TSTP Solution File: LCL777-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL777-1 : 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 : n027.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 08:20:35 EDT 2023
% Result : Unsatisfiable 4.72s 1.00s
% Output : Proof 4.72s
% 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 : LCL777-1 : 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
% 0.13/0.35 % Computer : n027.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 03:24:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.72/1.00 Command-line arguments: --no-flatten-goal
% 4.72/1.00
% 4.72/1.00 % SZS status Unsatisfiable
% 4.72/1.00
% 4.72/1.00 % SZS output start Proof
% 4.72/1.00 Take the following subset of the input axioms:
% 4.72/1.00 fof(cls_app__last_0, axiom, ![V_ts, V_t, V_u]: hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB)), V_u)=c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, c_List_Oappend(V_ts, c_List_Olist_OCons(V_u, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)).
% 4.72/1.00 fof(cls_conjecture_1, negated_conjecture, hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(v_r, v_s, c_HOL_Ozero__class_Ozero(tc_nat)), v_ss, tc_Lambda_OdB, tc_Lambda_OdB)), c_Lambda_OdB_OVar(v_i))))).
% 4.72/1.00 fof(cls_conjecture_4, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(v_r, v_s, c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Oappend(v_ss, c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))).
% 4.72/1.00 fof(cls_substn__subst__0_0, axiom, ![V_s, V_t2]: c_Lambda_Osubstn(V_t2, V_s, c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(V_t2, V_s, c_HOL_Ozero__class_Ozero(tc_nat))).
% 4.72/1.00
% 4.72/1.00 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.72/1.00 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.72/1.00 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.72/1.00 fresh(y, y, x1...xn) = u
% 4.72/1.00 C => fresh(s, t, x1...xn) = v
% 4.72/1.00 where fresh is a fresh function symbol and x1..xn are the free
% 4.72/1.00 variables of u and v.
% 4.72/1.00 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.72/1.00 input problem has no model of domain size 1).
% 4.72/1.00
% 4.72/1.00 The encoding turns the above axioms into the following unit equations and goals:
% 4.72/1.00
% 4.72/1.00 Axiom 1 (cls_substn__subst__0_0): c_Lambda_Osubstn(X, Y, c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X, Y, c_HOL_Ozero__class_Ozero(tc_nat)).
% 4.72/1.00 Axiom 2 (cls_app__last_0): hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, X, Y, tc_Lambda_OdB, tc_Lambda_OdB)), Z) = c_List_Ofoldl(c_Lambda_OdB_OApp, X, c_List_Oappend(Y, c_List_Olist_OCons(Z, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB).
% 4.72/1.00 Axiom 3 (cls_conjecture_1): hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(v_r, v_s, c_HOL_Ozero__class_Ozero(tc_nat)), v_ss, tc_Lambda_OdB, tc_Lambda_OdB)), c_Lambda_OdB_OVar(v_i)))) = true2.
% 4.72/1.00
% 4.72/1.00 Goal 1 (cls_conjecture_4): hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(v_r, v_s, c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Oappend(v_ss, c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB))) = true2.
% 4.72/1.00 Proof:
% 4.72/1.00 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(v_r, v_s, c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Oappend(v_ss, c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))
% 4.72/1.00 = { by axiom 1 (cls_substn__subst__0_0) R->L }
% 4.72/1.00 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubstn(v_r, v_s, c_HOL_Ozero__class_Ozero(tc_nat)), c_List_Oappend(v_ss, c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)))
% 4.72/1.00 = { by axiom 2 (cls_app__last_0) R->L }
% 4.72/1.00 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubstn(v_r, v_s, c_HOL_Ozero__class_Ozero(tc_nat)), v_ss, tc_Lambda_OdB, tc_Lambda_OdB)), c_Lambda_OdB_OVar(v_i))))
% 4.72/1.00 = { by axiom 1 (cls_substn__subst__0_0) }
% 4.72/1.00 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(v_r, v_s, c_HOL_Ozero__class_Ozero(tc_nat)), v_ss, tc_Lambda_OdB, tc_Lambda_OdB)), c_Lambda_OdB_OVar(v_i))))
% 4.72/1.00 = { by axiom 3 (cls_conjecture_1) }
% 4.72/1.00 true2
% 4.72/1.00 % SZS output end Proof
% 4.72/1.00
% 4.72/1.00 RESULT: Unsatisfiable (the axioms are contradictory).
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