TSTP Solution File: LCL818-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL818-1 : 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 08:20:49 EDT 2023
% Result : Unsatisfiable 42.13s 5.84s
% Output : Proof 42.13s
% 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 : LCL818-1 : 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 : n008.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 07:15:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 42.13/5.84 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 42.13/5.84
% 42.13/5.84 % SZS status Unsatisfiable
% 42.13/5.84
% 42.13/5.84 % SZS output start Proof
% 42.13/5.84 Take the following subset of the input axioms:
% 42.13/5.85 fof(cls_App_0, axiom, ![V_t, V_s, 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))))).
% 42.13/5.85 fof(cls_CHAINED_0, axiom, c_Type_Otyping(v_e____, c_Lambda_Osubst(v_a____, v_u____, v_i____), v_T_H_H____)).
% 42.13/5.85 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))).
% 42.13/5.85 fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otyping(v_e____, hAPP(hAPP(c_Lambda_OdB_OApp, v_u____), c_Lambda_Osubst(v_a____, v_u____, v_i____)), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))).
% 42.13/5.85 fof(cls_uT_0, axiom, c_Type_Otyping(v_e____, v_u____, v_T____)).
% 42.13/5.85
% 42.13/5.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 42.13/5.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 42.13/5.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 42.13/5.85 fresh(y, y, x1...xn) = u
% 42.13/5.85 C => fresh(s, t, x1...xn) = v
% 42.13/5.85 where fresh is a fresh function symbol and x1..xn are the free
% 42.13/5.85 variables of u and v.
% 42.13/5.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 42.13/5.85 input problem has no model of domain size 1).
% 42.13/5.85
% 42.13/5.85 The encoding turns the above axioms into the following unit equations and goals:
% 42.13/5.85
% 42.13/5.85 Axiom 1 (cls_uT_0): c_Type_Otyping(v_e____, v_u____, v_T____) = true2.
% 42.13/5.85 Axiom 2 (cls_CHAINED_0): c_Type_Otyping(v_e____, c_Lambda_Osubst(v_a____, v_u____, v_i____), v_T_H_H____) = true2.
% 42.13/5.85 Axiom 3 (cls_App_0): fresh231(X, X, Y, Z, W, V) = true2.
% 42.13/5.85 Axiom 4 (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)).
% 42.13/5.85 Axiom 5 (cls_App_0): fresh233(X, X, Y, Z, W, V, U) = c_Type_Otyping(Y, hAPP(hAPP(c_Lambda_OdB_OApp, Z), W), V).
% 42.13/5.85 Axiom 6 (cls_App_0): fresh233(c_Type_Otyping(X, Y, Z), true2, X, W, Y, V, Z) = fresh231(c_Type_Otyping(X, W, hAPP(hAPP(c_Type_Otype_OFun, Z), V)), true2, X, W, Y, V).
% 42.13/5.85
% 42.13/5.85 Goal 1 (cls_conjecture_0): c_Type_Otyping(v_e____, hAPP(hAPP(c_Lambda_OdB_OApp, v_u____), c_Lambda_Osubst(v_a____, v_u____, v_i____)), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)) = true2.
% 42.13/5.85 Proof:
% 42.13/5.85 c_Type_Otyping(v_e____, hAPP(hAPP(c_Lambda_OdB_OApp, v_u____), c_Lambda_Osubst(v_a____, v_u____, v_i____)), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))
% 42.13/5.85 = { by axiom 5 (cls_App_0) R->L }
% 42.13/5.85 fresh233(true2, true2, v_e____, v_u____, c_Lambda_Osubst(v_a____, v_u____, v_i____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), v_T_H_H____)
% 42.13/5.85 = { by axiom 2 (cls_CHAINED_0) R->L }
% 42.13/5.85 fresh233(c_Type_Otyping(v_e____, c_Lambda_Osubst(v_a____, v_u____, v_i____), v_T_H_H____), true2, v_e____, v_u____, c_Lambda_Osubst(v_a____, v_u____, v_i____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype), v_T_H_H____)
% 42.13/5.85 = { by axiom 6 (cls_App_0) }
% 42.13/5.85 fresh231(c_Type_Otyping(v_e____, v_u____, 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, v_e____, v_u____, c_Lambda_Osubst(v_a____, v_u____, v_i____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))
% 42.13/5.85 = { by axiom 4 (cls_T_0) R->L }
% 42.13/5.85 fresh231(c_Type_Otyping(v_e____, v_u____, v_T____), true2, v_e____, v_u____, c_Lambda_Osubst(v_a____, v_u____, v_i____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))
% 42.13/5.85 = { by axiom 1 (cls_uT_0) }
% 42.13/5.85 fresh231(true2, true2, v_e____, v_u____, c_Lambda_Osubst(v_a____, v_u____, v_i____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))
% 42.13/5.85 = { by axiom 3 (cls_App_0) }
% 42.13/5.85 true2
% 42.13/5.85 % SZS output end Proof
% 42.13/5.85
% 42.13/5.85 RESULT: Unsatisfiable (the axioms are contradictory).
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