%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL214-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 01:07:04 PM UTC 2026
% Result : Unsatisfiable 27.55s 27.80s
% Output : Refutation 27.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 13 unt; 0 nHn; 23 RR)
% Number of literals : 36 ( 0 equ; 16 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(or__dfg(p,q)),or__dfg(not__dfg(or__dfg(not__dfg(p),q)),q))),
file('LCL214-1.p',unknown),
[] ).
cnf(2,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
file('LCL214-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL214-1.p',unknown),
[] ).
cnf(5,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),or__dfg(v,or__dfg(u,w)))),
file('LCL214-1.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('LCL214-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL214-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL214-1.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('LCL214-1.p',unknown),
[] ).
cnf(12,plain,
( ~ theorem(or__dfg(not__dfg(u),or__dfg(not__dfg(or__dfg(not__dfg(p),q)),q)))
| ~ axiom(or__dfg(not__dfg(or__dfg(p,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(30,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.0,8.1')] ).
cnf(34,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(36,plain,
theorem(or__dfg(not__dfg(or__dfg(u,u)),u)),
inference(sor,[status(thm)],[23,34]),
[iquote('0:SoR:23.0,34.0')] ).
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(59,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(108,plain,
theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,v))),or__dfg(u,v))),
inference(sor,[status(thm)],[48,36]),
[iquote('0:SoR:48.0,36.0')] ).
cnf(284,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)],[6,59]),
[iquote('0:Res:6.0,59.0')] ).
cnf(1560,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)],[108,284]),
[iquote('0:Res:108.0,284.0')] ).
cnf(9940,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)],[23,1560]),
[iquote('0:SoR:23.0,1560.0')] ).
cnf(14108,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(not__dfg(or__dfg(not__dfg(v),u)),u))),
inference(sor,[status(thm)],[30,9940]),
[iquote('0:SoR:30.0,9940.0')] ).
cnf(16339,plain,
~ axiom(or__dfg(not__dfg(or__dfg(p,q)),or__dfg(q,p))),
inference(res,[status(thm),theory(equality)],[14108,12]),
[iquote('0:Res:14108.0,12.0')] ).
cnf(16367,plain,
$false,
inference(mrr,[status(thm)],[16339,4]),
[iquote('0:MRR:16339.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL214-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n013.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 22:34:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 27.55/27.80
% 27.55/27.80 SPASS V 3.9
% 27.55/27.80 SPASS beiseite: Proof found.
% 27.55/27.80 % SZS status Theorem
% 27.55/27.80 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.55/27.80 SPASS derived 16343 clauses, backtracked 0 clauses, performed 0 splits and kept 9503 clauses.
% 27.55/27.80 SPASS allocated 101130 KBytes.
% 27.55/27.80 SPASS spent 0:0:26.71 on the problem.
% 27.55/27.80 0:00:00.06 for the input.
% 27.55/27.80 0:00:00.00 for the FLOTTER CNF translation.
% 27.55/27.80 0:00:00.83 for inferences.
% 27.55/27.80 0:00:00.00 for the backtracking.
% 27.55/27.80 0:0:25.42 for the reduction.
% 27.55/27.80
% 27.55/27.80
% 27.55/27.80 Here is a proof with depth 9, length 23 :
% 27.55/27.80 % SZS output start Refutation
% See solution above
% 27.55/27.80 Formulae used in the proof : prove_this axiom_1_2 axiom_1_4 axiom_1_5 axiom_1_6 rule_1 rule_2 rule_3
% 27.55/27.80
%------------------------------------------------------------------------------