TSTP Solution File: LCL187-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL187-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 14:35:14 EDT 2022
% Result : Unsatisfiable 178.69s 178.95s
% Output : Refutation 178.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of clauses : 77 ( 52 unt; 0 nHn; 77 RR)
% Number of literals : 105 ( 0 equ; 29 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(p,implies__dfg(not__dfg(p),q))),
file('LCL187-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL187-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL187-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL187-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL187-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL187-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL187-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL187-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL187-3.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(30,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[18,5]),
[iquote('0:SoR:18.0,5.0')] ).
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(53,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)],[7,35]),
[iquote('0:SpR:7.0,35.0')] ).
cnf(55,plain,
axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,53]),
[iquote('0:Rew:7.0,53.0')] ).
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(95,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[18,55]),
[iquote('0:SoR:18.0,55.0')] ).
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(114,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[30,24]),
[iquote('0:SoR:30.0,24.1')] ).
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(273,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[114,163]),
[iquote('0:SoR:114.0,163.0')] ).
cnf(284,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(v)))),
inference(sor,[status(thm)],[30,273]),
[iquote('0:SoR:30.0,273.0')] ).
cnf(393,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)],[52,393]),
[iquote('0:SoR:52.0,393.0')] ).
cnf(476,plain,
( ~ axiom(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[95,8]),
[iquote('0:SoR:95.0,8.1')] ).
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(1460,plain,
theorem(implies__dfg(or__dfg(u,v),implies__dfg(implies__dfg(v,w),or__dfg(u,w)))),
inference(sor,[status(thm)],[476,6]),
[iquote('0:SoR:476.0,6.0')] ).
cnf(3826,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(3872,plain,
theorem(or__dfg(u,not__dfg(not__dfg(or__dfg(v,not__dfg(v)))))),
inference(sor,[status(thm)],[1349,284]),
[iquote('0:SoR:1349.0,284.0')] ).
cnf(3883,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(4160,plain,
theorem(not__dfg(not__dfg(or__dfg(u,not__dfg(u))))),
inference(sor,[status(thm)],[27,3872]),
[iquote('0:SoR:27.0,3872.0')] ).
cnf(5575,plain,
theorem(not__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))))),
inference(sor,[status(thm)],[27,3826]),
[iquote('0:SoR:27.0,3826.0')] ).
cnf(5773,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[25,3883]),
[iquote('0:SoR:25.0,3883.0')] ).
cnf(5788,plain,
( ~ theorem(not__dfg(u))
| theorem(implies__dfg(or__dfg(u,v),v)) ),
inference(sor,[status(thm)],[655,5773]),
[iquote('0:SoR:655.1,5773.0')] ).
cnf(7461,plain,
theorem(implies__dfg(or__dfg(not__dfg(or__dfg(u,not__dfg(u))),v),v)),
inference(sor,[status(thm)],[5788,4160]),
[iquote('0:SoR:5788.0,4160.0')] ).
cnf(7471,plain,
theorem(implies__dfg(or__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))),w),w)),
inference(sor,[status(thm)],[5788,5575]),
[iquote('0:SoR:5788.0,5575.0')] ).
cnf(7479,plain,
theorem(implies__dfg(implies__dfg(or__dfg(u,not__dfg(u)),v),v)),
inference(rew,[status(thm),theory(equality)],[7,7461]),
[iquote('0:Rew:7.0,7461.0')] ).
cnf(7488,plain,
theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,u)),w),w)),
inference(rew,[status(thm),theory(equality)],[7,7471]),
[iquote('0:Rew:7.0,7471.0')] ).
cnf(7520,plain,
( ~ theorem(implies__dfg(or__dfg(u,not__dfg(u)),v))
| theorem(v) ),
inference(sor,[status(thm)],[655,7479]),
[iquote('0:SoR:655.1,7479.0')] ).
cnf(11064,plain,
theorem(implies__dfg(implies__dfg(not__dfg(u),v),or__dfg(u,v))),
inference(sor,[status(thm)],[7520,1460]),
[iquote('0:SoR:7520.0,1460.0')] ).
cnf(11269,plain,
theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[7,11064]),
[iquote('0:SpR:7.0,11064.0')] ).
cnf(13076,plain,
( ~ theorem(implies__dfg(not__dfg(not__dfg(u)),v))
| theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[655,11269]),
[iquote('0:SoR:655.1,11269.0')] ).
cnf(14077,plain,
( ~ theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w))
| theorem(w) ),
inference(sor,[status(thm)],[655,7488]),
[iquote('0:SoR:655.1,7488.0')] ).
cnf(80795,plain,
theorem(implies__dfg(u,or__dfg(u,v))),
inference(sor,[status(thm)],[14077,194]),
[iquote('0:SoR:14077.0,194.0')] ).
cnf(81215,plain,
theorem(implies__dfg(u,or__dfg(not__dfg(not__dfg(u)),v))),
inference(sor,[status(thm)],[13076,80795]),
[iquote('0:SoR:13076.0,80795.0')] ).
cnf(81231,plain,
theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
inference(rew,[status(thm),theory(equality)],[7,81215]),
[iquote('0:Rew:7.0,81215.0')] ).
cnf(81232,plain,
$false,
inference(unc,[status(thm)],[81231,1]),
[iquote('0:UnC:81231.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL187-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 10:33:29 EDT 2022
% 0.14/0.34 % CPUTime :
% 178.69/178.95
% 178.69/178.95 SPASS V 3.9
% 178.69/178.95 SPASS beiseite: Proof found.
% 178.69/178.95 % SZS status Theorem
% 178.69/178.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 178.69/178.95 SPASS derived 74167 clauses, backtracked 0 clauses, performed 0 splits and kept 28527 clauses.
% 178.69/178.95 SPASS allocated 164814 KBytes.
% 178.69/178.95 SPASS spent 0:2:56.50 on the problem.
% 178.69/178.95 0:00:00.04 for the input.
% 178.69/178.95 0:00:00.00 for the FLOTTER CNF translation.
% 178.69/178.95 0:00:05.18 for inferences.
% 178.69/178.95 0:00:00.00 for the backtracking.
% 178.69/178.95 0:2:49.65 for the reduction.
% 178.69/178.95
% 178.69/178.95
% 178.69/178.95 Here is a proof with depth 20, length 77 :
% 178.69/178.95 % SZS output start Refutation
% See solution above
% 178.69/178.95 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
% 178.69/178.95
%------------------------------------------------------------------------------