDT 2023
% Result : Unsatisfiable 17.99s 2.83s
% Output : Proof 17.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL848-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.36 % Computer : n006.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri Aug 25 04:29:37 EDT 2023
% 0.16/0.36 % CPUTime :
% 17.99/2.83 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 17.99/2.83
% 17.99/2.83 % SZS status Unsatisfiable
% 17.99/2.83
% 17.99/2.83 % SZS output start Proof
% 17.99/2.83 Take the following subset of the input axioms:
% 17.99/2.83 fof(cls_CHAINED_0, axiom, c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)).
% 17.99/2.83 fof(cls_IT_OVar_0, axiom, ![V_n, V_rs]: (hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), V_rs, tc_Lambda_OdB, tc_Lambda_OdB))) | ~c_List_Olistsp(c_InductTermi_OIT, V_rs, tc_Lambda_OdB))).
% 17.99/2.83 fof(cls_conjecture_0, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))).
% 17.99/2.83
% 17.99/2.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 17.99/2.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 17.99/2.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 17.99/2.83 fresh(y, y, x1...xn) = u
% 17.99/2.83 C => fresh(s, t, x1...xn) = v
% 17.99/2.83 where fresh is a fresh function symbol and x1..xn are the free
% 17.99/2.83 variables of u and v.
% 17.99/2.83 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 17.99/2.83 input problem has no model of domain size 1).
% 17.99/2.83
% 17.99/2.83 The encoding turns the above axioms into the following unit equations and goals:
% 17.99/2.83
% 17.99/2.83 Axiom 1 (cls_IT_OVar_0): fresh404(X, X, Y, Z) = true2.
% 17.99/2.83 Axiom 2 (cls_IT_OVar_0): fresh404(c_List_Olistsp(c_InductTermi_OIT, X, tc_Lambda_OdB), true2, Y, X) = hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(Y), X, tc_Lambda_OdB, tc_Lambda_OdB))).
% 17.99/2.83 Axiom 3 (cls_CHAINED_0): c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB) = true2.
% 17.99/2.83
% 17.99/2.83 Goal 1 (cls_conjecture_0): hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB))) = true2.
% 17.99/2.83 Proof:
% 17.99/2.83 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))
% 17.99/2.83 = { by axiom 2 (cls_IT_OVar_0) R->L }
% 17.99/2.83 fresh404(c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), true2, c_HOL_Ozero__class_Ozero(tc_nat), c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB))
% 17.99/2.83 = { by axiom 3 (cls_CHAINED_0) }
% 17.99/2.83 fresh404(true2, true2, c_HOL_Ozero__class_Ozero(tc_nat), c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB))
% 17.99/2.83 = { by axiom 1 (cls_IT_OVar_0) }
% 17.99/2.83 true2
% 17.99/2.83 % SZS output end Proof
% 17.99/2.83
% 17.99/2.83 RESULT: Unsatisfiable (the axioms are contradictory).
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