%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL211-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 01:07:03 PM UTC 2026
% Result : Unsatisfiable 13.79s 14.07s
% Output : Refutation 13.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 13 unt; 0 nHn; 24 RR)
% Number of literals : 38 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(or__dfg(not__dfg(not__dfg(q)),or__dfg(not__dfg(or__dfg(p,q)),p))),
file('LCL211-1.p',unknown),
[] ).
cnf(2,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
file('LCL211-1.p',unknown),
[] ).
cnf(3,axiom,
axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
file('LCL211-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL211-1.p',unknown),
[] ).
cnf(6,axiom,
axiom(or__dfg(not__dfg(or__dfg(not__dfg(u),v)),or__dfg(not__dfg(or__dfg(w,u)),or__dfg(w,v)))),
file('LCL211-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL211-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL211-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(or__dfg(not__dfg(u),v))
| ~ axiom(or__dfg(not__dfg(w),u))
| theorem(or__dfg(not__dfg(w),v)) ),
file('LCL211-1.p',unknown),
[] ).
cnf(12,plain,
( ~ theorem(or__dfg(not__dfg(u),or__dfg(not__dfg(or__dfg(p,q)),p)))
| ~ axiom(or__dfg(not__dfg(not__dfg(q)),u)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.2,1.0')] ).
cnf(23,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.0,8.1')] ).
cnf(27,plain,
( ~ axiom(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[23,7]),
[iquote('0:SoR:23.0,7.1')] ).
cnf(43,plain,
theorem(or__dfg(u,not__dfg(or__dfg(u,u)))),
inference(sor,[status(thm)],[27,2]),
[iquote('0:SoR:27.0,2.0')] ).
cnf(45,plain,
theorem(or__dfg(not__dfg(or__dfg(u,u)),u)),
inference(sor,[status(thm)],[23,43]),
[iquote('0:SoR:23.0,43.0')] ).
cnf(48,plain,
( ~ theorem(or__dfg(not__dfg(u),v))
| theorem(or__dfg(not__dfg(or__dfg(w,u)),or__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.1')] ).
cnf(53,plain,
( ~ axiom(or__dfg(not__dfg(u),v))
| ~ theorem(or__dfg(not__dfg(v),w))
| theorem(or__dfg(w,not__dfg(u))) ),
inference(sor,[status(thm)],[23,9]),
[iquote('0:SoR:23.0,9.2')] ).
cnf(97,plain,
theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,v))),or__dfg(u,v))),
inference(sor,[status(thm)],[48,45]),
[iquote('0:SoR:48.0,45.0')] ).
cnf(280,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(w,not__dfg(or__dfg(v,u)))) ),
inference(res,[status(thm),theory(equality)],[4,53]),
[iquote('0:Res:4.0,53.0')] ).
cnf(282,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(u,w))),x))
| theorem(or__dfg(x,not__dfg(or__dfg(not__dfg(v),w)))) ),
inference(res,[status(thm),theory(equality)],[6,53]),
[iquote('0:Res:6.0,53.0')] ).
cnf(757,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(not__dfg(or__dfg(v,u)),w)) ),
inference(sor,[status(thm)],[23,280]),
[iquote('0:SoR:23.0,280.1')] ).
cnf(1501,plain,
theorem(or__dfg(or__dfg(not__dfg(or__dfg(u,v)),u),not__dfg(or__dfg(not__dfg(v),u)))),
inference(res,[status(thm),theory(equality)],[97,282]),
[iquote('0:Res:97.0,282.0')] ).
cnf(10237,plain,
theorem(or__dfg(not__dfg(or__dfg(not__dfg(u),v)),or__dfg(not__dfg(or__dfg(v,u)),v))),
inference(sor,[status(thm)],[23,1501]),
[iquote('0:SoR:23.0,1501.0')] ).
cnf(14175,plain,
theorem(or__dfg(not__dfg(or__dfg(u,not__dfg(v))),or__dfg(not__dfg(or__dfg(u,v)),u))),
inference(res,[status(thm),theory(equality)],[10237,757]),
[iquote('0:Res:10237.0,757.0')] ).
cnf(16434,plain,
~ axiom(or__dfg(not__dfg(not__dfg(q)),or__dfg(p,not__dfg(q)))),
inference(res,[status(thm),theory(equality)],[14175,12]),
[iquote('0:Res:14175.0,12.0')] ).
cnf(16458,plain,
$false,
inference(mrr,[status(thm)],[16434,3]),
[iquote('0:MRR:16434.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL211-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 19:32:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 13.79/14.07
% 13.79/14.07 SPASS V 3.9
% 13.79/14.07 SPASS beiseite: Proof found.
% 13.79/14.07 % SZS status Theorem
% 13.79/14.07 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.79/14.07 SPASS derived 16434 clauses, backtracked 0 clauses, performed 0 splits and kept 9580 clauses.
% 13.79/14.07 SPASS allocated 101163 KBytes.
% 13.79/14.07 SPASS spent 0:0:13.31 on the problem.
% 13.79/14.07 0:00:00.03 for the input.
% 13.79/14.07 0:00:00.00 for the FLOTTER CNF translation.
% 13.79/14.07 0:00:00.39 for inferences.
% 13.79/14.07 0:00:00.00 for the backtracking.
% 13.79/14.07 0:0:12.66 for the reduction.
% 13.79/14.07
% 13.79/14.07
% 13.79/14.07 Here is a proof with depth 9, length 24 :
% 13.79/14.07 % SZS output start Refutation
% See solution above
% 13.79/14.07 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_6 rule_1 rule_2 rule_3
% 13.79/14.07
%------------------------------------------------------------------------------