%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 7 unt; 0 nHn; 15 RR)
% Number of literals : 24 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_PropLog_Osat(c_insert(u,v,tc_PropLog_Opl(w)),x,w)
| c_PropLog_Osat(v,c_PropLog_Opl_Oop_A_N_62(u,x,w),w) ),
file('LCL433-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v,tc_PropLog_Opl(w))
| c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) ),
file('LCL433-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,x,w),c_PropLog_Othms(v,w),tc_PropLog_Opl(w))
| c_in(x,c_PropLog_Othms(v,w),tc_PropLog_Opl(w)) ),
file('LCL433-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,c_PropLog_Othms(v,w),tc_PropLog_Opl(w))
| c_in(u,c_PropLog_Othms(c_insert(x,v,tc_PropLog_Opl(w)),w),tc_PropLog_Opl(w)) ),
file('LCL433-2.p',unknown),
[] ).
cnf(5,axiom,
c_in(u,c_insert(u,v,w),w),
file('LCL433-2.p',unknown),
[] ).
cnf(6,axiom,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
file('LCL433-2.p',unknown),
[] ).
cnf(7,axiom,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('LCL433-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ c_PropLog_Osat(v_F,u,t_a)
| c_in(u,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
file('LCL433-2.p',unknown),
[] ).
cnf(9,plain,
c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a),
inference(res,[status(thm),theory(equality)],[6,1]),
[iquote('0:Res:6.0,1.0')] ).
cnf(12,plain,
( ~ c_in(u,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,v_xa,t_a),c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.2,7.0')] ).
cnf(13,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[9,8]),
[iquote('0:Res:9.0,8.0')] ).
cnf(34,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| ~ c_in(u,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.1,12.1')] ).
cnf(36,plain,
( ~ c_in(u,c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[2,34]),
[iquote('0:Res:2.1,34.1')] ).
cnf(48,plain,
~ c_in(v_x,c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[13,36]),
[iquote('0:Res:13.0,36.1')] ).
cnf(51,plain,
$false,
inference(mrr,[status(thm)],[48,5]),
[iquote('0:MRR:48.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 09:12:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.22/0.49
% 0.22/0.49 SPASS V 3.9
% 0.22/0.49 SPASS beiseite: Proof found.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.49 SPASS derived 41 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.22/0.49 SPASS allocated 63147 KBytes.
% 0.22/0.49 SPASS spent 0:00:00.10 on the problem.
% 0.22/0.49 0:00:00.06 for the input.
% 0.22/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.49 0:00:00.00 for inferences.
% 0.22/0.49 0:00:00.00 for the backtracking.
% 0.22/0.49 0:00:00.00 for the reduction.
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 Here is a proof with depth 4, length 15 :
% 0.22/0.49 % SZS output start Refutation
% See solution above
% 0.22/0.49 Formulae used in the proof : cls_PropLog_Osat__imp_0 cls_PropLog_Othms_OH_0 cls_PropLog_Othms_OMP_0 cls_PropLog_Oweaken__left__insert_0 cls_Set_OinsertCI_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4
% 0.22/0.49
%------------------------------------------------------------------------------