%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL793-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n001.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 01:08:26 PM UTC 2026
% Result : Unsatisfiable 0.66s 0.96s
% Output : Refutation 0.66s
% 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 : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1024,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
file('LCL793-1.p',unknown),
[] ).
cnf(1067,axiom,
( ~ c_InductTermi_OIT(u)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(u,c_Lambda_OdB_OVar(v))) ),
file('LCL793-1.p',unknown),
[] ).
cnf(1069,axiom,
c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('LCL793-1.p',unknown),
[] ).
cnf(1105,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))),
file('LCL793-1.p',unknown),
[] ).
cnf(1106,plain,
c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_Orderings_Obot__class_Obot(tc_nat))),
inference(rew,[status(thm),theory(equality)],[1024,1069]),
[iquote('0:Rew:1024.0,1069.0')] ).
cnf(1138,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_Orderings_Obot__class_Obot(tc_nat)),c_Lambda_OdB_OVar(c_Orderings_Obot__class_Obot(tc_nat)))),
inference(rew,[status(thm),theory(equality)],[1024,1105]),
[iquote('0:Rew:1024.0,1105.0')] ).
cnf(1273,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_Orderings_Obot__class_Obot(tc_nat))),
inference(res,[status(thm),theory(equality)],[1067,1138]),
[iquote('0:Res:1067.1,1138.0')] ).
cnf(1274,plain,
$false,
inference(mrr,[status(thm)],[1273,1106]),
[iquote('0:MRR:1273.0,1106.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL793-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 00:09:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.66/0.96
% 0.66/0.96 SPASS V 3.9
% 0.66/0.96 SPASS beiseite: Proof found.
% 0.66/0.96 % SZS status Theorem
% 0.66/0.96 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/0.96 SPASS derived 11 clauses, backtracked 0 clauses, performed 0 splits and kept 921 clauses.
% 0.66/0.96 SPASS allocated 77515 KBytes.
% 0.66/0.96 SPASS spent 0:00:00.56 on the problem.
% 0.66/0.96 0:00:00.11 for the input.
% 0.66/0.96 0:00:00.00 for the FLOTTER CNF translation.
% 0.66/0.96 0:00:00.00 for inferences.
% 0.66/0.96 0:00:00.00 for the backtracking.
% 0.66/0.96 0:00:00.30 for the reduction.
% 0.66/0.96
% 0.66/0.96
% 0.66/0.96 Here is a proof with depth 1, length 8 :
% 0.66/0.96 % SZS output start Refutation
% See solution above
% 0.66/0.96 Formulae used in the proof : cls_bot__nat__def_0 cls_app__Var__IT_0 cls_CHAINED_0 cls_conjecture_0
% 0.66/0.96
%------------------------------------------------------------------------------