TSTP Solution File: LCL813-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL813-1 : 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 : n008.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 08:20:47 EDT 2023
% Result : Unsatisfiable 44.66s 6.21s
% Output : Proof 45.19s
% 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 : LCL813-1 : 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
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Fri Aug 25 01:06:33 EDT 2023
% 0.16/0.35 % CPUTime :
% 44.66/6.21 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 44.66/6.21
% 44.66/6.21 % SZS status Unsatisfiable
% 44.66/6.21
% 45.19/6.21 % SZS output start Proof
% 45.19/6.21 Take the following subset of the input axioms:
% 45.19/6.21 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_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))).
% 45.19/6.21 fof(cls_shift__eq_0, axiom, ![T_a, V_e, V_x, V_T]: hAPP(c_Type_Oshift(V_e, V_x, V_T, T_a), V_x)=V_T).
% 45.19/6.21 fof(cls_typing_OVar_0, axiom, ![V_env, V_x2]: c_Type_Otyping(V_env, c_Lambda_OdB_OVar(V_x2), hAPP(V_env, V_x2))).
% 45.19/6.21
% 45.19/6.21 Now clausify the problem and encode Horn clauses using encoding 3 of
% 45.19/6.21 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 45.19/6.21 We repeatedly replace C & s=t => u=v by the two clauses:
% 45.19/6.21 fresh(y, y, x1...xn) = u
% 45.19/6.21 C => fresh(s, t, x1...xn) = v
% 45.19/6.21 where fresh is a fresh function symbol and x1..xn are the free
% 45.19/6.21 variables of u and v.
% 45.19/6.21 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 45.19/6.21 input problem has no model of domain size 1).
% 45.19/6.21
% 45.19/6.21 The encoding turns the above axioms into the following unit equations and goals:
% 45.19/6.21
% 45.19/6.21 Axiom 1 (cls_shift__eq_0): hAPP(c_Type_Oshift(X, Y, Z, W), Y) = Z.
% 45.19/6.21 Axiom 2 (cls_typing_OVar_0): c_Type_Otyping(X, c_Lambda_OdB_OVar(Y), hAPP(X, Y)) = true2.
% 45.19/6.21
% 45.19/6.21 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_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.
% 45.19/6.21 Proof:
% 45.19/6.21 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))
% 45.19/6.21 = { by axiom 1 (cls_shift__eq_0) R->L }
% 45.19/6.21 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)), hAPP(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_HOL_Ozero__class_Ozero(tc_nat)))
% 45.19/6.21 = { by axiom 2 (cls_typing_OVar_0) }
% 45.19/6.21 true2
% 45.19/6.21 % SZS output end Proof
% 45.19/6.21
% 45.19/6.21 RESULT: Unsatisfiable (the axioms are contradictory).
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