%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL848-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 01:08:35 PM UTC 2026
% Result : Unsatisfiable 0.45s 0.73s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 6 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(627,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,u,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v),u,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('LCL848-1.p',unknown),
[] ).
cnf(658,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('LCL848-1.p',unknown),
[] ).
cnf(723,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL848-1.p',unknown),
[] ).
cnf(755,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(res,[status(thm),theory(equality)],[627,723]),
[iquote('0:Res:627.1,723.0')] ).
cnf(763,plain,
$false,
inference(mrr,[status(thm)],[755,658]),
[iquote('0:MRR:755.0,658.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL848-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 21:12:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.45/0.73
% 0.45/0.73 SPASS V 3.9
% 0.45/0.73 SPASS beiseite: Proof found.
% 0.45/0.73 % SZS status Theorem
% 0.45/0.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.73 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 587 clauses.
% 0.45/0.73 SPASS allocated 76859 KBytes.
% 0.45/0.73 SPASS spent 0:00:00.33 on the problem.
% 0.45/0.73 0:00:00.09 for the input.
% 0.45/0.73 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.73 0:00:00.00 for inferences.
% 0.45/0.73 0:00:00.00 for the backtracking.
% 0.45/0.73 0:00:00.14 for the reduction.
% 0.45/0.73
% 0.45/0.73
% 0.45/0.73 Here is a proof with depth 1, length 5 :
% 0.45/0.73 % SZS output start Refutation
% See solution above
% 0.45/0.73 Formulae used in the proof : cls_IT_OVar_0 cls_CHAINED_0 cls_conjecture_0
% 0.45/0.73
%------------------------------------------------------------------------------