TSTP Solution File: LCL186-3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL186-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:35:13 EDT 2022
% Result : Unsatisfiable 167.20s 167.41s
% Output : Refutation 167.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of clauses : 59 ( 40 unt; 0 nHn; 59 RR)
% Number of literals : 81 ( 0 equ; 23 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(not__dfg(p),implies__dfg(p,q))),
file('LCL186-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL186-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL186-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL186-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL186-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL186-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL186-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL186-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL186-3.p',unknown),
[] ).
cnf(16,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(17,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(18,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(21,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[18,17]),
[iquote('0:SoR:18.0,17.0')] ).
cnf(24,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[18,3]),
[iquote('0:SoR:18.0,3.0')] ).
cnf(25,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[18,16]),
[iquote('0:SoR:18.0,16.0')] ).
cnf(26,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[18,4]),
[iquote('0:SoR:18.0,4.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[18,2]),
[iquote('0:SoR:18.0,2.0')] ).
cnf(31,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(32,plain,
axiom(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(35,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,31]),
[iquote('0:Rew:7.0,31.0')] ).
cnf(36,plain,
axiom(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,32]),
[iquote('0:Rew:7.0,32.0')] ).
cnf(42,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[18,6]),
[iquote('0:SoR:18.0,6.0')] ).
cnf(43,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(not__dfg(w),u),implies__dfg(w,v)))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(45,plain,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
inference(rew,[status(thm),theory(equality)],[7,43]),
[iquote('0:Rew:7.0,43.0')] ).
cnf(52,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[18,35]),
[iquote('0:SoR:18.0,35.0')] ).
cnf(63,plain,
( ~ theorem(or__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[18,36]),
[iquote('0:SoR:18.0,36.0')] ).
cnf(70,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[21,8]),
[iquote('0:SoR:21.0,8.1')] ).
cnf(71,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[18,45]),
[iquote('0:SoR:18.0,45.0')] ).
cnf(82,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[70,3]),
[iquote('0:SoR:70.0,3.0')] ).
cnf(86,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[70,4]),
[iquote('0:SoR:70.0,4.0')] ).
cnf(97,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[25,82]),
[iquote('0:SoR:25.0,82.0')] ).
cnf(124,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(sor,[status(thm)],[25,86]),
[iquote('0:SoR:25.0,86.0')] ).
cnf(157,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[52,97]),
[iquote('0:SoR:52.0,97.0')] ).
cnf(159,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,157]),
[iquote('0:SoR:27.0,157.0')] ).
cnf(163,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[21,159]),
[iquote('0:SoR:21.0,159.0')] ).
cnf(164,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[52,159]),
[iquote('0:SoR:52.0,159.0')] ).
cnf(168,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,163]),
[iquote('0:SpR:7.0,163.0')] ).
cnf(170,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[42,168]),
[iquote('0:SoR:42.0,168.0')] ).
cnf(176,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[63,24]),
[iquote('0:SoR:63.0,24.1')] ).
cnf(194,plain,
theorem(implies__dfg(implies__dfg(u,or__dfg(v,w)),implies__dfg(u,or__dfg(w,v)))),
inference(sor,[status(thm)],[71,124]),
[iquote('0:SoR:71.0,124.0')] ).
cnf(212,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
inference(sor,[status(thm)],[26,164]),
[iquote('0:SoR:26.0,164.0')] ).
cnf(214,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,164]),
[iquote('0:SpR:7.0,164.0')] ).
cnf(216,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,214]),
[iquote('0:Rew:7.0,214.0')] ).
cnf(250,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[216,9]),
[iquote('0:Res:216.0,9.1')] ).
cnf(392,plain,
theorem(implies__dfg(u,or__dfg(v,or__dfg(w,u)))),
inference(sor,[status(thm)],[176,97]),
[iquote('0:SoR:176.0,97.0')] ).
cnf(427,plain,
theorem(or__dfg(u,implies__dfg(v,or__dfg(w,v)))),
inference(sor,[status(thm)],[52,392]),
[iquote('0:SoR:52.0,392.0')] ).
cnf(655,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[250,9]),
[iquote('0:Res:250.1,9.1')] ).
cnf(1349,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[170,9]),
[iquote('0:Res:170.0,9.1')] ).
cnf(3825,plain,
theorem(or__dfg(u,not__dfg(not__dfg(implies__dfg(v,or__dfg(w,v)))))),
inference(sor,[status(thm)],[1349,427]),
[iquote('0:SoR:1349.0,427.0')] ).
cnf(3882,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),v),not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[1349,212]),
[iquote('0:SoR:1349.0,212.0')] ).
cnf(5574,plain,
theorem(not__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))))),
inference(sor,[status(thm)],[27,3825]),
[iquote('0:SoR:27.0,3825.0')] ).
cnf(5772,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[25,3882]),
[iquote('0:SoR:25.0,3882.0')] ).
cnf(5787,plain,
( ~ theorem(not__dfg(u))
| theorem(implies__dfg(or__dfg(u,v),v)) ),
inference(sor,[status(thm)],[655,5772]),
[iquote('0:SoR:655.1,5772.0')] ).
cnf(7470,plain,
theorem(implies__dfg(or__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))),w),w)),
inference(sor,[status(thm)],[5787,5574]),
[iquote('0:SoR:5787.0,5574.0')] ).
cnf(7487,plain,
theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,u)),w),w)),
inference(rew,[status(thm),theory(equality)],[7,7470]),
[iquote('0:Rew:7.0,7470.0')] ).
cnf(14076,plain,
( ~ theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w))
| theorem(w) ),
inference(sor,[status(thm)],[655,7487]),
[iquote('0:SoR:655.1,7487.0')] ).
cnf(80794,plain,
theorem(implies__dfg(u,or__dfg(u,v))),
inference(sor,[status(thm)],[14076,194]),
[iquote('0:SoR:14076.0,194.0')] ).
cnf(81227,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[7,80794]),
[iquote('0:SpR:7.0,80794.0')] ).
cnf(81230,plain,
$false,
inference(unc,[status(thm)],[81227,1]),
[iquote('0:UnC:81227.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL186-3 : TPTP v8.1.0. Released v2.3.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 11:27:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 167.20/167.41
% 167.20/167.41 SPASS V 3.9
% 167.20/167.41 SPASS beiseite: Proof found.
% 167.20/167.41 % SZS status Theorem
% 167.20/167.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 167.20/167.41 SPASS derived 74166 clauses, backtracked 0 clauses, performed 0 splits and kept 28527 clauses.
% 167.20/167.41 SPASS allocated 164782 KBytes.
% 167.20/167.41 SPASS spent 0:2:45.09 on the problem.
% 167.20/167.41 0:00:00.04 for the input.
% 167.20/167.41 0:00:00.00 for the FLOTTER CNF translation.
% 167.20/167.41 0:00:04.92 for inferences.
% 167.20/167.41 0:00:00.00 for the backtracking.
% 167.20/167.41 0:2:38.60 for the reduction.
% 167.20/167.41
% 167.20/167.41
% 167.20/167.41 Here is a proof with depth 18, length 59 :
% 167.20/167.41 % SZS output start Refutation
% See solution above
% 167.20/167.41 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
% 167.20/167.41
%------------------------------------------------------------------------------