TSTP Solution File: LCL811-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL811-1 : 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 : n011.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 08:20:46 EDT 2023
% Result : Unsatisfiable 15.73s 2.47s
% Output : Proof 15.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL811-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 16:58:07 EDT 2023
% 0.12/0.34 % CPUTime :
% 15.73/2.47 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 15.73/2.47
% 15.73/2.47 % SZS status Unsatisfiable
% 15.73/2.47
% 15.73/2.47 % SZS output start Proof
% 15.73/2.47 Take the following subset of the input axioms:
% 15.73/2.48 fof(cls_CHAINED_0, axiom, c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), v_u____), v_i____)), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_bs____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)).
% 15.73/2.48 fof(cls_COMBC__def_0, axiom, ![T_a, V_P, T_b, V_Q, T_c, V_R]: hAPP(c_COMBC(V_P, V_Q, T_b, T_c, T_a), V_R)=hAPP(hAPP(V_P, V_R), V_Q)).
% 15.73/2.48 fof(cls_conjecture_0, negated_conjecture, ~c_List_Olistsp(c_InductTermi_OIT, c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Olist_OCons(v_b____, v_bs____, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB)).
% 15.73/2.48 fof(cls_map__eq__Cons__conv_3, axiom, ![V_xa, V_x, V_f, T_a2, T_b2]: c_List_Omap(V_f, c_List_Olist_OCons(V_x, V_xa, T_b2), T_b2, T_a2)=c_List_Olist_OCons(hAPP(V_f, V_x), c_List_Omap(V_f, V_xa, T_b2, T_a2), T_a2)).
% 15.73/2.48
% 15.73/2.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 15.73/2.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 15.73/2.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 15.73/2.48 fresh(y, y, x1...xn) = u
% 15.73/2.48 C => fresh(s, t, x1...xn) = v
% 15.73/2.48 where fresh is a fresh function symbol and x1..xn are the free
% 15.73/2.48 variables of u and v.
% 15.73/2.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 15.73/2.48 input problem has no model of domain size 1).
% 15.73/2.48
% 15.73/2.48 The encoding turns the above axioms into the following unit equations and goals:
% 15.73/2.48
% 15.73/2.48 Axiom 1 (cls_COMBC__def_0): hAPP(c_COMBC(X, Y, Z, W, V), U) = hAPP(hAPP(X, U), Y).
% 15.73/2.48 Axiom 2 (cls_map__eq__Cons__conv_3): c_List_Omap(X, c_List_Olist_OCons(Y, Z, W), W, V) = c_List_Olist_OCons(hAPP(X, Y), c_List_Omap(X, Z, W, V), V).
% 15.73/2.48 Axiom 3 (cls_CHAINED_0): c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), v_u____), v_i____)), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_bs____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB) = true2.
% 15.73/2.48
% 15.73/2.48 Goal 1 (cls_conjecture_0): c_List_Olistsp(c_InductTermi_OIT, c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Olist_OCons(v_b____, v_bs____, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB) = true2.
% 15.73/2.48 Proof:
% 15.73/2.48 c_List_Olistsp(c_InductTermi_OIT, c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Olist_OCons(v_b____, v_bs____, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB)
% 15.73/2.48 = { by axiom 2 (cls_map__eq__Cons__conv_3) }
% 15.73/2.48 c_List_Olistsp(c_InductTermi_OIT, c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Olist_OCons(hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_b____), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_bs____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB)
% 15.73/2.48 = { by axiom 2 (cls_map__eq__Cons__conv_3) }
% 15.73/2.48 c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), hAPP(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_b____)), c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_bs____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)
% 15.73/2.48 = { by axiom 1 (cls_COMBC__def_0) }
% 15.73/2.48 c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), hAPP(hAPP(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_b____), v_i____)), c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_bs____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)
% 15.73/2.48 = { by axiom 1 (cls_COMBC__def_0) }
% 15.73/2.48 c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), v_u____), v_i____)), c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_bs____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)
% 15.73/2.48 = { by axiom 1 (cls_COMBC__def_0) }
% 15.73/2.48 c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_b____), v_u____), v_i____)), c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Omap(c_COMBC(c_Lambda_Olift, c_HOL_Ozero__class_Ozero(tc_nat), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_i____, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_bs____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)
% 15.73/2.48 = { by axiom 3 (cls_CHAINED_0) }
% 15.73/2.48 true2
% 15.73/2.48 % SZS output end Proof
% 15.73/2.48
% 15.73/2.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------