TSTP Solution File: LCL814-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL814-1 : 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 : n026.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 21.94s 3.20s
% Output : Proof 21.94s
% 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 : LCL814-1 : 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
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 05:09:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 21.94/3.20 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 21.94/3.20
% 21.94/3.20 % SZS status Unsatisfiable
% 21.94/3.20
% 21.94/3.20 % SZS output start Proof
% 21.94/3.20 Take the following subset of the input axioms:
% 21.94/3.20 fof(cls_argsT_0, axiom, c_Type_Otypings(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_as____, v_Ts____)).
% 21.94/3.20 fof(cls_conjecture_0, negated_conjecture, ~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____)).
% 21.94/3.20 fof(cls_substs__lemma_0, axiom, ![V_i, V_e, V_T, V_u, V_ts, V_Ts]: (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_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_Ts) | (~c_Type_Otypings(c_Type_Oshift(V_e, V_i, V_T, tc_Type_Otype), V_ts, V_Ts) | ~c_Type_Otyping(V_e, V_u, V_T)))).
% 21.94/3.20 fof(cls_uT_0, axiom, c_Type_Otyping(v_e____, v_u____, v_T____)).
% 21.94/3.20
% 21.94/3.20 Now clausify the problem and encode Horn clauses using encoding 3 of
% 21.94/3.20 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 21.94/3.20 We repeatedly replace C & s=t => u=v by the two clauses:
% 21.94/3.20 fresh(y, y, x1...xn) = u
% 21.94/3.20 C => fresh(s, t, x1...xn) = v
% 21.94/3.20 where fresh is a fresh function symbol and x1..xn are the free
% 21.94/3.20 variables of u and v.
% 21.94/3.20 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 21.94/3.20 input problem has no model of domain size 1).
% 21.94/3.20
% 21.94/3.20 The encoding turns the above axioms into the following unit equations and goals:
% 21.94/3.20
% 21.94/3.20 Axiom 1 (cls_uT_0): c_Type_Otyping(v_e____, v_u____, v_T____) = true2.
% 21.94/3.20 Axiom 2 (cls_argsT_0): c_Type_Otypings(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_as____, v_Ts____) = true2.
% 21.94/3.20 Axiom 3 (cls_substs__lemma_0): fresh375(X, X, Y, Z, W, V, U) = true2.
% 21.94/3.20 Axiom 4 (cls_substs__lemma_0): fresh374(X, X, Y, Z, W, V, U, T) = fresh375(c_Type_Otyping(Y, Z, T), true2, Y, Z, W, V, U).
% 21.94/3.20 Axiom 5 (cls_substs__lemma_0): fresh374(c_Type_Otypings(c_Type_Oshift(X, Y, Z, tc_Type_Otype), W, V), true2, X, U, Y, W, V, Z) = c_Type_Otypings(X, 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)), U), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), Y), W, tc_Lambda_OdB, tc_Lambda_OdB), V).
% 21.94/3.20
% 21.94/3.20 Goal 1 (cls_conjecture_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.
% 21.94/3.20 Proof:
% 21.94/3.20 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____)
% 21.94/3.20 = { by axiom 5 (cls_substs__lemma_0) R->L }
% 21.94/3.20 fresh374(c_Type_Otypings(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_as____, v_Ts____), true2, v_e____, v_u____, v_i____, v_as____, v_Ts____, v_T____)
% 21.94/3.20 = { by axiom 2 (cls_argsT_0) }
% 21.94/3.20 fresh374(true2, true2, v_e____, v_u____, v_i____, v_as____, v_Ts____, v_T____)
% 21.94/3.20 = { by axiom 4 (cls_substs__lemma_0) }
% 21.94/3.20 fresh375(c_Type_Otyping(v_e____, v_u____, v_T____), true2, v_e____, v_u____, v_i____, v_as____, v_Ts____)
% 21.94/3.20 = { by axiom 1 (cls_uT_0) }
% 21.94/3.20 fresh375(true2, true2, v_e____, v_u____, v_i____, v_as____, v_Ts____)
% 21.94/3.20 = { by axiom 3 (cls_substs__lemma_0) }
% 21.94/3.20 true2
% 21.94/3.20 % SZS output end Proof
% 21.94/3.20
% 21.94/3.20 RESULT: Unsatisfiable (the axioms are contradictory).
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