TSTP Solution File: LCL825-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL825-1 : 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 : n026.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 08:20:51 EDT 2023
% Result : Unsatisfiable 7.86s 1.46s
% Output : Proof 7.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL825-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 18:50:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 7.86/1.46 Command-line arguments: --no-flatten-goal
% 7.86/1.46
% 7.86/1.46 % SZS status Unsatisfiable
% 7.86/1.46
% 7.86/1.46 % SZS output start Proof
% 7.86/1.46 Take the following subset of the input axioms:
% 7.86/1.46 fof(cls_conjecture_0, negated_conjecture, ~c_List_Olistsp(c_InductTermi_OIT, c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB)).
% 7.86/1.46 fof(cls_listsp_ONil_0, axiom, ![T_a, V_A]: c_List_Olistsp(V_A, c_List_Olist_ONil(T_a), T_a)).
% 7.86/1.46 fof(cls_map__is__Nil__conv_1, axiom, ![V_f, T_b, T_a2]: c_List_Omap(V_f, c_List_Olist_ONil(T_b), T_b, T_a2)=c_List_Olist_ONil(T_a2)).
% 7.86/1.46
% 7.86/1.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.86/1.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.86/1.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.86/1.46 fresh(y, y, x1...xn) = u
% 7.86/1.46 C => fresh(s, t, x1...xn) = v
% 7.86/1.46 where fresh is a fresh function symbol and x1..xn are the free
% 7.86/1.46 variables of u and v.
% 7.86/1.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.86/1.46 input problem has no model of domain size 1).
% 7.86/1.46
% 7.86/1.46 The encoding turns the above axioms into the following unit equations and goals:
% 7.86/1.46
% 7.86/1.46 Axiom 1 (cls_listsp_ONil_0): c_List_Olistsp(X, c_List_Olist_ONil(Y), Y) = true2.
% 7.86/1.46 Axiom 2 (cls_map__is__Nil__conv_1): c_List_Omap(X, c_List_Olist_ONil(Y), Y, Z) = c_List_Olist_ONil(Z).
% 7.86/1.46
% 7.86/1.46 Goal 1 (cls_conjecture_0): c_List_Olistsp(c_InductTermi_OIT, c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB) = true2.
% 7.86/1.46 Proof:
% 7.86/1.46 c_List_Olistsp(c_InductTermi_OIT, c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), v_u____), tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), v_i____), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB)
% 7.86/1.46 = { by axiom 2 (cls_map__is__Nil__conv_1) }
% 7.86/1.46 c_List_Olistsp(c_InductTermi_OIT, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB)
% 7.86/1.46 = { by axiom 1 (cls_listsp_ONil_0) }
% 7.86/1.46 true2
% 7.86/1.46 % SZS output end Proof
% 7.86/1.46
% 7.86/1.46 RESULT: Unsatisfiable (the axioms are contradictory).
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