TSTP Solution File: LCL821-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL821-1 : 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 : n005.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 08:20:50 EDT 2023
% Result : Unsatisfiable 17.69s 2.60s
% Output : Proof 17.69s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : LCL821-1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.30 % Computer : n005.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Aug 24 17:55:23 EDT 2023
% 0.09/0.30 % CPUTime :
% 17.69/2.60 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 17.69/2.60
% 17.69/2.60 % SZS status Unsatisfiable
% 17.69/2.60
% 17.69/2.61 % SZS output start Proof
% 17.69/2.61 Take the following subset of the input axioms:
% 17.69/2.61 fof(cls_conjecture_0, negated_conjecture, ~v_thesis____).
% 17.69/2.61 fof(cls_conjecture_1, negated_conjecture, ![V_x]: (v_thesis____ | ~c_Type_Otypings(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_rs____, V_x))).
% 17.69/2.61 fof(cls_nT_0, axiom, c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)).
% 17.69/2.61 fof(cls_var__app__typesE_1, axiom, ![V_i, V_e, V_T, V_ts]: (c_Type_Otypings(V_e, V_ts, c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T, V_e, V_i, V_ts)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T))).
% 17.69/2.61
% 17.69/2.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 17.69/2.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 17.69/2.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 17.69/2.61 fresh(y, y, x1...xn) = u
% 17.69/2.61 C => fresh(s, t, x1...xn) = v
% 17.69/2.61 where fresh is a fresh function symbol and x1..xn are the free
% 17.69/2.61 variables of u and v.
% 17.69/2.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 17.69/2.61 input problem has no model of domain size 1).
% 17.69/2.61
% 17.69/2.61 The encoding turns the above axioms into the following unit equations and goals:
% 17.69/2.61
% 17.69/2.61 Axiom 1 (cls_conjecture_1): fresh176(X, X) = true2.
% 17.69/2.61 Axiom 2 (cls_var__app__typesE_1): fresh84(X, X, Y, Z, W, V) = true2.
% 17.69/2.61 Axiom 3 (cls_conjecture_1): fresh176(c_Type_Otypings(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_rs____, X), true2) = v_thesis____.
% 17.69/2.61 Axiom 4 (cls_nT_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____) = true2.
% 17.69/2.61 Axiom 5 (cls_var__app__typesE_1): fresh84(c_Type_Otyping(X, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(Y), Z, tc_Lambda_OdB, tc_Lambda_OdB), W), true2, X, Z, W, Y) = c_Type_Otypings(X, Z, c_Type_Osko__Type__Xvar__app__typesE__1__1(W, X, Y, Z)).
% 17.69/2.61
% 17.69/2.61 Goal 1 (cls_conjecture_0): v_thesis____ = true2.
% 17.69/2.61 Proof:
% 17.69/2.61 v_thesis____
% 17.69/2.61 = { by axiom 3 (cls_conjecture_1) R->L }
% 17.69/2.61 fresh176(c_Type_Otypings(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_rs____, c_Type_Osko__Type__Xvar__app__typesE__1__1(v_T_H____, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_n____, v_rs____)), true2)
% 17.69/2.61 = { by axiom 5 (cls_var__app__typesE_1) R->L }
% 17.69/2.61 fresh176(fresh84(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_rs____, v_T_H____, v_n____), true2)
% 17.69/2.61 = { by axiom 4 (cls_nT_0) }
% 17.69/2.61 fresh176(fresh84(true2, true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_rs____, v_T_H____, v_n____), true2)
% 17.69/2.61 = { by axiom 2 (cls_var__app__typesE_1) }
% 17.69/2.61 fresh176(true2, true2)
% 17.69/2.61 = { by axiom 1 (cls_conjecture_1) }
% 17.69/2.61 true2
% 17.69/2.61 % SZS output end Proof
% 17.69/2.61
% 17.69/2.61 RESULT: Unsatisfiable (the axioms are contradictory).
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