%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL805-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 01:08:28 PM UTC 2026
% Result : Unsatisfiable 0.55s 0.89s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 6 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(800,axiom,
equal(v_i____,v_n____),
file('LCL805-1.p',unknown),
[] ).
cnf(835,axiom,
c_List_Olistsp(u,c_List_Olist_ONil(v),v),
file('LCL805-1.p',unknown),
[] ).
cnf(840,axiom,
equal(c_List_Omap(u,c_List_Olist_ONil(v),v,w),c_List_Olist_ONil(w)),
file('LCL805-1.p',unknown),
[] ).
cnf(919,axiom,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('LCL805-1.p',unknown),
[] ).
cnf(987,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(rew,[status(thm),theory(equality)],[840,919,800]),
[iquote('0:Rew:840.0,919.0,840.0,919.0,800.0,919.0')] ).
cnf(988,plain,
$false,
inference(mrr,[status(thm)],[987,835]),
[iquote('0:MRR:987.0,835.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL805-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 17:42:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.55/0.89
% 0.55/0.89 SPASS V 3.9
% 0.55/0.89 SPASS beiseite: Proof found.
% 0.55/0.89 % SZS status Theorem
% 0.55/0.89 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.89 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 731 clauses.
% 0.55/0.89 SPASS allocated 77225 KBytes.
% 0.55/0.89 SPASS spent 0:00:00.48 on the problem.
% 0.55/0.89 0:00:00.10 for the input.
% 0.55/0.89 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.89 0:00:00.00 for inferences.
% 0.55/0.89 0:00:00.00 for the backtracking.
% 0.55/0.89 0:00:00.24 for the reduction.
% 0.55/0.89
% 0.55/0.89
% 0.55/0.89 Here is a proof with depth 0, length 6 :
% 0.55/0.89 % SZS output start Refutation
% See solution above
% 0.55/0.89 Formulae used in the proof : cls_True_0 cls_listsp_ONil_0 cls_Nil__is__map__conv_1 cls_conjecture_0
% 0.55/0.89
%------------------------------------------------------------------------------