TSTP Solution File: LCL785-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL785-1 : 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 : n007.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 08:20:37 EDT 2023
% Result : Unsatisfiable 12.80s 2.06s
% Output : Proof 12.80s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LCL785-1 : TPTP v8.1.2. Released v4.1.0.
% 0.05/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Aug 25 04:31:40 EDT 2023
% 0.10/0.32 % CPUTime :
% 12.80/2.06 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 12.80/2.06
% 12.80/2.06 % SZS status Unsatisfiable
% 12.80/2.06
% 12.80/2.06 % SZS output start Proof
% 12.80/2.06 Take the following subset of the input axioms:
% 12.80/2.06 fof(cls_Cons_0, axiom, v_rs____=c_List_Olist_OCons(v_a____, v_as____, tc_Lambda_OdB)).
% 12.80/2.06 fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)).
% 12.80/2.06 fof(cls_foldl__Cons_0, axiom, ![T_a, V_xs, V_x, V_a, T_b, V_f]: 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)).
% 12.80/2.06 fof(cls_nT_0, axiom, c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)).
% 12.80/2.06
% 12.80/2.06 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.80/2.06 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.80/2.06 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.80/2.06 fresh(y, y, x1...xn) = u
% 12.80/2.06 C => fresh(s, t, x1...xn) = v
% 12.80/2.06 where fresh is a fresh function symbol and x1..xn are the free
% 12.80/2.06 variables of u and v.
% 12.80/2.06 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.80/2.06 input problem has no model of domain size 1).
% 12.80/2.06
% 12.80/2.06 The encoding turns the above axioms into the following unit equations and goals:
% 12.80/2.06
% 12.80/2.06 Axiom 1 (cls_Cons_0): v_rs____ = c_List_Olist_OCons(v_a____, v_as____, tc_Lambda_OdB).
% 12.80/2.06 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).
% 12.80/2.06 Axiom 3 (cls_nT_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____) = true2.
% 12.80/2.06
% 12.80/2.06 Goal 1 (cls_conjecture_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____) = true2.
% 12.80/2.06 Proof:
% 12.80/2.06 c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 12.80/2.06 = { by axiom 2 (cls_foldl__Cons_0) R->L }
% 12.80/2.06 c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), c_List_Olist_OCons(v_a____, v_as____, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 12.80/2.06 = { by axiom 1 (cls_Cons_0) R->L }
% 12.80/2.06 c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 12.80/2.06 = { by axiom 3 (cls_nT_0) }
% 12.80/2.06 true2
% 12.80/2.06 % SZS output end Proof
% 12.80/2.06
% 12.80/2.06 RESULT: Unsatisfiable (the axioms are contradictory).
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