%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL432-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 01:07:30 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.49s
% Output : Refutation 0.24s
% 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 : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_PropLog_Osat(c_emptyset,u,v)
| c_in(u,c_PropLog_Othms(c_emptyset,v),tc_PropLog_Opl(v)) ),
file('LCL432-2.p',unknown),
[] ).
cnf(2,axiom,
c_PropLog_Osat(c_emptyset,v_x,t_a),
file('LCL432-2.p',unknown),
[] ).
cnf(3,axiom,
~ c_in(v_x,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file('LCL432-2.p',unknown),
[] ).
cnf(5,plain,
~ c_PropLog_Osat(c_emptyset,v_x,t_a),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.1,3.0')] ).
cnf(6,plain,
$false,
inference(mrr,[status(thm)],[5,2]),
[iquote('0:MRR:5.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL432-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 15:48:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.24/0.49
% 0.24/0.49 SPASS V 3.9
% 0.24/0.49 SPASS beiseite: Proof found.
% 0.24/0.49 % SZS status Theorem
% 0.24/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.49 SPASS derived 2 clauses, backtracked 0 clauses, performed 0 splits and kept 4 clauses.
% 0.24/0.49 SPASS allocated 63077 KBytes.
% 0.24/0.49 SPASS spent 0:00:00.10 on the problem.
% 0.24/0.49 0:00:00.06 for the input.
% 0.24/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.24/0.49 0:00:00.00 for inferences.
% 0.24/0.49 0:00:00.00 for the backtracking.
% 0.24/0.49 0:00:00.00 for the reduction.
% 0.24/0.49
% 0.24/0.49
% 0.24/0.49 Here is a proof with depth 1, length 5 :
% 0.24/0.49 % SZS output start Refutation
% See solution above
% 0.24/0.49 Formulae used in the proof : cls_PropLog_Ocompleteness__0_0 cls_conjecture_0 cls_conjecture_1
% 0.24/0.49
%------------------------------------------------------------------------------