%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL809-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:43:36 PM UTC 2026
% Result : Unsatisfiable 15.57s 15.82s
% Output : CNFRefutation 15.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 4 RR)
% Number of literals : 9 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 4 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_lift__IT_0,axiom,
( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
| ~ c_InductTermi_OIT(V_t) ) ).
cnf(cls_CHAINED_0,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ).
cnf(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))) ).
cnf(refute_0_0,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____))
| c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),X_949)) ),
inference(subst,[],[cls_lift__IT_0:[bind(V_i,$fot(X_949)),bind(V_t,$fot(c_Lambda_Osubst(v_b____,v_u____,v_i____)))]]) ).
cnf(refute_0_1,plain,
c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),X_949)),
inference(resolve,[$cnf( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) )],[cls_CHAINED_0,refute_0_0]) ).
cnf(refute_0_2,plain,
c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(subst,[],[refute_0_1:[bind(X_949,$fot(c_HOL_Ozero__class_Ozero(tc_nat)))]]) ).
cnf(refute_0_3,plain,
$false,
inference(resolve,[$cnf( c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))) )],[refute_0_2,cls_conjecture_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL809-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 21:44:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 15.57/15.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.57/15.82
% 15.57/15.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.57/15.83
%------------------------------------------------------------------------------