%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL756-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 01:08:20 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.60s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 2
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 3 RR)
% Number of literals : 3 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 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(754,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(u),v)),
file('LCL756-1.p',unknown),
[] ).
cnf(755,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
file('LCL756-1.p',unknown),
[] ).
cnf(756,plain,
$false,
inference(mrr,[status(thm)],[755,754]),
[iquote('0:MRR:755.0,754.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL756-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 11:52:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.32/0.60
% 0.32/0.60 SPASS V 3.9
% 0.32/0.60 SPASS beiseite: Proof found.
% 0.32/0.60 % SZS status Theorem
% 0.32/0.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.32/0.60 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 83 clauses.
% 0.32/0.60 SPASS allocated 76763 KBytes.
% 0.32/0.60 SPASS spent 0:00:00.21 on the problem.
% 0.32/0.60 0:00:00.09 for the input.
% 0.32/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.32/0.60 0:00:00.00 for inferences.
% 0.32/0.60 0:00:00.00 for the backtracking.
% 0.32/0.60 0:00:00.02 for the reduction.
% 0.32/0.60
% 0.32/0.60
% 0.32/0.60 Here is a proof with depth 0, length 3 :
% 0.32/0.60 % SZS output start Refutation
% See solution above
% 0.32/0.60 Formulae used in the proof : cls_conjecture_1 cls_conjecture_2
% 0.32/0.60
%------------------------------------------------------------------------------