TSTP Solution File: LCL839-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL839-1 : 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 : n023.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 08:20:55 EDT 2023
% Result : Unsatisfiable 11.81s 1.83s
% Output : Proof 11.81s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL839-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 24 22:08:42 EDT 2023
% 0.11/0.33 % CPUTime :
% 11.81/1.83 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 11.81/1.83
% 11.81/1.83 % SZS status Unsatisfiable
% 11.81/1.83
% 11.81/1.83 % SZS output start Proof
% 11.81/1.83 Take the following subset of the input axioms:
% 11.81/1.83 fof(cls_CHAINED_0, axiom, c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_Ua____)).
% 11.81/1.83 fof(cls_conjecture_0, negated_conjecture, ~v_thesis____).
% 11.81/1.83 fof(cls_conjecture_1, negated_conjecture, ![V_x]: (v_thesis____ | ~c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, V_x))).
% 11.81/1.83 fof(cls_typing__elims_I2_J_1, axiom, ![V_e, V_T, V_t, V_u]: (c_Type_Otyping(V_e, V_u, c_Type_Osko__Type__Xtyping__elims__2__1(V_T, V_e, V_t, V_u)) | ~c_Type_Otyping(V_e, hAPP(hAPP(c_Lambda_OdB_OApp, V_t), V_u), V_T))).
% 11.81/1.83
% 11.81/1.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.81/1.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.81/1.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.81/1.83 fresh(y, y, x1...xn) = u
% 11.81/1.83 C => fresh(s, t, x1...xn) = v
% 11.81/1.83 where fresh is a fresh function symbol and x1..xn are the free
% 11.81/1.83 variables of u and v.
% 11.81/1.83 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.81/1.83 input problem has no model of domain size 1).
% 11.81/1.83
% 11.81/1.83 The encoding turns the above axioms into the following unit equations and goals:
% 11.81/1.83
% 11.81/1.83 Axiom 1 (cls_conjecture_1): fresh194(X, X) = true2.
% 11.81/1.83 Axiom 2 (cls_typing__elims_I2_J_1): fresh85(X, X, Y, Z, W, V) = true2.
% 11.81/1.83 Axiom 3 (cls_conjecture_1): fresh194(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, X), true2) = v_thesis____.
% 11.81/1.83 Axiom 4 (cls_CHAINED_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_Ua____) = true2.
% 11.81/1.83 Axiom 5 (cls_typing__elims_I2_J_1): fresh85(c_Type_Otyping(X, hAPP(hAPP(c_Lambda_OdB_OApp, Y), Z), W), true2, X, Z, W, Y) = c_Type_Otyping(X, Z, c_Type_Osko__Type__Xtyping__elims__2__1(W, X, Y, Z)).
% 11.81/1.83
% 11.81/1.83 Goal 1 (cls_conjecture_0): v_thesis____ = true2.
% 11.81/1.83 Proof:
% 11.81/1.83 v_thesis____
% 11.81/1.83 = { by axiom 3 (cls_conjecture_1) R->L }
% 11.81/1.83 fresh194(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OAbs(v_r____), v_a____)), true2)
% 11.81/1.83 = { by axiom 5 (cls_typing__elims_I2_J_1) R->L }
% 11.81/1.83 fresh194(fresh85(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_Ua____), true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_Ua____, c_Lambda_OdB_OAbs(v_r____)), true2)
% 11.81/1.83 = { by axiom 4 (cls_CHAINED_0) }
% 11.81/1.83 fresh194(fresh85(true2, true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_Ua____, c_Lambda_OdB_OAbs(v_r____)), true2)
% 11.81/1.83 = { by axiom 2 (cls_typing__elims_I2_J_1) }
% 11.81/1.83 fresh194(true2, true2)
% 11.81/1.83 = { by axiom 1 (cls_conjecture_1) }
% 11.81/1.83 true2
% 11.81/1.83 % SZS output end Proof
% 11.81/1.83
% 11.81/1.83 RESULT: Unsatisfiable (the axioms are contradictory).
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