TSTP Solution File: LCL830-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL830-1 : 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 : n021.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 08:20:53 EDT 2023
% Result : Unsatisfiable 14.12s 2.26s
% Output : Proof 14.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL830-1 : 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 : n021.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 : Thu Aug 24 20:07:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 14.12/2.26 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 14.12/2.26
% 14.12/2.26 % SZS status Unsatisfiable
% 14.12/2.26
% 14.12/2.26 % SZS output start Proof
% 14.12/2.26 Take the following subset of the input axioms:
% 14.12/2.26 fof(cls_CHAINED_0, axiom, c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst, v_a____), v_u____), v_i____), 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_as____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)).
% 14.12/2.26 fof(cls_COMBC__def_0, axiom, ![T_a, V_P, T_b, T_c, V_Q, 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)).
% 14.12/2.26 fof(cls_conjecture_0, negated_conjecture, ~c_List_Olistsp(c_InductTermi_OIT, 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_a____, v_as____, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB)).
% 14.12/2.26 fof(cls_map__eq__Cons__conv_3, axiom, ![V_x, V_xa, 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)).
% 14.12/2.26
% 14.12/2.26 Now clausify the problem and encode Horn clauses using encoding 3 of
% 14.12/2.26 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 14.12/2.26 We repeatedly replace C & s=t => u=v by the two clauses:
% 14.12/2.26 fresh(y, y, x1...xn) = u
% 14.12/2.26 C => fresh(s, t, x1...xn) = v
% 14.12/2.26 where fresh is a fresh function symbol and x1..xn are the free
% 14.12/2.26 variables of u and v.
% 14.12/2.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 14.12/2.26 input problem has no model of domain size 1).
% 14.12/2.26
% 14.12/2.26 The encoding turns the above axioms into the following unit equations and goals:
% 14.12/2.26
% 14.12/2.26 Axiom 1 (cls_COMBC__def_0): hAPP(c_COMBC(X, Y, Z, W, V), U) = hAPP(hAPP(X, U), Y).
% 14.12/2.26 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).
% 14.12/2.26 Axiom 3 (cls_CHAINED_0): c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst, v_a____), v_u____), v_i____), 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_as____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB) = true2.
% 14.12/2.26
% 14.12/2.26 Goal 1 (cls_conjecture_0): c_List_Olistsp(c_InductTermi_OIT, 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_a____, v_as____, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB) = true2.
% 14.12/2.26 Proof:
% 14.12/2.26 c_List_Olistsp(c_InductTermi_OIT, 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_a____, v_as____, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB)
% 14.12/2.26 = { by axiom 2 (cls_map__eq__Cons__conv_3) }
% 14.12/2.26 c_List_Olistsp(c_InductTermi_OIT, 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_a____), 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_as____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)
% 14.12/2.26 = { by axiom 1 (cls_COMBC__def_0) }
% 14.12/2.26 c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(c_COMBC(c_Lambda_Osubst, v_u____, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_a____), v_i____), 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_as____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)
% 14.12/2.26 = { by axiom 1 (cls_COMBC__def_0) }
% 14.12/2.26 c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst, v_a____), v_u____), v_i____), 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_as____, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB)
% 14.12/2.26 = { by axiom 3 (cls_CHAINED_0) }
% 14.12/2.26 true2
% 14.12/2.26 % SZS output end Proof
% 14.12/2.26
% 14.12/2.26 RESULT: Unsatisfiable (the axioms are contradictory).
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