%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL755-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 01:08:19 PM UTC 2026
% Result : Unsatisfiable 0.45s 0.71s
% Output : Refutation 0.45s
% 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(710,axiom,
( ~ c_InductTermi_OIT(u)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(u)) ),
file('LCL755-1.p',unknown),
[] ).
cnf(754,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(u),v)),
file('LCL755-1.p',unknown),
[] ).
cnf(755,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
file('LCL755-1.p',unknown),
[] ).
cnf(820,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
inference(res,[status(thm),theory(equality)],[710,755]),
[iquote('0:Res:710.1,755.0')] ).
cnf(821,plain,
$false,
inference(mrr,[status(thm)],[820,754]),
[iquote('0:MRR:820.0,754.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL755-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 15:50:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.45/0.71
% 0.45/0.71 SPASS V 3.9
% 0.45/0.71 SPASS beiseite: Proof found.
% 0.45/0.71 % SZS status Theorem
% 0.45/0.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.71 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 600 clauses.
% 0.45/0.71 SPASS allocated 76867 KBytes.
% 0.45/0.71 SPASS spent 0:00:00.33 on the problem.
% 0.45/0.71 0:00:00.09 for the input.
% 0.45/0.71 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.71 0:00:00.00 for inferences.
% 0.45/0.71 0:00:00.00 for the backtracking.
% 0.45/0.71 0:00:00.15 for the reduction.
% 0.45/0.71
% 0.45/0.71
% 0.45/0.71 Here is a proof with depth 1, length 5 :
% 0.45/0.71 % SZS output start Refutation
% See solution above
% 0.45/0.71 Formulae used in the proof : cls_Lambda_0 cls_conjecture_1 cls_conjecture_2
% 0.45/0.71
%------------------------------------------------------------------------------