TSTP Solution File: LCL815-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL815-1 : 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 : n019.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 08:20:48 EDT 2023
% Result : Unsatisfiable 26.47s 3.79s
% Output : Proof 26.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL815-1 : 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 : n019.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 : Thu Aug 24 22:52:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 26.47/3.79 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 26.47/3.79
% 26.47/3.79 % SZS status Unsatisfiable
% 26.47/3.79
% 26.47/3.79 % SZS output start Proof
% 26.47/3.79 Take the following subset of the input axioms:
% 26.47/3.80 fof(cls_CHAINED_0, axiom, c_Type_Otypings(v_e____, c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_Ts____)).
% 26.47/3.80 fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otypings(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), tc_Type_Otype), c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), v_Ts____)).
% 26.47/3.80 fof(cls_lift__types_0, axiom, ![V_i, V_e, V_ts, V_U, V_Ts]: (c_Type_Otypings(c_Type_Oshift(V_e, V_i, V_U, tc_Type_Otype), c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_Ts) | ~c_Type_Otypings(V_e, V_ts, V_Ts))).
% 26.47/3.80
% 26.47/3.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 26.47/3.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 26.47/3.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 26.47/3.80 fresh(y, y, x1...xn) = u
% 26.47/3.80 C => fresh(s, t, x1...xn) = v
% 26.47/3.80 where fresh is a fresh function symbol and x1..xn are the free
% 26.47/3.80 variables of u and v.
% 26.47/3.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 26.47/3.80 input problem has no model of domain size 1).
% 26.47/3.80
% 26.47/3.80 The encoding turns the above axioms into the following unit equations and goals:
% 26.47/3.80
% 26.47/3.80 Axiom 1 (cls_lift__types_0): fresh305(X, X, Y, Z, W, V, U) = true2.
% 26.47/3.80 Axiom 2 (cls_lift__types_0): fresh305(c_Type_Otypings(X, Y, Z), true2, X, W, V, Y, Z) = c_Type_Otypings(c_Type_Oshift(X, W, V, tc_Type_Otype), c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), W), Y, tc_Lambda_OdB, tc_Lambda_OdB), Z).
% 26.47/3.80 Axiom 3 (cls_CHAINED_0): c_Type_Otypings(v_e____, c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_Ts____) = true2.
% 26.47/3.80
% 26.47/3.80 Goal 1 (cls_conjecture_0): c_Type_Otypings(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), tc_Type_Otype), c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), v_Ts____) = true2.
% 26.47/3.80 Proof:
% 26.47/3.80 c_Type_Otypings(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), tc_Type_Otype), c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), v_Ts____)
% 26.47/3.80 = { by axiom 2 (cls_lift__types_0) R->L }
% 26.47/3.80 fresh305(c_Type_Otypings(v_e____, c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_Ts____), true2, v_e____, c_HOL_Ozero__class_Ozero(tc_nat), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_Ts____)
% 26.47/3.80 = { by axiom 3 (cls_CHAINED_0) }
% 26.47/3.80 fresh305(true2, true2, v_e____, c_HOL_Ozero__class_Ozero(tc_nat), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_Ts____)
% 26.47/3.80 = { by axiom 1 (cls_lift__types_0) }
% 26.47/3.80 true2
% 26.47/3.80 % SZS output end Proof
% 26.47/3.80
% 26.47/3.80 RESULT: Unsatisfiable (the axioms are contradictory).
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