%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL441-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 01:07:32 PM UTC 2026
% Result : Unsatisfiable 0.96s 1.23s
% Output : Refutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 9 unt; 0 nHn; 12 RR)
% Number of literals : 15 ( 0 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_in(v_a,v_tt,t_a) ),
file('LCL441-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ c_in(v_a,v_tt,t_a)
| ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
file('LCL441-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ c_in(u,v,tc_PropLog_Opl(w))
| c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) ),
file('LCL441-1.p',unknown),
[] ).
cnf(196,axiom,
c_in(u,c_insert(u,v,w),w),
file('LCL441-1.p',unknown),
[] ).
cnf(3254,plain,
~ c_in(v_a,v_tt,t_a),
inference(spt,[spt(split,[position(s1)])],[9]),
[iquote('1:Spt:9.0')] ).
cnf(3255,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(mrr,[status(thm)],[8,3254]),
[iquote('1:MRR:8.1,3254.0')] ).
cnf(3394,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[20,3255]),
[iquote('1:Res:20.1,3255.0')] ).
cnf(3396,plain,
$false,
inference(mrr,[status(thm)],[3394,196]),
[iquote('1:MRR:3394.0,196.0')] ).
cnf(3397,plain,
c_in(v_a,v_tt,t_a),
inference(spt,[spt(split,[position(sa)])],[3396,3254]),
[iquote('1:Spt:3396.0,9.0,3254.0')] ).
cnf(3398,plain,
~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(spt,[spt(split,[position(s2)])],[9]),
[iquote('1:Spt:3396.0,9.1')] ).
cnf(3399,plain,
~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[20,3398]),
[iquote('1:Res:20.1,3398.0')] ).
cnf(3400,plain,
$false,
inference(mrr,[status(thm)],[3399,196]),
[iquote('1:MRR:3399.0,196.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL441-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 22:51:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.96/1.23
% 0.96/1.23 SPASS V 3.9
% 0.96/1.23 SPASS beiseite: Proof found.
% 0.96/1.23 % SZS status Theorem
% 0.96/1.23 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.96/1.23 SPASS derived 1727 clauses, backtracked 25 clauses, performed 2 splits and kept 2177 clauses.
% 0.96/1.23 SPASS allocated 80213 KBytes.
% 0.96/1.23 SPASS spent 0:00:00.83 on the problem.
% 0.96/1.23 0:00:00.06 for the input.
% 0.96/1.23 0:00:00.00 for the FLOTTER CNF translation.
% 0.96/1.23 0:00:00.07 for inferences.
% 0.96/1.23 0:00:00.00 for the backtracking.
% 0.96/1.23 0:00:00.53 for the reduction.
% 0.96/1.23
% 0.96/1.23
% 0.96/1.23 Here is a proof with depth 2, length 12 :
% 0.96/1.23 % SZS output start Refutation
% See solution above
% 0.96/1.23 Formulae used in the proof : cls_conjecture_1 cls_conjecture_2 cls_PropLog_Othms_OH_0 cls_Set_OinsertCI_1
% 0.96/1.23
%------------------------------------------------------------------------------