TSTP Solution File: LCL809-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL809-1 : 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 : n014.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 08:20:45 EDT 2023
% Result : Unsatisfiable 104.06s 13.80s
% Output : Proof 104.06s
% 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 : LCL809-1 : 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 : n014.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 18:27:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 104.06/13.80 Command-line arguments: --no-flatten-goal
% 104.06/13.80
% 104.06/13.80 % SZS status Unsatisfiable
% 104.06/13.80
% 104.06/13.81 % SZS output start Proof
% 104.06/13.81 Take the following subset of the input axioms:
% 104.06/13.81 fof(cls_CHAINED_0, axiom, c_InductTermi_OIT(c_Lambda_Osubst(v_b____, v_u____, v_i____))).
% 104.06/13.81 fof(cls_True_0, axiom, v_n____=v_i____).
% 104.06/13.81 fof(cls_char__size_0, axiom, ![V_c]: c_String_Ochar_Ochar__size(V_c)=c_HOL_Ozero__class_Ozero(tc_nat)).
% 104.06/13.81 fof(cls_conjecture_0, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat)))).
% 104.06/13.81 fof(cls_lift__IT_0, axiom, ![V_i, V_t]: (c_InductTermi_OIT(c_Lambda_Olift(V_t, V_i)) | ~c_InductTermi_OIT(V_t))).
% 104.06/13.81
% 104.06/13.81 Now clausify the problem and encode Horn clauses using encoding 3 of
% 104.06/13.81 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 104.06/13.81 We repeatedly replace C & s=t => u=v by the two clauses:
% 104.06/13.81 fresh(y, y, x1...xn) = u
% 104.06/13.81 C => fresh(s, t, x1...xn) = v
% 104.06/13.81 where fresh is a fresh function symbol and x1..xn are the free
% 104.06/13.81 variables of u and v.
% 104.06/13.81 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 104.06/13.81 input problem has no model of domain size 1).
% 104.06/13.81
% 104.06/13.81 The encoding turns the above axioms into the following unit equations and goals:
% 104.06/13.81
% 104.06/13.81 Axiom 1 (cls_True_0): v_n____ = v_i____.
% 104.06/13.81 Axiom 2 (cls_char__size_0): c_String_Ochar_Ochar__size(X) = c_HOL_Ozero__class_Ozero(tc_nat).
% 104.06/13.81 Axiom 3 (cls_lift__IT_0): fresh574(X, X, Y, Z) = true2.
% 104.06/13.81 Axiom 4 (cls_CHAINED_0): c_InductTermi_OIT(c_Lambda_Osubst(v_b____, v_u____, v_i____)) = true2.
% 104.06/13.81 Axiom 5 (cls_lift__IT_0): fresh574(c_InductTermi_OIT(X), true2, X, Y) = c_InductTermi_OIT(c_Lambda_Olift(X, Y)).
% 104.06/13.81
% 104.06/13.81 Goal 1 (cls_conjecture_0): c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat))) = true2.
% 104.06/13.81 Proof:
% 104.06/13.81 c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____, v_u____, v_i____), c_HOL_Ozero__class_Ozero(tc_nat)))
% 104.06/13.81 = { by axiom 1 (cls_True_0) R->L }
% 104.06/13.81 c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____, v_u____, v_n____), c_HOL_Ozero__class_Ozero(tc_nat)))
% 104.06/13.81 = { by axiom 2 (cls_char__size_0) R->L }
% 104.06/13.81 c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____, v_u____, v_n____), c_String_Ochar_Ochar__size(X)))
% 104.06/13.81 = { by axiom 5 (cls_lift__IT_0) R->L }
% 104.06/13.81 fresh574(c_InductTermi_OIT(c_Lambda_Osubst(v_b____, v_u____, v_n____)), true2, c_Lambda_Osubst(v_b____, v_u____, v_n____), c_String_Ochar_Ochar__size(X))
% 104.06/13.81 = { by axiom 1 (cls_True_0) }
% 104.06/13.81 fresh574(c_InductTermi_OIT(c_Lambda_Osubst(v_b____, v_u____, v_i____)), true2, c_Lambda_Osubst(v_b____, v_u____, v_n____), c_String_Ochar_Ochar__size(X))
% 104.06/13.81 = { by axiom 4 (cls_CHAINED_0) }
% 104.06/13.81 fresh574(true2, true2, c_Lambda_Osubst(v_b____, v_u____, v_n____), c_String_Ochar_Ochar__size(X))
% 104.06/13.81 = { by axiom 3 (cls_lift__IT_0) }
% 104.06/13.81 true2
% 104.06/13.81 % SZS output end Proof
% 104.06/13.81
% 104.06/13.81 RESULT: Unsatisfiable (the axioms are contradictory).
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