TSTP Solution File: LCL849-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL849-1 : 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 : n018.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 08:20:58 EDT 2023
% Result : Unsatisfiable 19.79s 2.93s
% Output : Proof 19.79s
% 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 : LCL849-1 : 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 : n018.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 05:59:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 19.79/2.93 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 19.79/2.93
% 19.79/2.93 % SZS status Unsatisfiable
% 19.79/2.93
% 19.79/2.99 % SZS output start Proof
% 19.79/2.99 Take the following subset of the input axioms:
% 19.79/2.99 fof(cls_conjecture_0, negated_conjecture, 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)!=hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))), hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)))).
% 19.79/2.99 fof(cls_foldl__Cons_0, axiom, ![T_a, V_a, V_x, V_xs, V_f, T_b]: c_List_Ofoldl(V_f, V_a, c_List_Olist_OCons(V_x, V_xs, T_b), T_a, T_b)=c_List_Ofoldl(V_f, hAPP(hAPP(V_f, V_a), V_x), V_xs, T_a, T_b)).
% 19.79/2.99 fof(cls_foldl__Nil_0, axiom, ![V_f2, T_a2, V_a2, T_b2]: c_List_Ofoldl(V_f2, V_a2, c_List_Olist_ONil(T_b2), T_a2, T_b2)=V_a2).
% 19.79/2.99
% 19.79/2.99 Now clausify the problem and encode Horn clauses using encoding 3 of
% 19.79/2.99 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 19.79/2.99 We repeatedly replace C & s=t => u=v by the two clauses:
% 19.79/2.99 fresh(y, y, x1...xn) = u
% 19.79/2.99 C => fresh(s, t, x1...xn) = v
% 19.79/2.99 where fresh is a fresh function symbol and x1..xn are the free
% 19.79/2.99 variables of u and v.
% 19.79/2.99 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 19.79/2.99 input problem has no model of domain size 1).
% 19.79/2.99
% 19.79/2.99 The encoding turns the above axioms into the following unit equations and goals:
% 19.79/2.99
% 19.79/2.99 Axiom 1 (cls_foldl__Nil_0): c_List_Ofoldl(X, Y, c_List_Olist_ONil(Z), W, Z) = Y.
% 19.79/2.99 Axiom 2 (cls_foldl__Cons_0): c_List_Ofoldl(X, Y, c_List_Olist_OCons(Z, W, V), U, V) = c_List_Ofoldl(X, hAPP(hAPP(X, Y), Z), W, U, V).
% 19.79/2.99
% 19.79/2.99 Goal 1 (cls_conjecture_0): 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) = hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))), hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat))).
% 19.79/2.99 Proof:
% 19.79/2.99 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)
% 19.79/2.99 = { by axiom 2 (cls_foldl__Cons_0) }
% 19.79/2.99 c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))), 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)
% 19.79/2.99 = { by axiom 1 (cls_foldl__Nil_0) }
% 19.79/2.99 hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))), hAPP(hAPP(c_Lambda_Olift, v_ta____), c_HOL_Ozero__class_Ozero(tc_nat)))
% 19.79/2.99 % SZS output end Proof
% 19.79/2.99
% 19.79/2.99 RESULT: Unsatisfiable (the axioms are contradictory).
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