%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL792-1 : 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 0.78s 1.06s
% Output : Refutation 0.78s
% 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 : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1169,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
file('LCL792-1.p',unknown),
[] ).
cnf(1191,axiom,
( ~ c_InductTermi_OIT(u)
| c_InductTermi_OIT(c_Lambda_Olift(u,v)) ),
file('LCL792-1.p',unknown),
[] ).
cnf(1192,axiom,
c_InductTermi_OIT(v_u____),
file('LCL792-1.p',unknown),
[] ).
cnf(1229,axiom,
~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('LCL792-1.p',unknown),
[] ).
cnf(1232,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_Orderings_Obot__class_Obot(tc_nat))),
inference(rew,[status(thm),theory(equality)],[1169,1229]),
[iquote('0:Rew:1169.0,1229.0')] ).
cnf(1397,plain,
~ c_InductTermi_OIT(v_u____),
inference(res,[status(thm),theory(equality)],[1191,1232]),
[iquote('0:Res:1191.1,1232.0')] ).
cnf(1398,plain,
$false,
inference(mrr,[status(thm)],[1397,1192]),
[iquote('0:MRR:1397.0,1192.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL792-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 6 01:54:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.78/1.06
% 0.78/1.06 SPASS V 3.9
% 0.78/1.06 SPASS beiseite: Proof found.
% 0.78/1.06 % SZS status Theorem
% 0.78/1.06 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/1.06 SPASS derived 12 clauses, backtracked 0 clauses, performed 0 splits and kept 1034 clauses.
% 0.78/1.06 SPASS allocated 77746 KBytes.
% 0.78/1.06 SPASS spent 0:00:00.65 on the problem.
% 0.78/1.06 0:00:00.12 for the input.
% 0.78/1.06 0:00:00.00 for the FLOTTER CNF translation.
% 0.78/1.06 0:00:00.00 for inferences.
% 0.78/1.06 0:00:00.00 for the backtracking.
% 0.78/1.06 0:00:00.35 for the reduction.
% 0.78/1.06
% 0.78/1.06
% 0.78/1.06 Here is a proof with depth 1, length 7 :
% 0.78/1.06 % SZS output start Refutation
% See solution above
% 0.78/1.06 Formulae used in the proof : cls_bot__nat__def_0 cls_lift__IT_0 cls_uIT_0 cls_conjecture_0
% 0.78/1.06
%------------------------------------------------------------------------------