%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL208-1 : TPTP v9.3.1. Released v1.1.0.
% 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 01:07:03 PM UTC 2026
% Result : Unsatisfiable 27.66s 28.03s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 17 unt; 0 nHn; 30 RR)
% Number of literals : 46 ( 0 equ; 19 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(not__dfg(p)),q))),
file('LCL208-1.p',unknown),
[] ).
cnf(2,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
file('LCL208-1.p',unknown),
[] ).
cnf(3,axiom,
axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
file('LCL208-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL208-1.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('LCL208-1.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('LCL208-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL208-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL208-1.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('LCL208-1.p',unknown),
[] ).
cnf(12,plain,
( ~ theorem(or__dfg(not__dfg(u),or__dfg(not__dfg(not__dfg(p)),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(39,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(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(94,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(281,plain,
( ~ theorem(or__dfg(not__dfg(or__dfg(u,v)),w))
| theorem(or__dfg(w,not__dfg(v))) ),
inference(res,[status(thm),theory(equality)],[3,53]),
[iquote('0:Res:3.0,53.0')] ).
cnf(282,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(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)],[6,53]),
[iquote('0:Res:6.0,53.0')] ).
cnf(758,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)],[23,282]),
[iquote('0:SoR:23.0,282.1')] ).
cnf(1520,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)],[94,284]),
[iquote('0:Res:94.0,284.0')] ).
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)],[23,1520]),
[iquote('0:SoR:23.0,1520.0')] ).
cnf(14143,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)],[10237,758]),
[iquote('0:Res:10237.0,758.0')] ).
cnf(16410,plain,
theorem(or__dfg(or__dfg(not__dfg(or__dfg(u,v)),u),not__dfg(not__dfg(v)))),
inference(res,[status(thm),theory(equality)],[14143,281]),
[iquote('0:Res:14143.0,281.0')] ).
cnf(16418,plain,
theorem(or__dfg(not__dfg(not__dfg(u)),or__dfg(not__dfg(or__dfg(v,u)),v))),
inference(sor,[status(thm)],[23,16410]),
[iquote('0:SoR:23.0,16410.0')] ).
cnf(16424,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(not__dfg(not__dfg(v)),u))),
inference(sor,[status(thm)],[39,16418]),
[iquote('0:SoR:39.0,16418.0')] ).
cnf(16480,plain,
~ axiom(or__dfg(not__dfg(or__dfg(p,q)),or__dfg(q,p))),
inference(res,[status(thm),theory(equality)],[16424,12]),
[iquote('0:Res:16424.0,12.0')] ).
cnf(16508,plain,
$false,
inference(mrr,[status(thm)],[16480,4]),
[iquote('0:MRR:16480.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL208-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 4 14:04:38 UTC 2026
% 0.09/0.38 % CPUTime :
% 27.66/28.03
% 27.66/28.03 SPASS V 3.9
% 27.66/28.03 SPASS beiseite: Proof found.
% 27.66/28.03 % SZS status Theorem
% 27.66/28.03 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.66/28.03 SPASS derived 16484 clauses, backtracked 0 clauses, performed 0 splits and kept 9623 clauses.
% 27.66/28.03 SPASS allocated 101341 KBytes.
% 27.66/28.03 SPASS spent 0:0:26.79 on the problem.
% 27.66/28.03 0:00:00.06 for the input.
% 27.66/28.03 0:00:00.00 for the FLOTTER CNF translation.
% 27.66/28.03 0:00:00.85 for inferences.
% 27.66/28.03 0:00:00.00 for the backtracking.
% 27.66/28.03 0:0:25.46 for the reduction.
% 27.66/28.03
% 27.66/28.03
% 27.66/28.03 Here is a proof with depth 12, length 30 :
% 27.66/28.03 % SZS output start Refutation
% See solution above
% 0.15/28.03 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 rule_1 rule_2 rule_3
% 0.15/28.03
%------------------------------------------------------------------------------