%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 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 01:07:30 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 8 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 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_minus(c_PropLog_Ohyps(u,w,v),c_PropLog_Ohyps(u,x,v),tc_set(tc_PropLog_Opl(v))),v),tc_PropLog_Opl(v)) ),
file('LCL431-2.p',unknown),
[] ).
cnf(2,axiom,
equal(c_minus(u,u,tc_set(v)),c_emptyset),
file('LCL431-2.p',unknown),
[] ).
cnf(3,axiom,
c_PropLog_Osat(c_emptyset,v,t_a),
file('LCL431-2.p',unknown),
[] ).
cnf(4,axiom,
~ c_in(v,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file('LCL431-2.p',unknown),
[] ).
cnf(5,plain,
c_in(v,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v,u,t_a),c_PropLog_Ohyps(v,v,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.0')] ).
cnf(7,plain,
c_in(v,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(8,plain,
$false,
inference(mrr,[status(thm)],[7,4]),
[iquote('0:MRR:7.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.36 % Computer : n027.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 4 17:25:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 6 clauses.
% 0.21/0.48 SPASS allocated 63091 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.10 on the problem.
% 0.21/0.48 0:00:00.06 for the input.
% 0.21/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.00 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.00 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 2, length 7 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : cls_PropLog_Ocompleteness__0__lemma__dest_0 cls_Set_ODiff__cancel_0 cls_conjecture_0 cls_conjecture_1
% 0.21/0.48
%------------------------------------------------------------------------------