TSTP Solution File: LCL778-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL778-1 : 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 : n019.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 13.24s 2.12s
% Output : Proof 13.24s
% 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 : LCL778-1 : 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
% 0.13/0.34 % Computer : n019.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 04:44:43 EDT 2023
% 0.20/0.34 % CPUTime :
% 13.24/2.12 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 13.24/2.12
% 13.24/2.12 % SZS status Unsatisfiable
% 13.24/2.12
% 13.24/2.12 % SZS output start Proof
% 13.24/2.12 Take the following subset of the input axioms:
% 13.24/2.13 fof(cls_conjecture_1, negated_conjecture, hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(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))))).
% 13.24/2.13 fof(cls_conjecture_4, negated_conjecture, ~hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(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))))).
% 13.24/2.13
% 13.24/2.13 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.24/2.13 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.24/2.13 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.24/2.13 fresh(y, y, x1...xn) = u
% 13.24/2.13 C => fresh(s, t, x1...xn) = v
% 13.24/2.13 where fresh is a fresh function symbol and x1..xn are the free
% 13.24/2.13 variables of u and v.
% 13.24/2.13 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.24/2.13 input problem has no model of domain size 1).
% 13.24/2.13
% 13.24/2.13 The encoding turns the above axioms into the following unit equations and goals:
% 13.24/2.13
% 13.24/2.13 Axiom 1 (cls_conjecture_1): hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(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.
% 13.24/2.13
% 13.24/2.13 Goal 1 (cls_conjecture_4): hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(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.
% 13.24/2.13 Proof:
% 13.24/2.13 hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(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))))
% 13.24/2.13 = { by axiom 1 (cls_conjecture_1) }
% 13.24/2.13 true2
% 13.24/2.13 % SZS output end Proof
% 13.24/2.13
% 13.24/2.13 RESULT: Unsatisfiable (the axioms are contradictory).
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