%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL779-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 01:08:23 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.59s
% 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 : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(547,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('LCL779-1.p',unknown),
[] ).
cnf(549,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('LCL779-1.p',unknown),
[] ).
cnf(550,plain,
$false,
inference(mrr,[status(thm)],[549,547]),
[iquote('0:MRR:549.0,547.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL779-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n027.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 10:51:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.32/0.59
% 0.32/0.59 SPASS V 3.9
% 0.32/0.59 SPASS beiseite: Proof found.
% 0.32/0.59 % SZS status Theorem
% 0.32/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.32/0.59 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.32/0.59 SPASS allocated 76576 KBytes.
% 0.32/0.59 SPASS spent 0:00:00.18 on the problem.
% 0.32/0.59 0:00:00.08 for the input.
% 0.32/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.32/0.59 0:00:00.00 for inferences.
% 0.32/0.59 0:00:00.00 for the backtracking.
% 0.32/0.59 0:00:00.02 for the reduction.
% 0.32/0.59
% 0.32/0.59
% 0.32/0.59 Here is a proof with depth 0, length 3 :
% 0.32/0.59 % SZS output start Refutation
% See solution above
% 0.32/0.59 Formulae used in the proof : cls_conjecture_2 cls_conjecture_4
% 0.32/0.59
%------------------------------------------------------------------------------