TSTP Solution File: LCL834-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL834-1 : 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 : n015.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 08:20:54 EDT 2023
% Result : Unsatisfiable 14.48s 2.26s
% Output : Proof 14.48s
% 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 : LCL834-1 : 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
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 04:28:36 EDT 2023
% 0.12/0.34 % CPUTime :
% 14.48/2.26 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 14.48/2.26
% 14.48/2.26 % SZS status Unsatisfiable
% 14.48/2.26
% 14.48/2.26 % SZS output start Proof
% 14.48/2.26 Take the following subset of the input axioms:
% 14.48/2.26 fof(cls_apps__preserves__beta_0, axiom, ![V_r, V_s, V_ss]: (hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, V_r, V_ss, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB))) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_r), V_s)))).
% 14.48/2.26 fof(cls_beta_0, axiom, ![V_t, V_s2]: hBOOL(hAPP(hAPP(c_Lambda_Obeta, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_s2)), V_t)), hAPP(hAPP(hAPP(c_Lambda_Osubst, V_s2), V_t), c_HOL_Ozero__class_Ozero(tc_nat))))).
% 14.48/2.26 fof(cls_conjecture_0, negated_conjecture, ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), 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)))).
% 14.48/2.26
% 14.48/2.26 Now clausify the problem and encode Horn clauses using encoding 3 of
% 14.48/2.26 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 14.48/2.26 We repeatedly replace C & s=t => u=v by the two clauses:
% 14.48/2.26 fresh(y, y, x1...xn) = u
% 14.48/2.26 C => fresh(s, t, x1...xn) = v
% 14.48/2.26 where fresh is a fresh function symbol and x1..xn are the free
% 14.48/2.26 variables of u and v.
% 14.48/2.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 14.48/2.26 input problem has no model of domain size 1).
% 14.48/2.26
% 14.48/2.26 The encoding turns the above axioms into the following unit equations and goals:
% 14.48/2.26
% 14.48/2.26 Axiom 1 (cls_apps__preserves__beta_0): fresh200(X, X, Y, Z, W) = true2.
% 14.48/2.26 Axiom 2 (cls_apps__preserves__beta_0): fresh200(hBOOL(hAPP(hAPP(c_Lambda_Obeta, X), Y)), true2, X, Z, Y) = hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, X, Z, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, Y, Z, tc_Lambda_OdB, tc_Lambda_OdB))).
% 14.48/2.26 Axiom 3 (cls_beta_0): hBOOL(hAPP(hAPP(c_Lambda_Obeta, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(X)), Y)), hAPP(hAPP(hAPP(c_Lambda_Osubst, X), Y), c_HOL_Ozero__class_Ozero(tc_nat)))) = true2.
% 14.48/2.26
% 14.48/2.26 Goal 1 (cls_conjecture_0): hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), 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))) = true2.
% 14.48/2.26 Proof:
% 14.48/2.26 hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), 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)))
% 14.48/2.26 = { by axiom 2 (cls_apps__preserves__beta_0) R->L }
% 14.48/2.26 fresh200(hBOOL(hAPP(hAPP(c_Lambda_Obeta, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____)), hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)))), true2, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)))
% 14.48/2.26 = { by axiom 3 (cls_beta_0) }
% 14.48/2.26 fresh200(true2, true2, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)))
% 14.48/2.26 = { by axiom 1 (cls_apps__preserves__beta_0) }
% 14.48/2.26 true2
% 14.48/2.26 % SZS output end Proof
% 14.48/2.26
% 14.48/2.26 RESULT: Unsatisfiable (the axioms are contradictory).
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