%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL858-1 : 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 01:08:36 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 6 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(158,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
| hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),u)) ),
file('LCL858-1.p',unknown),
[] ).
cnf(189,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
file('LCL858-1.p',unknown),
[] ).
cnf(204,axiom,
~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
file('LCL858-1.p',unknown),
[] ).
cnf(211,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(res,[status(thm),theory(equality)],[158,204]),
[iquote('0:Res:158.1,204.0')] ).
cnf(237,plain,
$false,
inference(mrr,[status(thm)],[211,189]),
[iquote('0:MRR:211.0,189.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL858-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.03/0.36 % Computer : n004.cluster.edu
% 0.03/0.36 % Model : x86_64 x86_64
% 0.03/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.36 % Memory : 8046.5625MB
% 0.03/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sat Sep 5 03:08:29 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.21/0.53
% 0.21/0.53 SPASS V 3.9
% 0.21/0.53 SPASS beiseite: Proof found.
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.53 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 184 clauses.
% 0.21/0.53 SPASS allocated 76002 KBytes.
% 0.21/0.53 SPASS spent 0:00:00.15 on the problem.
% 0.21/0.53 0:00:00.07 for the input.
% 0.21/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.53 0:00:00.00 for inferences.
% 0.21/0.53 0:00:00.00 for the backtracking.
% 0.21/0.53 0:00:00.03 for the reduction.
% 0.21/0.53
% 0.21/0.53
% 0.21/0.53 Here is a proof with depth 1, length 5 :
% 0.21/0.53 % SZS output start Refutation
% See solution above
% 0.21/0.53 Formulae used in the proof : cls_IT__implies__termi_0 cls_CHAINED_0 cls_conjecture_0
% 0.21/0.53
%------------------------------------------------------------------------------