%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL209-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 16.66s 16.94s
% Output : Refutation 16.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of clauses : 55 ( 35 unt; 0 nHn; 55 RR)
% Number of literals : 78 ( 0 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(implies__dfg(not__dfg(p),q),or__dfg(p,q))),
file('LCL209-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL209-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL209-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL209-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL209-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL209-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL209-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL209-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL209-3.p',unknown),
[] ).
cnf(15,plain,
axiom(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(16,plain,
axiom(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(20,plain,
( ~ axiom(implies__dfg(u,v))
| ~ theorem(u)
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.1')] ).
cnf(21,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[20,16]),
[iquote('0:SoR:20.0,16.0')] ).
cnf(24,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[20,15]),
[iquote('0:SoR:20.0,15.0')] ).
cnf(26,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[20,4]),
[iquote('0:SoR:20.0,4.0')] ).
cnf(27,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[20,3]),
[iquote('0:SoR:20.0,3.0')] ).
cnf(28,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[20,2]),
[iquote('0:SoR:20.0,2.0')] ).
cnf(29,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[20,5]),
[iquote('0:SoR:20.0,5.0')] ).
cnf(30,plain,
axiom(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(34,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,30]),
[iquote('0:Rew:7.0,30.0')] ).
cnf(43,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[20,6]),
[iquote('0:SoR:20.0,6.0')] ).
cnf(51,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[20,34]),
[iquote('0:SoR:20.0,34.0')] ).
cnf(52,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,34]),
[iquote('0:SpR:7.0,34.0')] ).
cnf(54,plain,
axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,52]),
[iquote('0:Rew:7.0,52.0')] ).
cnf(73,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[21,8]),
[iquote('0:SoR:21.0,8.1')] ).
cnf(88,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[73,3]),
[iquote('0:SoR:73.0,3.0')] ).
cnf(92,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[20,54]),
[iquote('0:SoR:20.0,54.0')] ).
cnf(99,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[24,88]),
[iquote('0:SoR:24.0,88.0')] ).
cnf(106,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[29,27]),
[iquote('0:SoR:29.0,27.1')] ).
cnf(150,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[51,99]),
[iquote('0:SoR:51.0,99.0')] ).
cnf(152,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[28,150]),
[iquote('0:SoR:28.0,150.0')] ).
cnf(156,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[21,152]),
[iquote('0:SoR:21.0,152.0')] ).
cnf(157,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[51,152]),
[iquote('0:SoR:51.0,152.0')] ).
cnf(161,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,156]),
[iquote('0:SpR:7.0,156.0')] ).
cnf(163,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[43,161]),
[iquote('0:SoR:43.0,161.0')] ).
cnf(201,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
inference(sor,[status(thm)],[26,157]),
[iquote('0:SoR:26.0,157.0')] ).
cnf(203,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,157]),
[iquote('0:SpR:7.0,157.0')] ).
cnf(205,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,203]),
[iquote('0:Rew:7.0,203.0')] ).
cnf(230,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[205,9]),
[iquote('0:Res:205.0,9.1')] ).
cnf(270,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[106,156]),
[iquote('0:SoR:106.0,156.0')] ).
cnf(281,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),
inference(sor,[status(thm)],[29,270]),
[iquote('0:SoR:29.0,270.0')] ).
cnf(471,plain,
( ~ axiom(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[92,8]),
[iquote('0:SoR:92.0,8.1')] ).
cnf(656,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[230,9]),
[iquote('0:Res:230.1,9.1')] ).
cnf(1334,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[163,9]),
[iquote('0:Res:163.0,9.1')] ).
cnf(1462,plain,
theorem(implies__dfg(or__dfg(u,v),implies__dfg(implies__dfg(v,w),or__dfg(u,w)))),
inference(sor,[status(thm)],[471,6]),
[iquote('0:SoR:471.0,6.0')] ).
cnf(3883,plain,
theorem(or__dfg(u,not__dfg(not__dfg(or__dfg(v,not__dfg(v)))))),
inference(sor,[status(thm)],[1334,281]),
[iquote('0:SoR:1334.0,281.0')] ).
cnf(3894,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[1334,201]),
[iquote('0:SoR:1334.0,201.0')] ).
cnf(4881,plain,
theorem(not__dfg(not__dfg(or__dfg(u,not__dfg(u))))),
inference(sor,[status(thm)],[28,3883]),
[iquote('0:SoR:28.0,3883.0')] ).
cnf(6843,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[24,3894]),
[iquote('0:SoR:24.0,3894.0')] ).
cnf(6846,plain,
( ~ theorem(not__dfg(u))
| theorem(implies__dfg(or__dfg(u,v),v)) ),
inference(sor,[status(thm)],[656,6843]),
[iquote('0:SoR:656.1,6843.0')] ).
cnf(8954,plain,
theorem(implies__dfg(or__dfg(not__dfg(or__dfg(u,not__dfg(u))),v),v)),
inference(sor,[status(thm)],[6846,4881]),
[iquote('0:SoR:6846.0,4881.0')] ).
cnf(8976,plain,
theorem(implies__dfg(implies__dfg(or__dfg(u,not__dfg(u)),v),v)),
inference(rew,[status(thm),theory(equality)],[7,8954]),
[iquote('0:Rew:7.0,8954.0')] ).
cnf(9009,plain,
( ~ theorem(implies__dfg(or__dfg(u,not__dfg(u)),v))
| theorem(v) ),
inference(sor,[status(thm)],[656,8976]),
[iquote('0:SoR:656.1,8976.0')] ).
cnf(13502,plain,
theorem(implies__dfg(implies__dfg(not__dfg(u),v),or__dfg(u,v))),
inference(sor,[status(thm)],[9009,1462]),
[iquote('0:SoR:9009.0,1462.0')] ).
cnf(13709,plain,
$false,
inference(unc,[status(thm)],[13502,1]),
[iquote('0:UnC:13502.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL209-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 16:31:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 16.66/16.94
% 16.66/16.94 SPASS V 3.9
% 16.66/16.94 SPASS beiseite: Proof found.
% 16.66/16.94 % SZS status Theorem
% 16.66/16.94 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.66/16.94 SPASS derived 12694 clauses, backtracked 0 clauses, performed 0 splits and kept 5882 clauses.
% 16.66/16.94 SPASS allocated 91903 KBytes.
% 16.66/16.94 SPASS spent 0:0:16.29 on the problem.
% 16.66/16.94 0:00:00.06 for the input.
% 16.66/16.94 0:00:00.00 for the FLOTTER CNF translation.
% 16.66/16.94 0:00:01.46 for inferences.
% 16.66/16.94 0:00:00.00 for the backtracking.
% 16.66/16.94 0:0:14.42 for the reduction.
% 16.66/16.94
% 16.66/16.94
% 16.66/16.94 Here is a proof with depth 17, length 55 :
% 16.66/16.94 % SZS output start Refutation
% See solution above
% 16.66/16.94 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2
% 16.66/16.94
%------------------------------------------------------------------------------