%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL809-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n002.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 0.79s 1.08s
% Output : Refutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 8 unt; 0 nHn; 9 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1170,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
file('LCL809-1.p',unknown),
[] ).
cnf(1198,axiom,
equal(v_i____,v_n____),
file('LCL809-1.p',unknown),
[] ).
cnf(1199,axiom,
( ~ c_InductTermi_OIT(u)
| c_InductTermi_OIT(c_Lambda_Olift(u,v)) ),
file('LCL809-1.p',unknown),
[] ).
cnf(1202,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
file('LCL809-1.p',unknown),
[] ).
cnf(1239,axiom,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
file('LCL809-1.p',unknown),
[] ).
cnf(1240,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_n____)),
inference(rew,[status(thm),theory(equality)],[1198,1202]),
[iquote('0:Rew:1198.0,1202.0')] ).
cnf(1269,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_n____),c_Orderings_Obot__class_Obot(tc_nat))),
inference(rew,[status(thm),theory(equality)],[1198,1239,1170]),
[iquote('0:Rew:1198.0,1239.0,1170.0,1239.0')] ).
cnf(1424,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_n____)),
inference(res,[status(thm),theory(equality)],[1199,1269]),
[iquote('0:Res:1199.1,1269.0')] ).
cnf(1425,plain,
$false,
inference(mrr,[status(thm)],[1424,1240]),
[iquote('0:MRR:1424.0,1240.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL809-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 21:47:35 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.79/1.08
% 0.79/1.08 SPASS V 3.9
% 0.79/1.08 SPASS beiseite: Proof found.
% 0.79/1.08 % SZS status Theorem
% 0.79/1.08 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.79/1.08 SPASS derived 12 clauses, backtracked 0 clauses, performed 0 splits and kept 1036 clauses.
% 0.79/1.08 SPASS allocated 77769 KBytes.
% 0.79/1.08 SPASS spent 0:00:00.66 on the problem.
% 0.79/1.08 0:00:00.12 for the input.
% 0.79/1.08 0:00:00.00 for the FLOTTER CNF translation.
% 0.79/1.08 0:00:00.00 for inferences.
% 0.79/1.08 0:00:00.00 for the backtracking.
% 0.79/1.08 0:00:00.36 for the reduction.
% 0.79/1.08
% 0.79/1.08
% 0.79/1.08 Here is a proof with depth 1, length 9 :
% 0.79/1.08 % SZS output start Refutation
% See solution above
% 0.79/1.08 Formulae used in the proof : cls_bot__nat__def_0 cls_True_0 cls_lift__IT_0 cls_CHAINED_0 cls_conjecture_0
% 0.79/1.08
%------------------------------------------------------------------------------