TSTP Solution File: LCL788-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL788-1 : 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 : n015.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 08:20:38 EDT 2023
% Result : Unsatisfiable 0.20s 0.69s
% Output : Proof 0.20s
% 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 : LCL788-1 : 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 : n015.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 01:16:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.69 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.69
% 0.20/0.69 % SZS status Unsatisfiable
% 0.20/0.69
% 0.20/0.69 % SZS output start Proof
% 0.20/0.69 Take the following subset of the input axioms:
% 0.20/0.69 fof(cls_True_0, axiom, v_n____=v_i____).
% 0.20/0.69 fof(cls_conjecture_0, negated_conjecture, 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))).
% 0.20/0.69 fof(cls_shift__eq_0, axiom, ![T_a, V_x, V_e, V_T]: hAPP(c_Type_Oshift(V_e, V_x, V_T, T_a), V_x)=V_T).
% 0.20/0.69 fof(cls_typing__elims_I1_J_0, axiom, ![V_i, V_T2, V_e2]: (hAPP(V_e2, V_i)=V_T2 | ~c_Type_Otyping(V_e2, c_Lambda_OdB_OVar(V_i), V_T2))).
% 0.20/0.69 fof(cls_varT_0, axiom, c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_n____), 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)))).
% 0.20/0.69
% 0.20/0.69 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.69 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.69 fresh(y, y, x1...xn) = u
% 0.20/0.69 C => fresh(s, t, x1...xn) = v
% 0.20/0.69 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.69 variables of u and v.
% 0.20/0.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.69 input problem has no model of domain size 1).
% 0.20/0.69
% 0.20/0.69 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.69
% 0.20/0.69 Axiom 1 (cls_True_0): v_n____ = v_i____.
% 0.20/0.69 Axiom 2 (cls_shift__eq_0): hAPP(c_Type_Oshift(X, Y, Z, W), Y) = Z.
% 0.20/0.69 Axiom 3 (cls_typing__elims_I1_J_0): fresh30(X, X, Y, Z, W) = W.
% 0.20/0.69 Axiom 4 (cls_typing__elims_I1_J_0): fresh30(c_Type_Otyping(X, c_Lambda_OdB_OVar(Y), Z), true2, X, Y, Z) = hAPP(X, Y).
% 0.20/0.69 Axiom 5 (cls_varT_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_n____), 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.
% 0.20/0.69
% 0.20/0.69 Goal 1 (cls_conjecture_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)).
% 0.20/0.69 Proof:
% 0.20/0.69 v_T____
% 0.20/0.69 = { by axiom 2 (cls_shift__eq_0) R->L }
% 0.20/0.69 hAPP(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_i____)
% 0.20/0.69 = { by axiom 4 (cls_typing__elims_I1_J_0) R->L }
% 0.20/0.69 fresh30(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_i____), 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, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_i____, 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)))
% 0.20/0.69 = { by axiom 1 (cls_True_0) R->L }
% 0.20/0.69 fresh30(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_n____), 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, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_i____, 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)))
% 0.20/0.69 = { by axiom 5 (cls_varT_0) }
% 0.20/0.69 fresh30(true2, true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_i____, 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)))
% 0.20/0.69 = { by axiom 3 (cls_typing__elims_I1_J_0) }
% 0.20/0.69 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))
% 0.20/0.69 % SZS output end Proof
% 0.20/0.69
% 0.20/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
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