%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL812-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %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 01:08:29 PM UTC 2026
% Result : Unsatisfiable 0.46s 0.73s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 9 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(535,axiom,
equal(v_i____,v_n____),
file('LCL812-1.p',unknown),
[] ).
cnf(563,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('LCL812-1.p',unknown),
[] ).
cnf(587,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),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('LCL812-1.p',unknown),
[] ).
cnf(653,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_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),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL812-1.p',unknown),
[] ).
cnf(700,plain,
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_n____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(rew,[status(thm),theory(equality)],[535,587]),
[iquote('0:Rew:535.0,587.0')] ).
cnf(710,plain,
~ 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_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_n____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(rew,[status(thm),theory(equality)],[535,653]),
[iquote('0:Rew:535.0,653.0')] ).
cnf(717,plain,
~ 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_n____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(res,[status(thm),theory(equality)],[563,710]),
[iquote('0:Res:563.1,710.0')] ).
cnf(720,plain,
$false,
inference(mrr,[status(thm)],[717,700]),
[iquote('0:MRR:717.0,700.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL812-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 23:22:14 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.46/0.73
% 0.46/0.73 SPASS V 3.9
% 0.46/0.73 SPASS beiseite: Proof found.
% 0.46/0.73 % SZS status Theorem
% 0.46/0.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.73 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 526 clauses.
% 0.46/0.73 SPASS allocated 76817 KBytes.
% 0.46/0.73 SPASS spent 0:00:00.34 on the problem.
% 0.46/0.73 0:00:00.08 for the input.
% 0.46/0.73 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.73 0:00:00.00 for inferences.
% 0.46/0.73 0:00:00.00 for the backtracking.
% 0.46/0.73 0:00:00.16 for the reduction.
% 0.46/0.73
% 0.46/0.73
% 0.46/0.73 Here is a proof with depth 1, length 8 :
% 0.46/0.73 % SZS output start Refutation
% See solution above
% 0.46/0.73 Formulae used in the proof : cls_True_0 cls_IT_OVar_0 cls_CHAINED_0 cls_conjecture_0
% 0.46/0.73
%------------------------------------------------------------------------------