%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL241-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 01:07:09 PM UTC 2026
% Result : Unsatisfiable 14.54s 14.86s
% Output : Refutation 14.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 26 unt; 0 nHn; 39 RR)
% Number of literals : 54 ( 0 equ; 16 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(and__dfg(p,q),q)),
file('LCL241-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL241-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL241-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL241-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL241-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL241-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL241-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL241-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL241-3.p',unknown),
[] ).
cnf(10,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL241-3.p',unknown),
[] ).
cnf(11,plain,
equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.0')] ).
cnf(18,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(19,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(38,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(39,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[38,19]),
[iquote('0:SoR:38.0,19.0')] ).
cnf(41,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[38,3]),
[iquote('0:SoR:38.0,3.0')] ).
cnf(42,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[38,18]),
[iquote('0:SoR:38.0,18.0')] ).
cnf(44,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[38,2]),
[iquote('0:SoR:38.0,2.0')] ).
cnf(48,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[38,5]),
[iquote('0:SoR:38.0,5.0')] ).
cnf(49,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(53,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,49]),
[iquote('0:Rew:7.0,49.0')] ).
cnf(62,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[38,6]),
[iquote('0:SoR:38.0,6.0')] ).
cnf(110,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[38,53]),
[iquote('0:SoR:38.0,53.0')] ).
cnf(121,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[39,8]),
[iquote('0:SoR:39.0,8.1')] ).
cnf(135,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[121,3]),
[iquote('0:SoR:121.0,3.0')] ).
cnf(160,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[42,135]),
[iquote('0:SoR:42.0,135.0')] ).
cnf(312,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[48,41]),
[iquote('0:SoR:48.0,41.1')] ).
cnf(356,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[110,160]),
[iquote('0:SoR:110.0,160.0')] ).
cnf(358,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[44,356]),
[iquote('0:SoR:44.0,356.0')] ).
cnf(363,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[39,358]),
[iquote('0:SoR:39.0,358.0')] ).
cnf(370,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,363]),
[iquote('0:SpR:7.0,363.0')] ).
cnf(372,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[62,370]),
[iquote('0:SoR:62.0,370.0')] ).
cnf(680,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[372,9]),
[iquote('0:Res:372.0,9.1')] ).
cnf(1061,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[312,363]),
[iquote('0:SoR:312.0,363.0')] ).
cnf(1085,plain,
theorem(or__dfg(u,implies__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,1061]),
[iquote('0:SpR:7.0,1061.0')] ).
cnf(13521,plain,
theorem(or__dfg(u,not__dfg(not__dfg(implies__dfg(v,not__dfg(u)))))),
inference(sor,[status(thm)],[680,1085]),
[iquote('0:SoR:680.0,1085.0')] ).
cnf(13568,plain,
theorem(or__dfg(u,not__dfg(and__dfg(v,u)))),
inference(rew,[status(thm),theory(equality)],[11,13521]),
[iquote('0:Rew:11.0,13521.0')] ).
cnf(13697,plain,
theorem(implies__dfg(and__dfg(u,v),v)),
inference(sor,[status(thm)],[42,13568]),
[iquote('0:SoR:42.0,13568.0')] ).
cnf(13709,plain,
$false,
inference(unc,[status(thm)],[13697,1]),
[iquote('0:UnC:13697.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL241-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.36 % Computer : n027.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Sep 5 20:07:28 UTC 2026
% 0.13/0.36 % CPUTime :
% 14.54/14.86
% 14.54/14.86 SPASS V 3.9
% 14.54/14.86 SPASS beiseite: Proof found.
% 14.54/14.86 % SZS status Theorem
% 14.54/14.86 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.54/14.86 SPASS derived 11095 clauses, backtracked 0 clauses, performed 0 splits and kept 4172 clauses.
% 14.54/14.86 SPASS allocated 101402 KBytes.
% 14.54/14.86 SPASS spent 0:0:14.13 on the problem.
% 14.54/14.86 0:00:00.06 for the input.
% 14.54/14.86 0:00:00.00 for the FLOTTER CNF translation.
% 14.54/14.86 0:00:00.61 for inferences.
% 14.54/14.86 0:00:00.00 for the backtracking.
% 14.54/14.86 0:0:13.29 for the reduction.
% 14.54/14.86
% 14.54/14.86
% 14.54/14.86 Here is a proof with depth 13, length 39 :
% 14.54/14.86 % SZS output start Refutation
% See solution above
% 14.54/14.86 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 and_defn
% 14.54/14.86
%------------------------------------------------------------------------------