%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL815-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 01:08:30 PM UTC 2026
% Result : Unsatisfiable 0.55s 0.85s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 8 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(689,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
file('LCL815-1.p',unknown),
[] ).
cnf(783,axiom,
( ~ c_Type_Otypings(u,v,w)
| c_Type_Otypings(c_Type_Oshift(u,x,y,tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),x),v,tc_Lambda_OdB,tc_Lambda_OdB),w) ),
file('LCL815-1.p',unknown),
[] ).
cnf(785,axiom,
c_Type_Otypings(v_e____,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____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('LCL815-1.p',unknown),
[] ).
cnf(817,axiom,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),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____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('LCL815-1.p',unknown),
[] ).
cnf(984,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Orderings_Obot__class_Obot(tc_nat)),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____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(rew,[status(thm),theory(equality)],[689,817]),
[iquote('0:Rew:689.0,817.0')] ).
cnf(986,plain,
~ c_Type_Otypings(v_e____,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____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(res,[status(thm),theory(equality)],[783,984]),
[iquote('0:Res:783.1,984.0')] ).
cnf(987,plain,
$false,
inference(mrr,[status(thm)],[986,785]),
[iquote('0:MRR:986.0,785.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL815-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 17:20:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.55/0.85
% 0.55/0.85 SPASS V 3.9
% 0.55/0.85 SPASS beiseite: Proof found.
% 0.55/0.85 % SZS status Theorem
% 0.55/0.85 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.85 SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 646 clauses.
% 0.55/0.85 SPASS allocated 77198 KBytes.
% 0.55/0.85 SPASS spent 0:00:00.46 on the problem.
% 0.55/0.85 0:00:00.09 for the input.
% 0.55/0.85 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.85 0:00:00.00 for inferences.
% 0.55/0.85 0:00:00.00 for the backtracking.
% 0.55/0.85 0:00:00.25 for the reduction.
% 0.55/0.85
% 0.55/0.85
% 0.55/0.85 Here is a proof with depth 1, length 7 :
% 0.55/0.85 % SZS output start Refutation
% See solution above
% 0.55/0.85 Formulae used in the proof : cls_bot__nat__def_0 cls_lift__types_0 cls_CHAINED_0 cls_conjecture_0
% 0.55/0.85
%------------------------------------------------------------------------------