TSTP Solution File: LCL206-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL206-3 : TPTP v8.1.0. Bugfixed v2.4.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:35:26 EDT 2022
% Result : Unsatisfiable 2.20s 2.37s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of clauses : 57 ( 37 unt; 0 nHn; 57 RR)
% Number of literals : 80 ( 0 equ; 24 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(not__dfg(implies__dfg(p,q)),implies__dfg(not__dfg(p),not__dfg(q)))),
file('LCL206-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL206-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL206-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL206-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL206-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL206-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL206-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL206-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL206-3.p',unknown),
[] ).
cnf(13,plain,
axiom(implies__dfg(u,implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
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(24,plain,
( ~ theorem(u)
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[19,13]),
[iquote('0:SoR:19.0,13.0')] ).
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(26,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[19,3]),
[iquote('0:SoR:19.0,3.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(35,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[19,5]),
[iquote('0:SoR:19.0,5.0')] ).
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(144,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[35,26]),
[iquote('0:SoR:35.0,26.1')] ).
cnf(185,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(189,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,implies__dfg(w,v))) ),
inference(sor,[status(thm)],[76,24]),
[iquote('0:SoR:76.0,24.1')] ).
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(197,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[76,192]),
[iquote('0:SoR:76.0,192.0')] ).
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(262,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),v)),
inference(sor,[status(thm)],[25,185]),
[iquote('0:SoR:25.0,185.0')] ).
cnf(268,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,197]),
[iquote('0:SpR:7.0,197.0')] ).
cnf(270,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,268]),
[iquote('0:Rew:7.0,268.0')] ).
cnf(281,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[144,196]),
[iquote('0:SoR:144.0,196.0')] ).
cnf(289,plain,
theorem(or__dfg(or__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[25,281]),
[iquote('0:SoR:25.0,281.0')] ).
cnf(298,plain,
theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(spr,[status(thm),theory(equality)],[7,289]),
[iquote('0:SpR:7.0,289.0')] ).
cnf(344,plain,
theorem(or__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(w,v))),
inference(sor,[status(thm)],[189,298]),
[iquote('0:SoR:189.0,298.0')] ).
cnf(443,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[270,9]),
[iquote('0:Res:270.0,9.1')] ).
cnf(842,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[443,9]),
[iquote('0:Res:443.1,9.1')] ).
cnf(1385,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(3768,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),not__dfg(not__dfg(v)))),
inference(sor,[status(thm)],[1385,262]),
[iquote('0:SoR:1385.0,262.0')] ).
cnf(4783,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(v,u),v))),
inference(sor,[status(thm)],[23,3768]),
[iquote('0:SoR:23.0,3768.0')] ).
cnf(4800,plain,
theorem(implies__dfg(or__dfg(u,v),implies__dfg(not__dfg(v),u))),
inference(sor,[status(thm)],[131,4783]),
[iquote('0:SoR:131.0,4783.0')] ).
cnf(4803,plain,
( ~ theorem(or__dfg(u,v))
| theorem(implies__dfg(not__dfg(v),u)) ),
inference(sor,[status(thm)],[842,4800]),
[iquote('0:SoR:842.1,4800.0')] ).
cnf(6164,plain,
theorem(implies__dfg(not__dfg(implies__dfg(u,v)),implies__dfg(w,not__dfg(v)))),
inference(sor,[status(thm)],[4803,344]),
[iquote('0:SoR:4803.0,344.0')] ).
cnf(6396,plain,
$false,
inference(unc,[status(thm)],[6164,1]),
[iquote('0:UnC:6164.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL206-3 : TPTP v8.1.0. Bugfixed v2.4.1.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.32 % Computer : n011.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Sun Jul 3 02:56:20 EDT 2022
% 0.13/0.32 % CPUTime :
% 2.20/2.37
% 2.20/2.37 SPASS V 3.9
% 2.20/2.37 SPASS beiseite: Proof found.
% 2.20/2.37 % SZS status Theorem
% 2.20/2.37 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.20/2.37 SPASS derived 6056 clauses, backtracked 0 clauses, performed 0 splits and kept 2813 clauses.
% 2.20/2.37 SPASS allocated 83838 KBytes.
% 2.20/2.37 SPASS spent 0:00:01.99 on the problem.
% 2.20/2.37 0:00:00.04 for the input.
% 2.20/2.37 0:00:00.00 for the FLOTTER CNF translation.
% 2.20/2.37 0:00:00.23 for inferences.
% 2.20/2.37 0:00:00.00 for the backtracking.
% 2.20/2.37 0:00:01.65 for the reduction.
% 2.20/2.37
% 2.20/2.37
% 2.20/2.37 Here is a proof with depth 16, length 57 :
% 2.20/2.37 % SZS output start Refutation
% See solution above
% 2.20/2.37 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
% 2.20/2.37
%------------------------------------------------------------------------------