TSTP Solution File: LCL794-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL794-1 : 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 : n031.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 08:20:40 EDT 2023
% Result : Unsatisfiable 201.20s 26.27s
% Output : Proof 201.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL794-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.35 % Computer : n031.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Aug 25 05:44:21 EDT 2023
% 0.12/0.35 % CPUTime :
% 201.20/26.27 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 201.20/26.27
% 201.20/26.27 % SZS status Unsatisfiable
% 201.20/26.27
% 201.20/26.27 % SZS output start Proof
% 201.20/26.27 Take the following subset of the input axioms:
% 201.20/26.27 fof(cls_App_0, axiom, ![V_s, V_T, V_t, V_U, V_env]: (c_Type_Otyping(V_env, hAPP(hAPP(c_Lambda_OdB_OApp, V_s), V_t), V_U) | (~c_Type_Otyping(V_env, V_t, V_T) | ~c_Type_Otyping(V_env, V_s, hAPP(hAPP(c_Type_Otype_OFun, V_T), V_U))))).
% 201.20/26.27 fof(cls_T_0, axiom, v_T____=hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))).
% 201.20/26.27 fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat))), 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))).
% 201.20/26.27 fof(cls_lift__type_0, axiom, ![V_e, V_i, V_T2, V_t2, V_U2]: (c_Type_Otyping(c_Type_Oshift(V_e, V_i, V_U2, tc_Type_Otype), c_Lambda_Olift(V_t2, V_i), V_T2) | ~c_Type_Otyping(V_e, V_t2, V_T2))).
% 201.20/26.27 fof(cls_shift__eq_0, axiom, ![T_a, V_x, V_T2, V_e2]: hAPP(c_Type_Oshift(V_e2, V_x, V_T2, T_a), V_x)=V_T2).
% 201.20/26.27 fof(cls_typing_OVar_0, axiom, ![V_x2, V_env2]: c_Type_Otyping(V_env2, c_Lambda_OdB_OVar(V_x2), hAPP(V_env2, V_x2))).
% 201.20/26.27 fof(cls_uT_0, axiom, c_Type_Otyping(v_e____, v_u____, v_T____)).
% 201.20/26.27
% 201.20/26.27 Now clausify the problem and encode Horn clauses using encoding 3 of
% 201.20/26.27 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 201.20/26.27 We repeatedly replace C & s=t => u=v by the two clauses:
% 201.20/26.27 fresh(y, y, x1...xn) = u
% 201.20/26.27 C => fresh(s, t, x1...xn) = v
% 201.20/26.27 where fresh is a fresh function symbol and x1..xn are the free
% 201.20/26.27 variables of u and v.
% 201.20/26.27 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 201.20/26.27 input problem has no model of domain size 1).
% 201.20/26.27
% 201.20/26.27 The encoding turns the above axioms into the following unit equations and goals:
% 201.20/26.27
% 201.20/26.27 Axiom 1 (cls_uT_0): c_Type_Otyping(v_e____, v_u____, v_T____) = true2.
% 201.20/26.27 Axiom 2 (cls_shift__eq_0): hAPP(c_Type_Oshift(X, Y, Z, W), Y) = Z.
% 201.20/26.27 Axiom 3 (cls_typing_OVar_0): c_Type_Otyping(X, c_Lambda_OdB_OVar(Y), hAPP(X, Y)) = true2.
% 201.20/26.27 Axiom 4 (cls_App_0): fresh253(X, X, Y, Z, W, V) = true2.
% 201.20/26.27 Axiom 5 (cls_App_0): fresh255(X, X, Y, Z, W, V, U) = c_Type_Otyping(Y, hAPP(hAPP(c_Lambda_OdB_OApp, Z), W), V).
% 201.20/26.27 Axiom 6 (cls_lift__type_0): fresh157(X, X, Y, Z, W, V, U) = true2.
% 201.20/26.27 Axiom 7 (cls_T_0): v_T____ = hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)).
% 201.20/26.27 Axiom 8 (cls_lift__type_0): fresh157(c_Type_Otyping(X, Y, Z), true2, X, W, V, Y, Z) = c_Type_Otyping(c_Type_Oshift(X, W, V, tc_Type_Otype), c_Lambda_Olift(Y, W), Z).
% 201.20/26.27 Axiom 9 (cls_App_0): fresh255(c_Type_Otyping(X, Y, Z), true2, X, W, Y, V, Z) = fresh253(c_Type_Otyping(X, W, hAPP(hAPP(c_Type_Otype_OFun, Z), V)), true2, X, W, Y, V).
% 201.20/26.27
% 201.20/26.28 Goal 1 (cls_conjecture_0): c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat))), 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.
% 201.20/26.28 Proof:
% 201.20/26.28 c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat))), 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))
% 201.20/26.28 = { by axiom 5 (cls_App_0) R->L }
% 201.20/26.28 fresh255(true2, true2, c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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), v_T_H_H____)
% 201.20/26.28 = { by axiom 3 (cls_typing_OVar_0) R->L }
% 201.20/26.28 fresh255(c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), hAPP(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_HOL_Ozero__class_Ozero(tc_nat))), true2, c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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), v_T_H_H____)
% 201.20/26.28 = { by axiom 2 (cls_shift__eq_0) }
% 201.20/26.28 fresh255(c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), v_T_H_H____), true2, c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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), v_T_H_H____)
% 201.20/26.28 = { by axiom 9 (cls_App_0) }
% 201.20/26.28 fresh253(c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), 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), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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))
% 201.20/26.28 = { by axiom 7 (cls_T_0) R->L }
% 201.20/26.28 fresh253(c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), v_T____), true2, c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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))
% 201.20/26.28 = { by axiom 8 (cls_lift__type_0) R->L }
% 201.20/26.28 fresh253(fresh157(c_Type_Otyping(v_e____, v_u____, v_T____), true2, v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, v_u____, v_T____), true2, c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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))
% 201.20/26.28 = { by axiom 1 (cls_uT_0) }
% 201.20/26.28 fresh253(fresh157(true2, true2, v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, v_u____, v_T____), true2, c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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))
% 201.20/26.28 = { by axiom 6 (cls_lift__type_0) }
% 201.20/26.28 fresh253(true2, true2, c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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))
% 201.20/26.28 = { by axiom 4 (cls_App_0) }
% 201.20/26.28 true2
% 201.20/26.28 % SZS output end Proof
% 201.20/26.28
% 201.20/26.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------