TSTP Solution File: LCL776-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL776-1 : 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 : n023.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 08:20:34 EDT 2023
% Result : Unsatisfiable 50.43s 6.73s
% Output : Proof 50.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL776-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % 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 : n023.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 : Fri Aug 25 00:57:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 50.43/6.73 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 50.43/6.73
% 50.43/6.73 % SZS status Unsatisfiable
% 50.43/6.73
% 50.43/6.73 % SZS output start Proof
% 50.43/6.73 Take the following subset of the input axioms:
% 50.43/6.74 fof(cls_Beta_0, axiom, ![V_r, V_s, V_ss]: (hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_r)), V_s), V_ss, tc_Lambda_OdB, tc_Lambda_OdB))) | (~hBOOL(hAPP(c_InductTermi_OIT, V_s)) | ~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)), V_ss, tc_Lambda_OdB, tc_Lambda_OdB)))))).
% 50.43/6.74 fof(cls_app__last_0, axiom, ![V_u, V_t, V_ts]: 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)).
% 50.43/6.74 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))))).
% 50.43/6.74 fof(cls_conjecture_2, negated_conjecture, hBOOL(hAPP(c_InductTermi_OIT, v_s))).
% 50.43/6.74 fof(cls_conjecture_4, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r)), v_s), 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)))).
% 50.43/6.74
% 50.43/6.74 Now clausify the problem and encode Horn clauses using encoding 3 of
% 50.43/6.74 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 50.43/6.74 We repeatedly replace C & s=t => u=v by the two clauses:
% 50.43/6.74 fresh(y, y, x1...xn) = u
% 50.43/6.74 C => fresh(s, t, x1...xn) = v
% 50.43/6.74 where fresh is a fresh function symbol and x1..xn are the free
% 50.43/6.74 variables of u and v.
% 50.43/6.74 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 50.43/6.74 input problem has no model of domain size 1).
% 50.43/6.74
% 50.43/6.74 The encoding turns the above axioms into the following unit equations and goals:
% 50.43/6.74
% 50.43/6.74 Axiom 1 (cls_conjecture_2): hBOOL(hAPP(c_InductTermi_OIT, v_s)) = true2.
% 50.43/6.74 Axiom 2 (cls_Beta_0): fresh478(X, X, Y, Z, W) = true2.
% 50.43/6.74 Axiom 3 (cls_Beta_0): fresh477(X, X, Y, Z, W) = fresh478(hBOOL(hAPP(c_InductTermi_OIT, Z)), true2, Y, Z, W).
% 50.43/6.74 Axiom 4 (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).
% 50.43/6.74 Axiom 5 (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.
% 50.43/6.74 Axiom 6 (cls_Beta_0): fresh477(hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(X, Y, c_HOL_Ozero__class_Ozero(tc_nat)), Z, tc_Lambda_OdB, tc_Lambda_OdB))), true2, X, Y, Z) = hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(X)), Y), Z, tc_Lambda_OdB, tc_Lambda_OdB))).
% 50.43/6.74
% 50.43/6.74 Goal 1 (cls_conjecture_4): hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r)), v_s), 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.
% 50.43/6.74 Proof:
% 50.43/6.74 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r)), v_s), 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)))
% 50.43/6.74 = { by axiom 6 (cls_Beta_0) R->L }
% 50.43/6.74 fresh477(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, v_r, v_s, 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))
% 50.43/6.74 = { by axiom 4 (cls_app__last_0) R->L }
% 50.43/6.74 fresh477(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, v_r, v_s, 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))
% 50.43/6.74 = { by axiom 5 (cls_conjecture_1) }
% 50.43/6.74 fresh477(true2, true2, v_r, v_s, 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))
% 50.43/6.74 = { by axiom 3 (cls_Beta_0) }
% 50.43/6.74 fresh478(hBOOL(hAPP(c_InductTermi_OIT, v_s)), true2, v_r, v_s, 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))
% 50.43/6.74 = { by axiom 1 (cls_conjecture_2) }
% 50.43/6.74 fresh478(true2, true2, v_r, v_s, 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))
% 50.43/6.74 = { by axiom 2 (cls_Beta_0) }
% 50.43/6.74 true2
% 50.43/6.74 % SZS output end Proof
% 50.43/6.74
% 50.43/6.74 RESULT: Unsatisfiable (the axioms are contradictory).
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