TSTP Solution File: LCL537+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL537+1 : TPTP v8.1.0. Released v3.3.0.
% 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 14:37:34 EDT 2022
% Result : Theorem 64.03s 64.21s
% Output : Refutation 74.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 44
% Syntax : Number of clauses : 151 ( 102 unt; 0 nHn; 151 RR)
% Number of literals : 205 ( 0 equ; 57 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 24 ( 23 usr; 22 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
op_or,
file('LCL537+1.p',unknown),
[] ).
cnf(2,axiom,
op_implies_and,
file('LCL537+1.p',unknown),
[] ).
cnf(3,axiom,
op_equiv,
file('LCL537+1.p',unknown),
[] ).
cnf(4,axiom,
modus_ponens,
file('LCL537+1.p',unknown),
[] ).
cnf(6,axiom,
implies_1,
file('LCL537+1.p',unknown),
[] ).
cnf(7,axiom,
implies_2,
file('LCL537+1.p',unknown),
[] ).
cnf(8,axiom,
implies_3,
file('LCL537+1.p',unknown),
[] ).
cnf(9,axiom,
and_1,
file('LCL537+1.p',unknown),
[] ).
cnf(11,axiom,
and_3,
file('LCL537+1.p',unknown),
[] ).
cnf(12,axiom,
or_1,
file('LCL537+1.p',unknown),
[] ).
cnf(14,axiom,
or_3,
file('LCL537+1.p',unknown),
[] ).
cnf(16,axiom,
equivalence_2,
file('LCL537+1.p',unknown),
[] ).
cnf(18,axiom,
substitution_of_equivalents,
file('LCL537+1.p',unknown),
[] ).
cnf(19,axiom,
op_possibly,
file('LCL537+1.p',unknown),
[] ).
cnf(20,axiom,
necessitation,
file('LCL537+1.p',unknown),
[] ).
cnf(21,axiom,
axiom_K,
file('LCL537+1.p',unknown),
[] ).
cnf(22,axiom,
axiom_M,
file('LCL537+1.p',unknown),
[] ).
cnf(23,axiom,
axiom_4,
file('LCL537+1.p',unknown),
[] ).
cnf(24,axiom,
axiom_B,
file('LCL537+1.p',unknown),
[] ).
cnf(25,axiom,
~ axiom_5,
file('LCL537+1.p',unknown),
[] ).
cnf(26,axiom,
is_a_theorem(skc95),
file('LCL537+1.p',unknown),
[] ).
cnf(32,axiom,
is_a_theorem(implies__dfg(skc95,skc94)),
file('LCL537+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL537+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL537+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ or_1
| is_a_theorem(implies__dfg(u,or__dfg(u,v))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ r1
| is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
file('LCL537+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ is_a_theorem(implies__dfg(or__dfg(skc138,skc138),skc138))
| r1 ),
file('LCL537+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL537+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ axiom_B
| is_a_theorem(implies__dfg(u,necessarily(possibly(u)))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ axiom_4
| is_a_theorem(implies__dfg(necessarily(u),necessarily(necessarily(u)))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ is_a_theorem(implies__dfg(possibly(skc161),necessarily(possibly(skc161))))
| axiom_5 ),
file('LCL537+1.p',unknown),
[] ).
cnf(86,axiom,
( ~ op_possibly
| equal(not__dfg(necessarily(not__dfg(u))),possibly(u)) ),
file('LCL537+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
file('LCL537+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ equivalence_2
| is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(v,u))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL537+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL537+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL537+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL537+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ axiom_K
| is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ implies_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(136,axiom,
( ~ or_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,v),implies__dfg(or__dfg(u,w),v)))) ),
file('LCL537+1.p',unknown),
[] ).
cnf(142,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[41,22]),
[iquote('0:MRR:41.0,22.0')] ).
cnf(143,plain,
is_a_theorem(implies__dfg(u,necessarily(possibly(u)))),
inference(mrr,[status(thm)],[64,24]),
[iquote('0:MRR:64.0,24.0')] ).
cnf(144,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[63,20]),
[iquote('0:MRR:63.1,20.0')] ).
cnf(147,plain,
is_a_theorem(implies__dfg(u,or__dfg(u,v))),
inference(mrr,[status(thm)],[51,12]),
[iquote('0:MRR:51.0,12.0')] ).
cnf(149,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[47,9]),
[iquote('0:MRR:47.0,9.0')] ).
cnf(151,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(mrr,[status(thm)],[45,6]),
[iquote('0:MRR:45.0,6.0')] ).
cnf(152,plain,
equal(not__dfg(necessarily(not__dfg(u))),possibly(u)),
inference(mrr,[status(thm)],[86,19]),
[iquote('0:MRR:86.0,19.0')] ).
cnf(153,plain,
~ is_a_theorem(implies__dfg(possibly(skc161),necessarily(possibly(skc161)))),
inference(mrr,[status(thm)],[77,25]),
[iquote('0:MRR:77.1,25.0')] ).
cnf(154,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(necessarily(u)))),
inference(mrr,[status(thm)],[74,23]),
[iquote('0:MRR:74.0,23.0')] ).
cnf(155,plain,
is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(v,u))),
inference(mrr,[status(thm)],[93,16]),
[iquote('0:MRR:93.0,16.0')] ).
cnf(157,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[89,11]),
[iquote('0:MRR:89.0,11.0')] ).
cnf(158,plain,
( ~ is_a_theorem(equiv__dfg(u,v))
| equal(u,v) ),
inference(mrr,[status(thm)],[88,18]),
[iquote('0:MRR:88.0,18.0')] ).
cnf(159,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[102,2]),
[iquote('0:MRR:102.0,2.0')] ).
cnf(160,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[159,108]),
[iquote('0:Rew:159.0,108.1')] ).
cnf(161,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[160,1]),
[iquote('0:MRR:160.0,1.0')] ).
cnf(167,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[106,7]),
[iquote('0:MRR:106.0,7.0')] ).
cnf(170,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[103,4]),
[iquote('0:MRR:103.1,4.0')] ).
cnf(171,plain,
is_a_theorem(implies__dfg(necessarily(implies__dfg(u,v)),implies__dfg(necessarily(u),necessarily(v)))),
inference(mrr,[status(thm)],[115,21]),
[iquote('0:MRR:115.0,21.0')] ).
cnf(172,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[114,3]),
[iquote('0:MRR:114.0,3.0')] ).
cnf(174,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[120,8]),
[iquote('0:MRR:120.0,8.0')] ).
cnf(178,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,v),implies__dfg(or__dfg(u,w),v)))),
inference(mrr,[status(thm)],[136,14]),
[iquote('0:MRR:136.0,14.0')] ).
cnf(244,plain,
equal(not__dfg(necessarily(implies__dfg(u,v))),possibly(and__dfg(u,not__dfg(v)))),
inference(spr,[status(thm),theory(equality)],[159,152]),
[iquote('0:SpR:159.0,152.0')] ).
cnf(377,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(skc94) ),
inference(res,[status(thm),theory(equality)],[32,170]),
[iquote('0:Res:32.0,170.1')] ).
cnf(378,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[142,170]),
[iquote('0:Res:142.0,170.1')] ).
cnf(386,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[151,170]),
[iquote('0:Res:151.0,170.1')] ).
cnf(387,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,and__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[157,170]),
[iquote('0:Res:157.0,170.1')] ).
cnf(400,plain,
is_a_theorem(skc94),
inference(ssi,[status(thm)],[377,26]),
[iquote('0:SSi:377.0,26.0')] ).
cnf(405,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[167,170]),
[iquote('0:Res:167.0,170.1')] ).
cnf(416,plain,
( ~ is_a_theorem(necessarily(implies__dfg(u,v)))
| is_a_theorem(implies__dfg(necessarily(u),necessarily(v))) ),
inference(res,[status(thm),theory(equality)],[171,170]),
[iquote('0:Res:171.0,170.1')] ).
cnf(505,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,u),equiv__dfg(u,v))) ),
inference(spr,[status(thm),theory(equality)],[172,387]),
[iquote('0:SpR:172.0,387.1')] ).
cnf(629,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[174,170]),
[iquote('0:Res:174.0,170.1')] ).
cnf(1134,plain,
equal(possibly(and__dfg(not__dfg(u),not__dfg(v))),not__dfg(necessarily(or__dfg(u,v)))),
inference(spr,[status(thm),theory(equality)],[161,244]),
[iquote('0:SpR:161.0,244.0')] ).
cnf(1592,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(u,u),v))),
inference(sor,[status(thm)],[405,178]),
[iquote('0:SoR:405.0,178.0')] ).
cnf(1598,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(sor,[status(thm)],[405,157]),
[iquote('0:SoR:405.0,157.0')] ).
cnf(1599,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[405,151]),
[iquote('0:SoR:405.0,151.0')] ).
cnf(2546,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(necessarily(u),necessarily(v))) ),
inference(sor,[status(thm)],[416,144]),
[iquote('0:SoR:416.0,144.1')] ).
cnf(5318,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(and__dfg(u,u)))),
inference(sor,[status(thm)],[2546,1598]),
[iquote('0:SoR:2546.0,1598.0')] ).
cnf(5323,plain,
is_a_theorem(implies__dfg(necessarily(u),necessarily(implies__dfg(v,u)))),
inference(sor,[status(thm)],[2546,151]),
[iquote('0:SoR:2546.0,151.0')] ).
cnf(5425,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(skc95,u))),
inference(sor,[status(thm)],[629,32]),
[iquote('0:SoR:629.0,32.0')] ).
cnf(5668,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(implies__dfg(skc95,u)) ),
inference(res,[status(thm),theory(equality)],[5425,170]),
[iquote('0:Res:5425.0,170.1')] ).
cnf(5817,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(necessarily(and__dfg(u,u))) ),
inference(res,[status(thm),theory(equality)],[5318,170]),
[iquote('0:Res:5318.0,170.1')] ).
cnf(5828,plain,
( ~ is_a_theorem(necessarily(u))
| is_a_theorem(necessarily(implies__dfg(v,u))) ),
inference(res,[status(thm),theory(equality)],[5323,170]),
[iquote('0:Res:5323.0,170.1')] ).
cnf(7342,plain,
is_a_theorem(implies__dfg(skc95,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[5668,1598]),
[iquote('0:SoR:5668.0,1598.0')] ).
cnf(7347,plain,
is_a_theorem(implies__dfg(skc95,implies__dfg(u,skc94))),
inference(sor,[status(thm)],[5668,151]),
[iquote('0:SoR:5668.0,151.0')] ).
cnf(7359,plain,
is_a_theorem(implies__dfg(necessarily(skc95),necessarily(and__dfg(skc94,skc94)))),
inference(sor,[status(thm)],[2546,7342]),
[iquote('0:SoR:2546.0,7342.0')] ).
cnf(7383,plain,
( ~ is_a_theorem(skc95)
| is_a_theorem(implies__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[7347,170]),
[iquote('0:Res:7347.0,170.1')] ).
cnf(7384,plain,
is_a_theorem(implies__dfg(u,skc94)),
inference(ssi,[status(thm)],[7383,26]),
[iquote('0:SSi:7383.0,26.0')] ).
cnf(7386,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),implies__dfg(v,u))),
inference(sor,[status(thm)],[629,7384]),
[iquote('0:SoR:629.0,7384.0')] ).
cnf(7710,plain,
( ~ is_a_theorem(necessarily(skc95))
| is_a_theorem(necessarily(and__dfg(skc94,skc94))) ),
inference(res,[status(thm),theory(equality)],[7359,170]),
[iquote('0:Res:7359.0,170.1')] ).
cnf(7711,plain,
is_a_theorem(necessarily(and__dfg(skc94,skc94))),
inference(ssi,[status(thm)],[7710,144,26]),
[iquote('0:SSi:7710.0,144.0,26.1')] ).
cnf(10461,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),u)),
inference(sor,[status(thm)],[405,7386]),
[iquote('0:SoR:405.0,7386.0')] ).
cnf(15830,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(and__dfg(u,u))) ),
inference(sor,[status(thm)],[5817,144]),
[iquote('0:SoR:5817.0,144.1')] ).
cnf(15892,plain,
( ~ is_a_theorem(implies__dfg(u,u))
| is_a_theorem(necessarily(equiv__dfg(u,u))) ),
inference(spr,[status(thm),theory(equality)],[172,15830]),
[iquote('0:SpR:172.0,15830.1')] ).
cnf(15894,plain,
is_a_theorem(necessarily(equiv__dfg(u,u))),
inference(ssi,[status(thm)],[15892,1599]),
[iquote('0:SSi:15892.0,1599.0')] ).
cnf(16639,plain,
is_a_theorem(necessarily(implies__dfg(u,equiv__dfg(v,v)))),
inference(sor,[status(thm)],[5828,15894]),
[iquote('0:SoR:5828.0,15894.0')] ).
cnf(16714,plain,
is_a_theorem(necessarily(implies__dfg(u,and__dfg(skc94,skc94)))),
inference(sor,[status(thm)],[5828,7711]),
[iquote('0:SoR:5828.0,7711.0')] ).
cnf(17066,plain,
is_a_theorem(implies__dfg(u,and__dfg(skc94,skc94))),
inference(sor,[status(thm)],[378,16714]),
[iquote('0:SoR:378.0,16714.0')] ).
cnf(17988,plain,
is_a_theorem(implies__dfg(u,equiv__dfg(v,v))),
inference(sor,[status(thm)],[378,16639]),
[iquote('0:SoR:378.0,16639.0')] ).
cnf(23486,plain,
( ~ r1
| is_a_theorem(implies__dfg(implies__dfg(u,or__dfg(u,u)),equiv__dfg(or__dfg(u,u),u))) ),
inference(sor,[status(thm)],[505,59]),
[iquote('0:SoR:505.0,59.1')] ).
cnf(23501,plain,
is_a_theorem(implies__dfg(implies__dfg(skc94,u),equiv__dfg(u,skc94))),
inference(sor,[status(thm)],[505,7384]),
[iquote('0:SoR:505.0,7384.0')] ).
cnf(23542,plain,
is_a_theorem(implies__dfg(implies__dfg(and__dfg(u,u),u),equiv__dfg(u,and__dfg(u,u)))),
inference(sor,[status(thm)],[505,1598]),
[iquote('0:SoR:505.0,1598.0')] ).
cnf(23598,plain,
is_a_theorem(implies__dfg(implies__dfg(necessarily(necessarily(u)),necessarily(u)),equiv__dfg(necessarily(u),necessarily(necessarily(u))))),
inference(sor,[status(thm)],[505,154]),
[iquote('0:SoR:505.0,154.0')] ).
cnf(23655,plain,
( ~ is_a_theorem(implies__dfg(skc94,u))
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(res,[status(thm),theory(equality)],[23501,170]),
[iquote('0:Res:23501.0,170.1')] ).
cnf(37458,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equiv__dfg(u,skc94)) ),
inference(sor,[status(thm)],[23655,386]),
[iquote('0:SoR:23655.0,386.1')] ).
cnf(37468,plain,
is_a_theorem(equiv__dfg(equiv__dfg(u,u),skc94)),
inference(sor,[status(thm)],[23655,17988]),
[iquote('0:SoR:23655.0,17988.0')] ).
cnf(37518,plain,
is_a_theorem(equiv__dfg(and__dfg(skc94,skc94),skc94)),
inference(sor,[status(thm)],[23655,17066]),
[iquote('0:SoR:23655.0,17066.0')] ).
cnf(41065,plain,
equal(and__dfg(skc94,skc94),skc94),
inference(res,[status(thm),theory(equality)],[37518,158]),
[iquote('0:Res:37518.0,158.0')] ).
cnf(44899,plain,
equal(equiv__dfg(u,u),skc94),
inference(res,[status(thm),theory(equality)],[37468,158]),
[iquote('0:Res:37468.0,158.0')] ).
cnf(45285,plain,
is_a_theorem(implies__dfg(skc94,implies__dfg(u,u))),
inference(spr,[status(thm),theory(equality)],[44899,155]),
[iquote('0:SpR:44899.0,155.0')] ).
cnf(45351,plain,
is_a_theorem(equiv__dfg(implies__dfg(u,u),skc94)),
inference(sor,[status(thm)],[23655,45285]),
[iquote('0:SoR:23655.0,45285.0')] ).
cnf(45439,plain,
equal(implies__dfg(u,u),skc94),
inference(res,[status(thm),theory(equality)],[45351,158]),
[iquote('0:Res:45351.0,158.0')] ).
cnf(45567,plain,
is_a_theorem(implies__dfg(skc94,implies__dfg(or__dfg(u,u),u))),
inference(spr,[status(thm),theory(equality)],[45439,1592]),
[iquote('0:SpR:45439.0,1592.0')] ).
cnf(47721,plain,
( ~ is_a_theorem(u)
| equal(u,skc94) ),
inference(res,[status(thm),theory(equality)],[37458,158]),
[iquote('0:Res:37458.1,158.0')] ).
cnf(48076,plain,
equal(implies__dfg(implies__dfg(skc94,u),u),skc94),
inference(ems,[status(thm)],[47721,10461]),
[iquote('0:EmS:47721.0,10461.0')] ).
cnf(48213,plain,
equal(implies__dfg(and__dfg(u,v),u),skc94),
inference(ems,[status(thm)],[47721,149]),
[iquote('0:EmS:47721.0,149.0')] ).
cnf(48231,plain,
equal(implies__dfg(u,implies__dfg(v,u)),skc94),
inference(ems,[status(thm)],[47721,151]),
[iquote('0:EmS:47721.0,151.0')] ).
cnf(48235,plain,
equal(implies__dfg(u,or__dfg(u,v)),skc94),
inference(ems,[status(thm)],[47721,147]),
[iquote('0:EmS:47721.0,147.0')] ).
cnf(48242,plain,
equal(implies__dfg(u,necessarily(possibly(u))),skc94),
inference(ems,[status(thm)],[47721,143]),
[iquote('0:EmS:47721.0,143.0')] ).
cnf(48261,plain,
equal(implies__dfg(necessarily(u),u),skc94),
inference(ems,[status(thm)],[47721,142]),
[iquote('0:EmS:47721.0,142.0')] ).
cnf(48342,plain,
is_a_theorem(implies__dfg(skc94,equiv__dfg(necessarily(u),necessarily(necessarily(u))))),
inference(rew,[status(thm),theory(equality)],[48261,23598]),
[iquote('0:Rew:48261.0,23598.0')] ).
cnf(48572,plain,
is_a_theorem(implies__dfg(skc94,equiv__dfg(u,and__dfg(u,u)))),
inference(rew,[status(thm),theory(equality)],[48213,23542]),
[iquote('0:Rew:48213.0,23542.0')] ).
cnf(48626,plain,
( ~ r1
| is_a_theorem(implies__dfg(skc94,equiv__dfg(or__dfg(u,u),u))) ),
inference(rew,[status(thm),theory(equality)],[48235,23486]),
[iquote('0:Rew:48235.0,23486.1')] ).
cnf(51078,plain,
equal(and__dfg(implies__dfg(u,implies__dfg(skc94,u)),skc94),equiv__dfg(u,implies__dfg(skc94,u))),
inference(spr,[status(thm),theory(equality)],[48076,172]),
[iquote('0:SpR:48076.0,172.0')] ).
cnf(51107,plain,
equal(equiv__dfg(u,implies__dfg(skc94,u)),and__dfg(skc94,skc94)),
inference(rew,[status(thm),theory(equality)],[48231,51078]),
[iquote('0:Rew:48231.0,51078.0')] ).
cnf(51108,plain,
equal(equiv__dfg(u,implies__dfg(skc94,u)),skc94),
inference(rew,[status(thm),theory(equality)],[41065,51107]),
[iquote('0:Rew:41065.0,51107.0')] ).
cnf(51457,plain,
( ~ is_a_theorem(skc94)
| equal(implies__dfg(skc94,u),u) ),
inference(spl,[status(thm),theory(equality)],[51108,158]),
[iquote('0:SpL:51108.0,158.0')] ).
cnf(51459,plain,
equal(implies__dfg(skc94,u),u),
inference(mrr,[status(thm)],[51457,400]),
[iquote('0:MRR:51457.0,400.0')] ).
cnf(51533,plain,
is_a_theorem(equiv__dfg(necessarily(u),necessarily(necessarily(u)))),
inference(rew,[status(thm),theory(equality)],[51459,48342]),
[iquote('0:Rew:51459.0,48342.0')] ).
cnf(51534,plain,
( ~ r1
| is_a_theorem(equiv__dfg(or__dfg(u,u),u)) ),
inference(rew,[status(thm),theory(equality)],[51459,48626]),
[iquote('0:Rew:51459.0,48626.1')] ).
cnf(51538,plain,
is_a_theorem(equiv__dfg(u,and__dfg(u,u))),
inference(rew,[status(thm),theory(equality)],[51459,48572]),
[iquote('0:Rew:51459.0,48572.0')] ).
cnf(51577,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),u)),
inference(rew,[status(thm),theory(equality)],[51459,45567]),
[iquote('0:Rew:51459.0,45567.0')] ).
cnf(51700,plain,
r1,
inference(mrr,[status(thm)],[60,51577]),
[iquote('0:MRR:60.0,51577.0')] ).
cnf(52270,plain,
is_a_theorem(equiv__dfg(or__dfg(u,u),u)),
inference(mrr,[status(thm)],[51534,51700]),
[iquote('0:MRR:51534.0,51700.0')] ).
cnf(52929,plain,
equal(and__dfg(u,u),u),
inference(res,[status(thm),theory(equality)],[51538,158]),
[iquote('0:Res:51538.0,158.0')] ).
cnf(53177,plain,
equal(implies__dfg(not__dfg(u),u),not__dfg(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[52929,159]),
[iquote('0:SpR:52929.0,159.0')] ).
cnf(53186,plain,
equal(not__dfg(necessarily(or__dfg(u,u))),possibly(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[52929,1134]),
[iquote('0:SpR:52929.0,1134.0')] ).
cnf(53194,plain,
equal(or__dfg(u,u),not__dfg(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[161,53177]),
[iquote('0:Rew:161.0,53177.0')] ).
cnf(53443,plain,
equal(or__dfg(u,u),u),
inference(res,[status(thm),theory(equality)],[52270,158]),
[iquote('0:Res:52270.0,158.0')] ).
cnf(53480,plain,
equal(not__dfg(necessarily(u)),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[53443,53186]),
[iquote('0:Rew:53443.0,53186.0')] ).
cnf(53491,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[53443,53194]),
[iquote('0:Rew:53443.0,53194.0')] ).
cnf(61920,plain,
equal(necessarily(necessarily(u)),necessarily(u)),
inference(res,[status(thm),theory(equality)],[51533,158]),
[iquote('0:Res:51533.0,158.0')] ).
cnf(64368,plain,
equal(possibly(not__dfg(necessarily(u))),not__dfg(necessarily(u))),
inference(spr,[status(thm),theory(equality)],[61920,53480]),
[iquote('0:SpR:61920.0,53480.0')] ).
cnf(64375,plain,
equal(possibly(possibly(not__dfg(u))),possibly(not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[53480,64368]),
[iquote('0:Rew:53480.0,64368.0')] ).
cnf(67033,plain,
equal(possibly(possibly(u)),possibly(u)),
inference(spr,[status(thm),theory(equality)],[53491,64375]),
[iquote('0:SpR:53491.0,64375.0')] ).
cnf(67127,plain,
equal(implies__dfg(possibly(u),necessarily(possibly(u))),skc94),
inference(spr,[status(thm),theory(equality)],[67033,48242]),
[iquote('0:SpR:67033.0,48242.0')] ).
cnf(67142,plain,
~ is_a_theorem(skc94),
inference(rew,[status(thm),theory(equality)],[67127,153]),
[iquote('0:Rew:67127.0,153.0')] ).
cnf(67143,plain,
$false,
inference(mrr,[status(thm)],[67142,400]),
[iquote('0:MRR:67142.0,400.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : LCL537+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jul 5 01:18:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 64.03/64.21
% 64.03/64.21 SPASS V 3.9
% 64.03/64.21 SPASS beiseite: Proof found.
% 64.03/64.21 % SZS status Theorem
% 64.03/64.21 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 64.03/64.21 SPASS derived 47694 clauses, backtracked 0 clauses, performed 2 splits and kept 20614 clauses.
% 64.03/64.21 SPASS allocated 173216 KBytes.
% 64.03/64.21 SPASS spent 0:01:03.76 on the problem.
% 64.03/64.21 0:00:00.04 for the input.
% 64.03/64.21 0:00:00.06 for the FLOTTER CNF translation.
% 64.03/64.21 0:00:00.71 for inferences.
% 64.03/64.21 0:00:00.13 for the backtracking.
% 64.03/64.21 0:01:02.05 for the reduction.
% 64.03/64.21
% 64.03/64.21
% 64.03/64.21 Here is a proof with depth 14, length 151 :
% 64.03/64.21 % SZS output start Refutation
% See solution above
% 74.86/75.12 Formulae used in the proof : hilbert_op_or hilbert_op_implies_and hilbert_op_equiv hilbert_modus_ponens hilbert_implies_1 hilbert_implies_2 hilbert_implies_3 hilbert_and_1 hilbert_and_3 hilbert_or_1 hilbert_or_3 hilbert_equivalence_2 substitution_of_equivalents km4b_op_possibly km4b_necessitation km4b_axiom_K km4b_axiom_M km4b_axiom_4 km4b_axiom_B km5_axiom_5 modus_ponens axiom_M and_3 implies_1 and_1 or_1 r1 necessitation axiom_B axiom_4 axiom_5 op_possibly equivalence_2 op_implies_and implies_2 op_or op_equiv axiom_K implies_3 or_3
% 74.86/75.12
%------------------------------------------------------------------------------