TSTP Solution File: LCL205-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL205-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 14:35:25 EDT 2022
% Result : Unsatisfiable 2.25s 2.41s
% Output : Refutation 2.25s
% 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(p,not__dfg(q)))),
file('LCL205-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL205-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL205-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL205-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL205-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL205-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL205-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL205-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL205-3.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(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(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(260,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(266,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(268,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,266]),
[iquote('0:Rew:7.0,266.0')] ).
cnf(288,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(297,plain,
theorem(or__dfg(or__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[25,288]),
[iquote('0:SoR:25.0,288.0')] ).
cnf(306,plain,
theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
inference(spr,[status(thm),theory(equality)],[7,297]),
[iquote('0:SpR:7.0,297.0')] ).
cnf(352,plain,
theorem(or__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(w,v))),
inference(sor,[status(thm)],[189,306]),
[iquote('0:SoR:189.0,306.0')] ).
cnf(436,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[268,9]),
[iquote('0:Res:268.0,9.1')] ).
cnf(840,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[436,9]),
[iquote('0:Res:436.1,9.1')] ).
cnf(1383,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(3748,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),not__dfg(not__dfg(v)))),
inference(sor,[status(thm)],[1383,260]),
[iquote('0:SoR:1383.0,260.0')] ).
cnf(4780,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(v,u),v))),
inference(sor,[status(thm)],[23,3748]),
[iquote('0:SoR:23.0,3748.0')] ).
cnf(4789,plain,
theorem(implies__dfg(or__dfg(u,v),implies__dfg(not__dfg(v),u))),
inference(sor,[status(thm)],[131,4780]),
[iquote('0:SoR:131.0,4780.0')] ).
cnf(4792,plain,
( ~ theorem(or__dfg(u,v))
| theorem(implies__dfg(not__dfg(v),u)) ),
inference(sor,[status(thm)],[840,4789]),
[iquote('0:SoR:840.1,4789.0')] ).
cnf(6161,plain,
theorem(implies__dfg(not__dfg(implies__dfg(u,v)),implies__dfg(w,not__dfg(v)))),
inference(sor,[status(thm)],[4792,352]),
[iquote('0:SoR:4792.0,352.0')] ).
cnf(6393,plain,
$false,
inference(unc,[status(thm)],[6161,1]),
[iquote('0:UnC:6161.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL205-3 : TPTP v8.1.0. Released v2.3.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 11:00:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.25/2.41
% 2.25/2.41 SPASS V 3.9
% 2.25/2.41 SPASS beiseite: Proof found.
% 2.25/2.41 % SZS status Theorem
% 2.25/2.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.25/2.41 SPASS derived 6053 clauses, backtracked 0 clauses, performed 0 splits and kept 2812 clauses.
% 2.25/2.41 SPASS allocated 83834 KBytes.
% 2.25/2.41 SPASS spent 0:00:02.02 on the problem.
% 2.25/2.41 0:00:00.04 for the input.
% 2.25/2.41 0:00:00.00 for the FLOTTER CNF translation.
% 2.25/2.41 0:00:00.24 for inferences.
% 2.25/2.41 0:00:00.00 for the backtracking.
% 2.25/2.41 0:00:01.68 for the reduction.
% 2.25/2.41
% 2.25/2.41
% 2.25/2.41 Here is a proof with depth 16, length 57 :
% 2.25/2.41 % SZS output start Refutation
% See solution above
% 2.25/2.41 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
% 2.25/2.41
%------------------------------------------------------------------------------