%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 01:07:33 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 8 unt; 0 nHn; 13 RR)
% Number of literals : 19 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 1 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_in(u,c_PropLog_Othms(c_insert(v,w,tc_PropLog_Opl(x)),x),tc_PropLog_Opl(x))
| c_in(c_PropLog_Opl_Oop_A_N_62(v,u,x),c_PropLog_Othms(w,x),tc_PropLog_Opl(x)) ),
file('LCL445-2.p',unknown),
[] ).
cnf(2,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('LCL445-2.p',unknown),
[] ).
cnf(3,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(u,v,w),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Ofalse,w),v,w),v,w),w),c_PropLog_Othms(x,w),tc_PropLog_Opl(w)),
file('LCL445-2.p',unknown),
[] ).
cnf(4,axiom,
c_in(v_q,c_PropLog_Othms(c_insert(v,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('LCL445-2.p',unknown),
[] ).
cnf(5,axiom,
c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('LCL445-2.p',unknown),
[] ).
cnf(6,axiom,
~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('LCL445-2.p',unknown),
[] ).
cnf(7,plain,
( ~ c_in(u,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.2,6.0')] ).
cnf(8,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.0')] ).
cnf(10,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[5,1]),
[iquote('0:Res:5.0,1.0')] ).
cnf(22,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,v,w),c_PropLog_Othms(x,w),tc_PropLog_Opl(w))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Ofalse,w),v,w),v,w),c_PropLog_Othms(x,w),tc_PropLog_Opl(w)) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.0,2.1')] ).
cnf(23,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(u,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(u,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(res,[status(thm),theory(equality)],[22,7]),
[iquote('0:Res:22.1,7.1')] ).
cnf(27,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(res,[status(thm),theory(equality)],[10,23]),
[iquote('0:Res:10.0,23.1')] ).
cnf(28,plain,
$false,
inference(mrr,[status(thm)],[27,8]),
[iquote('0:MRR:27.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 21:50:53 UTC 2026
% 0.09/0.36 % 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/sandbox/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 21 clauses, backtracked 0 clauses, performed 0 splits and kept 20 clauses.
% 0.21/0.48 SPASS allocated 63151 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 3, length 13 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : cls_PropLog_Odeduction_0 cls_PropLog_Othms_OMP_0 cls_PropLog_Othms__excluded__middle_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.21/0.48
%------------------------------------------------------------------------------