TSTP Solution File: LCL773-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL773-1 : 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 : n026.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 08:20:33 EDT 2023
% Result : Unsatisfiable 85.97s 11.60s
% Output : Proof 85.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL773-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 18:33:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 85.97/11.60 Command-line arguments: --no-flatten-goal
% 85.97/11.60
% 85.97/11.60 % SZS status Unsatisfiable
% 85.97/11.60
% 85.97/11.60 % SZS output start Proof
% 85.97/11.60 Take the following subset of the input axioms:
% 85.97/11.60 fof(cls_conjecture_0, negated_conjecture, c_InductTermi_OIT(v_r)).
% 85.97/11.60 fof(cls_conjecture_2, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_Osubst(v_r, c_Lambda_OdB_OVar(v_i), c_HOL_Ozero__class_Ozero(tc_nat)))).
% 85.97/11.60 fof(cls_subst__Var__IT_0, axiom, ![V_i, V_j, V_r]: (c_InductTermi_OIT(c_Lambda_Osubst(V_r, c_Lambda_OdB_OVar(V_i), V_j)) | ~c_InductTermi_OIT(V_r))).
% 85.97/11.60
% 85.97/11.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 85.97/11.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 85.97/11.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 85.97/11.60 fresh(y, y, x1...xn) = u
% 85.97/11.60 C => fresh(s, t, x1...xn) = v
% 85.97/11.60 where fresh is a fresh function symbol and x1..xn are the free
% 85.97/11.60 variables of u and v.
% 85.97/11.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 85.97/11.60 input problem has no model of domain size 1).
% 85.97/11.60
% 85.97/11.60 The encoding turns the above axioms into the following unit equations and goals:
% 85.97/11.60
% 85.97/11.60 Axiom 1 (cls_conjecture_0): c_InductTermi_OIT(v_r) = true2.
% 85.97/11.60 Axiom 2 (cls_subst__Var__IT_0): fresh177(X, X, Y, Z, W) = true2.
% 85.97/11.60 Axiom 3 (cls_subst__Var__IT_0): fresh177(c_InductTermi_OIT(X), true2, X, Y, Z) = c_InductTermi_OIT(c_Lambda_Osubst(X, c_Lambda_OdB_OVar(Y), Z)).
% 85.97/11.60
% 85.97/11.60 Goal 1 (cls_conjecture_2): c_InductTermi_OIT(c_Lambda_Osubst(v_r, c_Lambda_OdB_OVar(v_i), c_HOL_Ozero__class_Ozero(tc_nat))) = true2.
% 85.97/11.60 Proof:
% 85.97/11.60 c_InductTermi_OIT(c_Lambda_Osubst(v_r, c_Lambda_OdB_OVar(v_i), c_HOL_Ozero__class_Ozero(tc_nat)))
% 85.97/11.60 = { by axiom 3 (cls_subst__Var__IT_0) R->L }
% 85.97/11.60 fresh177(c_InductTermi_OIT(v_r), true2, v_r, v_i, c_HOL_Ozero__class_Ozero(tc_nat))
% 85.97/11.60 = { by axiom 1 (cls_conjecture_0) }
% 85.97/11.60 fresh177(true2, true2, v_r, v_i, c_HOL_Ozero__class_Ozero(tc_nat))
% 85.97/11.60 = { by axiom 2 (cls_subst__Var__IT_0) }
% 85.97/11.60 true2
% 85.97/11.60 % SZS output end Proof
% 85.97/11.60
% 85.97/11.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------