%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL182-3 : 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 01:06:57 PM UTC 2026
% Result : Unsatisfiable 2.66s 2.93s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 41 ( 29 unt; 0 nHn; 41 RR)
% Number of literals : 55 ( 0 equ; 15 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(implies__dfg(p,q),implies__dfg(not__dfg(q),not__dfg(p)))),
file('LCL182-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL182-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL182-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL182-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL182-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL182-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL182-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL182-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL182-3.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(19,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(20,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[19,16]),
[iquote('0:SoR:19.0,16.0')] ).
cnf(23,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[19,15]),
[iquote('0:SoR:19.0,15.0')] ).
cnf(25,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[19,4]),
[iquote('0:SoR:19.0,4.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(36,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(40,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,36]),
[iquote('0:Rew:7.0,36.0')] ).
cnf(48,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[19,6]),
[iquote('0:SoR:19.0,6.0')] ).
cnf(60,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[20,8]),
[iquote('0:SoR:20.0,8.1')] ).
cnf(71,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[60,4]),
[iquote('0:SoR:60.0,4.0')] ).
cnf(72,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[60,3]),
[iquote('0:SoR:60.0,3.0')] ).
cnf(76,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[19,40]),
[iquote('0:SoR:19.0,40.0')] ).
cnf(77,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)],[7,40]),
[iquote('0:SpR:7.0,40.0')] ).
cnf(79,plain,
axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,77]),
[iquote('0:Rew:7.0,77.0')] ).
cnf(87,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[23,72]),
[iquote('0:SoR:23.0,72.0')] ).
cnf(119,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(sor,[status(thm)],[23,71]),
[iquote('0:SoR:23.0,71.0')] ).
cnf(131,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[19,79]),
[iquote('0:SoR:19.0,79.0')] ).
cnf(187,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(v,u),v))),
inference(sor,[status(thm)],[76,119]),
[iquote('0:SoR:76.0,119.0')] ).
cnf(190,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[76,87]),
[iquote('0:SoR:76.0,87.0')] ).
cnf(192,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,190]),
[iquote('0:SoR:27.0,190.0')] ).
cnf(196,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[20,192]),
[iquote('0:SoR:20.0,192.0')] ).
cnf(201,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,196]),
[iquote('0:SpR:7.0,196.0')] ).
cnf(203,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[48,201]),
[iquote('0:SoR:48.0,201.0')] ).
cnf(248,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),v)),
inference(sor,[status(thm)],[25,187]),
[iquote('0:SoR:25.0,187.0')] ).
cnf(1373,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[203,9]),
[iquote('0:Res:203.0,9.1')] ).
cnf(3753,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),not__dfg(not__dfg(v)))),
inference(sor,[status(thm)],[1373,248]),
[iquote('0:SoR:1373.0,248.0')] ).
cnf(4762,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(v,u),v))),
inference(sor,[status(thm)],[23,3753]),
[iquote('0:SoR:23.0,3753.0')] ).
cnf(4788,plain,
theorem(implies__dfg(or__dfg(u,v),implies__dfg(not__dfg(v),u))),
inference(sor,[status(thm)],[131,4762]),
[iquote('0:SoR:131.0,4762.0')] ).
cnf(4798,plain,
theorem(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(v),not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,4788]),
[iquote('0:SpR:7.0,4788.0')] ).
cnf(4800,plain,
$false,
inference(unc,[status(thm)],[4798,1]),
[iquote('0:UnC:4798.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL182-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.12/0.37 % Computer : n027.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 5 06:25:28 UTC 2026
% 0.12/0.38 % CPUTime :
% 2.66/2.93
% 2.66/2.93 SPASS V 3.9
% 2.66/2.93 SPASS beiseite: Proof found.
% 2.66/2.93 % SZS status Theorem
% 2.66/2.93 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.66/2.93 SPASS derived 4508 clauses, backtracked 0 clauses, performed 0 splits and kept 2098 clauses.
% 2.66/2.93 SPASS allocated 81654 KBytes.
% 2.66/2.93 SPASS spent 0:00:02.47 on the problem.
% 2.66/2.93 0:00:00.06 for the input.
% 2.66/2.93 0:00:00.00 for the FLOTTER CNF translation.
% 2.66/2.93 0:00:00.37 for inferences.
% 2.66/2.93 0:00:00.00 for the backtracking.
% 2.66/2.93 0:00:01.93 for the reduction.
% 2.66/2.93
% 2.66/2.93
% 2.66/2.93 Here is a proof with depth 15, length 41 :
% 2.66/2.93 % SZS output start Refutation
% See solution above
% 2.66/2.93 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
% 2.66/2.93
%------------------------------------------------------------------------------