%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL235-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 01:07:08 PM UTC 2026
% Result : Unsatisfiable 0.14s 23.20s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 25 unt; 0 nHn; 35 RR)
% Number of literals : 47 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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(not__dfg(and__dfg(p,q)),or__dfg(not__dfg(p),not__dfg(q)))),
file('LCL235-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL235-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL235-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL235-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL235-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL235-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL235-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL235-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL235-3.p',unknown),
[] ).
cnf(10,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL235-3.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(12,plain,
~ theorem(implies__dfg(not__dfg(and__dfg(p,q)),implies__dfg(p,not__dfg(q)))),
inference(rew,[status(thm),theory(equality)],[7,1]),
[iquote('0:Rew:7.0,1.0')] ).
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(29,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(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[29,18]),
[iquote('0:SoR:29.0,18.0')] ).
cnf(41,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[29,19]),
[iquote('0:SoR:29.0,19.0')] ).
cnf(44,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[29,2]),
[iquote('0:SoR:29.0,2.0')] ).
cnf(52,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(56,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,52]),
[iquote('0:Rew:7.0,52.0')] ).
cnf(63,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[29,6]),
[iquote('0:SoR:29.0,6.0')] ).
cnf(116,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[41,8]),
[iquote('0:SoR:41.0,8.1')] ).
cnf(123,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[29,56]),
[iquote('0:SoR:29.0,56.0')] ).
cnf(140,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[116,3]),
[iquote('0:SoR:116.0,3.0')] ).
cnf(162,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[39,140]),
[iquote('0:SoR:39.0,140.0')] ).
cnf(380,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[123,162]),
[iquote('0:SoR:123.0,162.0')] ).
cnf(382,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[44,380]),
[iquote('0:SoR:44.0,380.0')] ).
cnf(387,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[41,382]),
[iquote('0:SoR:41.0,382.0')] ).
cnf(394,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,387]),
[iquote('0:SpR:7.0,387.0')] ).
cnf(396,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[63,394]),
[iquote('0:SoR:63.0,394.0')] ).
cnf(701,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[396,9]),
[iquote('0:Res:396.0,9.1')] ).
cnf(15538,plain,
theorem(or__dfg(u,not__dfg(not__dfg(not__dfg(u))))),
inference(sor,[status(thm)],[701,387]),
[iquote('0:SoR:701.0,387.0')] ).
cnf(15792,plain,
theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[39,15538]),
[iquote('0:SoR:39.0,15538.0')] ).
cnf(15821,plain,
theorem(implies__dfg(not__dfg(and__dfg(u,v)),implies__dfg(u,not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[11,15792]),
[iquote('0:SpR:11.0,15792.0')] ).
cnf(15830,plain,
$false,
inference(unc,[status(thm)],[15821,12]),
[iquote('0:UnC:15821.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL235-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.36 % Computer : n004.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
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sat Sep 5 15:56:59 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.14/23.20
% 0.14/23.20 SPASS V 3.9
% 0.14/23.20 SPASS beiseite: Proof found.
% 0.14/23.20 % SZS status Theorem
% 0.14/23.20 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/23.20 SPASS derived 12309 clauses, backtracked 0 clauses, performed 0 splits and kept 4986 clauses.
% 0.14/23.20 SPASS allocated 113370 KBytes.
% 0.14/23.20 SPASS spent 0:0:22.34 on the problem.
% 0.14/23.20 0:00:00.06 for the input.
% 0.14/23.20 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/23.20 0:00:00.66 for inferences.
% 0.14/23.20 0:00:00.00 for the backtracking.
% 0.14/23.20 0:0:21.44 for the reduction.
% 0.14/23.20
% 0.14/23.20
% 0.14/23.20 Here is a proof with depth 14, length 35 :
% 0.14/23.20 % SZS output start Refutation
% See solution above
% 0.14/23.20 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
% 0.14/23.20
%------------------------------------------------------------------------------