TSTP Solution File: LCL760-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL760-1 : 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 : n016.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 08:20:29 EDT 2023
% Result : Unsatisfiable 19.50s 2.90s
% Output : Proof 19.50s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL760-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 18:15:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 19.50/2.90 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 19.50/2.90
% 19.50/2.90 % SZS status Unsatisfiable
% 19.50/2.90
% 19.50/2.90 % SZS output start Proof
% 19.50/2.90 Take the following subset of the input axioms:
% 19.50/2.90 fof(cls_conjecture_1, negated_conjecture, ![V_j, V_i]: hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_ra), c_Lambda_OdB_OVar(c_Suc(V_i))), c_Suc(V_j))), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_s), c_Lambda_OdB_OVar(V_i)), V_j)), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, c_Lambda_OdB_OVar(V_i), tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), V_j, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_ss, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))).
% 19.50/2.90 fof(cls_conjecture_4, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_ra), c_Lambda_OdB_OVar(c_Suc(v_ia))), c_Suc(v_ja))), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_s), c_Lambda_OdB_OVar(v_ia)), v_ja)), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, c_Lambda_OdB_OVar(v_ia), tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_ja, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_ss, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))).
% 19.50/2.90
% 19.50/2.90 Now clausify the problem and encode Horn clauses using encoding 3 of
% 19.50/2.90 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 19.50/2.90 We repeatedly replace C & s=t => u=v by the two clauses:
% 19.50/2.90 fresh(y, y, x1...xn) = u
% 19.50/2.90 C => fresh(s, t, x1...xn) = v
% 19.50/2.90 where fresh is a fresh function symbol and x1..xn are the free
% 19.50/2.90 variables of u and v.
% 19.50/2.90 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 19.50/2.90 input problem has no model of domain size 1).
% 19.50/2.90
% 19.50/2.90 The encoding turns the above axioms into the following unit equations and goals:
% 19.50/2.90
% 19.50/2.90 Axiom 1 (cls_conjecture_1): hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_ra), c_Lambda_OdB_OVar(c_Suc(X))), c_Suc(Y))), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_s), c_Lambda_OdB_OVar(X)), Y)), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, c_Lambda_OdB_OVar(X), tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), Y, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_ss, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB))) = true2.
% 19.50/2.90
% 19.50/2.90 Goal 1 (cls_conjecture_4): hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_ra), c_Lambda_OdB_OVar(c_Suc(v_ia))), c_Suc(v_ja))), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_s), c_Lambda_OdB_OVar(v_ia)), v_ja)), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, c_Lambda_OdB_OVar(v_ia), tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_ja, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_ss, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB))) = true2.
% 19.50/2.90 Proof:
% 19.50/2.90 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_ra), c_Lambda_OdB_OVar(c_Suc(v_ia))), c_Suc(v_ja))), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_s), c_Lambda_OdB_OVar(v_ia)), v_ja)), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, c_Lambda_OdB_OVar(v_ia), tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_ja, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_ss, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))
% 19.50/2.90 = { by axiom 1 (cls_conjecture_1) }
% 19.50/2.90 true2
% 19.50/2.90 % SZS output end Proof
% 19.50/2.90
% 19.50/2.90 RESULT: Unsatisfiable (the axioms are contradictory).
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