TSTP Solution File: LCL795-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL795-1 : 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 : n006.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 08:20:41 EDT 2023
% Result : Unsatisfiable 41.15s 5.62s
% Output : Proof 41.15s
% 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 : LCL795-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 06:13:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 41.15/5.62 Command-line arguments: --no-flatten-goal
% 41.15/5.62
% 41.15/5.62 % SZS status Unsatisfiable
% 41.15/5.62
% 41.15/5.62 % SZS output start Proof
% 41.15/5.62 Take the following subset of the input axioms:
% 41.15/5.62 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))).
% 41.15/5.62 fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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)))).
% 41.15/5.63 fof(cls_lift__type_0, axiom, ![V_e, V_i, V_t, V_T, V_U]: (c_Type_Otyping(c_Type_Oshift(V_e, V_i, V_U, tc_Type_Otype), c_Lambda_Olift(V_t, V_i), V_T) | ~c_Type_Otyping(V_e, V_t, V_T))).
% 41.15/5.63 fof(cls_uT_0, axiom, c_Type_Otyping(v_e____, v_u____, v_T____)).
% 41.15/5.63
% 41.15/5.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 41.15/5.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 41.15/5.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 41.15/5.63 fresh(y, y, x1...xn) = u
% 41.15/5.63 C => fresh(s, t, x1...xn) = v
% 41.15/5.63 where fresh is a fresh function symbol and x1..xn are the free
% 41.15/5.63 variables of u and v.
% 41.15/5.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 41.15/5.63 input problem has no model of domain size 1).
% 41.15/5.63
% 41.15/5.63 The encoding turns the above axioms into the following unit equations and goals:
% 41.15/5.63
% 41.15/5.63 Axiom 1 (cls_uT_0): c_Type_Otyping(v_e____, v_u____, v_T____) = true2.
% 41.15/5.63 Axiom 2 (cls_lift__type_0): fresh443(X, X, Y, Z, W, V, U) = true2.
% 41.15/5.63 Axiom 3 (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)).
% 41.15/5.63 Axiom 4 (cls_lift__type_0): fresh443(c_Type_Otyping(X, Y, Z), true2, X, W, V, Y, Z) = c_Type_Otyping(c_Type_Oshift(X, W, V, tc_Type_Otype), c_Lambda_Olift(Y, W), Z).
% 41.15/5.63
% 41.15/5.63 Goal 1 (cls_conjecture_0): c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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.
% 41.15/5.63 Proof:
% 41.15/5.63 c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), 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)))
% 41.15/5.63 = { by axiom 3 (cls_T_0) R->L }
% 41.15/5.63 c_Type_Otyping(c_Type_Oshift(v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, tc_Type_Otype), c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), v_T____)
% 41.15/5.63 = { by axiom 4 (cls_lift__type_0) R->L }
% 41.15/5.63 fresh443(c_Type_Otyping(v_e____, v_u____, v_T____), true2, v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, v_u____, v_T____)
% 41.15/5.63 = { by axiom 1 (cls_uT_0) }
% 41.15/5.63 fresh443(true2, true2, v_e____, c_HOL_Ozero__class_Ozero(tc_nat), v_T_H_H____, v_u____, v_T____)
% 41.15/5.63 = { by axiom 2 (cls_lift__type_0) }
% 41.15/5.63 true2
% 41.15/5.63 % SZS output end Proof
% 41.15/5.63
% 41.15/5.63 RESULT: Unsatisfiable (the axioms are contradictory).
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