TSTP Solution File: LCL837-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL837-1 : 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 : n031.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 08:20:55 EDT 2023
% Result : Unsatisfiable 21.67s 3.13s
% Output : Proof 21.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL837-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % 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 : n031.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 17:35:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 21.67/3.13 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 21.67/3.13
% 21.67/3.13 % SZS status Unsatisfiable
% 21.67/3.13
% 21.67/3.13 % SZS output start Proof
% 21.67/3.13 Take the following subset of the input axioms:
% 21.67/3.13 fof(cls_CHAINED_0, axiom, hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), v_u____), v_i____)))).
% 21.67/3.13 fof(cls_Suc__eq__plus1_0, axiom, ![V_n]: c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), V_n), c_HOL_Oone__class_Oone(tc_nat))).
% 21.67/3.13 fof(cls_conjecture_0, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), hAPP(hAPP(c_Lambda_Olift, v_u____), c_HOL_Ozero__class_Ozero(tc_nat))), c_Suc(v_i____))), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_a____), v_u____), v_i____)), c_HOL_Ozero__class_Ozero(tc_nat)), 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)))).
% 21.67/3.13 fof(cls_subst__map_0, axiom, ![V_i, V_u, V_t, V_ts]: hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB)), V_u), V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, V_t), 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_ts, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)).
% 21.67/3.13 fof(cls_subst__subst_0, axiom, ![V_j, V_v, V_i2, V_u2, V_t2]: (hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, V_t2), hAPP(hAPP(c_Lambda_Olift, V_v), V_i2)), c_Suc(V_j))), hAPP(hAPP(hAPP(c_Lambda_Osubst, V_u2), V_v), V_j)), V_i2)=hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, V_t2), V_u2), V_i2)), V_v), V_j) | ~c_HOL_Oord__class_Oless(V_i2, hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), V_j), c_HOL_Oone__class_Oone(tc_nat)), tc_nat))).
% 21.67/3.13 fof(cls_zero__less__Suc_0, axiom, ![V_n2]: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(V_n2), tc_nat)).
% 21.67/3.13
% 21.67/3.13 Now clausify the problem and encode Horn clauses using encoding 3 of
% 21.67/3.13 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 21.67/3.13 We repeatedly replace C & s=t => u=v by the two clauses:
% 21.67/3.13 fresh(y, y, x1...xn) = u
% 21.67/3.13 C => fresh(s, t, x1...xn) = v
% 21.67/3.13 where fresh is a fresh function symbol and x1..xn are the free
% 21.67/3.13 variables of u and v.
% 21.67/3.13 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 21.67/3.13 input problem has no model of domain size 1).
% 21.67/3.13
% 21.67/3.13 The encoding turns the above axioms into the following unit equations and goals:
% 21.67/3.13
% 21.67/3.13 Axiom 1 (cls_Suc__eq__plus1_0): c_Suc(X) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), X), c_HOL_Oone__class_Oone(tc_nat)).
% 21.67/3.13 Axiom 2 (cls_zero__less__Suc_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(X), tc_nat) = true2.
% 21.67/3.13 Axiom 3 (cls_subst__subst_0): fresh130(X, X, Y, Z, W, V, U) = hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, Y), U), W)), Z), V).
% 21.67/3.13 Axiom 4 (cls_subst__subst_0): fresh130(c_HOL_Oord__class_Oless(X, hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), Y), c_HOL_Oone__class_Oone(tc_nat)), tc_nat), true2, Z, W, X, Y, V) = hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, Z), hAPP(hAPP(c_Lambda_Olift, W), X)), c_Suc(Y))), hAPP(hAPP(hAPP(c_Lambda_Osubst, V), W), Y)), X).
% 21.67/3.13 Axiom 5 (cls_CHAINED_0): hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), v_u____), v_i____))) = true2.
% 21.67/3.13 Axiom 6 (cls_subst__map_0): hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, X, Y, tc_Lambda_OdB, tc_Lambda_OdB)), Z), W) = c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, X), Z), W), c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst, Z, tc_Lambda_OdB, tc_Lambda_OdB, tc_fun(tc_nat, tc_Lambda_OdB)), W, tc_Lambda_OdB, tc_nat, tc_Lambda_OdB), Y, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB).
% 21.67/3.13
% 21.67/3.13 Goal 1 (cls_conjecture_0): hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), hAPP(hAPP(c_Lambda_Olift, v_u____), c_HOL_Ozero__class_Ozero(tc_nat))), c_Suc(v_i____))), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_a____), v_u____), v_i____)), c_HOL_Ozero__class_Ozero(tc_nat)), 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.
% 21.67/3.13 Proof:
% 21.67/3.13 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), hAPP(hAPP(c_Lambda_Olift, v_u____), c_HOL_Ozero__class_Ozero(tc_nat))), c_Suc(v_i____))), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_a____), v_u____), v_i____)), c_HOL_Ozero__class_Ozero(tc_nat)), 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)))
% 21.67/3.13 = { by axiom 4 (cls_subst__subst_0) R->L }
% 21.67/3.13 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, fresh130(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat), v_i____), c_HOL_Oone__class_Oone(tc_nat)), tc_nat), true2, v_r____, v_u____, c_HOL_Ozero__class_Ozero(tc_nat), v_i____, 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)))
% 21.67/3.13 = { by axiom 1 (cls_Suc__eq__plus1_0) R->L }
% 21.67/3.13 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, fresh130(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(v_i____), tc_nat), true2, v_r____, v_u____, c_HOL_Ozero__class_Ozero(tc_nat), v_i____, 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)))
% 21.67/3.13 = { by axiom 2 (cls_zero__less__Suc_0) }
% 21.67/3.13 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, fresh130(true2, true2, v_r____, v_u____, c_HOL_Ozero__class_Ozero(tc_nat), v_i____, 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)))
% 21.67/3.13 = { by axiom 3 (cls_subst__subst_0) }
% 21.67/3.13 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat))), 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)))
% 21.67/3.13 = { by axiom 6 (cls_subst__map_0) R->L }
% 21.67/3.13 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(hAPP(c_Lambda_Osubst, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), v_u____), v_i____)))
% 21.67/3.13 = { by axiom 5 (cls_CHAINED_0) }
% 21.67/3.13 true2
% 21.67/3.13 % SZS output end Proof
% 21.67/3.13
% 21.67/3.13 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------