%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL212-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n031.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 36.65s 37.02s
% Output : Refutation 36.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 14 unt; 0 nHn; 25 RR)
% Number of literals : 39 ( 0 equ; 15 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(not__dfg(not__dfg(p)),q)),or__dfg(not__dfg(or__dfg(not__dfg(p),q)),q))),
file('LCL212-1.p',unknown),
[] ).
cnf(2,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
file('LCL212-1.p',unknown),
[] ).
cnf(4,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
file('LCL212-1.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('LCL212-1.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('LCL212-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL212-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ theorem(u)
| ~ axiom(or__dfg(not__dfg(u),v))
| theorem(v) ),
file('LCL212-1.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('LCL212-1.p',unknown),
[] ).
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(39,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(62,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(89,plain,
theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,v))),or__dfg(u,v))),
inference(sor,[status(thm)],[39,36]),
[iquote('0:SoR:39.0,36.0')] ).
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)],[4,62]),
[iquote('0:Res:4.0,62.0')] ).
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)],[6,62]),
[iquote('0:Res:6.0,62.0')] ).
cnf(775,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(1593,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)],[89,282]),
[iquote('0:Res:89.0,282.0')] ).
cnf(9937,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)],[23,1593]),
[iquote('0:SoR:23.0,1593.0')] ).
cnf(14078,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)],[30,9937]),
[iquote('0:SoR:30.0,9937.0')] ).
cnf(16326,plain,
theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(not__dfg(or__dfg(not__dfg(u),v)),v))),
inference(res,[status(thm),theory(equality)],[14078,775]),
[iquote('0:Res:14078.0,775.0')] ).
cnf(18168,plain,
theorem(or__dfg(not__dfg(or__dfg(not__dfg(u),v)),or__dfg(not__dfg(or__dfg(u,v)),v))),
inference(sor,[status(thm)],[30,16326]),
[iquote('0:SoR:30.0,16326.0')] ).
cnf(18198,plain,
$false,
inference(unc,[status(thm)],[18168,1]),
[iquote('0:UnC:18168.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL212-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n031.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 15:11:09 UTC 2026
% 0.09/0.35 % CPUTime :
% 36.65/37.02
% 36.65/37.02 SPASS V 3.9
% 36.65/37.02 SPASS beiseite: Proof found.
% 36.65/37.02 % SZS status Theorem
% 36.65/37.02 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.65/37.02 SPASS derived 18174 clauses, backtracked 0 clauses, performed 0 splits and kept 10722 clauses.
% 36.65/37.02 SPASS allocated 104437 KBytes.
% 36.65/37.02 SPASS spent 0:0:35.67 on the problem.
% 36.65/37.02 0:00:00.06 for the input.
% 36.65/37.02 0:00:00.00 for the FLOTTER CNF translation.
% 36.65/37.02 0:00:00.98 for inferences.
% 36.65/37.02 0:00:00.00 for the backtracking.
% 36.65/37.02 0:0:34.17 for the reduction.
% 36.65/37.02
% 36.65/37.02
% 36.65/37.02 Here is a proof with depth 10, length 25 :
% 36.65/37.02 % SZS output start Refutation
% See solution above
% 36.65/37.02 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
% 36.65/37.02
%------------------------------------------------------------------------------