TSTP Solution File: LCL800-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL800-1 : 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 08:20:42 EDT 2023
% Result : Unsatisfiable 7.67s 1.55s
% Output : Proof 8.23s
% 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 : LCL800-1 : 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 : n026.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 : Thu Aug 24 19:11:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.67/1.55 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 7.67/1.55
% 7.67/1.55 % SZS status Unsatisfiable
% 7.67/1.55
% 7.67/1.56 % SZS output start Proof
% 7.67/1.56 Take the following subset of the input axioms:
% 7.67/1.56 fof(cls_CHAINED_0, axiom, c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))), c_Lambda_Osubst(v_a____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat)))).
% 7.67/1.56 fof(cls_conjecture_0, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____, c_Lambda_Osubst(v_a____, v_u____, v_i____)))).
% 7.67/1.56 fof(cls_subst__App_0, axiom, ![V_k, V_u, V_t, V_s]: c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t, V_u), V_s, V_k)=c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t, V_s, V_k), c_Lambda_Osubst(V_u, V_s, V_k))).
% 7.67/1.56 fof(cls_subst__eq_0, axiom, ![V_k2, V_u2]: c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k2), V_u2, V_k2)=V_u2).
% 7.67/1.56 fof(cls_subst__lift_0, axiom, ![V_k2, V_t2, V_s2]: c_Lambda_Osubst(c_Lambda_Olift(V_t2, V_k2), V_s2, V_k2)=V_t2).
% 7.67/1.56
% 7.67/1.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.67/1.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.67/1.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.67/1.56 fresh(y, y, x1...xn) = u
% 7.67/1.56 C => fresh(s, t, x1...xn) = v
% 7.67/1.56 where fresh is a fresh function symbol and x1..xn are the free
% 7.67/1.56 variables of u and v.
% 7.67/1.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.67/1.56 input problem has no model of domain size 1).
% 7.67/1.56
% 7.67/1.56 The encoding turns the above axioms into the following unit equations and goals:
% 7.67/1.56
% 7.67/1.56 Axiom 1 (cls_subst__eq_0): c_Lambda_Osubst(c_Lambda_OdB_OVar(X), Y, X) = Y.
% 7.67/1.56 Axiom 2 (cls_subst__lift_0): c_Lambda_Osubst(c_Lambda_Olift(X, Y), Z, Y) = X.
% 7.67/1.56 Axiom 3 (cls_subst__App_0): c_Lambda_Osubst(c_Lambda_OdB_OApp(X, Y), Z, W) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X, Z, W), c_Lambda_Osubst(Y, Z, W)).
% 7.67/1.56 Axiom 4 (cls_CHAINED_0): c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))), c_Lambda_Osubst(v_a____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat))) = true2.
% 7.67/1.56
% 7.67/1.56 Goal 1 (cls_conjecture_0): c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____, c_Lambda_Osubst(v_a____, v_u____, v_i____))) = true2.
% 7.67/1.56 Proof:
% 7.67/1.56 c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____, c_Lambda_Osubst(v_a____, v_u____, v_i____)))
% 7.67/1.56 = { by axiom 2 (cls_subst__lift_0) R->L }
% 7.67/1.56 c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), c_Lambda_Osubst(v_a____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat)), c_Lambda_Osubst(v_a____, v_u____, v_i____)))
% 7.67/1.56 = { by axiom 1 (cls_subst__eq_0) R->L }
% 7.67/1.56 c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), c_Lambda_Osubst(v_a____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat)), c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)), c_Lambda_Osubst(v_a____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat))))
% 8.23/1.56 = { by axiom 3 (cls_subst__App_0) R->L }
% 8.23/1.56 c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____, c_HOL_Ozero__class_Ozero(tc_nat)), c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))), c_Lambda_Osubst(v_a____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat)))
% 8.23/1.56 = { by axiom 4 (cls_CHAINED_0) }
% 8.23/1.56 true2
% 8.23/1.56 % SZS output end Proof
% 8.23/1.56
% 8.23/1.56 RESULT: Unsatisfiable (the axioms are contradictory).
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