%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL825-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 12:43:39 PM UTC 2026
% Result : Unsatisfiable 1.17s 1.43s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 12 ( 3 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 5 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_listsp_ONil_0,axiom,
c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_map__is__Nil__conv_1,axiom,
c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ).
cnf(refute_0_0,plain,
c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB),
inference(subst,[],[cls_map__is__Nil__conv_1:[bind(T_a,$fot(tc_Lambda_OdB)),bind(T_b,$fot(tc_Lambda_OdB)),bind(V_f,$fot(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____)))]]) ).
cnf(refute_0_1,plain,
( c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
introduced(tautology,[equality,[$cnf( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),[1],$fot(c_List_Olist_ONil(tc_Lambda_OdB))]]) ).
cnf(refute_0_2,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(resolve,[$cnf( $equal(c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),c_List_Olist_ONil(tc_Lambda_OdB)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(resolve,[$cnf( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) )],[refute_0_2,cls_conjecture_0]) ).
cnf(refute_0_4,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(subst,[],[cls_listsp_ONil_0:[bind(T_a,$fot(tc_Lambda_OdB)),bind(V_A,$fot(c_InductTermi_OIT))]]) ).
cnf(refute_0_5,plain,
$false,
inference(resolve,[$cnf( c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB) )],[refute_0_4,refute_0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL825-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n017.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 : Sat Sep 5 23:52:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.17/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.17/1.43
% 1.17/1.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.17/1.43
%------------------------------------------------------------------------------