TSTP Solution File: LCL846-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL846-1 : 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 : n005.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 08:20:57 EDT 2023
% Result : Unsatisfiable 91.29s 11.95s
% Output : Proof 91.29s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL846-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 19:16:53 EDT 2023
% 0.12/0.33 % CPUTime :
% 91.29/11.95 Command-line arguments: --no-flatten-goal
% 91.29/11.95
% 91.29/11.95 % SZS status Unsatisfiable
% 91.29/11.95
% 91.29/11.96 % SZS output start Proof
% 91.29/11.96 Take the following subset of the input axioms:
% 91.29/11.96 fof(cls_App_I4_J_0, axiom, c_InductTermi_OIT(v_ta____)).
% 91.29/11.96 fof(cls_char__size_0, axiom, ![V_c]: c_String_Ochar_Ochar__size(V_c)=c_HOL_Ozero__class_Ozero(tc_nat)).
% 91.29/11.96 fof(cls_conjecture_0, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_Olift(v_ta____, c_HOL_Ozero__class_Ozero(tc_nat)))).
% 91.29/11.96 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))).
% 91.29/11.96
% 91.29/11.96 Now clausify the problem and encode Horn clauses using encoding 3 of
% 91.29/11.96 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 91.29/11.96 We repeatedly replace C & s=t => u=v by the two clauses:
% 91.29/11.96 fresh(y, y, x1...xn) = u
% 91.29/11.96 C => fresh(s, t, x1...xn) = v
% 91.29/11.96 where fresh is a fresh function symbol and x1..xn are the free
% 91.29/11.96 variables of u and v.
% 91.29/11.96 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 91.29/11.96 input problem has no model of domain size 1).
% 91.29/11.96
% 91.29/11.96 The encoding turns the above axioms into the following unit equations and goals:
% 91.29/11.96
% 91.29/11.96 Axiom 1 (cls_App_I4_J_0): c_InductTermi_OIT(v_ta____) = true2.
% 91.29/11.96 Axiom 2 (cls_char__size_0): c_String_Ochar_Ochar__size(X) = c_HOL_Ozero__class_Ozero(tc_nat).
% 91.29/11.96 Axiom 3 (cls_lift__IT_0): fresh564(X, X, Y, Z) = true2.
% 91.29/11.96 Axiom 4 (cls_lift__IT_0): fresh564(c_InductTermi_OIT(X), true2, X, Y) = c_InductTermi_OIT(c_Lambda_Olift(X, Y)).
% 91.29/11.96
% 91.29/11.96 Goal 1 (cls_conjecture_0): c_InductTermi_OIT(c_Lambda_Olift(v_ta____, c_HOL_Ozero__class_Ozero(tc_nat))) = true2.
% 91.29/11.96 Proof:
% 91.29/11.96 c_InductTermi_OIT(c_Lambda_Olift(v_ta____, c_HOL_Ozero__class_Ozero(tc_nat)))
% 91.29/11.96 = { by axiom 2 (cls_char__size_0) R->L }
% 91.29/11.96 c_InductTermi_OIT(c_Lambda_Olift(v_ta____, c_String_Ochar_Ochar__size(X)))
% 91.29/11.96 = { by axiom 4 (cls_lift__IT_0) R->L }
% 91.29/11.96 fresh564(c_InductTermi_OIT(v_ta____), true2, v_ta____, c_String_Ochar_Ochar__size(X))
% 91.29/11.96 = { by axiom 1 (cls_App_I4_J_0) }
% 91.29/11.96 fresh564(true2, true2, v_ta____, c_String_Ochar_Ochar__size(X))
% 91.29/11.96 = { by axiom 3 (cls_lift__IT_0) }
% 91.29/11.96 true2
% 91.29/11.96 % SZS output end Proof
% 91.29/11.96
% 91.29/11.96 RESULT: Unsatisfiable (the axioms are contradictory).
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