TSTP Solution File: LCL816-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL816-1 : 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 : n025.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 176.48s 22.94s
% Output : Proof 176.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL816-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 01:53:51 EDT 2023
% 0.12/0.33 % CPUTime :
% 176.48/22.94 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 176.48/22.94
% 176.48/22.94 % SZS status Unsatisfiable
% 176.48/22.94
% 176.79/22.94 % SZS output start Proof
% 176.79/22.94 Take the following subset of the input axioms:
% 176.79/22.94 fof(cls_CHAINED_0, axiom, 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____)).
% 176.79/22.94 fof(cls_CHAINED_0_01, axiom, c_Type_Otyping(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_Lambda_OdB_OVar(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))).
% 176.79/22.94 fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otyping(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_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), 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), tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)).
% 176.79/22.94 fof(cls_list__app__typeI_0, axiom, ![V_t, V_e, V_T, V_ts, V_Ts]: (c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) | (~c_Type_Otypings(V_e, V_ts, V_Ts) | ~c_Type_Otyping(V_e, V_t, c_List_Ofoldr(c_Type_Otype_OFun, V_Ts, V_T, tc_Type_Otype, tc_Type_Otype))))).
% 176.79/22.94
% 176.79/22.94 Now clausify the problem and encode Horn clauses using encoding 3 of
% 176.79/22.94 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 176.79/22.94 We repeatedly replace C & s=t => u=v by the two clauses:
% 176.79/22.94 fresh(y, y, x1...xn) = u
% 176.79/22.94 C => fresh(s, t, x1...xn) = v
% 176.79/22.94 where fresh is a fresh function symbol and x1..xn are the free
% 176.79/22.94 variables of u and v.
% 176.79/22.94 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 176.79/22.94 input problem has no model of domain size 1).
% 176.79/22.94
% 176.79/22.94 The encoding turns the above axioms into the following unit equations and goals:
% 176.79/22.94
% 176.79/22.94 Axiom 1 (cls_list__app__typeI_0): fresh168(X, X, Y, Z, W, V) = true2.
% 176.79/22.94 Axiom 2 (cls_list__app__typeI_0): fresh169(X, X, Y, Z, W, V, U) = c_Type_Otyping(Y, c_List_Ofoldl(c_Lambda_OdB_OApp, Z, W, tc_Lambda_OdB, tc_Lambda_OdB), V).
% 176.79/22.94 Axiom 3 (cls_list__app__typeI_0): fresh169(c_Type_Otypings(X, Y, Z), true2, X, W, Y, V, Z) = fresh168(c_Type_Otyping(X, W, c_List_Ofoldr(c_Type_Otype_OFun, Z, V, tc_Type_Otype, tc_Type_Otype)), true2, X, W, Y, V).
% 176.79/22.94 Axiom 4 (cls_CHAINED_0_01): c_Type_Otyping(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_Lambda_OdB_OVar(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)) = true2.
% 176.79/22.94 Axiom 5 (cls_CHAINED_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.
% 176.79/22.94
% 176.79/22.94 Goal 1 (cls_conjecture_0): c_Type_Otyping(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_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), 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), tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____) = true2.
% 176.79/22.94 Proof:
% 176.79/22.94 c_Type_Otyping(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_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), 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), tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 176.79/22.95 = { by axiom 2 (cls_list__app__typeI_0) R->L }
% 176.79/22.95 fresh169(true2, true2, 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_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), 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_T_H____, v_Ts____)
% 176.79/22.95 = { by axiom 5 (cls_CHAINED_0) R->L }
% 176.79/22.95 fresh169(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, 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_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), 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_T_H____, v_Ts____)
% 176.79/22.95 = { by axiom 3 (cls_list__app__typeI_0) }
% 176.79/22.95 fresh168(c_Type_Otyping(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_Lambda_OdB_OVar(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)), true2, 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_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), 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_T_H____)
% 176.79/22.95 = { by axiom 4 (cls_CHAINED_0_01) }
% 176.79/22.95 fresh168(true2, true2, 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_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), 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_T_H____)
% 176.79/22.95 = { by axiom 1 (cls_list__app__typeI_0) }
% 176.79/22.95 true2
% 176.79/22.95 % SZS output end Proof
% 176.79/22.95
% 176.79/22.95 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------